-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/

-- | Lenses, Folds and Traversals
--   
--   This package comes "Batteries Included" with many useful lenses for
--   the types commonly used from the Haskell Platform, and with tools for
--   automatically generating lenses and isomorphisms for user-supplied
--   data types.
--   
--   The combinators in Control.Lens provide a highly generic
--   toolbox for composing families of getters, folds, isomorphisms,
--   traversals, setters and lenses and their indexed variants.
--   
--   An overview, with a large number of examples can be found in the
--   README:
--   https://github.com/ekmett/lens#lens-lenses-folds-and-traversals
--   
--   A video on how to use lenses and how they are constructed is available
--   from youtube: http://youtu.be/cefnmjtAolY?hd=1
--   
--   Slides can be obtained here:
--   http://comonad.com/haskell/Lenses-Folds-and-Traversals-NYC.pdf
--   
--   More information on the care and feeding of lenses, including a brief
--   tutorial and motivation for their types can be found on the lens wiki:
--   https://github.com/ekmett/lens/wiki
--   
--   A small game of pong and other more complex examples that
--   manage their state using lenses can be found in the example folder:
--   https://github.com/ekmett/lens/blob/master/examples/
--   
--   Lenses, Folds and Traversals
--   
--   The core of the hierarchy of lens-like constructions looks like:
--   
--   
--   Local copy (Hierarchy.png)
--   
--   You can compose any two elements of the hierarchy above using
--   (.) from the Prelude, and you can use any element of
--   the hierarchy as any type it linked to above it.
--   
--   The result is their lowest upper bound in the hierarchy (or an error
--   if that bound doesn't exist).
--   
--   For instance:
--   
--   
--   
- You can use any Traversal as a Fold or as a
--   Setter.
--   
- The composition of a Traversal and a Getter yields a
--   Fold.
--   
--   
--   Minimizing Dependencies
--   
--   If you want to provide lenses and traversals for your own types in
--   your own libraries, then you can do so without incurring a dependency
--   on this (or any other) lens package at all.
--   
--   e.g. for a data type:
--   
--   
--   data Foo a = Foo Int Int a
--   
--   
--   You can define lenses such as
--   
--   
--   -- bar :: Lens' (Foo a) Int
--   bar :: Functor f => (Int -> f Int) -> Foo a -> f (Foo a)
--   bar f (Foo a b c) = fmap (\a' -> Foo a' b c) (f a)
--   
--   
--   
--   -- baz :: Lens (Foo a) (Foo b) a b
--   quux :: Functor f => (a -> f b) -> Foo a -> f (Foo b)
--   quux f (Foo a b c) = fmap (Foo a b) (f c)
--   
--   
--   without the need to use any type that isn't already defined in the
--   Prelude.
--   
--   And you can define a traversal of multiple fields with
--   Control.Applicative.Applicative:
--   
--   
--   -- traverseBarAndBaz :: Traversal' (Foo a) Int
--   traverseBarAndBaz :: Applicative f => (Int -> f Int) -> Foo a -> f (Foo a)
--   traverseBarAndBaz f (Foo a b c) = Foo <$> f a <*> f b <*> pure c
--   
--   
--   What is provided in this library is a number of stock lenses and
--   traversals for common haskell types, a wide array of combinators for
--   working them, and more exotic functionality, (e.g. getters,
--   setters, indexed folds, isomorphisms).
@package lens
@version 3.10

-- | This module includes orphan instances for (,), Either
--   and Const that should be supplied by base.
module Control.Lens.Internal.Instances
instance Traversable (Const m)
instance Foldable (Const m)
instance Traversable (Either a)
instance Foldable (Either a)
instance Traversable1 ((,) b)
instance Traversable ((,) b)
instance Foldable1 ((,) b)
instance Foldable ((,) b)

module Control.Lens.Internal.Prism

-- | This type is used internally by the Prism code to provide
--   efficient access to the two parts of a Prism.
data Market a b s t
Market :: (b -> t) -> (s -> Either t a) -> Market a b s t

-- | 
--   type Market' a s t = Market a a s t
--   
type Market' a = Market a a
instance Choice (Market a b)
instance Profunctor (Market a b)
instance Functor (Market a b s)

module Control.Lens.Internal.Iso

-- | This is used internally by the Iso code to provide efficient
--   access to the two functions that make up an isomorphism.
data Exchange a b s t
Exchange :: (s -> a) -> (b -> t) -> Exchange a b s t

-- | This class provides a generalized notion of list reversal extended to
--   other containers.
class Reversing t
reversing :: Reversing t => t -> t
instance Storable a => Reversing (Vector a)
instance Unbox a => Reversing (Vector a)
instance Prim a => Reversing (Vector a)
instance Reversing (Seq a)
instance Reversing (Vector a)
instance Reversing Text
instance Reversing Text
instance Reversing ByteString
instance Reversing ByteString
instance Reversing [a]
instance Profunctor (Exchange a b)
instance Functor (Exchange a b s)

-- | This module provides implementation details of the combinators in
--   Control.Lens.Level, which provides for the breadth-first
--   Traversal of an arbitrary Traversal.
module Control.Lens.Internal.Level

-- | This data type represents a path-compressed copy of one level of a
--   source data structure. We can safely use path-compression because we
--   know the depth of the tree.
--   
--   Path compression is performed by viewing a Level as a PATRICIA
--   trie of the paths into the structure to leaves at a given depth,
--   similar in many ways to a IntMap, but unlike a regular PATRICIA
--   trie we do not need to store the mask bits merely the depth of the
--   fork.
--   
--   One invariant of this structure is that underneath a Two node
--   you will not find any Zero nodes, so Zero can only occur
--   at the root.
data Level i a
Two :: {-# UNPACK #-} !Word -> !(Level i a) -> !(Level i a) -> Level i a
One :: i -> a -> Level i a
Zero :: Level i a

-- | This is an illegal Monoid used to construct a single
--   Level.
newtype Deepening i a
Deepening :: (forall r. Int -> (Level i a -> Bool -> r) -> r) -> Deepening i a
runDeepening :: Deepening i a -> forall r. Int -> (Level i a -> Bool -> r) -> r

-- | Generate the leaf of a given Deepening based on whether or not
--   we're at the correct depth.
deepening :: i -> a -> Deepening i a

-- | This is an illegal Applicative used to replace the contents of
--   a list of consecutive Level values representing each layer of a
--   structure into the original shape that they were derived from.
--   
--   Attempting to Flow something back into a shape other than the
--   one it was taken from will fail.
newtype Flows i b a
Flows :: ([Level i b] -> a) -> Flows i b a
runFlows :: Flows i b a -> [Level i b] -> a
instance (Eq i, Eq a) => Eq (Level i a)
instance (Ord i, Ord a) => Ord (Level i a)
instance (Show i, Show a) => Show (Level i a)
instance (Read i, Read a) => Read (Level i a)
instance Applicative (Flows i b)
instance Apply (Flows i b)
instance Functor (Flows i b)
instance Monoid (Deepening i a)
instance Semigroup (Deepening i a)
instance Traversable (Level i)
instance Foldable (Level i)
instance Functor (Level i)

module Control.Lens.Internal.Setter

-- | Anything Settable must be isomorphic to the Identity
--   Functor.
class (Applicative f, Distributive f, Traversable f) => Settable f where untaintedDot g = g `seq` rmap untainted g taintedDot g = g `seq` rmap pure g
untainted :: Settable f => f a -> a
untaintedDot :: (Settable f, Profunctor p) => p a (f b) -> p a b
taintedDot :: (Settable f, Profunctor p) => p a b -> p a (f b)

-- | Mutator is just a renamed Identity Functor to
--   give better error messages when someone attempts to use a
--   Getter as a Setter.
--   
--   Most user code will never need to see this type.
newtype Mutator a
Mutator :: a -> Mutator a
runMutator :: Mutator a -> a
instance Settable Mutator
instance Traversable Mutator
instance Foldable Mutator
instance Distributive Mutator
instance ComonadApply Mutator
instance Comonad Mutator
instance Extend Mutator
instance Monad Mutator
instance Bind Mutator
instance Applicative Mutator
instance Apply Mutator
instance Functor Mutator
instance (Settable f, Settable g) => Settable (Compose f g)
instance Settable f => Settable (Backwards f)
instance Settable Identity

module Control.Lens.Internal.Review

-- | This class is provided mostly for backwards compatibility with lens
--   3.8, but it can also shorten type signatures.
class (Profunctor p, Bifunctor p) => Reviewable p

-- | This is a profunctor used internally to implement Review
--   
--   It plays a role similar to that of Accessor or Const do
--   for Control.Lens.Getter
retagged :: (Profunctor p, Bifunctor p) => p a b -> p s b
newtype Reviewed a b
Reviewed :: b -> Reviewed a b
runReviewed :: Reviewed a b -> b
instance Corepresentable Reviewed
instance Choice Reviewed
instance Profunctor Reviewed
instance Distributive (Reviewed a)
instance Bitraversable Reviewed
instance Bifoldable Reviewed
instance Bifunctor Reviewed
instance Traversable (Reviewed a)
instance Foldable (Reviewed a)
instance MonadFix (Reviewed a)
instance Monad (Reviewed a)
instance Bind (Reviewed a)
instance ComonadApply (Reviewed a)
instance Comonad (Reviewed a)
instance Applicative (Reviewed a)
instance Apply (Reviewed a)
instance Functor (Reviewed a)
instance (Profunctor p, Bifunctor p) => Reviewable p

module Control.Lens.Internal.Getter

-- | This class is provided mostly for backwards compatibility with lens
--   3.8, but it can also shorten type signatures.
class (Contravariant f, Functor f) => Gettable f

-- | This Generalizes Const so we can apply simple
--   Applicative transformations to it and so we can get nicer error
--   messages.
--   
--   A Functor you can coerce ignores its argument, which it
--   carries solely as a phantom type parameter.
--   
--   By the Functor and Contravariant laws, an instance of
--   Gettable will necessarily satisfy:
--   
--   
--   id = fmap f = coerce = contramap g
--   
coerce :: (Contravariant f, Functor f) => f a -> f b

-- | The mempty equivalent for a Gettable Applicative
--   Functor.
noEffect :: (Contravariant f, Applicative f) => f a

-- | Used instead of Const to report
--   
--   
--   No instance for (Settable Accessor)
--   
--   
--   when the user attempts to misuse a Setter as a Getter,
--   rather than a monolithic unification error.
newtype Accessor r a
Accessor :: r -> Accessor r a
runAccessor :: Accessor r a -> r
instance Monoid r => Applicative (Accessor r)
instance Semigroup r => Apply (Accessor r)
instance Contravariant (Accessor r)
instance Functor (Accessor r)
instance (Contravariant f, Functor f) => Gettable f

-- | Internal implementation details for Indexed lens-likes
module Control.Lens.Internal.Indexed

-- | A function with access to a index. This constructor may be useful when
--   you need to store an Indexable in a container to avoid
--   ImpredicativeTypes.
--   
--   
--   index :: Indexed i a b -> i -> a -> b
--   
newtype Indexed i a b
Indexed :: (i -> a -> b) -> Indexed i a b
runIndexed :: Indexed i a b -> i -> a -> b

-- | This is a Profunctor that is both Corepresentable by
--   f and Representable by g such that f
--   is left adjoint to g. From this you can derive a lot of
--   structure due to the preservation of limits and colimits.
class (Choice p, Corepresentable p, Comonad (Corep p), Traversable (Corep p), Strong p, Representable p, Monad (Rep p), MonadFix (Rep p), Distributive (Rep p), ArrowLoop p, ArrowApply p, ArrowChoice p) => Conjoined p where distrib = tabulate . collect . rep conjoined _ r = r
distrib :: (Conjoined p, Functor f) => p a b -> p (f a) (f b)
conjoined :: Conjoined p => (p ~ (->) => q (a -> b) r) -> q (p a b) r -> q (p a b) r

-- | This class permits overloading of function application for things that
--   also admit a notion of a key or index.
class Conjoined p => Indexable i p
indexed :: Indexable i p => p a b -> i -> a -> b

-- | Applicative composition of State Int
--   with a Functor, used by indexed.
newtype Indexing f a
Indexing :: (Int -> (Int, f a)) -> Indexing f a
runIndexing :: Indexing f a -> Int -> (Int, f a)

-- | Transform a Traversal into an IndexedTraversal or a
--   Fold into an IndexedFold, etc.
--   
--   
--   indexing :: Traversal s t a b -> IndexedTraversal Int s t a b
--   indexing :: Prism s t a b     -> IndexedTraversal Int s t a b
--   indexing :: Lens s t a b      -> IndexedLens Int  s t a b
--   indexing :: Iso s t a b       -> IndexedLens Int s t a b
--   indexing :: Fold s a          -> IndexedFold Int s a
--   indexing :: Getter s a        -> IndexedGetter Int s a
--   
--   
--   
--   indexing :: Indexable Int p => LensLike (Indexing f) s t a b -> Overloading p (->) f s t a b
--   
indexing :: Indexable Int p => ((a -> Indexing f b) -> s -> Indexing f t) -> p a (f b) -> s -> f t

-- | Applicative composition of State Int64
--   with a Functor, used by indexed64.
newtype Indexing64 f a
Indexing64 :: (Int64 -> (Int64, f a)) -> Indexing64 f a
runIndexing64 :: Indexing64 f a -> Int64 -> (Int64, f a)

-- | Transform a Traversal into an IndexedTraversal or a
--   Fold into an IndexedFold, etc.
--   
--   This combinator is like indexing except that it handles large
--   traversals and folds gracefully.
--   
--   
--   indexing64 :: Traversal s t a b -> IndexedTraversal Int64 s t a b
--   indexing64 :: Prism s t a b     -> IndexedTraversal Int64 s t a b
--   indexing64 :: Lens s t a b      -> IndexedLens Int64 s t a b
--   indexing64 :: Iso s t a b       -> IndexedLens Int64 s t a b
--   indexing64 :: Fold s a          -> IndexedFold Int64 s a
--   indexing64 :: Getter s a        -> IndexedGetter Int64 s a
--   
--   
--   
--   indexing64 :: Indexable Int64 p => LensLike (Indexing64 f) s t a b -> Overloading p (->) f s t a b
--   
indexing64 :: Indexable Int64 p => ((a -> Indexing64 f b) -> s -> Indexing64 f t) -> p a (f b) -> s -> f t
instance Contravariant f => Contravariant (Indexing64 f)
instance Applicative f => Applicative (Indexing64 f)
instance Apply f => Apply (Indexing64 f)
instance Functor f => Functor (Indexing64 f)
instance Contravariant f => Contravariant (Indexing f)
instance Applicative f => Applicative (Indexing f)
instance Apply f => Apply (Indexing f)
instance Functor f => Functor (Indexing f)
instance i ~ j => Indexable i (Indexed j)
instance Conjoined (Indexed i)
instance ArrowLoop (Indexed i)
instance ArrowApply (Indexed i)
instance ArrowChoice (Indexed i)
instance Arrow (Indexed i)
instance Category (Indexed i)
instance Strong (Indexed i)
instance Choice (Indexed i)
instance Representable (Indexed i)
instance Corepresentable (Indexed i)
instance Profunctor (Indexed i)
instance MonadFix (Indexed i a)
instance Monad (Indexed i a)
instance Bind (Indexed i a)
instance Applicative (Indexed i a)
instance Apply (Indexed i a)
instance Functor (Indexed i a)
instance Indexable i (->)
instance Conjoined (->)

module Control.Lens.Internal.Context

-- | This is a Bob Atkey -style 2-argument indexed functor.
--   
--   It exists as a superclass for IndexedComonad and expresses the
--   functoriality of an IndexedComonad in its third argument.
class IndexedFunctor w
ifmap :: IndexedFunctor w => (s -> t) -> w a b s -> w a b t

-- | This is a Bob Atkey -style 2-argument indexed comonad.
--   
--   It exists as a superclass for IndexedComonad and expresses the
--   functoriality of an IndexedComonad in its third argument.
--   
--   The notion of indexed monads is covered in more depth in Bob Atkey's
--   Parameterized Notions of Computation
--   http://bentnib.org/paramnotions-jfp.pdf and that construction
--   is dualized here.
class IndexedFunctor w => IndexedComonad w where iduplicate = iextend id iextend f = ifmap f . iduplicate
iextract :: IndexedComonad w => w a a t -> t
iduplicate :: IndexedComonad w => w a c t -> w a b (w b c t)
iextend :: IndexedComonad w => (w b c t -> r) -> w a c t -> w a b r

-- | This is an indexed analogue to ComonadStore for when you are
--   working with an IndexedComonad.
class IndexedComonad w => IndexedComonadStore w where ipeek c = iextract . iseek c ipeeks f = iextract . iseeks f iexperiment bfc wbct = (`ipeek` wbct) <$> bfc (ipos wbct) context wabt = Context (`ipeek` wabt) (ipos wabt)
ipos :: IndexedComonadStore w => w a c t -> a
ipeek :: IndexedComonadStore w => c -> w a c t -> t
ipeeks :: IndexedComonadStore w => (a -> c) -> w a c t -> t
iseek :: IndexedComonadStore w => b -> w a c t -> w b c t
iseeks :: IndexedComonadStore w => (a -> b) -> w a c t -> w b c t
iexperiment :: (IndexedComonadStore w, Functor f) => (b -> f c) -> w b c t -> f t
context :: IndexedComonadStore w => w a b t -> Context a b t

-- | This is used internally to construct a Bazaar, Context
--   or Pretext from a singleton value.
class Corepresentable p => Sellable p w | w -> p
sell :: Sellable p w => p a (w a b b)

-- | The indexed store can be used to characterize a Lens and is
--   used by clone.
--   
--   Context a b t is isomorphic to newtype
--   Context a b t = Context { runContext :: forall f.
--   Functor f => (a -> f b) -> f t }, and to
--   exists s. (s, Lens s t a b).
--   
--   A Context is like a Lens that has already been applied
--   to a some structure.
data Context a b t
Context :: (b -> t) -> a -> Context a b t

-- | 
--   type Context' a s = Context a a s
--   
type Context' a = Context a a

-- | This is a generalized form of Context that can be repeatedly
--   cloned with less impact on its performance, and which permits the use
--   of an arbitrary Conjoined Profunctor
newtype Pretext p a b t
Pretext :: (forall f. Functor f => p a (f b) -> f t) -> Pretext p a b t
runPretext :: Pretext p a b t -> forall f. Functor f => p a (f b) -> f t

-- | 
--   type Pretext' p a s = Pretext p a a s
--   
type Pretext' p a = Pretext p a a

-- | This is a generalized form of Context that can be repeatedly
--   cloned with less impact on its performance, and which permits the use
--   of an arbitrary Conjoined Profunctor.
--   
--   The extra phantom Functor is used to let us lie and claim a
--   Gettable instance under limited circumstances. This is used
--   internally to permit a number of combinators to gracefully degrade
--   when applied to a Fold, Getter or Action.
newtype PretextT p (g :: * -> *) a b t
PretextT :: (forall f. Functor f => p a (f b) -> f t) -> PretextT p a b t
runPretextT :: PretextT p a b t -> forall f. Functor f => p a (f b) -> f t

-- | 
--   type PretextT' p g a s = PretextT p g a a s
--   
type PretextT' p g a = PretextT p g a a
instance (Profunctor p, Contravariant g) => Contravariant (PretextT p g a b)
instance Corepresentable p => Sellable p (PretextT p g)
instance (a ~ b, Conjoined p) => ComonadStore a (PretextT p g a b)
instance Conjoined p => IndexedComonadStore (PretextT p g)
instance (a ~ b, Conjoined p) => Comonad (PretextT p g a b)
instance Conjoined p => IndexedComonad (PretextT p g)
instance Functor (PretextT p g a b)
instance IndexedFunctor (PretextT p g)
instance Corepresentable p => Sellable p (Pretext p)
instance (a ~ b, Conjoined p) => ComonadStore a (Pretext p a b)
instance Conjoined p => IndexedComonadStore (Pretext p)
instance (a ~ b, Conjoined p) => Comonad (Pretext p a b)
instance Conjoined p => IndexedComonad (Pretext p)
instance Functor (Pretext p a b)
instance IndexedFunctor (Pretext p)
instance Sellable (->) Context
instance a ~ b => ComonadStore a (Context a b)
instance a ~ b => Comonad (Context a b)
instance Functor (Context a b)
instance IndexedComonadStore Context
instance IndexedComonad Context
instance IndexedFunctor Context

module Control.Lens.Internal.Bazaar

-- | This class is used to run the various Bazaar variants used in
--   this library.
class Profunctor p => Bizarre p w | w -> p
bazaar :: (Bizarre p w, Applicative f) => p a (f b) -> w a b t -> f t

-- | This is used to characterize a Traversal.
--   
--   a.k.a. indexed Cartesian store comonad, indexed Kleene store comonad,
--   or an indexed FunList.
--   
--   http://twanvl.nl/blog/haskell/non-regular1
--   
--   A Bazaar is like a Traversal that has already been
--   applied to some structure.
--   
--   Where a Context a b t holds an a and a
--   function from b to t, a Bazaar a b t
--   holds N as and a function from N
--   bs to t, (where N might be infinite).
--   
--   Mnemonically, a Bazaar holds many stores and you can easily add
--   more.
--   
--   This is a final encoding of Bazaar.
newtype Bazaar p a b t
Bazaar :: (forall f. Applicative f => p a (f b) -> f t) -> Bazaar p a b t
runBazaar :: Bazaar p a b t -> forall f. Applicative f => p a (f b) -> f t

-- | This alias is helpful when it comes to reducing repetition in type
--   signatures.
--   
--   
--   type Bazaar' p a t = Bazaar p a a t
--   
type Bazaar' p a = Bazaar p a a

-- | BazaarT is like Bazaar, except that it provides a
--   questionable Contravariant instance To protect this instance it
--   relies on the soundness of another Contravariant type, and
--   usage conventions.
--   
--   For example. This lets us write a suitably polymorphic and lazy
--   taking, but there must be a better way!
newtype BazaarT p (g :: * -> *) a b t
BazaarT :: (forall f. Applicative f => p a (f b) -> f t) -> BazaarT p a b t
runBazaarT :: BazaarT p a b t -> forall f. Applicative f => p a (f b) -> f t

-- | This alias is helpful when it comes to reducing repetition in type
--   signatures.
--   
--   
--   type BazaarT' p g a t = BazaarT p g a a t
--   
type BazaarT' p g a = BazaarT p g a a
instance (Profunctor p, Contravariant g) => Contravariant (BazaarT p g a b)
instance (a ~ b, Conjoined p) => ComonadApply (BazaarT p g a b)
instance (a ~ b, Conjoined p) => Comonad (BazaarT p g a b)
instance Applicative (BazaarT p g a b)
instance Apply (BazaarT p g a b)
instance Functor (BazaarT p g a b)
instance Profunctor p => Bizarre p (BazaarT p g)
instance Corepresentable p => Sellable p (BazaarT p g)
instance Conjoined p => IndexedComonad (BazaarT p g)
instance IndexedFunctor (BazaarT p g)
instance (a ~ b, Conjoined p) => ComonadApply (Bazaar p a b)
instance (a ~ b, Conjoined p) => Comonad (Bazaar p a b)
instance Applicative (Bazaar p a b)
instance Apply (Bazaar p a b)
instance Functor (Bazaar p a b)
instance Profunctor p => Bizarre p (Bazaar p)
instance Corepresentable p => Sellable p (Bazaar p)
instance Conjoined p => IndexedComonad (Bazaar p)
instance IndexedFunctor (Bazaar p)

module Control.Lens.Internal.Magma

-- | This provides a way to peek at the internal structure of a
--   Traversal or IndexedTraversal
data Magma i t b a
MagmaAp :: Magma i (x -> y) b a -> Magma i x b a -> Magma i y b a
MagmaPure :: x -> Magma i x b a
MagmaFmap :: (x -> y) -> Magma i x b a -> Magma i y b a
Magma :: i -> a -> Magma i b b a

-- | Run a Magma where all the individual leaves have been converted
--   to the expected type
runMagma :: Magma i t a a -> t

-- | This is a a non-reassociating initially encoded version of
--   Bazaar.
newtype Molten i a b t
Molten :: Magma i t b a -> Molten i a b t
runMolten :: Molten i a b t -> Magma i t b a

-- | This is used to generate an indexed magma from an unindexed source
--   
--   By constructing it this way we avoid infinite reassociations in sums
--   where possible.
data Mafic a b t
Mafic :: Int -> (Int -> Magma Int t b a) -> Mafic a b t

-- | Generate a Magma using from a prefix sum.
runMafic :: Mafic a b t -> Magma Int t b a

-- | This is used to generate an indexed magma from an unindexed source
--   
--   By constructing it this way we avoid infinite reassociations where
--   possible.
data TakingWhile p (g :: * -> *) a b t
TakingWhile :: Bool -> t -> (Bool -> Magma () t b (Corep p a)) -> TakingWhile p a b t

-- | Generate a Magma with leaves only while the predicate holds
--   from left to right.
runTakingWhile :: Corepresentable p => TakingWhile p f a b t -> Magma () t b (Corep p a)
instance IndexedFunctor (TakingWhile p f)
instance Contravariant f => Contravariant (TakingWhile p f a b)
instance Corepresentable p => Bizarre p (TakingWhile p g)
instance Applicative (TakingWhile p f a b)
instance Apply (TakingWhile p f a b)
instance Functor (TakingWhile p f a b)
instance IndexedFunctor Mafic
instance Bizarre (Indexed Int) Mafic
instance Sellable (->) Mafic
instance Applicative (Mafic a b)
instance Apply (Mafic a b)
instance Functor (Mafic a b)
instance a ~ b => Comonad (Molten i a b)
instance IndexedComonad (Molten i)
instance IndexedFunctor (Molten i)
instance Bizarre (Indexed i) (Molten i)
instance Sellable (Indexed i) (Molten i)
instance Applicative (Molten i a b)
instance Apply (Molten i a b)
instance Functor (Molten i a b)
instance (Show i, Show a) => Show (Magma i t b a)
instance Traversable (Magma i t b)
instance Foldable (Magma i t b)
instance Functor (Magma i t b)

module Control.Lens.Internal.Fold

-- | A Monoid for a Contravariant Applicative.
newtype Folding f a
Folding :: f a -> Folding f a
getFolding :: Folding f a -> f a

-- | Used internally by traverseOf_ and the like.
--   
--   The argument a of the result should not be used!
newtype Traversed a f
Traversed :: f a -> Traversed a f
getTraversed :: Traversed a f -> f a

-- | Used internally by mapM_ and the like.
--   
--   The argument a of the result should not be used!
newtype Sequenced a m
Sequenced :: m a -> Sequenced a m
getSequenced :: Sequenced a m -> m a

-- | Used for maximumOf.
data Max a
NoMax :: Max a
Max :: a -> Max a

-- | Obtain the maximum.
getMax :: Max a -> Maybe a

-- | Used for minimumOf.
data Min a
NoMin :: Min a
Min :: a -> Min a

-- | Obtain the minimum.
getMin :: Min a -> Maybe a

-- | Used for preview.
data Leftmost a
LPure :: Leftmost a
LLeaf :: a -> Leftmost a
LStep :: (Leftmost a) -> Leftmost a

-- | Extract the Leftmost element. This will fairly eagerly
--   determine that it can return Just the moment it sees any
--   element at all.
getLeftmost :: Leftmost a -> Maybe a

-- | Used for lastOf.
data Rightmost a
RPure :: Rightmost a
RLeaf :: a -> Rightmost a
RStep :: (Rightmost a) -> Rightmost a

-- | Extract the Rightmost element. This will fairly eagerly
--   determine that it can return Just the moment it sees any
--   element at all.
getRightmost :: Rightmost a -> Maybe a
instance Monoid (Rightmost a)
instance Semigroup (Rightmost a)
instance Monoid (Leftmost a)
instance Semigroup (Leftmost a)
instance Ord a => Monoid (Max a)
instance Ord a => Semigroup (Max a)
instance Ord a => Monoid (Min a)
instance Ord a => Semigroup (Min a)
instance Monad m => Monoid (Sequenced a m)
instance Apply m => Semigroup (Sequenced a m)
instance Applicative f => Monoid (Traversed a f)
instance Apply f => Semigroup (Traversed a f)
instance (Contravariant f, Applicative f) => Monoid (Folding f a)
instance (Contravariant f, Apply f) => Semigroup (Folding f a)

module Control.Lens.Internal.Action

-- | An Effective Functor ignores its argument and is
--   isomorphic to a Monad wrapped around a value.
--   
--   That said, the Monad is possibly rather unrelated to any
--   Applicative structure.
class (Monad m, Functor f, Contravariant f) => Effective m r f | f -> m r
effective :: Effective m r f => m r -> f a
ineffective :: Effective m r f => f a -> m r

-- | Wrap a monadic effect with a phantom type argument.
newtype Effect m r a
Effect :: m r -> Effect m r a
getEffect :: Effect m r a -> m r
instance (Monad m, Monoid r) => Applicative (Effect m r)
instance (Apply m, Semigroup r) => Apply (Effect m r)
instance (Monad m, Monoid r) => Monoid (Effect m r a)
instance (Apply m, Semigroup r) => Semigroup (Effect m r a)
instance Monad m => Effective m r (Effect m r)
instance Contravariant (Effect m r)
instance Functor (Effect m r)
instance Effective Identity r (Accessor r)
instance Effective m r f => Effective m (Dual r) (Backwards f)

module Control.Lens.Internal.Zoom

-- | This type family is used by Zoom to describe the common effect
--   type.

-- | Used by Zoom to zoom into StateT.
newtype Focusing m s a
Focusing :: m (s, a) -> Focusing m s a
unfocusing :: Focusing m s a -> m (s, a)

-- | Used by Zoom to zoom into RWST.
newtype FocusingWith w m s a
FocusingWith :: m (s, a, w) -> FocusingWith w m s a
unfocusingWith :: FocusingWith w m s a -> m (s, a, w)

-- | Used by Zoom to zoom into WriterT.
newtype FocusingPlus w k s a
FocusingPlus :: k (s, w) a -> FocusingPlus w k s a
unfocusingPlus :: FocusingPlus w k s a -> k (s, w) a

-- | Used by Zoom to zoom into MaybeT or ListT.
newtype FocusingOn f k s a
FocusingOn :: k (f s) a -> FocusingOn f k s a
unfocusingOn :: FocusingOn f k s a -> k (f s) a

-- | Used by Zoom to zoom into ErrorT.
newtype FocusingMay k s a
FocusingMay :: k (May s) a -> FocusingMay k s a
unfocusingMay :: FocusingMay k s a -> k (May s) a

-- | Make a Monoid out of Maybe for error handling.
newtype May a
May :: Maybe a -> May a
getMay :: May a -> Maybe a

-- | Used by Zoom to zoom into ErrorT.
newtype FocusingErr e k s a
FocusingErr :: k (Err e s) a -> FocusingErr e k s a
unfocusingErr :: FocusingErr e k s a -> k (Err e s) a

-- | Make a Monoid out of Either for error handling.
newtype Err e a
Err :: Either e a -> Err e a
getErr :: Err e a -> Either e a

-- | This type family is used by Magnify to describe the common
--   effect type.

-- | Wrap a monadic effect with a phantom type argument. Used when
--   magnifying RWST.
newtype EffectRWS w st m s a
EffectRWS :: (st -> m (s, st, w)) -> EffectRWS w st m s a
getEffectRWS :: EffectRWS w st m s a -> st -> m (s, st, w)
instance Contravariant (EffectRWS w st m s)
instance (Monoid s, Monoid w, Monad m) => Applicative (EffectRWS w st m s)
instance (Semigroup s, Semigroup w, Bind m) => Apply (EffectRWS w st m s)
instance Functor (EffectRWS w st m s)
instance Applicative (k (Err e s)) => Applicative (FocusingErr e k s)
instance Apply (k (Err e s)) => Apply (FocusingErr e k s)
instance Functor (k (Err e s)) => Functor (FocusingErr e k s)
instance Monoid a => Monoid (Err e a)
instance Semigroup a => Semigroup (Err e a)
instance Applicative (k (May s)) => Applicative (FocusingMay k s)
instance Apply (k (May s)) => Apply (FocusingMay k s)
instance Functor (k (May s)) => Functor (FocusingMay k s)
instance Monoid a => Monoid (May a)
instance Semigroup a => Semigroup (May a)
instance Applicative (k (f s)) => Applicative (FocusingOn f k s)
instance Apply (k (f s)) => Apply (FocusingOn f k s)
instance Functor (k (f s)) => Functor (FocusingOn f k s)
instance Applicative (k (s, w)) => Applicative (FocusingPlus w k s)
instance Apply (k (s, w)) => Apply (FocusingPlus w k s)
instance Functor (k (s, w)) => Functor (FocusingPlus w k s)
instance (Monad m, Monoid s, Monoid w) => Applicative (FocusingWith w m s)
instance (Monad m, Semigroup s, Semigroup w) => Apply (FocusingWith w m s)
instance Monad m => Functor (FocusingWith w m s)
instance (Monad m, Monoid s) => Applicative (Focusing m s)
instance (Monad m, Semigroup s) => Apply (Focusing m s)
instance Monad m => Functor (Focusing m s)

-- | This module exports the majority of the types that need to appear in
--   user signatures or in documentation when talking about lenses. The
--   remaining types for consuming lenses are distributed across various
--   modules in the hierarchy.
module Control.Lens.Type

-- | A witness that (a ~ s, b ~ t).
--   
--   Note: Composition with an Equality is index-preserving.
type Equality s t a b = forall p (f :: * -> *). p a (f b) -> p s (f t)

-- | A Simple Equality.
type Equality' s a = Equality s s a a

-- | Isomorphism families can be composed with another Lens using
--   (.) and id.
--   
--   Note: Composition with an Iso is index- and measure-
--   preserving.
type Iso s t a b = forall p f. (Profunctor p, Functor f) => p a (f b) -> p s (f t)

-- | 
--   type Iso' = Simple Iso
--   
type Iso' s a = Iso s s a a

-- | A Prism l is a 0-or-1 target Traversal that can
--   also be turned around with re to obtain a Getter in the
--   opposite direction.
--   
--   There are two laws that a Prism should satisfy:
--   
--   First, if I re or review a value with a Prism and
--   then preview or use (^?), I will get it back:
--   
--   
--   preview l (review l b) ≡ Just b
--   
--   
--   Second, if you can extract a value a using a Prism
--   l from a value s, then the value s is
--   completely described my l and a:
--   
--   If preview l s ≡ Just a then review
--   l a ≡ s
--   
--   These two laws imply that the Traversal laws hold for every
--   Prism and that we traverse at most 1 element:
--   
--   
--   lengthOf l x <= 1
--   
--   
--   It may help to think of this as a Iso that can be partial in
--   one direction.
--   
--   Every Prism is a valid Traversal.
--   
--   Every Iso is a valid Prism.
--   
--   For example, you might have a Prism' Integer
--   Natural allows you to always go from a Natural to
--   an Integer, and provide you with tools to check if an
--   Integer is a Natural and/or to edit one if it is.
--   
--   
--   nat :: Prism' Integer Natural
--   nat = prism toInteger $ \ i ->
--      if i < 0
--      then Left i
--      else Right (fromInteger i)
--   
--   
--   Now we can ask if an Integer is a Natural.
--   
--   
--   >>> 5^?nat
--   Just 5
--   
--   
--   
--   >>> (-5)^?nat
--   Nothing
--   
--   
--   We can update the ones that are:
--   
--   
--   >>> (-3,4) & both.nat *~ 2
--   (-3,8)
--   
--   
--   And we can then convert from a Natural to an Integer.
--   
--   
--   >>> 5 ^. re nat -- :: Natural
--   5
--   
--   
--   Similarly we can use a Prism to traverse the Left
--   half of an Either:
--   
--   
--   >>> Left "hello" & _Left %~ length
--   Left 5
--   
--   
--   or to construct an Either:
--   
--   
--   >>> 5^.re _Left
--   Left 5
--   
--   
--   such that if you query it with the Prism, you will get your
--   original input back.
--   
--   
--   >>> 5^.re _Left ^? _Left
--   Just 5
--   
--   
--   Another interesting way to think of a Prism is as the
--   categorical dual of a Lens -- a co-Lens, so to speak.
--   This is what permits the construction of outside.
--   
--   Note: Composition with a Prism is index-preserving.
type Prism s t a b = forall p f. (Choice p, Applicative f) => p a (f b) -> p s (f t)

-- | A Simple Prism.
type Prism' s a = Prism s s a a

-- | A Lens is actually a lens family as described in
--   http://comonad.com/reader/2012/mirrored-lenses/.
--   
--   With great power comes great responsibility and a Lens is
--   subject to the three common sense Lens laws:
--   
--   1) You get back what you put in:
--   
--   
--   view l (set l b a)  ≡ b
--   
--   
--   2) Putting back what you got doesn't change anything:
--   
--   
--   set l (view l a) a  ≡ a
--   
--   
--   3) Setting twice is the same as setting once:
--   
--   
--   set l c (set l b a) ≡ set l c a
--   
--   
--   These laws are strong enough that the 4 type parameters of a
--   Lens cannot vary fully independently. For more on how they
--   interact, read the "Why is it a Lens Family?" section of
--   http://comonad.com/reader/2012/mirrored-lenses/.
--   
--   Every Lens can be used directly as a Setter or
--   Traversal.
--   
--   You can also use a Lens for Getting as if it were a
--   Fold or Getter.
--   
--   Since every Lens is a valid Traversal, the
--   Traversal laws are required of any Lens you create:
--   
--   
--   l pure ≡ pure
--   fmap (l f) . l g ≡ getCompose . l (Compose . fmap f . g)
--   
--   
--   
--   type Lens s t a b = forall f. Functor f => LensLike f s t a b
--   
type Lens s t a b = forall f. Functor f => (a -> f b) -> s -> f t

-- | 
--   type Lens' = Simple Lens
--   
type Lens' s a = Lens s s a a

-- | A Traversal can be used directly as a Setter or a
--   Fold (but not as a Lens) and provides the ability to
--   both read and update multiple fields, subject to some relatively weak
--   Traversal laws.
--   
--   These have also been known as multilenses, but they have the signature
--   and spirit of
--   
--   
--   traverse :: Traversable f => Traversal (f a) (f b) a b
--   
--   
--   and the more evocative name suggests their application.
--   
--   Most of the time the Traversal you will want to use is just
--   traverse, but you can also pass any Lens or Iso
--   as a Traversal, and composition of a Traversal (or
--   Lens or Iso) with a Traversal (or Lens or
--   Iso) using (.) forms a valid Traversal.
--   
--   The laws for a Traversal t follow from the laws for
--   Traversable as stated in "The Essence of the Iterator Pattern".
--   
--   
--   t pure ≡ pure
--   fmap (t f) . t g ≡ getCompose . t (Compose . fmap f . g)
--   
--   
--   One consequence of this requirement is that a Traversal needs
--   to leave the same number of elements as a candidate for subsequent
--   Traversal that it started with. Another testament to the
--   strength of these laws is that the caveat expressed in section 5.5 of
--   the "Essence of the Iterator Pattern" about exotic Traversable
--   instances that traverse the same entry multiple times was
--   actually already ruled out by the second law in that same paper!
type Traversal s t a b = forall f. Applicative f => (a -> f b) -> s -> f t

-- | 
--   type Traversal' = Simple Traversal
--   
type Traversal' s a = Traversal s s a a

-- | The only LensLike law that can apply to a Setter
--   l is that
--   
--   
--   set l y (set l x a) ≡ set l y a
--   
--   
--   You can't view a Setter in general, so the other two
--   laws are irrelevant.
--   
--   However, two Functor laws apply to a Setter:
--   
--   
--   over l id ≡ id
--   over l f . over l g ≡ over l (f . g)
--   
--   
--   These can be stated more directly:
--   
--   
--   l pure ≡ pure
--   l f . untainted . l g ≡ l (f . untainted . g)
--   
--   
--   You can compose a Setter with a Lens or a
--   Traversal using (.) from the Prelude and the
--   result is always only a Setter and nothing more.
--   
--   
--   >>> over traverse f [a,b,c,d]
--   [f a,f b,f c,f d]
--   
--   
--   
--   >>> over _1 f (a,b)
--   (f a,b)
--   
--   
--   
--   >>> over (traverse._1) f [(a,b),(c,d)]
--   [(f a,b),(f c,d)]
--   
--   
--   
--   >>> over both f (a,b)
--   (f a,f b)
--   
--   
--   
--   >>> over (traverse.both) f [(a,b),(c,d)]
--   [(f a,f b),(f c,f d)]
--   
type Setter s t a b = forall f. Settable f => (a -> f b) -> s -> f t

-- | A Setter' is just a Setter that doesn't change the
--   types.
--   
--   These are particularly common when talking about monomorphic
--   containers. e.g.
--   
--   
--   sets Data.Text.map :: Setter' Text Char
--   
--   
--   
--   type Setter' = Setter'
--   
type Setter' s a = Setter s s a a

-- | A Getter describes how to retrieve a single value in a way that
--   can be composed with other LensLike constructions.
--   
--   Unlike a Lens a Getter is read-only. Since a
--   Getter cannot be used to write back there are no Lens
--   laws that can be applied to it. In fact, it is isomorphic to an
--   arbitrary function from (a -> s).
--   
--   Moreover, a Getter can be used directly as a Fold, since
--   it just ignores the Applicative.
type Getter s a = forall f. (Contravariant f, Functor f) => (a -> f a) -> s -> f s

-- | A Fold describes how to retrieve multiple values in a way that
--   can be composed with other LensLike constructions.
--   
--   A Fold s a provides a structure with operations very
--   similar to those of the Foldable typeclass, see
--   foldMapOf and the other Fold combinators.
--   
--   By convention, if there exists a foo method that expects a
--   Foldable (f a), then there should be a fooOf
--   method that takes a Fold s a and a value of type
--   s.
--   
--   A Getter is a legal Fold that just ignores the supplied
--   Monoid.
--   
--   Unlike a Traversal a Fold is read-only. Since a
--   Fold cannot be used to write back there are no Lens laws
--   that apply.
type Fold s a = forall f. (Contravariant f, Applicative f) => (a -> f a) -> s -> f s

-- | An Action is a Getter enriched with access to a
--   Monad for side-effects.
--   
--   Every Getter can be used as an Action.
--   
--   You can compose an Action with another Action using
--   (.) from the Prelude.
type Action m s a = forall f r. Effective m r f => (a -> f a) -> s -> f s

-- | A MonadicFold is a Fold enriched with access to a
--   Monad for side-effects.
--   
--   Every Fold can be used as a MonadicFold, that simply
--   ignores the access to the Monad.
--   
--   You can compose a MonadicFold with another MonadicFold
--   using (.) from the Prelude.
type MonadicFold m s a = forall f r. (Effective m r f, Applicative f) => (a -> f a) -> s -> f s

-- | Every IndexedLens is a valid Lens and a valid
--   IndexedTraversal.
type IndexedLens i s t a b = forall f p. (Indexable i p, Functor f) => p a (f b) -> s -> f t

-- | 
--   type IndexedLens' i = Simple (IndexedLens i)
--   
type IndexedLens' i s a = IndexedLens i s s a a

-- | Every IndexedTraversal is a valid Traversal or
--   IndexedFold.
--   
--   The Indexed constraint is used to allow an
--   IndexedTraversal to be used directly as a Traversal.
--   
--   The Traversal laws are still required to hold.
type IndexedTraversal i s t a b = forall p f. (Indexable i p, Applicative f) => p a (f b) -> s -> f t

-- | 
--   type IndexedTraversal' i = Simple (IndexedTraversal i)
--   
type IndexedTraversal' i s a = IndexedTraversal i s s a a

-- | Every IndexedSetter is a valid Setter.
--   
--   The Setter laws are still required to hold.
type IndexedSetter i s t a b = forall f p. (Indexable i p, Settable f) => p a (f b) -> s -> f t

-- | 
--   type IndexedSetter' i = Simple (IndexedSetter i)
--   
type IndexedSetter' i s a = IndexedSetter i s s a a

-- | Every IndexedGetter is a valid IndexedFold and can be
--   used for Getting like a Getter.
type IndexedGetter i s a = forall p f. (Indexable i p, Contravariant f, Functor f) => p a (f a) -> s -> f s

-- | Every IndexedFold is a valid Fold and can be used for
--   Getting.
type IndexedFold i s a = forall p f. (Indexable i p, Contravariant f, Applicative f) => p a (f a) -> s -> f s

-- | An IndexedAction is an IndexedGetter enriched with
--   access to a Monad for side-effects.
--   
--   Every Getter can be used as an Action.
--   
--   You can compose an Action with another Action using
--   (.) from the Prelude.
type IndexedAction i m s a = forall p f r. (Indexable i p, Effective m r f) => p a (f a) -> s -> f s

-- | An IndexedMonadicFold is an IndexedFold enriched with
--   access to a Monad for side-effects.
--   
--   Every IndexedFold can be used as an IndexedMonadicFold,
--   that simply ignores the access to the Monad.
--   
--   You can compose an IndexedMonadicFold with another
--   IndexedMonadicFold using (.) from the Prelude.
type IndexedMonadicFold i m s a = forall p f r. (Indexable i p, Effective m r f, Applicative f) => p a (f a) -> s -> f s

-- | An IndexPreservingLens leaves any index it is composed with
--   alone.
type IndexPreservingLens s t a b = forall p f. (Conjoined p, Functor f) => p a (f b) -> p s (f t)

-- | 
--   type IndexPreservingLens' = Simple IndexPreservingLens
--   
type IndexPreservingLens' s a = IndexPreservingLens s s a a

-- | An IndexPreservingLens leaves any index it is composed with
--   alone.
type IndexPreservingTraversal s t a b = forall p f. (Conjoined p, Applicative f) => p a (f b) -> p s (f t)

-- | 
--   type IndexPreservingTraversal' = Simple IndexPreservingTraversal
--   
type IndexPreservingTraversal' s a = IndexPreservingTraversal s s a a

-- | An IndexPreservingSetter can be composed with a
--   IndexedSetter, IndexedTraversal or IndexedLens
--   and leaves the index intact, yielding an IndexedSetter.
type IndexPreservingSetter s t a b = forall p f. (Conjoined p, Settable f) => p a (f b) -> p s (f t)

-- | 
--   type IndexedPreservingSetter' i = Simple IndexedPreservingSetter
--   
type IndexPreservingSetter' s a = IndexPreservingSetter s s a a

-- | An IndexPreservingGetter can be used as a Getter, but
--   when composed with an IndexedTraversal, IndexedFold, or
--   IndexedLens yields an IndexedFold, IndexedFold or
--   IndexedGetter respectively.
type IndexPreservingGetter s a = forall p f. (Conjoined p, Contravariant f, Functor f) => p a (f a) -> p s (f s)

-- | An IndexPreservingFold can be used as a Fold, but when
--   composed with an IndexedTraversal, IndexedFold, or
--   IndexedLens yields an IndexedFold respectively.
type IndexPreservingFold s a = forall p f. (Conjoined p, Contravariant f, Applicative f) => p a (f a) -> p s (f s)

-- | An IndexPreservingAction can be used as a Action, but
--   when composed with an IndexedTraversal, IndexedFold, or
--   IndexedLens yields an IndexedMonadicFold,
--   IndexedMonadicFold or IndexedAction respectively.
type IndexPreservingAction m s a = forall p f r. (Conjoined p, Effective m r f) => p a (f a) -> p s (f s)

-- | An IndexPreservingFold can be used as a Fold, but when
--   composed with an IndexedTraversal, IndexedFold, or
--   IndexedLens yields an IndexedFold respectively.
type IndexPreservingMonadicFold m s a = forall p f r. (Conjoined p, Effective m r f, Applicative f) => p a (f a) -> p s (f s)

-- | A Simple Lens, Simple Traversal, ... can
--   be used instead of a Lens,Traversal, ... whenever the
--   type variables don't change upon setting a value.
--   
--   
--   _imagPart :: Simple Lens (Complex a) a
--   traversed :: Simple (IndexedTraversal Int) [a] a
--   
--   
--   Note: To use this alias in your own code with LensLike
--   f or Setter, you may have to turn on
--   LiberalTypeSynonyms.
--   
--   This is commonly abbreviated as a "prime" marker, e.g.
--   Lens' = Simple Lens.
type Simple f s a = f s s a a

-- | Many combinators that accept a Lens can also accept a
--   Traversal in limited situations.
--   
--   They do so by specializing the type of Functor that they
--   require of the caller.
--   
--   If a function accepts a LensLike f s t a b for some
--   Functor f, then they may be passed a Lens.
--   
--   Further, if f is an Applicative, they may also be
--   passed a Traversal.
type LensLike f s t a b = (a -> f b) -> s -> f t

-- | 
--   type LensLike' f = Simple (LensLike f)
--   
type LensLike' f s a = LensLike f s s a a

-- | This is a convenient alias for use when you need to consume either
--   indexed or non-indexed lens-likes based on context.
type Over p f s t a b = p a (f b) -> s -> f t

-- | This is a convenient alias for use when you need to consume either
--   indexed or non-indexed lens-likes based on context.
--   
--   
--   type Over' p f = Simple (Over p f)
--   
type Over' p f s a = Over p f s s a a

-- | Convenient alias for constructing indexed lenses and their ilk.
type IndexedLensLike i f s t a b = forall p. Indexable i p => p a (f b) -> s -> f t

-- | Convenient alias for constructing simple indexed lenses and their ilk.
type IndexedLensLike' i f s a = IndexedLensLike i f s s a a

-- | 
--   type LensLike f s t a b = Overloading (->) (->) f s t a b
--   
type Overloading p q f s t a b = p a (f b) -> q s (f t)

-- | 
--   type Overloading' p q f s a = Simple (Overloading p q f) s a
--   
type Overloading' p q f s a = Overloading p q f s s a a

-- | 
--   type LensLike f s t a b = Overloaded (->) f s t a b
--   
type Overloaded p f s t a b = p a (f b) -> p s (f t)

-- | 
--   type Overloaded' p q f s a = Simple (Overloaded p q f) s a
--   
type Overloaded' p f s a = Overloaded p f s s a a

module Control.Lens.Reified

-- | Reify a Lens so it can be stored safely in a container.
newtype ReifiedLens s t a b
ReifyLens :: Lens s t a b -> ReifiedLens s t a b
reflectLens :: ReifiedLens s t a b -> Lens s t a b

-- | 
--   type ReifiedLens' = Simple ReifiedLens
--   
type ReifiedLens' s a = ReifiedLens s s a a

-- | Reify an IndexedLens so it can be stored safely in a container.
newtype ReifiedIndexedLens i s t a b
ReifyIndexedLens :: IndexedLens i s t a b -> ReifiedIndexedLens i s t a b
reflectIndexedLens :: ReifiedIndexedLens i s t a b -> IndexedLens i s t a b

-- | 
--   type ReifiedIndexedLens' i = Simple (ReifiedIndexedLens i)
--   
type ReifiedIndexedLens' i s a = ReifiedIndexedLens i s s a a

-- | Reify an IndexedTraversal so it can be stored safely in a
--   container.
newtype ReifiedIndexedTraversal i s t a b
ReifyIndexedTraversal :: IndexedTraversal i s t a b -> ReifiedIndexedTraversal i s t a b
reflectIndexedTraversal :: ReifiedIndexedTraversal i s t a b -> IndexedTraversal i s t a b

-- | 
--   type ReifiedIndexedTraversal' i = Simple (ReifiedIndexedTraversal i)
--   
type ReifiedIndexedTraversal' i s a = ReifiedIndexedTraversal i s s a a

-- | A form of Traversal that can be stored monomorphically in a
--   container.
data ReifiedTraversal s t a b
ReifyTraversal :: Traversal s t a b -> ReifiedTraversal s t a b
reflectTraversal :: ReifiedTraversal s t a b -> Traversal s t a b

-- | 
--   type ReifiedTraversal' = Simple ReifiedTraversal
--   
type ReifiedTraversal' s a = ReifiedTraversal s s a a

-- | Reify a Getter so it can be stored safely in a container.
newtype ReifiedGetter s a
ReifyGetter :: Getter s a -> ReifiedGetter s a
reflectGetter :: ReifiedGetter s a -> Getter s a

-- | Reify an IndexedGetter so it can be stored safely in a
--   container.
newtype ReifiedIndexedGetter i s a
ReifyIndexedGetter :: IndexedGetter i s a -> ReifiedIndexedGetter i s a
reflectIndexedGetter :: ReifiedIndexedGetter i s a -> IndexedGetter i s a

-- | Reify a Fold so it can be stored safely in a container.
newtype ReifiedFold s a
ReifyFold :: Fold s a -> ReifiedFold s a
reflectFold :: ReifiedFold s a -> Fold s a

-- | Reify a Setter so it can be stored safely in a container.
newtype ReifiedSetter s t a b
ReifySetter :: Setter s t a b -> ReifiedSetter s t a b
reflectSetter :: ReifiedSetter s t a b -> Setter s t a b

-- | 
--   type ReifiedSetter' = Simple ReifiedSetter
--   
type ReifiedSetter' s a = ReifiedSetter s s a a

-- | Reify an IndexedSetter so it can be stored safely in a
--   container.
newtype ReifiedIndexedSetter i s t a b
ReifyIndexedSetter :: IndexedSetter i s t a b -> ReifiedIndexedSetter i s t a b
reflectIndexedSetter :: ReifiedIndexedSetter i s t a b -> IndexedSetter i s t a b

-- | 
--   type ReifiedIndexedSetter' i = Simple (ReifiedIndexedSetter i)
--   
type ReifiedIndexedSetter' i s a = ReifiedIndexedSetter i s s a a

-- | Reify an Iso so it can be stored safely in a container.
newtype ReifiedIso s t a b
ReifyIso :: Iso s t a b -> ReifiedIso s t a b
reflectIso :: ReifiedIso s t a b -> Iso s t a b

-- | 
--   type ReifiedIso' = Simple ReifiedIso
--   
type ReifiedIso' s a = ReifiedIso s s a a

-- | Reify a Prism so it can be stored safely in a container.
newtype ReifiedPrism s t a b
ReifyPrism :: Prism s t a b -> ReifiedPrism s t a b
reflectPrism :: ReifiedPrism s t a b -> Prism s t a b

-- | 
--   type ReifiedPrism' = Simple ReifiedPrism
--   
type ReifiedPrism' s a = ReifiedPrism s s a a

module Control.Lens.Equality

-- | A witness that (a ~ s, b ~ t).
--   
--   Note: Composition with an Equality is index-preserving.
type Equality s t a b = forall p (f :: * -> *). p a (f b) -> p s (f t)

-- | A Simple Equality.
type Equality' s a = Equality s s a a

-- | When you see this as an argument to a function, it expects an
--   Equality.
type AnEquality s t a b = Identical a (Mutator b) a (Mutator b) -> Identical a (Mutator b) s (Mutator t)

-- | A Simple AnEquality.
type AnEquality' s a = AnEquality s s a a

-- | Extract a witness of type Equality.
runEq :: AnEquality s t a b -> Identical s t a b

-- | Substituting types with Equality.
substEq :: AnEquality s t a b -> ((s ~ a, t ~ b) => r) -> r

-- | We can use Equality to do substitution into anything.
mapEq :: AnEquality s t a b -> f s -> f a

-- | Equality is symmetric.
fromEq :: AnEquality s t a b -> Equality b a t s

-- | This is an adverb that can be used to modify many other Lens
--   combinators to make them require simple lenses, simple traversals,
--   simple prisms or simple isos as input.
simply :: (Overloaded' p f s a -> r) -> Overloaded' p f s a -> r

-- | Provides witness that (s ~ a, b ~ t) holds.
data Identical a b s t
Identical :: Identical a b a b

module Control.Lens.Action

-- | An Action is a Getter enriched with access to a
--   Monad for side-effects.
--   
--   Every Getter can be used as an Action.
--   
--   You can compose an Action with another Action using
--   (.) from the Prelude.
type Action m s a = forall f r. Effective m r f => (a -> f a) -> s -> f s

-- | Construct an Action from a monadic side-effect.
--   
--   
--   >>> ["hello","world"]^!folded.act (\x -> [x,x ++ "!"])
--   ["helloworld","helloworld!","hello!world","hello!world!"]
--   
--   
--   
--   act :: Monad m => (s -> m a) -> Action m s a
--   act sma afb a = effective (sma a >>= ineffective . afb)
--   
act :: Monad m => (s -> m a) -> IndexPreservingAction m s a

-- | A self-running Action, analogous to join.
--   
--   
--   acts ≡ act id
--   
--   
--   
--   >>> (1,"hello")^!_2.acts.to succ
--   "ifmmp"
--   
acts :: Action m (m a) a

-- | Perform an Action.
--   
--   
--   perform ≡ flip (^!)
--   
perform :: Monad m => Acting m a s t a b -> s -> m a

-- | Perform an Action and modify the result.
--   
--   
--   performs :: Monad m => Acting m e s t a b -> (a -> e) -> s -> m e
--   
performs :: (Profunctor p, Monad m) => Over p (Effect m e) s t a b -> p a e -> s -> m e

-- | Apply a Monad transformer to an Action.
liftAct :: (MonadTrans trans, Monad m) => Acting m a s t a b -> Action (trans m) s a

-- | Perform an Action.
--   
--   
--   >>> ["hello","world"]^!folded.act putStrLn
--   hello
--   world
--   
(^!) :: Monad m => s -> Acting m a s t a b -> m a

-- | Perform a MonadicFold and collect all of the results in a list.
--   
--   
--   >>> ["ab","cd","ef"]^!!folded.acts
--   ["ace","acf","ade","adf","bce","bcf","bde","bdf"]
--   
(^!!) :: Monad m => s -> Acting m [a] s t a b -> m [a]

-- | Perform a MonadicFold and collect the leftmost result.
--   
--   Note: this still causes all effects for all elements.
--   
--   
--   >>> [Just 1, Just 2, Just 3]^!?folded.acts
--   Just (Just 1)
--   
--   >>> [Just 1, Nothing]^!?folded.acts
--   Nothing
--   
(^!?) :: Monad m => s -> Acting m (Leftmost a) s t a b -> m (Maybe a)

-- | An IndexedAction is an IndexedGetter enriched with
--   access to a Monad for side-effects.
--   
--   Every Getter can be used as an Action.
--   
--   You can compose an Action with another Action using
--   (.) from the Prelude.
type IndexedAction i m s a = forall p f r. (Indexable i p, Effective m r f) => p a (f a) -> s -> f s

-- | Construct an IndexedAction from a monadic side-effect.
iact :: Monad m => (s -> m (i, a)) -> IndexedAction i m s a

-- | Perform an IndexedAction.
--   
--   
--   iperform ≡ flip (^@!)
--   
iperform :: Monad m => IndexedActing i m (i, a) s t a b -> s -> m (i, a)

-- | Perform an IndexedAction and modify the result.
iperforms :: Monad m => IndexedActing i m e s t a b -> (i -> a -> e) -> s -> m e

-- | Perform an IndexedAction.
(^@!) :: Monad m => s -> IndexedActing i m (i, a) s t a b -> m (i, a)

-- | Obtain a list of all of the results of an IndexedMonadicFold.
(^@!!) :: Monad m => s -> IndexedActing i m [(i, a)] s t a b -> m [(i, a)]

-- | Perform an IndexedMonadicFold and collect the Leftmost
--   result.
--   
--   Note: this still causes all effects for all elements.
(^@!?) :: Monad m => s -> IndexedActing i m (Leftmost (i, a)) s t a b -> m (Maybe (i, a))

-- | A MonadicFold is a Fold enriched with access to a
--   Monad for side-effects.
--   
--   Every Fold can be used as a MonadicFold, that simply
--   ignores the access to the Monad.
--   
--   You can compose a MonadicFold with another MonadicFold
--   using (.) from the Prelude.
type MonadicFold m s a = forall f r. (Effective m r f, Applicative f) => (a -> f a) -> s -> f s

-- | An IndexedMonadicFold is an IndexedFold enriched with
--   access to a Monad for side-effects.
--   
--   Every IndexedFold can be used as an IndexedMonadicFold,
--   that simply ignores the access to the Monad.
--   
--   You can compose an IndexedMonadicFold with another
--   IndexedMonadicFold using (.) from the Prelude.
type IndexedMonadicFold i m s a = forall p f r. (Indexable i p, Effective m r f, Applicative f) => p a (f a) -> s -> f s

-- | Used to evaluate an Action.
type Acting m r s t a b = LensLike (Effect m r) s t a b

-- | Used to evaluate an IndexedAction.
type IndexedActing i m r s t a b = Over (Indexed i) (Effect m r) s t a b

-- | An Effective Functor ignores its argument and is
--   isomorphic to a Monad wrapped around a value.
--   
--   That said, the Monad is possibly rather unrelated to any
--   Applicative structure.
class (Monad m, Functor f, Contravariant f) => Effective m r f | f -> m r

-- | These are some of the explicit Functor instances that leak into
--   the type signatures of Control.Lens. You shouldn't need to
--   import this module directly for most use-cases.
module Control.Lens.Internal

-- | A Setter s t a b is a generalization of fmap
--   from Functor. It allows you to map into a structure and change
--   out the contents, but it isn't strong enough to allow you to enumerate
--   those contents. Starting with fmap :: Functor f
--   => (a -> b) -> f a -> f b we monomorphize the type to
--   obtain (a -> b) -> s -> t and then decorate it with
--   Identity to obtain:
--   
--   
--   type Setter s t a b = (a -> Identity b) -> s -> Identity t
--   
--   
--   Every Traversal is a valid Setter, since Identity
--   is Applicative.
--   
--   Everything you can do with a Functor, you can do with a
--   Setter. There are combinators that generalize fmap and
--   (<$).
module Control.Lens.Setter

-- | The only LensLike law that can apply to a Setter
--   l is that
--   
--   
--   set l y (set l x a) ≡ set l y a
--   
--   
--   You can't view a Setter in general, so the other two
--   laws are irrelevant.
--   
--   However, two Functor laws apply to a Setter:
--   
--   
--   over l id ≡ id
--   over l f . over l g ≡ over l (f . g)
--   
--   
--   These can be stated more directly:
--   
--   
--   l pure ≡ pure
--   l f . untainted . l g ≡ l (f . untainted . g)
--   
--   
--   You can compose a Setter with a Lens or a
--   Traversal using (.) from the Prelude and the
--   result is always only a Setter and nothing more.
--   
--   
--   >>> over traverse f [a,b,c,d]
--   [f a,f b,f c,f d]
--   
--   
--   
--   >>> over _1 f (a,b)
--   (f a,b)
--   
--   
--   
--   >>> over (traverse._1) f [(a,b),(c,d)]
--   [(f a,b),(f c,d)]
--   
--   
--   
--   >>> over both f (a,b)
--   (f a,f b)
--   
--   
--   
--   >>> over (traverse.both) f [(a,b),(c,d)]
--   [(f a,f b),(f c,f d)]
--   
type Setter s t a b = forall f. Settable f => (a -> f b) -> s -> f t

-- | A Setter' is just a Setter that doesn't change the
--   types.
--   
--   These are particularly common when talking about monomorphic
--   containers. e.g.
--   
--   
--   sets Data.Text.map :: Setter' Text Char
--   
--   
--   
--   type Setter' = Setter'
--   
type Setter' s a = Setter s s a a

-- | Every IndexedSetter is a valid Setter.
--   
--   The Setter laws are still required to hold.
type IndexedSetter i s t a b = forall f p. (Indexable i p, Settable f) => p a (f b) -> s -> f t

-- | 
--   type IndexedSetter' i = Simple (IndexedSetter i)
--   
type IndexedSetter' i s a = IndexedSetter i s s a a

-- | Running a Setter instantiates it to a concrete type.
--   
--   When consuming a setter directly to perform a mapping, you can use
--   this type, but most user code will not need to use this type.
--   
--   By choosing Mutator rather than Identity, we get nicer
--   error messages.
type ASetter s t a b = (a -> Mutator b) -> s -> Mutator t

-- | This is a useful alias for use when consuming a Setter'.
--   
--   Most user code will never have to use this type.
--   
--   
--   type ASetter' = Simple ASetter
--   
type ASetter' s a = ASetter s s a a

-- | Running an IndexedSetter instantiates it to a concrete type.
--   
--   When consuming a setter directly to perform a mapping, you can use
--   this type, but most user code will not need to use this type.
--   
--   By choosing Mutator rather than Identity, we get nicer
--   error messages.
type AnIndexedSetter i s t a b = Indexed i a (Mutator b) -> s -> Mutator t

-- | 
--   type AnIndexedSetter' i = Simple (AnIndexedSetter i)
--   
type AnIndexedSetter' i s a = AnIndexedSetter i s s a a

-- | This is a convenient alias when defining highly polymorphic code that
--   takes both ASetter and AnIndexedSetter as appropriate.
--   If a function takes this it is expecting one of those two things based
--   on context.
type Setting p s t a b = p a (Mutator b) -> s -> Mutator t

-- | This is a convenient alias when defining highly polymorphic code that
--   takes both ASetter' and AnIndexedSetter' as appropriate.
--   If a function takes this it is expecting one of those two things based
--   on context.
type Setting' p s a = Setting p s s a a

-- | Build a Setter, IndexedSetter or
--   IndexPreservingSetter depending on your choice of
--   Profunctor.
--   
--   
--   sets :: ((a -> b) -> s -> t) -> Setter s t a b
--   
sets :: (Profunctor p, Profunctor q, Settable f) => (p a b -> q s t) -> Overloading p q f s t a b

-- | Build an index-preserving Setter from a map-like function.
--   
--   Your supplied function f is required to satisfy:
--   
--   
--   f id ≡ id
--   f g . f h ≡ f (g . h)
--   
--   
--   Equational reasoning:
--   
--   
--   setting . over ≡ id
--   over . setting ≡ id
--   
--   
--   Another way to view sets is that it takes a "semantic editor
--   combinator" and transforms it into a Setter.
--   
--   
--   setting :: ((a -> b) -> s -> t) -> Setter s t a b
--   
setting :: ((a -> b) -> s -> t) -> IndexPreservingSetter s t a b

-- | Restore ASetter to a full Setter.
cloneSetter :: ASetter s t a b -> Setter s t a b

-- | Build an IndexPreservingSetter from any Setter.
cloneIndexPreservingSetter :: ASetter s t a b -> IndexPreservingSetter s t a b

-- | Clone an IndexedSetter.
cloneIndexedSetter :: AnIndexedSetter i s t a b -> IndexedSetter i s t a b

-- | This Setter can be used to map over all of the values in a
--   Functor.
--   
--   
--   fmap ≡ over mapped
--   fmapDefault ≡ over traverse
--   (<$) ≡ set mapped
--   
--   
--   
--   >>> over mapped f [a,b,c]
--   [f a,f b,f c]
--   
--   
--   
--   >>> over mapped (+1) [1,2,3]
--   [2,3,4]
--   
--   
--   
--   >>> set mapped x [a,b,c]
--   [x,x,x]
--   
--   
--   
--   >>> [[a,b],[c]] & mapped.mapped +~ x
--   [[a + x,b + x],[c + x]]
--   
--   
--   
--   >>> over (mapped._2) length [("hello","world"),("leaders","!!!")]
--   [("hello",5),("leaders",3)]
--   
--   
--   
--   mapped :: Functor f => Setter (f a) (f b) a b
--   
--   
--   If you want an IndexPreservingSetter use setting
--   fmap.
mapped :: Functor f => Setter (f a) (f b) a b

-- | This setter can be used to modify all of the values in a
--   Monad.
--   
--   You sometimes have to use this rather than mapped -- due to
--   temporary insanity Functor is not a superclass of Monad.
--   
--   
--   liftM ≡ over lifted
--   
--   
--   
--   >>> over lifted f [a,b,c]
--   [f a,f b,f c]
--   
--   
--   
--   >>> set lifted b (Just a)
--   Just b
--   
--   
--   If you want an IndexPreservingSetter use setting
--   liftM.
lifted :: Monad m => Setter (m a) (m b) a b

-- | This Setter can be used to map over all of the inputs to a
--   Contravariant.
--   
--   
--   contramap ≡ over contramapped
--   
--   
--   
--   >>> getPredicate (over contramapped (*2) (Predicate even)) 5
--   True
--   
--   
--   
--   >>> getOp (over contramapped (*5) (Op show)) 100
--   "500"
--   
--   
--   
--   >>> Prelude.map ($ 1) $ over (mapped . wrapping Op . contramapped) (*12) [(*2),(+1),(^3)]
--   [24,13,1728]
--   
contramapped :: Contravariant f => Setter (f b) (f a) a b

-- | This Setter can be used to map over the input of a
--   Profunctor.
--   
--   The most common Profunctor to use this with is
--   (->).
--   
--   
--   >>> (argument %~ f) g x
--   g (f x)
--   
--   
--   
--   >>> (argument %~ show) length [1,2,3]
--   7
--   
--   
--   
--   >>> (argument %~ f) h x y
--   h (f x) y
--   
--   
--   Map over the argument of the result of a function -- i.e., its second
--   argument:
--   
--   
--   >>> (mapped.argument %~ f) h x y
--   h x (f y)
--   
--   
--   
--   argument :: Setter (b -> r) (a -> r) a b
--   
argument :: Profunctor p => Setter (p b r) (p a r) a b

-- | Modify the target of a Lens or all the targets of a
--   Setter or Traversal with a function.
--   
--   
--   fmap ≡ over mapped
--   fmapDefault ≡ over traverse
--   sets . over ≡ id
--   over . sets ≡ id
--   
--   
--   Given any valid Setter l, you can also rely on the
--   law:
--   
--   
--   over l f . over l g = over l (f . g)
--   
--   
--   e.g.
--   
--   
--   >>> over mapped f (over mapped g [a,b,c]) == over mapped (f . g) [a,b,c]
--   True
--   
--   
--   Another way to view over is to say that it transforms a
--   Setter into a "semantic editor combinator".
--   
--   
--   >>> over mapped f (Just a)
--   Just (f a)
--   
--   
--   
--   >>> over mapped (*10) [1,2,3]
--   [10,20,30]
--   
--   
--   
--   >>> over _1 f (a,b)
--   (f a,b)
--   
--   
--   
--   >>> over _1 show (10,20)
--   ("10",20)
--   
--   
--   
--   over :: Setter s t a b -> (a -> b) -> s -> t
--   over :: ASetter s t a b -> (a -> b) -> s -> t
--   
over :: Profunctor p => Setting p s t a b -> p a b -> s -> t

-- | Replace the target of a Lens or all of the targets of a
--   Setter or Traversal with a constant value.
--   
--   
--   (<$) ≡ set mapped
--   
--   
--   
--   >>> set _2 "hello" (1,())
--   (1,"hello")
--   
--   
--   
--   >>> set mapped () [1,2,3,4]
--   [(),(),(),()]
--   
--   
--   Note: Attempting to set a Fold or Getter will
--   fail at compile time with an relatively nice error message.
--   
--   
--   set :: Setter s t a b    -> b -> s -> t
--   set :: Iso s t a b       -> b -> s -> t
--   set :: Lens s t a b      -> b -> s -> t
--   set :: Traversal s t a b -> b -> s -> t
--   
set :: ASetter s t a b -> b -> s -> t

-- | Replace the target of a Lens or all of the targets of a
--   Setter or Traversal with a constant value.
--   
--   This is an infix version of set, provided for consistency with
--   (.=).
--   
--   
--   f <$ a ≡ mapped .~ f $ a
--   
--   
--   
--   >>> (a,b,c,d) & _4 .~ e
--   (a,b,c,e)
--   
--   
--   
--   >>> (42,"world") & _1 .~ "hello"
--   ("hello","world")
--   
--   
--   
--   >>> (a,b) & both .~ c
--   (c,c)
--   
--   
--   
--   (.~) :: Setter s t a b    -> b -> s -> t
--   (.~) :: Iso s t a b       -> b -> s -> t
--   (.~) :: Lens s t a b      -> b -> s -> t
--   (.~) :: Traversal s t a b -> b -> s -> t
--   
(.~) :: ASetter s t a b -> b -> s -> t

-- | Modifies the target of a Lens or all of the targets of a
--   Setter or Traversal with a user supplied function.
--   
--   This is an infix version of over.
--   
--   
--   fmap f ≡ mapped %~ f
--   fmapDefault f ≡ traverse %~ f
--   
--   
--   
--   >>> (a,b,c) & _3 %~ f
--   (a,b,f c)
--   
--   
--   
--   >>> (a,b) & both %~ f
--   (f a,f b)
--   
--   
--   
--   >>> _2 %~ length $ (1,"hello")
--   (1,5)
--   
--   
--   
--   >>> traverse %~ f $ [a,b,c]
--   [f a,f b,f c]
--   
--   
--   
--   >>> traverse %~ even $ [1,2,3]
--   [False,True,False]
--   
--   
--   
--   >>> traverse.traverse %~ length $ [["hello","world"],["!!!"]]
--   [[5,5],[3]]
--   
--   
--   
--   (%~) :: Setter s t a b    -> (a -> b) -> s -> t
--   (%~) :: Iso s t a b       -> (a -> b) -> s -> t
--   (%~) :: Lens s t a b      -> (a -> b) -> s -> t
--   (%~) :: Traversal s t a b -> (a -> b) -> s -> t
--   
(%~) :: Profunctor p => Setting p s t a b -> p a b -> s -> t

-- | Increment the target(s) of a numerically valued Lens,
--   Setter or Traversal.
--   
--   
--   >>> (a,b) & _1 +~ c
--   (a + c,b)
--   
--   
--   
--   >>> (a,b) & both +~ c
--   (a + c,b + c)
--   
--   
--   
--   >>> (1,2) & _2 +~ 1
--   (1,3)
--   
--   
--   
--   >>> [(a,b),(c,d)] & traverse.both +~ e
--   [(a + e,b + e),(c + e,d + e)]
--   
--   
--   
--   (+~) :: Num a => Setter' s a    -> a -> s -> s
--   (+~) :: Num a => Iso' s a       -> a -> s -> s
--   (+~) :: Num a => Lens' s a      -> a -> s -> s
--   (+~) :: Num a => Traversal' s a -> a -> s -> s
--   
(+~) :: Num a => ASetter s t a a -> a -> s -> t

-- | Decrement the target(s) of a numerically valued Lens,
--   Iso, Setter or Traversal.
--   
--   
--   >>> (a,b) & _1 -~ c
--   (a - c,b)
--   
--   
--   
--   >>> (a,b) & both -~ c
--   (a - c,b - c)
--   
--   
--   
--   >>> _1 -~ 2 $ (1,2)
--   (-1,2)
--   
--   
--   
--   >>> mapped.mapped -~ 1 $ [[4,5],[6,7]]
--   [[3,4],[5,6]]
--   
--   
--   
--   (-~) :: Num a => Setter' s a    -> a -> s -> s
--   (-~) :: Num a => Iso' s a       -> a -> s -> s
--   (-~) :: Num a => Lens' s a      -> a -> s -> s
--   (-~) :: Num a => Traversal' s a -> a -> s -> s
--   
(-~) :: Num a => ASetter s t a a -> a -> s -> t

-- | Multiply the target(s) of a numerically valued Lens,
--   Iso, Setter or Traversal.
--   
--   
--   >>> (a,b) & _1 *~ c
--   (a * c,b)
--   
--   
--   
--   >>> (a,b) & both *~ c
--   (a * c,b * c)
--   
--   
--   
--   >>> (1,2) & _2 *~ 4
--   (1,8)
--   
--   
--   
--   >>> Just 24 & mapped *~ 2
--   Just 48
--   
--   
--   
--   (*~) :: Num a => Setter' s a    -> a -> s -> s
--   (*~) :: Num a => Iso' s a       -> a -> s -> s
--   (*~) :: Num a => Lens' s a      -> a -> s -> s
--   (*~) :: Num a => Traversal' s a -> a -> s -> s
--   
(*~) :: Num a => ASetter s t a a -> a -> s -> t

-- | Divide the target(s) of a numerically valued Lens, Iso,
--   Setter or Traversal.
--   
--   
--   >>> (a,b) & _1 //~ c
--   (a / c,b)
--   
--   
--   
--   >>> (a,b) & both //~ c
--   (a / c,b / c)
--   
--   
--   
--   >>> ("Hawaii",10) & _2 //~ 2
--   ("Hawaii",5.0)
--   
--   
--   
--   (//~) :: Fractional a => Setter' s a    -> a -> s -> s
--   (//~) :: Fractional a => Iso' s a       -> a -> s -> s
--   (//~) :: Fractional a => Lens' s a      -> a -> s -> s
--   (//~) :: Fractional a => Traversal' s a -> a -> s -> s
--   
(//~) :: Fractional a => ASetter s t a a -> a -> s -> t

-- | Raise the target(s) of a numerically valued Lens, Setter
--   or Traversal to a non-negative integral power.
--   
--   
--   >>> (1,3) & _2 ^~ 2
--   (1,9)
--   
--   
--   
--   (^~) :: (Num a, Integral e) => Setter' s a    -> e -> s -> s
--   (^~) :: (Num a, Integral e) => Iso' s a       -> e -> s -> s
--   (^~) :: (Num a, Integral e) => Lens' s a      -> e -> s -> s
--   (^~) :: (Num a, Integral e) => Traversal' s a -> e -> s -> s
--   
(^~) :: (Num a, Integral e) => ASetter s t a a -> e -> s -> t

-- | Raise the target(s) of a fractionally valued Lens,
--   Setter or Traversal to an integral power.
--   
--   
--   >>> (1,2) & _2 ^^~ (-1)
--   (1,0.5)
--   
--   
--   
--   (^^~) :: (Fractional a, Integral e) => Setter' s a    -> e -> s -> s
--   (^^~) :: (Fractional a, Integral e) => Iso' s a       -> e -> s -> s
--   (^^~) :: (Fractional a, Integral e) => Lens' s a      -> e -> s -> s
--   (^^~) :: (Fractional a, Integral e) => Traversal' s a -> e -> s -> s
--   
(^^~) :: (Fractional a, Integral e) => ASetter s t a a -> e -> s -> t

-- | Raise the target(s) of a floating-point valued Lens,
--   Setter or Traversal to an arbitrary power.
--   
--   
--   >>> (a,b) & _1 **~ c
--   (a**c,b)
--   
--   
--   
--   >>> (a,b) & both **~ c
--   (a**c,b**c)
--   
--   
--   
--   >>> _2 **~ 10 $ (3,2)
--   (3,1024.0)
--   
--   
--   
--   (**~) :: Floating a => Setter' s a    -> a -> s -> s
--   (**~) :: Floating a => Iso' s a       -> a -> s -> s
--   (**~) :: Floating a => Lens' s a      -> a -> s -> s
--   (**~) :: Floating a => Traversal' s a -> a -> s -> s
--   
(**~) :: Floating a => ASetter s t a a -> a -> s -> t

-- | Logically || the target(s) of a Bool-valued Lens
--   or Setter.
--   
--   
--   >>> both ||~ True $ (False,True)
--   (True,True)
--   
--   
--   
--   >>> both ||~ False $ (False,True)
--   (False,True)
--   
--   
--   
--   (||~) :: Setter' s Bool    -> Bool -> s -> s
--   (||~) :: Iso' s Bool       -> Bool -> s -> s
--   (||~) :: Lens' s Bool      -> Bool -> s -> s
--   (||~) :: Traversal' s Bool -> Bool -> s -> s
--   
(||~) :: ASetter s t Bool Bool -> Bool -> s -> t

-- | Modify the target of a monoidally valued by mappending another
--   value.
--   
--   
--   >>> (Sum a,b) & _1 <>~ Sum c
--   (Sum {getSum = a + c},b)
--   
--   
--   
--   >>> (Sum a,Sum b) & both <>~ Sum c
--   (Sum {getSum = a + c},Sum {getSum = b + c})
--   
--   
--   
--   >>> both <>~ "!!!" $ ("hello","world")
--   ("hello!!!","world!!!")
--   
--   
--   
--   (<>~) :: Monoid a => Setter s t a a    -> a -> s -> t
--   (<>~) :: Monoid a => Iso s t a a       -> a -> s -> t
--   (<>~) :: Monoid a => Lens s t a a      -> a -> s -> t
--   (<>~) :: Monoid a => Traversal s t a a -> a -> s -> t
--   
(<>~) :: Monoid a => ASetter s t a a -> a -> s -> t

-- | Logically && the target(s) of a Bool-valued
--   Lens or Setter.
--   
--   
--   >>> both &&~ True $ (False, True)
--   (False,True)
--   
--   
--   
--   >>> both &&~ False $ (False, True)
--   (False,False)
--   
--   
--   
--   (&&~) :: Setter' s Bool    -> Bool -> s -> s
--   (&&~) :: Iso' s Bool       -> Bool -> s -> s
--   (&&~) :: Lens' s Bool      -> Bool -> s -> s
--   (&&~) :: Traversal' s Bool -> Bool -> s -> s
--   
(&&~) :: ASetter s t Bool Bool -> Bool -> s -> t

-- | Set with pass-through.
--   
--   This is mostly present for consistency, but may be useful for for
--   chaining assignments.
--   
--   If you do not need a copy of the intermediate result, then using l
--   .~ t directly is a good idea.
--   
--   
--   >>> (a,b) & _1 <.~ c
--   (c,(c,b))
--   
--   
--   
--   >>> ("good","morning","vietnam") & _3 <.~ "world"
--   ("world",("good","morning","world"))
--   
--   
--   
--   >>> (42,Map.fromList [("goodnight","gracie")]) & _2.at "hello" <.~ Just "world"
--   (Just "world",(42,fromList [("goodnight","gracie"),("hello","world")]))
--   
--   
--   
--   (<.~) :: Setter s t a b    -> b -> s -> (b, t)
--   (<.~) :: Iso s t a b       -> b -> s -> (b, t)
--   (<.~) :: Lens s t a b      -> b -> s -> (b, t)
--   (<.~) :: Traversal s t a b -> b -> s -> (b, t)
--   
(<.~) :: ASetter s t a b -> b -> s -> (b, t)

-- | Set the target of a Lens, Traversal or Setter to
--   Just a value.
--   
--   
--   l ?~ t ≡ set l (Just t)
--   
--   
--   
--   >>> Nothing & id ?~ a
--   Just a
--   
--   
--   
--   >>> Map.empty & at 3 ?~ x
--   fromList [(3,x)]
--   
--   
--   
--   (?~) :: Setter s t a (Maybe b)    -> b -> s -> t
--   (?~) :: Iso s t a (Maybe b)       -> b -> s -> t
--   (?~) :: Lens s t a (Maybe b)      -> b -> s -> t
--   (?~) :: Traversal s t a (Maybe b) -> b -> s -> t
--   
(?~) :: ASetter s t a (Maybe b) -> b -> s -> t

-- | Set to Just a value with pass-through.
--   
--   This is mostly present for consistency, but may be useful for for
--   chaining assignments.
--   
--   If you do not need a copy of the intermediate result, then using l
--   ?~ d directly is a good idea.
--   
--   
--   >>> import Data.Map as Map
--   
--   >>> _2.at "hello" <?~ "world" $ (42,Map.fromList [("goodnight","gracie")])
--   ("world",(42,fromList [("goodnight","gracie"),("hello","world")]))
--   
--   
--   
--   (<?~) :: Setter s t a (Maybe b)    -> b -> s -> (b, t)
--   (<?~) :: Iso s t a (Maybe b)       -> b -> s -> (b, t)
--   (<?~) :: Lens s t a (Maybe b)      -> b -> s -> (b, t)
--   (<?~) :: Traversal s t a (Maybe b) -> b -> s -> (b, t)
--   
(<?~) :: ASetter s t a (Maybe b) -> b -> s -> (b, t)

-- | Replace the target of a Lens or all of the targets of a
--   Setter or Traversal in our monadic state with a new
--   value, irrespective of the old.
--   
--   This is an alias for (.=).
--   
--   
--   >>> execState (do assign _1 c; assign _2 d) (a,b)
--   (c,d)
--   
--   
--   
--   >>> execState (both .= c) (a,b)
--   (c,c)
--   
--   
--   
--   assign :: MonadState s m => Iso' s a       -> a -> m ()
--   assign :: MonadState s m => Lens' s a      -> a -> m ()
--   assign :: MonadState s m => Traversal' s a -> a -> m ()
--   assign :: MonadState s m => Setter' s a    -> a -> m ()
--   
assign :: MonadState s m => ASetter s s a b -> b -> m ()

-- | Replace the target of a Lens or all of the targets of a
--   Setter or Traversal in our monadic state with a new
--   value, irrespective of the old.
--   
--   This is an infix version of assign.
--   
--   
--   >>> execState (do _1 .= c; _2 .= d) (a,b)
--   (c,d)
--   
--   
--   
--   >>> execState (both .= c) (a,b)
--   (c,c)
--   
--   
--   
--   (.=) :: MonadState s m => Iso' s a       -> a -> m ()
--   (.=) :: MonadState s m => Lens' s a      -> a -> m ()
--   (.=) :: MonadState s m => Traversal' s a -> a -> m ()
--   (.=) :: MonadState s m => Setter' s a    -> a -> m ()
--   
--   
--   It puts the state in the monad or it gets the hose again.
(.=) :: MonadState s m => ASetter s s a b -> b -> m ()

-- | Map over the target of a Lens or all of the targets of a
--   Setter or Traversal in our monadic state.
--   
--   
--   >>> execState (do _1 %= f;_2 %= g) (a,b)
--   (f a,g b)
--   
--   
--   
--   >>> execState (do both %= f) (a,b)
--   (f a,f b)
--   
--   
--   
--   (%=) :: MonadState s m => Iso' s a       -> (a -> a) -> m ()
--   (%=) :: MonadState s m => Lens' s a      -> (a -> a) -> m ()
--   (%=) :: MonadState s m => Traversal' s a -> (a -> a) -> m ()
--   (%=) :: MonadState s m => Setter' s a    -> (a -> a) -> m ()
--   
--   
--   
--   (%=) :: MonadState s m => ASetter s s a b -> (a -> b) -> m ()
--   
(%=) :: (Profunctor p, MonadState s m) => Setting p s s a b -> p a b -> m ()

-- | Modify the target(s) of a Lens', Iso, Setter or
--   Traversal by adding a value.
--   
--   Example:
--   
--   
--   fresh :: MonadState Int m => m Int
--   fresh = do
--     id += 1
--     use id
--   
--   
--   
--   >>> execState (do _1 += c; _2 += d) (a,b)
--   (a + c,b + d)
--   
--   
--   
--   >>> execState (do _1.at 1.non 0 += 10) (Map.fromList [(2,100)],"hello")
--   (fromList [(1,10),(2,100)],"hello")
--   
--   
--   
--   (+=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
--   (+=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
--   (+=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
--   (+=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()
--   
(+=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m ()

-- | Modify the target(s) of a Lens', Iso, Setter or
--   Traversal by subtracting a value.
--   
--   
--   >>> execState (do _1 -= c; _2 -= d) (a,b)
--   (a - c,b - d)
--   
--   
--   
--   (-=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
--   (-=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
--   (-=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
--   (-=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()
--   
(-=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m ()

-- | Modify the target(s) of a Lens', Iso, Setter or
--   Traversal by multiplying by value.
--   
--   
--   >>> execState (do _1 *= c; _2 *= d) (a,b)
--   (a * c,b * d)
--   
--   
--   
--   (*=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
--   (*=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
--   (*=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
--   (*=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()
--   
(*=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m ()

-- | Modify the target(s) of a Lens', Iso, Setter or
--   Traversal by dividing by a value.
--   
--   
--   >>> execState (do _1 //= c; _2 //= d) (a,b)
--   (a / c,b / d)
--   
--   
--   
--   (//=) :: (MonadState s m, Fractional a) => Setter' s a    -> a -> m ()
--   (//=) :: (MonadState s m, Fractional a) => Iso' s a       -> a -> m ()
--   (//=) :: (MonadState s m, Fractional a) => Lens' s a      -> a -> m ()
--   (//=) :: (MonadState s m, Fractional a) => Traversal' s a -> a -> m ()
--   
(//=) :: (MonadState s m, Fractional a) => ASetter' s a -> a -> m ()

-- | Raise the target(s) of a numerically valued Lens, Setter
--   or Traversal to a non-negative integral power.
--   
--   
--   (^=) ::  (MonadState s m, Num a, Integral e) => Setter' s a    -> e -> m ()
--   (^=) ::  (MonadState s m, Num a, Integral e) => Iso' s a       -> e -> m ()
--   (^=) ::  (MonadState s m, Num a, Integral e) => Lens' s a      -> e -> m ()
--   (^=) ::  (MonadState s m, Num a, Integral e) => Traversal' s a -> e -> m ()
--   
(^=) :: (MonadState s m, Num a, Integral e) => ASetter' s a -> e -> m ()

-- | Raise the target(s) of a numerically valued Lens, Setter
--   or Traversal to an integral power.
--   
--   
--   (^^=) ::  (MonadState s m, Fractional a, Integral e) => Setter' s a    -> e -> m ()
--   (^^=) ::  (MonadState s m, Fractional a, Integral e) => Iso' s a       -> e -> m ()
--   (^^=) ::  (MonadState s m, Fractional a, Integral e) => Lens' s a      -> e -> m ()
--   (^^=) ::  (MonadState s m, Fractional a, Integral e) => Traversal' s a -> e -> m ()
--   
(^^=) :: (MonadState s m, Fractional a, Integral e) => ASetter' s a -> e -> m ()

-- | Raise the target(s) of a numerically valued Lens, Setter
--   or Traversal to an arbitrary power
--   
--   
--   >>> execState (do _1 **= c; _2 **= d) (a,b)
--   (a**c,b**d)
--   
--   
--   
--   (**=) ::  (MonadState s m, Floating a) => Setter' s a    -> a -> m ()
--   (**=) ::  (MonadState s m, Floating a) => Iso' s a       -> a -> m ()
--   (**=) ::  (MonadState s m, Floating a) => Lens' s a      -> a -> m ()
--   (**=) ::  (MonadState s m, Floating a) => Traversal' s a -> a -> m ()
--   
(**=) :: (MonadState s m, Floating a) => ASetter' s a -> a -> m ()

-- | Modify the target(s) of a Lens', 'Iso, Setter or
--   Traversal by taking their logical || with a value.
--   
--   
--   >>> execState (do _1 ||= True; _2 ||= False; _3 ||= True; _4 ||= False) (True,True,False,False)
--   (True,True,True,False)
--   
--   
--   
--   (||=) :: MonadState s m => Setter' s Bool    -> Bool -> m ()
--   (||=) :: MonadState s m => Iso' s Bool       -> Bool -> m ()
--   (||=) :: MonadState s m => Lens' s Bool      -> Bool -> m ()
--   (||=) :: MonadState s m => Traversal' s Bool -> Bool -> m ()
--   
(||=) :: MonadState s m => ASetter' s Bool -> Bool -> m ()

-- | Modify the target(s) of a Lens', Iso, Setter or
--   Traversal by mappending a value.
--   
--   
--   >>> execState (do _1 <>= Sum c; _2 <>= Product d) (Sum a,Product b)
--   (Sum {getSum = a + c},Product {getProduct = b * d})
--   
--   
--   
--   >>> execState (both <>= "!!!") ("hello","world")
--   ("hello!!!","world!!!")
--   
--   
--   
--   (<>=) :: (MonadState s m, Monoid a) => Setter' s a -> a -> m ()
--   (<>=) :: (MonadState s m, Monoid a) => Iso' s a -> a -> m ()
--   (<>=) :: (MonadState s m, Monoid a) => Lens' s a -> a -> m ()
--   (<>=) :: (MonadState s m, Monoid a) => Traversal' s a -> a -> m ()
--   
(<>=) :: (MonadState s m, Monoid a) => ASetter' s a -> a -> m ()

-- | Modify the target(s) of a Lens', Iso, Setter or
--   Traversal by taking their logical && with a
--   value.
--   
--   
--   >>> execState (do _1 &&= True; _2 &&= False; _3 &&= True; _4 &&= False) (True,True,False,False)
--   (True,False,False,False)
--   
--   
--   
--   (&&=) :: MonadState s m => Setter' s Bool    -> Bool -> m ()
--   (&&=) :: MonadState s m => Iso' s Bool       -> Bool -> m ()
--   (&&=) :: MonadState s m => Lens' s Bool      -> Bool -> m ()
--   (&&=) :: MonadState s m => Traversal' s Bool -> Bool -> m ()
--   
(&&=) :: MonadState s m => ASetter' s Bool -> Bool -> m ()

-- | Set with pass-through
--   
--   This is useful for chaining assignment without round-tripping through
--   your Monad stack.
--   
--   
--   do x <- _2 <.= ninety_nine_bottles_of_beer_on_the_wall
--   
--   
--   If you do not need a copy of the intermediate result, then using l
--   .= d will avoid unused binding warnings.
--   
--   
--   (<.=) :: MonadState s m => Setter s s a b    -> b -> m b
--   (<.=) :: MonadState s m => Iso s s a b       -> b -> m b
--   (<.=) :: MonadState s m => Lens s s a b      -> b -> m b
--   (<.=) :: MonadState s m => Traversal s s a b -> b -> m b
--   
(<.=) :: MonadState s m => ASetter s s a b -> b -> m b

-- | Replace the target of a Lens or all of the targets of a
--   Setter or Traversal in our monadic state with
--   Just a new value, irrespective of the old.
--   
--   
--   >>> execState (do at 1 ?= a; at 2 ?= b) Map.empty
--   fromList [(1,a),(2,b)]
--   
--   
--   
--   >>> execState (do _1 ?= b; _2 ?= c) (Just a, Nothing)
--   (Just b,Just c)
--   
--   
--   
--   (?=) :: MonadState s m => Iso' s (Maybe a)       -> a -> m ()
--   (?=) :: MonadState s m => Lens' s (Maybe a)      -> a -> m ()
--   (?=) :: MonadState s m => Traversal' s (Maybe a) -> a -> m ()
--   (?=) :: MonadState s m => Setter' s (Maybe a)    -> a -> m ()
--   
(?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m ()

-- | Set Just a value with pass-through
--   
--   This is useful for chaining assignment without round-tripping through
--   your Monad stack.
--   
--   
--   do x <- at foo <?= ninety_nine_bottles_of_beer_on_the_wall
--   
--   
--   If you do not need a copy of the intermediate result, then using l
--   ?= d will avoid unused binding warnings.
--   
--   
--   (<?=) :: MonadState s m => Setter s s a (Maybe b)    -> b -> m b
--   (<?=) :: MonadState s m => Iso s s a (Maybe b)       -> b -> m b
--   (<?=) :: MonadState s m => Lens s s a (Maybe b)      -> b -> m b
--   (<?=) :: MonadState s m => Traversal s s a (Maybe b) -> b -> m b
--   
(<?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m b

-- | Run a monadic action, and set all of the targets of a Lens,
--   Setter or Traversal to its result.
--   
--   
--   (<~) :: MonadState s m => Iso s s a b       -> m b -> m ()
--   (<~) :: MonadState s m => Lens s s a b      -> m b -> m ()
--   (<~) :: MonadState s m => Traversal s s a b -> m b -> m ()
--   (<~) :: MonadState s m => Setter s s a b    -> m b -> m ()
--   
--   
--   As a reasonable mnemonic, this lets you store the result of a monadic
--   action in a Lens rather than in a local variable.
--   
--   
--   do foo <- bar
--      ...
--   
--   
--   will store the result in a variable, while
--   
--   
--   do foo <~ bar
--      ...
--   
--   
--   will store the result in a Lens, Setter, or
--   Traversal.
(<~) :: MonadState s m => ASetter s s a b -> m b -> m ()

-- | Write to a fragment of a larger Writer format.
scribe :: (MonadWriter t m, Monoid s) => ASetter s t a b -> b -> m ()

-- | This is a generalization of pass that alows you to modify just
--   a portion of the resulting MonadWriter.
passing :: MonadWriter w m => Setter w w u v -> m (a, u -> v) -> m a

-- | This is a generalization of pass that alows you to modify just
--   a portion of the resulting MonadWriter with access to the index
--   of an IndexedSetter.
ipassing :: MonadWriter w m => IndexedSetter i w w u v -> m (a, i -> u -> v) -> m a

-- | This is a generalization of censor that alows you to
--   censor just a portion of the resulting MonadWriter.
censoring :: MonadWriter w m => Setter w w u v -> (u -> v) -> m a -> m a

-- | This is a generalization of censor that alows you to
--   censor just a portion of the resulting MonadWriter, with
--   access to the index of an IndexedSetter.
icensoring :: MonadWriter w m => IndexedSetter i w w u v -> (i -> u -> v) -> m a -> m a

-- | Replace the target of a Lens or all of the targets of a
--   Setter' or Traversal with a constant value, without
--   changing its type.
--   
--   This is a type restricted version of set, which retains the
--   type of the original.
--   
--   
--   >>> set' mapped x [a,b,c,d]
--   [x,x,x,x]
--   
--   
--   
--   >>> set' _2 "hello" (1,"world")
--   (1,"hello")
--   
--   
--   
--   >>> set' mapped 0 [1,2,3,4]
--   [0,0,0,0]
--   
--   
--   Note: Attempting to adjust set' a Fold or Getter
--   will fail at compile time with an relatively nice error message.
--   
--   
--   set' :: Setter' s a    -> a -> s -> s
--   set' :: Iso' s a       -> a -> s -> s
--   set' :: Lens' s a      -> a -> s -> s
--   set' :: Traversal' s a -> a -> s -> s
--   
set' :: ASetter' s a -> a -> s -> s

-- | Map with index. (Deprecated alias for iover).
--   
--   When you do not need access to the index, then mapOf is more
--   liberal in what it can accept.
--   
--   
--   mapOf l ≡ imapOf l . const
--   
--   
--   
--   imapOf :: IndexedSetter i s t a b    -> (i -> a -> b) -> s -> t
--   imapOf :: IndexedLens i s t a b      -> (i -> a -> b) -> s -> t
--   imapOf :: IndexedTraversal i s t a b -> (i -> a -> b) -> s -> t
--   

-- | Deprecated: Use iover 
imapOf :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t

-- | Map with index. This is an alias for imapOf.
--   
--   When you do not need access to the index, then over is more
--   liberal in what it can accept.
--   
--   
--   over l ≡ iover l . const
--   iover l ≡ over l . Indexed
--   
--   
--   
--   iover :: IndexedSetter i s t a b    -> (i -> a -> b) -> s -> t
--   iover :: IndexedLens i s t a b      -> (i -> a -> b) -> s -> t
--   iover :: IndexedTraversal i s t a b -> (i -> a -> b) -> s -> t
--   
iover :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t

-- | Build an IndexedSetter from an imap-like function.
--   
--   Your supplied function f is required to satisfy:
--   
--   
--   f id ≡ id
--   f g . f h ≡ f (g . h)
--   
--   
--   Equational reasoning:
--   
--   
--   isets . iover ≡ id
--   iover . isets ≡ id
--   
--   
--   Another way to view sets is that it takes a "semantic editor
--   combinator" and transforms it into a Setter.
isets :: ((i -> a -> b) -> s -> t) -> IndexedSetter i s t a b

-- | Adjust every target of an IndexedSetter, IndexedLens or
--   IndexedTraversal with access to the index.
--   
--   
--   (%@~) ≡ imapOf
--   
--   
--   When you do not need access to the index then (%@~) is more
--   liberal in what it can accept.
--   
--   
--   l %~ f ≡ l %@~ const f
--   
--   
--   
--   (%@~) :: IndexedSetter i s t a b    -> (i -> a -> b) -> s -> t
--   (%@~) :: IndexedLens i s t a b      -> (i -> a -> b) -> s -> t
--   (%@~) :: IndexedTraversal i s t a b -> (i -> a -> b) -> s -> t
--   
(%@~) :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t

-- | Adjust every target in the current state of an IndexedSetter,
--   IndexedLens or IndexedTraversal with access to the
--   index.
--   
--   When you do not need access to the index then (%=) is more
--   liberal in what it can accept.
--   
--   
--   l %= f ≡ l %@= const f
--   
--   
--   
--   (%@=) :: MonadState s m => IndexedSetter i s s a b    -> (i -> a -> b) -> m ()
--   (%@=) :: MonadState s m => IndexedLens i s s a b      -> (i -> a -> b) -> m ()
--   (%@=) :: MonadState s m => IndexedTraversal i s t a b -> (i -> a -> b) -> m ()
--   
(%@=) :: MonadState s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m ()

-- | Anything Settable must be isomorphic to the Identity
--   Functor.
class (Applicative f, Distributive f, Traversable f) => Settable f where untaintedDot g = g `seq` rmap untainted g taintedDot g = g `seq` rmap pure g

-- | Mutator is just a renamed Identity Functor to
--   give better error messages when someone attempts to use a
--   Getter as a Setter.
--   
--   Most user code will never need to see this type.
data Mutator a

-- | mapOf is a deprecated alias for over.

-- | Deprecated: Use over 
mapOf :: Profunctor p => Setting p s t a b -> p a b -> s -> t

-- | Deprecated names for simple lenses, etc.
module Control.Lens.Simple

-- | Deprecated. Use Lens'.

-- | Deprecated: use Lens' 
type SimpleLens s a = Lens s s a a

-- | Deprecated. Use ReifiedLens'.

-- | Deprecated: use Lens' 
type SimpleReifiedLens s a = Lens s s a a

-- | Deprecated. Use Traversal'.

-- | Deprecated: use Traversal' 
type SimpleTraversal s a = Traversal s s a a

-- | Deprecated. Use ReifiedTraversal'.

-- | Deprecated: use ReifiedTraversal' 
type SimpleReifiedTraversal s a = ReifiedTraversal s s a a

-- | Deprecated. Use IndexedTraversal'.

-- | Deprecated: use IndexedTraversal' 
type SimpleIndexedTraversal i s a = IndexedTraversal i s s a a

-- | Deprecated. Use ReifiedIndexedTraversal'.

-- | Deprecated: use ReifiedIndexedTraversal' 
type SimpleReifiedIndexedTraversal i s a = ReifiedIndexedTraversal i s s a a

-- | Deprecated. Use Setter'.

-- | Deprecated: use Setter' 
type SimpleSetter s a = Setter s s a a

-- | Deprecated. Use ReifiedSetter'.

-- | Deprecated: use ReifiedSetter' 
type SimpleReifiedSetter s a = ReifiedSetter s s a a

-- | Deprecated. Use IndexedSetter'.

-- | Deprecated: use IndexedSetter' 
type SimpleIndexedSetter i s a = IndexedSetter i s s a a

-- | Deprecated. Use ReifiedIndexedSetter'.

-- | Deprecated: use ReifiedIndexedSetter' 
type SimpleReifiedIndexedSetter i s a = ReifiedIndexedSetter i s s a a

-- | Deprecated. Use Iso'.

-- | Deprecated: use Iso' 
type SimpleIso s a = Iso s s a a

-- | Deprecated. Use Prism'.

-- | Deprecated: use Prism' 
type SimplePrism s a = Prism s s a a

module Control.Lens.Iso

-- | Isomorphism families can be composed with another Lens using
--   (.) and id.
--   
--   Note: Composition with an Iso is index- and measure-
--   preserving.
type Iso s t a b = forall p f. (Profunctor p, Functor f) => p a (f b) -> p s (f t)

-- | 
--   type Iso' = Simple Iso
--   
type Iso' s a = Iso s s a a

-- | When you see this as an argument to a function, it expects an
--   Iso.
type AnIso s t a b = Exchange a b a (Mutator b) -> Exchange a b s (Mutator t)

-- | A Simple AnIso.
type AnIso' s a = AnIso s s a a

-- | Build a simple isomorphism from a pair of inverse functions.
--   
--   
--   view (iso f g) ≡ f
--   view (from (iso f g)) ≡ g
--   set (iso f g) h ≡ g . h . f
--   set (from (iso f g)) h ≡ f . h . g
--   
iso :: (s -> a) -> (b -> t) -> Iso s t a b

-- | Invert an isomorphism.
--   
--   
--   from (from l) ≡ l
--   
from :: AnIso s t a b -> Iso b a t s

-- | Convert from AnIso back to any Iso.
--   
--   This is useful when you need to store an isomorphism as a data type
--   inside a container and later reconstitute it as an overloaded
--   function.
--   
--   See cloneLens or cloneTraversal for more information on
--   why you might want to do this.
cloneIso :: AnIso s t a b -> Iso s t a b

-- | Extract the two functions, one from s -> a and one from
--   b -> t that characterize an Iso.
withIso :: AnIso s t a b -> ((s -> a) -> (b -> t) -> r) -> r

-- | Based on ala from Conor McBride's work on Epigram.
--   
--   This version is generalized to accept any Iso, not just a
--   newtype.
--   
--   
--   >>> au (wrapping Sum) foldMap [1,2,3,4]
--   10
--   
au :: AnIso s t a b -> ((s -> a) -> e -> b) -> e -> t

-- | Based on ala' from Conor McBride's work on Epigram.
--   
--   This version is generalized to accept any Iso, not just a
--   newtype.
--   
--   For a version you pass the name of the newtype constructor
--   to, see alaf.
--   
--   Mnemonically, the German auf plays a similar role to à
--   la, and the combinator is au with an extra function
--   argument.
--   
--   
--   >>> auf (wrapping Sum) (foldMapOf both) Prelude.length ("hello","world")
--   10
--   
auf :: AnIso s t a b -> ((r -> a) -> e -> b) -> (r -> s) -> e -> t

-- | The opposite of working over a Setter is working
--   under an isomorphism.
--   
--   
--   under ≡ over . from
--   
--   
--   
--   under :: Iso s t a b -> (t -> s) -> b -> a
--   
under :: AnIso s t a b -> (t -> s) -> b -> a

-- | This can be used to lift any Iso into an arbitrary
--   Functor.
mapping :: Functor f => AnIso s t a b -> Iso (f s) (f t) (f a) (f b)

-- | Composition with this isomorphism is occasionally useful when your
--   Lens, Traversal or Iso has a constraint on an
--   unused argument to force that argument to agree with the type of a
--   used argument and avoid ScopedTypeVariables or other
--   ugliness.
simple :: Iso' a a

-- | If v is an element of a type a, and a' is
--   a sans the element v, then non v is
--   an isomorphism from Maybe a' to a.
--   
--   Keep in mind this is only a real isomorphism if you treat the domain
--   as being Maybe (a sans v).
--   
--   This is practically quite useful when you want to have a Map
--   where all the entries should have non-zero values.
--   
--   
--   >>> Map.fromList [("hello",1)] & at "hello" . non 0 +~ 2
--   fromList [("hello",3)]
--   
--   
--   
--   >>> Map.fromList [("hello",1)] & at "hello" . non 0 -~ 1
--   fromList []
--   
--   
--   
--   >>> Map.fromList [("hello",1)] ^. at "hello" . non 0
--   1
--   
--   
--   
--   >>> Map.fromList [] ^. at "hello" . non 0
--   0
--   
--   
--   This combinator is also particularly useful when working with nested
--   maps.
--   
--   e.g. When you want to create the nested Map when it is
--   missing:
--   
--   
--   >>> Map.empty & at "hello" . non Map.empty . at "world" ?~ "!!!"
--   fromList [("hello",fromList [("world","!!!")])]
--   
--   
--   and when have deleting the last entry from the nested Map mean
--   that we should delete its entry from the surrounding one:
--   
--   
--   >>> fromList [("hello",fromList [("world","!!!")])] & at "hello" . non Map.empty . at "world" .~ Nothing
--   fromList []
--   
non :: Eq a => a -> Iso' (Maybe a) a

-- | anon a p generalizes non a to take any
--   value and a predicate.
--   
--   This function assumes that p a holds True and
--   generates an isomorphism between Maybe (a | not (p
--   a)) and a.
--   
--   
--   >>> Map.empty & at "hello" . anon Map.empty Map.null . at "world" ?~ "!!!"
--   fromList [("hello",fromList [("world","!!!")])]
--   
--   
--   
--   >>> fromList [("hello",fromList [("world","!!!")])] & at "hello" . anon Map.empty Map.null . at "world" .~ Nothing
--   fromList []
--   
anon :: a -> (a -> Bool) -> Iso' (Maybe a) a

-- | This isomorphism can be used to convert to or from an instance of
--   Enum.
--   
--   
--   >>> LT^.from enum
--   0
--   
--   
--   
--   >>> 97^.enum :: Char
--   'a'
--   
--   
--   Note: this is only an isomorphism from the numeric range actually used
--   and it is a bit of a pleasant fiction, since there are questionable
--   Enum instances for Double, and Float that exist
--   solely for [1.0 .. 4.0] sugar and the instances for those and
--   Integer don't cover all values in their range.
enum :: Enum a => Iso' Int a

-- | The canonical isomorphism for currying and uncurrying a function.
--   
--   
--   curried = iso curry uncurry
--   
--   
--   
--   >>> (fst^.curried) 3 4
--   3
--   
--   
--   
--   >>> view curried fst 3 4
--   3
--   
curried :: Iso ((a, b) -> c) ((d, e) -> f) (a -> b -> c) (d -> e -> f)

-- | The canonical isomorphism for uncurrying and currying a function.
--   
--   
--   uncurried = iso uncurry curry
--   
--   
--   
--   uncurried = from curried
--   
--   
--   
--   >>> ((+)^.uncurried) (1,2)
--   3
--   
uncurried :: Iso (a -> b -> c) (d -> e -> f) ((a, b) -> c) ((d, e) -> f)

-- | The isomorphism for flipping a function.
--   
--   
--   >>> ((,)^.flipped) 1 2
--   (2,1)
--   
flipped :: Iso (a -> b -> c) (a' -> b' -> c') (b -> a -> c) (b' -> a' -> c')

-- | This class provides for symmetric bifunctors.
class Bifunctor p => Swapped p
swapped :: Swapped p => Iso (p a b) (p c d) (p b a) (p d c)

-- | Ad hoc conversion between "strict" and "lazy" versions of a structure,
--   such as Text or ByteString.
class Strict s a | s -> a, a -> s
strict :: Strict s a => Iso' s a

-- | This class provides a generalized notion of list reversal extended to
--   other containers.
class Reversing t
reversing :: Reversing t => t -> t

-- | An Iso between a list, ByteString, Text fragment,
--   etc. and its reversal.
--   
--   
--   >>> "live" ^. reversed
--   "evil"
--   
--   
--   
--   >>> "live" & reversed %~ ('d':)
--   "lived"
--   
reversed :: Reversing a => Iso' a a

-- | Given a function that is its own inverse, this gives you an Iso
--   using it in both directions.
--   
--   
--   involuted ≡ join iso
--   
--   
--   
--   >>> "live" ^. involuted reverse
--   "evil"
--   
--   
--   
--   >>> "live" & involuted reverse %~ ('d':)
--   "lived"
--   
involuted :: (a -> a) -> Iso' a a

-- | This isomorphism can be used to inspect a Traversal to see how
--   it associates the structure and it can also be used to bake the
--   Traversal into a Magma so that you can traverse over it
--   multiple times.
magma :: LensLike (Mafic a b) s t a b -> Iso s u (Magma Int t b a) (Magma j u c c)

-- | This isomorphism can be used to inspect an IndexedTraversal to
--   see how it associates the structure and it can also be used to bake
--   the IndexedTraversal into a Magma so that you can
--   traverse over it multiple times with access to the original indices.
imagma :: Overloading (Indexed i) (->) (Molten i a b) s t a b -> Iso s t' (Magma i t b a) (Magma j t' c c)

-- | This provides a way to peek at the internal structure of a
--   Traversal or IndexedTraversal
data Magma i t b a

-- | Lift an Iso into a Contravariant functor.
--   
--   
--   contramapping :: Contravariant f => Iso s t a b -> Iso (f a) (f b) (f s) (f t)
--   contramapping :: Contravariant f => Iso' s a -> Iso' (f a) (f s)
--   
contramapping :: Contravariant f => AnIso s t a b -> Iso (f a) (f b) (f s) (f t)

-- | Formally, the class Profunctor represents a profunctor from
--   Hask -> Hask.
--   
--   Intuitively it is a bifunctor where the first argument is
--   contravariant and the second argument is covariant.
--   
--   You can define a Profunctor by either defining dimap or
--   by defining both lmap and rmap.
--   
--   If you supply dimap, you should ensure that:
--   
--   
--   dimap id id ≡ id
--   
--   
--   If you supply lmap and rmap, ensure:
--   
--   
--   lmap id ≡ id
--   rmap id ≡ id
--   
--   
--   If you supply both, you should also ensure:
--   
--   
--   dimap f g ≡ lmap f . rmap g
--   
--   
--   These ensure by parametricity:
--   
--   
--   dimap (f . g) (h . i) ≡ dimap g h . dimap f i
--   lmap (f . g) ≡ lmap g . lmap f
--   rmap (f . g) ≡ rmap f . rmap g
--   
class Profunctor (p :: * -> * -> *)
dimap :: Profunctor p => (a -> b) -> (c -> d) -> p b c -> p a d
lmap :: Profunctor p => (a -> b) -> p b c -> p a c
rmap :: Profunctor p => (b -> c) -> p a b -> p a c

-- | Lift two Isos into both arguments of a Profunctor
--   simultaneously.
--   
--   
--   dimapping :: Profunctor p => Iso s t a b -> Iso s' t' a' b' -> Iso (p a s') (p b t') (p s a') (p t b')
--   dimapping :: Profunctor p => Iso' s a -> Iso' s' a' -> Iso' (p a s') (p s a')
--   
dimapping :: Profunctor p => AnIso s t a b -> AnIso s' t' a' b' -> Iso (p a s') (p b t') (p s a') (p t b')

-- | Lift an Iso contravariantly into the left argument of a
--   Profunctor.
--   
--   
--   lmapping :: Profunctor p => Iso s t a b -> Iso (p a x) (p b y) (p s x) (p t y)
--   lmapping :: Profunctor p => Iso' s a -> Iso' (p a x) (p s x)
--   
lmapping :: Profunctor p => AnIso s t a b -> Iso (p a x) (p b y) (p s x) (p t y)

-- | Lift an Iso covariantly into the right argument of a
--   Profunctor.
--   
--   
--   rmapping :: Profunctor p => Iso s t a b -> Iso (p x s) (p y t) (p x a) (p y b)
--   rmapping :: Profunctor p => Iso' s a -> Iso' (p x s) (p x a)
--   
rmapping :: Profunctor p => AnIso s t a b -> Iso (p x s) (p y t) (p x a) (p y b)
instance Strict (RWST r w s m a) (RWST r w s m a)
instance Strict (WriterT w m a) (WriterT w m a)
instance Strict (StateT s m a) (StateT s m a)
instance Strict Text Text
instance Strict ByteString ByteString
instance Swapped Either
instance Swapped (,)

-- | A Getter s a is just any function (s ->
--   a), which we've flipped into continuation passing style, (a
--   -> r) -> s -> r and decorated with Accessor to
--   obtain:
--   
--   
--   type Getting r s t a b = (a -> Accessor r b) -> s -> Accessor r t
--   
--   
--   If we restrict access to knowledge about the type r and can
--   work for any b and t, we could get:
--   
--   
--   type Getter s a = forall r. Getting r s s a a
--   
--   
--   But we actually hide the use of Accessor behind a class
--   Gettable to error messages from type class resolution rather
--   than at unification time, where they are much uglier.
--   
--   
--   type Getter s a = forall f. Gettable f => (a -> f a) -> s -> f s
--   
--   
--   Everything you can do with a function, you can do with a
--   Getter, but note that because of the continuation passing style
--   (.) composes them in the opposite order.
--   
--   Since it is only a function, every Getter obviously only
--   retrieves a single value for a given input.
module Control.Lens.Getter

-- | A Getter describes how to retrieve a single value in a way that
--   can be composed with other LensLike constructions.
--   
--   Unlike a Lens a Getter is read-only. Since a
--   Getter cannot be used to write back there are no Lens
--   laws that can be applied to it. In fact, it is isomorphic to an
--   arbitrary function from (a -> s).
--   
--   Moreover, a Getter can be used directly as a Fold, since
--   it just ignores the Applicative.
type Getter s a = forall f. (Contravariant f, Functor f) => (a -> f a) -> s -> f s

-- | Every IndexedGetter is a valid IndexedFold and can be
--   used for Getting like a Getter.
type IndexedGetter i s a = forall p f. (Indexable i p, Contravariant f, Functor f) => p a (f a) -> s -> f s

-- | When you see this in a type signature it indicates that you can pass
--   the function a Lens, Getter, Traversal,
--   Fold, Prism, Iso, or one of the indexed variants,
--   and it will just "do the right thing".
--   
--   Most Getter combinators are able to be used with both a
--   Getter or a Fold in limited situations, to do so, they
--   need to be monomorphic in what we are going to extract with
--   Const. To be compatible with Lens, Traversal and
--   Iso we also restricted choices of the irrelevant t and
--   b parameters.
--   
--   If a function accepts a Getting r s t a b, then when
--   r is a Monoid, then you can pass a Fold (or
--   Traversal), otherwise you can only pass this a Getter or
--   Lens.
type Getting r s a = (a -> Accessor r a) -> s -> Accessor r s

-- | Used to consume an IndexedFold.
type IndexedGetting i m s a = Indexed i a (Accessor m a) -> s -> Accessor m s

-- | This is a convenient alias used when consuming (indexed) getters and
--   (indexed) folds in a highly general fashion.
type Accessing p m s a = p a (Accessor m a) -> s -> Accessor m s

-- | Build a Getter from an arbitrary Haskell function.
--   
--   
--   to f . to g ≡ to (g . f)
--   
--   
--   
--   a ^. to f ≡ f a
--   
--   
--   
--   >>> a ^.to f
--   f a
--   
--   
--   
--   >>> ("hello","world")^.to snd
--   "world"
--   
--   
--   
--   >>> 5^.to succ
--   6
--   
--   
--   
--   >>> (0, -5)^._2.to abs
--   5
--   
to :: (s -> a) -> IndexPreservingGetter s a

-- | View the value pointed to by a Getter or Lens or the
--   result of folding over all the results of a Fold or
--   Traversal that points at a monoidal values.
--   
--   This is the same operation as view with the arguments flipped.
--   
--   The fixity and semantics are such that subsequent field accesses can
--   be performed with (.).
--   
--   
--   >>> (a,b)^._2
--   b
--   
--   
--   
--   >>> ("hello","world")^._2
--   "world"
--   
--   
--   
--   >>> import Data.Complex
--   
--   >>> ((0, 1 :+ 2), 3)^._1._2.to magnitude
--   2.23606797749979
--   
--   
--   
--   (^.) ::             s -> Getter s a     -> a
--   (^.) :: Monoid m => s -> Fold s m       -> m
--   (^.) ::             s -> Iso' s a       -> a
--   (^.) ::             s -> Lens' s a      -> a
--   (^.) :: Monoid m => s -> Traversal' s m -> m
--   
(^.) :: s -> Getting a s a -> a

-- | View the value pointed to by a Getter, Iso or
--   Lens or the result of folding over all the results of a
--   Fold or Traversal that points at a monoidal value.
--   
--   
--   view . to ≡ id
--   
--   
--   
--   >>> view (to f) a
--   f a
--   
--   
--   
--   >>> view _2 (1,"hello")
--   "hello"
--   
--   
--   
--   >>> view (to succ) 5
--   6
--   
--   
--   
--   >>> view (_2._1) ("hello",("world","!!!"))
--   "world"
--   
--   
--   As view is commonly used to access the target of a
--   Getter or obtain a monoidal summary of the targets of a
--   Fold, It may be useful to think of it as having one of these
--   more restricted signatures:
--   
--   
--   view ::             Getter s a     -> s -> a
--   view :: Monoid m => Fold s m       -> s -> m
--   view ::             Iso' s a       -> s -> a
--   view ::             Lens' s a      -> s -> a
--   view :: Monoid m => Traversal' s m -> s -> m
--   
--   
--   In a more general setting, such as when working with a Monad
--   transformer stack you can use:
--   
--   
--   view :: MonadReader s m             => Getter s a     -> m a
--   view :: (MonadReader s m, Monoid a) => Fold s a       -> m a
--   view :: MonadReader s m             => Iso' s a       -> m a
--   view :: MonadReader s m             => Lens' s a      -> m a
--   view :: (MonadReader s m, Monoid a) => Traversal' s a -> m a
--   
view :: MonadReader s m => Getting a s a -> m a

-- | View a function of the value pointed to by a Getter or
--   Lens or the result of folding over the result of mapping the
--   targets of a Fold or Traversal.
--   
--   
--   views l f ≡ view (l . to f)
--   
--   
--   
--   >>> views (to f) g a
--   g (f a)
--   
--   
--   
--   >>> views _2 length (1,"hello")
--   5
--   
--   
--   As views is commonly used to access the target of a
--   Getter or obtain a monoidal summary of the targets of a
--   Fold, It may be useful to think of it as having one of these
--   more restricted signatures:
--   
--   
--   views ::             Getter s a     -> (a -> r) -> s -> r
--   views :: Monoid m => Fold s a       -> (a -> m) -> s -> m
--   views ::             Iso' s a       -> (a -> r) -> s -> r
--   views ::             Lens' s a      -> (a -> r) -> s -> r
--   views :: Monoid m => Traversal' s a -> (a -> m) -> s -> m
--   
--   
--   In a more general setting, such as when working with a Monad
--   transformer stack you can use:
--   
--   
--   view :: MonadReader s m             => Getter s a     -> m a
--   view :: (MonadReader s m, Monoid a) => Fold s a       -> m a
--   view :: MonadReader s m             => Iso' s a       -> m a
--   view :: MonadReader s m             => Lens' s a      -> m a
--   view :: (MonadReader s m, Monoid a) => Traversal' s a -> m a
--   
--   
--   
--   views :: MonadReader s m => Getting r s a -> (a -> r) -> m r
--   
views :: (Profunctor p, MonadReader s m) => Overloading p (->) (Accessor r) s s a a -> p a r -> m r

-- | Use the target of a Lens, Iso, or Getter in the
--   current state, or use a summary of a Fold or Traversal
--   that points to a monoidal value.
--   
--   
--   >>> evalState (use _1) (a,b)
--   a
--   
--   
--   
--   >>> evalState (use _1) ("hello","world")
--   "hello"
--   
--   
--   
--   use :: MonadState s m             => Getter s a     -> m a
--   use :: (MonadState s m, Monoid r) => Fold s r       -> m r
--   use :: MonadState s m             => Iso' s a       -> m a
--   use :: MonadState s m             => Lens' s a      -> m a
--   use :: (MonadState s m, Monoid r) => Traversal' s r -> m r
--   
use :: MonadState s m => Getting a s a -> m a

-- | Use the target of a Lens, Iso or Getter in the
--   current state, or use a summary of a Fold or Traversal
--   that points to a monoidal value.
--   
--   
--   >>> evalState (uses _1 length) ("hello","world")
--   5
--   
--   
--   
--   uses :: MonadState s m             => Getter s a     -> (a -> r) -> m r
--   uses :: (MonadState s m, Monoid r) => Fold s a       -> (a -> r) -> m r
--   uses :: MonadState s m             => Lens' s a      -> (a -> r) -> m r
--   uses :: MonadState s m             => Iso' s a       -> (a -> r) -> m r
--   uses :: (MonadState s m, Monoid r) => Traversal' s a -> (a -> r) -> m r
--   
--   
--   
--   uses :: MonadState s m => Getting r s t a b -> (a -> r) -> m r
--   
uses :: (Profunctor p, MonadState s m) => Overloading p (->) (Accessor r) s s a a -> p a r -> m r

-- | This is a generalized form of listen that only extracts the
--   portion of the log that is focused on by a Getter. If given a
--   Fold or a Traversal then a monoidal summary of the parts
--   of the log that are visited will be returned.
--   
--   
--   listening :: MonadWriter w m             => Getter w u     -> m a -> m (a, u)
--   listening :: MonadWriter w m             => Lens' w u      -> m a -> m (a, u)
--   listening :: MonadWriter w m             => Iso' w u       -> m a -> m (a, u)
--   listening :: (MonadWriter w m, Monoid u) => Fold w u       -> m a -> m (a, u)
--   listening :: (MonadWriter w m, Monoid u) => Traversal' w u -> m a -> m (a, u)
--   listening :: (MonadWriter w m, Monoid u) => Prism' w u     -> m a -> m (a, u)
--   
listening :: MonadWriter w m => Getting u w u -> m a -> m (a, u)

-- | This is a generalized form of listen that only extracts the
--   portion of the log that is focused on by a Getter. If given a
--   Fold or a Traversal then a monoidal summary of the parts
--   of the log that are visited will be returned.
--   
--   
--   listenings :: MonadWriter w m             => Getter w u     -> (u -> v) -> m a -> m (a, v)
--   listenings :: MonadWriter w m             => Lens' w u      -> (u -> v) -> m a -> m (a, v)
--   listenings :: MonadWriter w m             => Iso' w u       -> (u -> v) -> m a -> m (a, v)
--   listenings :: (MonadWriter w m, Monoid v) => Fold w u       -> (u -> v) -> m a -> m (a, v)
--   listenings :: (MonadWriter w m, Monoid v) => Traversal' w u -> (u -> v) -> m a -> m (a, v)
--   listenings :: (MonadWriter w m, Monoid v) => Prism' w u     -> (u -> v) -> m a -> m (a, v)
--   
listenings :: MonadWriter w m => Getting v w u -> (u -> v) -> m a -> m (a, v)

-- | View the value pointed to by a Getter or Lens.
--   
--   This is the same operation as iview with the arguments flipped.
--   
--   The fixity and semantics are such that subsequent field accesses can
--   be performed with (.).
--   
--   
--   >>> (a,b,c,d)^@._2
--   (1,b)
--   
--   
--   
--   >>> ("hello","world","!!!")^@._2
--   (1,"world")
--   
--   
--   
--   (^@.) :: s -> IndexedGetter i s a -> (i, a)
--   (^@.) :: s -> IndexedLens' i s a  -> (i, a)
--   
--   
--   The result probably doesn't have much meaning when applied to an
--   IndexedFold.
(^@.) :: s -> IndexedGetting i (i, a) s a -> (i, a)

-- | View the index and value of an IndexedGetter into the current
--   environment as a pair.
--   
--   When applied to an IndexedFold the result will most likely be a
--   nonsensical monoidal summary of the indices tupled with a monoidal
--   summary of the values and probably not whatever it is you wanted.
iview :: MonadReader s m => IndexedGetting i (i, a) s a -> m (i, a)

-- | View a function of the index and value of an IndexedGetter into
--   the current environment.
--   
--   When applied to an IndexedFold the result will be a monoidal
--   summary instead of a single answer.
--   
--   
--   iviews ≡ ifoldMapOf
--   
iviews :: MonadReader s m => IndexedGetting i r s a -> (i -> a -> r) -> m r

-- | Use the index and value of an IndexedGetter into the current
--   state as a pair.
--   
--   When applied to an IndexedFold the result will most likely be a
--   nonsensical monoidal summary of the indices tupled with a monoidal
--   summary of the values and probably not whatever it is you wanted.
iuse :: MonadState s m => IndexedGetting i (i, a) s a -> m (i, a)

-- | Use a function of the index and value of an IndexedGetter into
--   the current state.
--   
--   When applied to an IndexedFold the result will be a monoidal
--   summary instead of a single answer.
iuses :: MonadState s m => IndexedGetting i r s a -> (i -> a -> r) -> m r

-- | This is a generalized form of listen that only extracts the
--   portion of the log that is focused on by a Getter. If given a
--   Fold or a Traversal then a monoidal summary of the parts
--   of the log that are visited will be returned.
--   
--   
--   ilistening :: MonadWriter w m             => IndexedGetter i w u     -> m a -> m (a, (i, u))
--   ilistening :: MonadWriter w m             => IndexedLens' i w u      -> m a -> m (a, (i, u))
--   ilistening :: (MonadWriter w m, Monoid u) => IndexedFold i w u       -> m a -> m (a, (i, u))
--   ilistening :: (MonadWriter w m, Monoid u) => IndexedTraversal' i w u -> m a -> m (a, (i, u))
--   
ilistening :: MonadWriter w m => IndexedGetting i (i, u) w u -> m a -> m (a, (i, u))

-- | This is a generalized form of listen that only extracts the
--   portion of the log that is focused on by a Getter. If given a
--   Fold or a Traversal then a monoidal summary of the parts
--   of the log that are visited will be returned.
--   
--   
--   ilistenings :: MonadWriter w m             => IndexedGetter w u     -> (i -> u -> v) -> m a -> m (a, v)
--   ilistenings :: MonadWriter w m             => IndexedLens' w u      -> (i -> u -> v) -> m a -> m (a, v)
--   ilistenings :: (MonadWriter w m, Monoid v) => IndexedFold w u       -> (i -> u -> v) -> m a -> m (a, v)
--   ilistenings :: (MonadWriter w m, Monoid v) => IndexedTraversal' w u -> (i -> u -> v) -> m a -> m (a, v)
--   
ilistenings :: MonadWriter w m => IndexedGetting i v w u -> (i -> u -> v) -> m a -> m (a, v)

-- | Any instance should be subject to the following laws:
--   
--   
--   contramap id = id
--   contramap f . contramap g = contramap (g . f)
--   
--   
--   Note, that the second law follows from the free theorem of the type of
--   contramap and the first law, so you need only check that the
--   former condition holds.
class Contravariant (f :: * -> *)
contramap :: Contravariant f => (a -> b) -> f b -> f a

-- | This Generalizes Const so we can apply simple
--   Applicative transformations to it and so we can get nicer error
--   messages.
--   
--   A Functor you can coerce ignores its argument, which it
--   carries solely as a phantom type parameter.
--   
--   By the Functor and Contravariant laws, an instance of
--   Gettable will necessarily satisfy:
--   
--   
--   id = fmap f = coerce = contramap g
--   
coerce :: (Contravariant f, Functor f) => f a -> f b

-- | Coerce a Gettable LensLike to a Simple
--   LensLike. This is useful when using a Traversal that is
--   not simple as a Getter or a Fold.
coerced :: (Functor f, Contravariant f) => LensLike f s t a b -> LensLike' f s a

-- | Used instead of Const to report
--   
--   
--   No instance for (Settable Accessor)
--   
--   
--   when the user attempts to misuse a Setter as a Getter,
--   rather than a monolithic unification error.
newtype Accessor r a
Accessor :: r -> Accessor r a
runAccessor :: Accessor r a -> r

-- | This class is provided mostly for backwards compatibility with lens
--   3.8, but it can also shorten type signatures.
class (Contravariant f, Functor f) => Gettable f

module Data.Set.Lens

-- | This Setter can be used to change the type of a Set by
--   mapping the elements to new values.
--   
--   Sadly, you can't create a valid Traversal for a Set, but
--   you can manipulate it by reading using folded and reindexing it
--   via setmapped.
--   
--   
--   >>> over setmapped (+1) (fromList [1,2,3,4])
--   fromList [2,3,4,5]
--   
setmapped :: (Ord i, Ord j) => IndexPreservingSetter (Set i) (Set j) i j

-- | Construct a set from a Getter, Fold, Traversal,
--   Lens or Iso.
--   
--   
--   >>> setOf folded ["hello","world"]
--   fromList ["hello","world"]
--   
--   
--   
--   >>> setOf (folded._2) [("hello",1),("world",2),("!!!",3)]
--   fromList [1,2,3]
--   
--   
--   
--   setOf ::          Getter s a     -> s -> Set a
--   setOf :: Ord a => Fold s a       -> s -> Set a
--   setOf ::          Iso' s a       -> s -> Set a
--   setOf ::          Lens' s a      -> s -> Set a
--   setOf :: Ord a => Traversal' s a -> s -> Set a
--   
setOf :: Getting (Set a) s a -> s -> Set a

-- | A Review is a type-restricted form of a Prism that can
--   only be used for writing back via re, review,
--   reuse.
module Control.Lens.Review

-- | This is a limited form of a Prism that can only be used for
--   re operations.
--   
--   Like with a Getter, there are no laws to state for a
--   Review.
--   
--   You can generate a Review by using unto. You can also
--   use any Prism or Iso directly as a Review.
type Review s t a b = forall p f. (Profunctor p, Bifunctor p, Settable f) => Overloaded p f s t a b

-- | A Simple Review
type Review' t b = Review t t b b

-- | If you see this in a signature for a function, the function is
--   expecting a Review (in practice, this usually means a
--   Prism).
type AReview s t a b = Overloaded Reviewed Identity s t a b

-- | A Simple AReview
type AReview' t b = AReview t t b b

-- | An analogue of to for review.
--   
--   
--   unto :: (b -> t) -> Review' t b
--   
unto :: (Profunctor p, Bifunctor p, Functor f) => (b -> t) -> Overloaded p f s t a b

-- | Turn a Prism or Iso around to build a Getter.
--   
--   If you have an Iso, from is a more powerful version of
--   this function that will return an Iso instead of a mere
--   Getter.
--   
--   
--   >>> 5 ^.re _Left
--   Left 5
--   
--   
--   
--   >>> 6 ^.re (_Left.unto succ)
--   Left 7
--   
--   
--   
--   review  ≡ view  . re
--   reviews ≡ views . re
--   reuse   ≡ use   . re
--   reuses  ≡ uses  . re
--   
--   
--   
--   re :: Prism s t a b -> Getter b t
--   re :: Iso s t a b   -> Getter b t
--   
re :: AReview s t a b -> Getter b t

-- | This can be used to turn an Iso or Prism around and
--   view a value (or the current environment) through it the other
--   way.
--   
--   
--   review ≡ view . re
--   review . unto ≡ id
--   
--   
--   
--   >>> review _Left "mustard"
--   Left "mustard"
--   
--   
--   
--   >>> review (unto succ) 5
--   6
--   
--   
--   Usually review is used in the (->) Monad
--   with a Prism or Iso, in which case it may be useful to
--   think of it as having one of these more restricted type signatures:
--   
--   
--   review :: Iso' s a   -> a -> s
--   review :: Prism' s a -> a -> s
--   
--   
--   However, when working with a Monad transformer stack, it is
--   sometimes useful to be able to review the current environment,
--   in which case one of these more slightly more liberal type signatures
--   may be beneficial to think of it as having:
--   
--   
--   review :: MonadReader a m => Iso' s a   -> m s
--   review :: MonadReader a m => Prism' s a -> m s
--   
review :: MonadReader b m => AReview s t a b -> m t

-- | This can be used to turn an Iso or Prism around and
--   view a value (or the current environment) through it the other
--   way, applying a function.
--   
--   
--   reviews ≡ views . re
--   reviews (unto f) g ≡ g . f
--   
--   
--   
--   >>> reviews _Left isRight "mustard"
--   False
--   
--   
--   
--   >>> reviews (unto succ) (*2) 3
--   8
--   
--   
--   Usually this function is used in the (->) Monad
--   with a Prism or Iso, in which case it may be useful to
--   think of it as having one of these more restricted type signatures:
--   
--   
--   reviews :: Iso' s a   -> (s -> r) -> a -> r
--   reviews :: Prism' s a -> (s -> r) -> a -> r
--   
--   
--   However, when working with a Monad transformer stack, it is
--   sometimes useful to be able to review the current environment,
--   in which case one of these more slightly more liberal type signatures
--   may be beneficial to think of it as having:
--   
--   
--   reviews :: MonadReader a m => Iso' s a   -> (s -> r) -> m r
--   reviews :: MonadReader a m => Prism' s a -> (s -> r) -> m r
--   
reviews :: MonadReader b m => AReview s t a b -> (t -> r) -> m r

-- | This can be used to turn an Iso or Prism around and
--   use a value (or the current environment) through it the other
--   way.
--   
--   
--   reuse ≡ use . re
--   reuse . unto ≡ gets
--   
--   
--   
--   >>> evalState (reuse _Left) 5
--   Left 5
--   
--   
--   
--   >>> evalState (reuse (unto succ)) 5
--   6
--   
--   
--   
--   reuse :: MonadState a m => Prism' s a -> m s
--   reuse :: MonadState a m => Iso' s a   -> m s
--   
reuse :: MonadState b m => AReview s t a b -> m t

-- | This can be used to turn an Iso or Prism around and
--   use the current state through it the other way, applying a
--   function.
--   
--   
--   reuses ≡ uses . re
--   reuses (unto f) g ≡ gets (g . f)
--   
--   
--   
--   >>> evalState (reuses _Left isLeft) (5 :: Int)
--   True
--   
--   
--   
--   reuses :: MonadState a m => Prism' s a -> (s -> r) -> m r
--   reuses :: MonadState a m => Iso' s a   -> (s -> r) -> m r
--   
reuses :: MonadState b m => AReview s t a b -> (t -> r) -> m r

-- | An infix alias for review.
--   
--   
--   unto f # x ≡ f x
--   l # x ≡ x ^. re l
--   
--   
--   This is commonly used when using a Prism as a smart
--   constructor.
--   
--   
--   >>> _Left # 4
--   Left 4
--   
--   
--   But it can be used for any Prism
--   
--   
--   >>> base 16 # 123
--   "7b"
--   
--   
--   
--   (#) :: Iso'      s a -> a -> s
--   (#) :: Prism'    s a -> a -> s
--   (#) :: Review'   s a -> a -> s
--   (#) :: Equality' s a -> a -> s
--   
(#) :: AReview s t a b -> b -> t

-- | Minimal definition either bimap or first and
--   second
--   
--   Formally, the class Bifunctor represents a bifunctor from
--   Hask -> Hask.
--   
--   Intuitively it is a bifunctor where both the first and second
--   arguments are covariant.
--   
--   You can define a Bifunctor by either defining bimap or
--   by defining both first and second.
--   
--   If you supply bimap, you should ensure that:
--   
--   
--   bimap id id ≡ id
--   
--   
--   If you supply first and second, ensure:
--   
--   
--   first id ≡ id
--   second id ≡ id
--   
--   
--   If you supply both, you should also ensure:
--   
--   
--   bimap f g ≡ first f . second g
--   
--   
--   These ensure by parametricity:
--   
--   
--   bimap  (f . g) (h . i) ≡ bimap f h . bimap g i
--   first  (f . g) ≡ first  f . first  g
--   second (f . g) ≡ second f . second g
--   
class Bifunctor (p :: * -> * -> *)
bimap :: Bifunctor p => (a -> b) -> (c -> d) -> p a c -> p b d

-- | This is a profunctor used internally to implement Review
--   
--   It plays a role similar to that of Accessor or Const do
--   for Control.Lens.Getter
retagged :: (Profunctor p, Bifunctor p) => p a b -> p s b

-- | This class is provided mostly for backwards compatibility with lens
--   3.8, but it can also shorten type signatures.
class (Profunctor p, Bifunctor p) => Reviewable p

-- | The Wrapped class provides similar functionality as
--   Control.Newtype, from the newtype package, but in a
--   more convenient and efficient form.
--   
--   There are a few functions from newtype that are not provided
--   here, because they can be done with the Iso directly:
--   
--   
--   Control.Newtype.over Sum f ≡ wrapping Sum %~ f
--   Control.Newtype.under Sum f ≡ unwrapping Sum %~ f
--   Control.Newtype.overF Sum f ≡ mapping (wrapping Sum) %~ f
--   Control.Newtype.underF Sum f ≡ mapping (unwrapping Sum) %~ f
--   
--   
--   under can also be used with wrapping to provide the
--   equivalent of Control.Newtype.under. Also, most use cases
--   don't need full polymorphism, so only the single constructor
--   wrapping functions would be needed.
--   
--   These equivalences aren't 100% honest, because newtype's
--   operators need to rely on two Newtype constraints. This means
--   that the wrapper used for the output is not necessarily the same as
--   the input.
module Control.Lens.Wrapped

-- | Wrapped provides isomorphisms to wrap and unwrap newtypes or
--   data types with one constructor.
class Wrapped s t a b | a -> s, b -> t, a t -> s, b s -> t
wrapped :: Wrapped s t a b => Iso s t a b

-- | This is a convenient alias for from wrapped.
--   
--   
--   >>> Const "hello" & unwrapped %~ length & getConst
--   5
--   
unwrapped :: Wrapped t s b a => Iso a b s t

-- | A convenient type-restricted version of wrapped for aiding type
--   inference.
wrapped' :: Wrapped s s a a => Iso' s a

-- | A convenient type-restricted version of unwrapped for aiding
--   type inference.
unwrapped' :: Wrapped s s a a => Iso' a s

-- | This is a convenient version of wrapped with an argument that's
--   ignored.
--   
--   The argument is used to specify which newtype the user intends to wrap
--   by using the constructor for that newtype.
--   
--   The user supplied function is ignored, merely its type is used.
wrapping :: Wrapped s s a a => (s -> a) -> Iso s s a a

-- | This is a convenient version of unwrapped with an argument
--   that's ignored.
--   
--   The argument is used to specify which newtype the user intends to
--   remove by using the constructor for that newtype.
--   
--   The user supplied function is ignored, merely its type is used.
unwrapping :: Wrapped s s a a => (s -> a) -> Iso a a s s

-- | This is a convenient version of wrapped with two arguments that
--   are ignored.
--   
--   These arguments are used to which newtype the user intends to wrap and
--   should both be the same constructor. This redundancy is necessary in
--   order to find the full polymorphic isomorphism family.
--   
--   The user supplied functions are ignored, merely their types are
--   used.
wrappings :: Wrapped s t a b => (s -> a) -> (t -> b) -> Iso s t a b

-- | This is a convenient version of unwrapped with two arguments
--   that are ignored.
--   
--   These arguments are used to which newtype the user intends to remove
--   and should both be the same constructor. This redundancy is necessary
--   in order to find the full polymorphic isomorphism family.
--   
--   The user supplied functions are ignored, merely their types are
--   used.
unwrappings :: Wrapped t s b a => (s -> a) -> (t -> b) -> Iso a b s t

-- | Given the constructor for a Wrapped type, return a
--   deconstructor that is its inverse.
--   
--   Assuming the Wrapped instance is legal, these laws hold:
--   
--   
--   op f . f ≡ id
--   f . op f ≡ id
--   
--   
--   
--   >>> op Identity (Identity 4)
--   4
--   
--   
--   
--   >>> op Const (Const "hello")
--   "hello"
--   
op :: Wrapped s s a a => (s -> a) -> a -> s

-- | This combinator is based on ala from Conor McBride's work on
--   Epigram.
--   
--   As with wrapping, the user supplied function for the newtype is
--   ignored.
--   
--   
--   >>> ala Sum foldMap [1,2,3,4]
--   10
--   
--   
--   
--   >>> ala All foldMap [True,True]
--   True
--   
--   
--   
--   >>> ala All foldMap [True,False]
--   False
--   
--   
--   
--   >>> ala Any foldMap [False,False]
--   False
--   
--   
--   
--   >>> ala Any foldMap [True,False]
--   True
--   
--   
--   
--   >>> ala Sum foldMap [1,2,3,4]
--   10
--   
--   
--   
--   >>> ala Product foldMap [1,2,3,4]
--   24
--   
ala :: Wrapped s s a a => (s -> a) -> ((s -> a) -> e -> a) -> e -> s

-- | This combinator is based on ala' from Conor McBride's work on
--   Epigram.
--   
--   As with wrapping, the user supplied function for the newtype is
--   ignored.
--   
--   
--   >>> alaf Sum foldMap length ["hello","world"]
--   10
--   
alaf :: Wrapped s s a a => (s -> a) -> ((r -> a) -> e -> a) -> (r -> s) -> e -> s
instance Wrapped String String ErrorCall ErrorCall
instance Wrapped String String RecUpdError RecUpdError
instance Wrapped String String RecSelError RecSelError
instance Wrapped String String RecConError RecConError
instance Wrapped String String PatternMatchFail PatternMatchFail
instance Wrapped String String NoMethodError NoMethodError
instance Wrapped String String AssertionFailed AssertionFailed
instance Wrapped a b (Tagged k s a) (Tagged k1 t b)
instance Wrapped (f (g a)) (f' (g' a')) (ComposeCF f g a) (ComposeFC f' g' a')
instance Wrapped (f (g a)) (f' (g' a')) (ComposeFC f g a) (ComposeFC f' g' a')
instance Wrapped (f (g a)) (f' (g' a')) (Compose f g a) (Compose f' g' a')
instance Wrapped (b -> a) (b' -> a') (Op a b) (Op a' b')
instance Wrapped (a -> a -> Bool) (a' -> a' -> Bool) (Equivalence a) (Equivalence a')
instance Wrapped (a -> a -> Ordering) (a' -> a' -> Ordering) (Comparison a) (Comparison a')
instance Wrapped (a -> Bool) (a' -> Bool) (Predicate a) (Predicate a')
instance Wrapped [a] [b] (Seq a) (Seq b)
instance (Ord a, Ord b) => Wrapped [a] [b] (Set a) (Set b)
instance (Ord k, Ord k') => Wrapped [(k, a)] [(k', b)] (Map k a) (Map k' b)
instance Wrapped [Int] [Int] IntSet IntSet
instance Wrapped [(Int, a)] [(Int, b)] (IntMap a) (IntMap b)
instance (Hashable a, Eq a, Hashable b, Eq b) => Wrapped [a] [b] (HashSet a) (HashSet b)
instance (Hashable k, Eq k, Hashable k', Eq k') => Wrapped [(k, a)] [(k', b)] (HashMap k a) (HashMap k' b)
instance Wrapped (w (m -> a)) (w' (m' -> a')) (TracedT m w a) (TracedT m' w' a')
instance Wrapped (Either (f a) (g a)) (Either (f' a') (g' a')) (Coproduct f g a) (Coproduct f' g' a')
instance Wrapped (m (a, w)) (m' (a', w')) (WriterT w m a) (WriterT w' m' a')
instance Wrapped (m (a, w)) (m' (a', w')) (WriterT w m a) (WriterT w' m' a')
instance Wrapped (s -> m (a, s)) (s' -> m' (a', s')) (StateT s m a) (StateT s' m' a')
instance Wrapped (s -> m (a, s)) (s' -> m' (a', s')) (StateT s m a) (StateT s' m' a')
instance Wrapped (r -> s -> m (a, s, w)) (r' -> s' -> m' (a', s', w')) (RWST r w s m a) (RWST r' w' s' m' a')
instance Wrapped (r -> s -> m (a, s, w)) (r' -> s' -> m' (a', s', w')) (RWST r w s m a) (RWST r' w' s' m' a')
instance Wrapped (f a) (f' a') (Reverse f a) (Reverse f' a')
instance Wrapped (r -> m a) (r' -> m' a') (ReaderT r m a) (ReaderT r' m' a')
instance Wrapped (m (Maybe a)) (m' (Maybe a')) (MaybeT m a) (MaybeT m' a')
instance Wrapped (m [a]) (m' [a']) (ListT m a) (ListT m' a')
instance Wrapped (m a) (m' a') (IdentityT m a) (IdentityT m' a')
instance Wrapped a a' (Identity a) (Identity a')
instance Wrapped (m (Either e a)) (m' (Either e' a')) (ErrorT e m a) (ErrorT e' m' a')
instance Wrapped ((a -> m r) -> m r) ((a' -> m' r') -> m' r') (ContT r m a) (ContT r' m' a')
instance Wrapped a a' (Constant a b) (Constant a' b')
instance Wrapped (f (g a)) (f' (g' a')) (Compose f g a) (Compose f' g' a')
instance Wrapped (f a) (f' a') (Backwards f a) (Backwards f' a')
instance Wrapped a b (Reviewed s a) (Reviewed t b)
instance (ArrowApply m, ArrowApply n) => Wrapped (m () a) (n () b) (ArrowMonad m a) (ArrowMonad n b)
instance Wrapped (Maybe a) (Maybe b) (Last a) (Last b)
instance Wrapped (Maybe a) (Maybe b) (First a) (First b)
instance Wrapped (a -> a) (b -> b) (Endo a) (Endo b)
instance Wrapped a b (Dual a) (Dual b)
instance Wrapped a b (Const a x) (Const b y)
instance Wrapped [a] [b] (ZipList a) (ZipList b)
instance Wrapped (a b c) (u v w) (WrappedArrow a b c) (WrappedArrow u v w)
instance Wrapped (m a) (n b) (WrappedMonad m a) (WrappedMonad n b)
instance Wrapped (a -> m b) (u -> n v) (Kleisli m a b) (Kleisli n u v)
instance Wrapped a b (Product a) (Product b)
instance Wrapped a b (Sum a) (Sum b)
instance Wrapped Bool Bool Any Any
instance Wrapped Bool Bool All All

module Control.Lens.Zoom

-- | This class allows us to use magnify part of the environment,
--   changing the environment supplied by many different Monad
--   transformers. Unlike zoom this can change the environment of a
--   deeply nested Monad transformer.
--   
--   Also, unlike zoom, this can be used with any valid
--   Getter, but cannot be used with a Traversal or
--   Fold.
class (Magnified m ~ Magnified n, MonadReader b m, MonadReader a n) => Magnify m n b a | m -> b, n -> a, m a -> n, n b -> m
magnify :: Magnify m n b a => LensLike' (Magnified m c) a b -> m c -> n c

-- | This class allows us to use zoom in, changing the State
--   supplied by many different Monad transformers, potentially
--   quite deep in a Monad transformer stack.
class (Zoomed m ~ Zoomed n, MonadState s m, MonadState t n) => Zoom m n s t | m -> s, n -> t, m t -> n, n s -> m
zoom :: Zoom m n s t => LensLike' (Zoomed m c) t s -> m c -> n c
instance Magnify m n b a => Magnify (IdentityT m) (IdentityT n) b a
instance (Monad m, Monoid w) => Magnify (RWST b w s m) (RWST a w s m) b a
instance (Monad m, Monoid w) => Magnify (RWST b w s m) (RWST a w s m) b a
instance Magnify ((->) b) ((->) a) b a
instance Monad m => Magnify (ReaderT b m) (ReaderT a m) b a
instance (Error e, Zoom m n s t) => Zoom (ErrorT e m) (ErrorT e n) s t
instance Zoom m n s t => Zoom (MaybeT m) (MaybeT n) s t
instance Zoom m n s t => Zoom (ListT m) (ListT n) s t
instance (Monoid w, Zoom m n s t) => Zoom (WriterT w m) (WriterT w n) s t
instance (Monoid w, Zoom m n s t) => Zoom (WriterT w m) (WriterT w n) s t
instance (Monoid w, Monad z) => Zoom (RWST r w s z) (RWST r w t z) s t
instance (Monoid w, Monad z) => Zoom (RWST r w s z) (RWST r w t z) s t
instance Zoom m n s t => Zoom (IdentityT m) (IdentityT n) s t
instance Zoom m n s t => Zoom (ReaderT e m) (ReaderT e n) s t
instance Monad z => Zoom (StateT s z) (StateT t z) s t
instance Monad z => Zoom (StateT s z) (StateT t z) s t

module Data.HashSet.Lens

-- | This Setter can be used to change the type of a HashSet
--   by mapping the elements to new values.
--   
--   Sadly, you can't create a valid Traversal for a Set,
--   but you can manipulate it by reading using folded and
--   reindexing it via setmapped.
setmapped :: (Eq i, Hashable i, Eq j, Hashable j) => IndexPreservingSetter (HashSet i) (HashSet j) i j

-- | Construct a set from a Getter, Fold, Traversal,
--   Lens or Iso.
--   
--   
--   setOf :: Hashable a         => Getter s a     -> s -> HashSet a
--   setOf :: (Eq a, Hashable a) => Fold s a       -> s -> HashSet a
--   setOf :: Hashable a         => Iso' s a       -> s -> HashSet a
--   setOf :: Hashable a         => Lens' s a      -> s -> HashSet a
--   setOf :: (Eq a, Hashable a) => Traversal' s a -> s -> HashSet a
--   
setOf :: Hashable a => Getting (HashSet a) s a -> s -> HashSet a

-- | A Fold s a is a generalization of something
--   Foldable. It allows you to extract multiple results from a
--   container. A Foldable container can be characterized by the
--   behavior of foldMap :: (Foldable t, Monoid m)
--   => (a -> m) -> t a -> m. Since we want to be able to
--   work with monomorphic containers, we could generalize this signature
--   to forall m. Monoid m => (a -> m) -> s ->
--   m, and then decorate it with Accessor to obtain
--   
--   
--   type Fold s a = forall m. Monoid m => Getting m s a
--   
--   
--   Every Getter is a valid Fold that simply doesn't use the
--   Monoid it is passed.
--   
--   In practice the type we use is slightly more complicated to allow for
--   better error messages and for it to be transformed by certain
--   Applicative transformers.
--   
--   Everything you can do with a Foldable container, you can with
--   with a Fold and there are combinators that generalize the usual
--   Foldable operations here.
module Control.Lens.Fold

-- | A Fold describes how to retrieve multiple values in a way that
--   can be composed with other LensLike constructions.
--   
--   A Fold s a provides a structure with operations very
--   similar to those of the Foldable typeclass, see
--   foldMapOf and the other Fold combinators.
--   
--   By convention, if there exists a foo method that expects a
--   Foldable (f a), then there should be a fooOf
--   method that takes a Fold s a and a value of type
--   s.
--   
--   A Getter is a legal Fold that just ignores the supplied
--   Monoid.
--   
--   Unlike a Traversal a Fold is read-only. Since a
--   Fold cannot be used to write back there are no Lens laws
--   that apply.
type Fold s a = forall f. (Contravariant f, Applicative f) => (a -> f a) -> s -> f s

-- | Every IndexedFold is a valid Fold and can be used for
--   Getting.
type IndexedFold i s a = forall p f. (Indexable i p, Contravariant f, Applicative f) => p a (f a) -> s -> f s

-- | A convenient infix (flipped) version of toListOf.
--   
--   
--   >>> [[1,2],[3]]^..traverse.traverse
--   [1,2,3]
--   
--   
--   
--   >>> (1,2)^..both
--   [1,2]
--   
--   
--   
--   toList xs ≡ xs ^.. folded
--   (^..) ≡ flip toListOf
--   
--   
--   
--   (^..) :: s -> Getter s a     -> [a]
--   (^..) :: s -> Fold s a       -> [a]
--   (^..) :: s -> Lens' s a      -> [a]
--   (^..) :: s -> Iso' s a       -> [a]
--   (^..) :: s -> Traversal' s a -> [a]
--   (^..) :: s -> Prism' s a     -> [a]
--   
(^..) :: s -> Getting (Endo [a]) s a -> [a]

-- | Perform a safe head of a Fold or Traversal or
--   retrieve Just the result from a Getter or Lens.
--   
--   When using a Traversal as a partial Lens, or a
--   Fold as a partial Getter this can be a convenient way to
--   extract the optional value.
--   
--   Note: if you get stack overflows due to this, you may want to use
--   firstOf instead, which can deal more gracefully with heavily
--   left-biased trees.
--   
--   
--   >>> Left 4 ^?_Left
--   Just 4
--   
--   
--   
--   >>> Right 4 ^?_Left
--   Nothing
--   
--   
--   
--   >>> "world" ^? ix 3
--   Just 'l'
--   
--   
--   
--   >>> "world" ^? ix 20
--   Nothing
--   
--   
--   
--   (^?) ≡ flip preview
--   
--   
--   
--   (^?) :: s -> Getter s a     -> Maybe a
--   (^?) :: s -> Fold s a       -> Maybe a
--   (^?) :: s -> Lens' s a      -> Maybe a
--   (^?) :: s -> Iso' s a       -> Maybe a
--   (^?) :: s -> Traversal' s a -> Maybe a
--   
(^?) :: s -> Getting (First a) s a -> Maybe a

-- | Perform an *UNSAFE* head of a Fold or Traversal
--   assuming that it is there.
--   
--   
--   >>> Left 4 ^?! _Left
--   4
--   
--   
--   
--   >>> "world" ^?! ix 3
--   'l'
--   
--   
--   
--   (^?!) :: s -> Getter s a     -> a
--   (^?!) :: s -> Fold s a       -> a
--   (^?!) :: s -> Lens' s a      -> a
--   (^?!) :: s -> Iso' s a       -> a
--   (^?!) :: s -> Traversal' s a -> a
--   
(^?!) :: s -> Getting (Endo a) s a -> a

-- | This converts a Fold to a IndexPreservingGetter that
--   returns the first element, if it exists, as a Maybe.
--   
--   
--   pre :: Getter s a           -> IndexPreservingGetter s (Maybe a)
--   pre :: Fold s a             -> IndexPreservingGetter s (Maybe a)
--   pre :: Simple Traversal s a -> IndexPreservingGetter s (Maybe a)
--   pre :: Simple Lens s a      -> IndexPreservingGetter s (Maybe a)
--   pre :: Simple Iso s a       -> IndexPreservingGetter s (Maybe a)
--   pre :: Simple Prism s a     -> IndexPreservingGetter s (Maybe a)
--   
pre :: Getting (First a) s a -> IndexPreservingGetter s (Maybe a)

-- | This converts an IndexedFold to an IndexPreservingGetter
--   that returns the first index and element, if they exist, as a
--   Maybe.
--   
--   
--   ipre :: IndexedGetter i s a             -> IndexPreservingGetter s (Maybe (i, a))
--   ipre :: IndexedFold i s a               -> IndexPreservingGetter s (Maybe (i, a))
--   ipre :: Simple (IndexedTraversal i) s a -> IndexPreservingGetter s (Maybe (i, a))
--   ipre :: Simple (IndexedLens i) s a      -> IndexPreservingGetter s (Maybe (i, a))
--   
ipre :: IndexedGetting i (First (i, a)) s a -> IndexPreservingGetter s (Maybe (i, a))

-- | Retrieve the first value targeted by a Fold or Traversal
--   (or Just the result from a Getter or Lens). See
--   also (^?).
--   
--   
--   listToMaybe . toList ≡ preview folded
--   
--   
--   This is usually applied in the Reader Monad (->)
--   s.
--   
--   
--   preview = view . pre
--   
--   
--   
--   preview :: Getter s a     -> s -> Maybe a
--   preview :: Fold s a       -> s -> Maybe a
--   preview :: Lens' s a      -> s -> Maybe a
--   preview :: Iso' s a       -> s -> Maybe a
--   preview :: Traversal' s a -> s -> Maybe a
--   
--   
--   However, it may be useful to think of its full generality when working
--   with a Monad transformer stack:
--   
--   
--   preview :: MonadReader s m => Getter s a     -> m (Maybe a)
--   preview :: MonadReader s m => Fold s a       -> m (Maybe a)
--   preview :: MonadReader s m => Lens' s a      -> m (Maybe a)
--   preview :: MonadReader s m => Iso' s a       -> m (Maybe a)
--   preview :: MonadReader s m => Traversal' s a -> m (Maybe a)
--   
preview :: MonadReader s m => Getting (First a) s a -> m (Maybe a)

-- | Retrieve a function of the first value targeted by a Fold or
--   Traversal (or Just the result from a Getter or
--   Lens).
--   
--   This is usually applied in the Reader Monad (->)
--   s.
previews :: MonadReader s m => Getting (First r) s a -> (a -> r) -> m (Maybe r)

-- | Retrieve the first index and value targeted by a Fold or
--   Traversal (or Just the result from a Getter or
--   Lens). See also (^@?).
--   
--   
--   ipreview = view . ipre
--   
--   
--   This is usually applied in the Reader Monad (->)
--   s.
--   
--   
--   ipreview :: IndexedGetter i s a     -> s -> Maybe (i, a)
--   ipreview :: IndexedFold i s a       -> s -> Maybe (i, a)
--   ipreview :: IndexedLens' i s a      -> s -> Maybe (i, a)
--   ipreview :: IndexedTraversal' i s a -> s -> Maybe (i, a)
--   
--   
--   However, it may be useful to think of its full generality when working
--   with a Monad transformer stack:
--   
--   
--   ipreview :: MonadReader s m => IndexedGetter s a     -> m (Maybe (i, a))
--   ipreview :: MonadReader s m => IndexedFold s a       -> m (Maybe (i, a))
--   ipreview :: MonadReader s m => IndexedLens' s a      -> m (Maybe (i, a))
--   ipreview :: MonadReader s m => IndexedTraversal' s a -> m (Maybe (i, a))
--   
ipreview :: MonadReader s m => IndexedGetting i (First (i, a)) s a -> m (Maybe (i, a))

-- | Retrieve a function of the first index and value targeted by an
--   IndexedFold or IndexedTraversal (or Just the
--   result from an IndexedGetter or IndexedLens). See also
--   (^@?).
--   
--   
--   ipreviews = views . ipre
--   
--   
--   This is usually applied in the Reader Monad (->)
--   s.
--   
--   
--   ipreviews :: IndexedGetter i s a     -> (i -> a -> r) -> s -> Maybe r
--   ipreviews :: IndexedFold i s a       -> (i -> a -> r) -> s -> Maybe r
--   ipreviews :: IndexedLens' i s a      -> (i -> a -> r) -> s -> Maybe r
--   ipreviews :: IndexedTraversal' i s a -> (i -> a -> r) -> s -> Maybe r
--   
--   
--   However, it may be useful to think of its full generality when working
--   with a Monad transformer stack:
--   
--   
--   ipreviews :: MonadReader s m => IndexedGetter i s a     -> (i -> a -> r) -> m (Maybe r)
--   ipreviews :: MonadReader s m => IndexedFold i s a       -> (i -> a -> r) -> m (Maybe r)
--   ipreviews :: MonadReader s m => IndexedLens' i s a      -> (i -> a -> r) -> m (Maybe r)
--   ipreviews :: MonadReader s m => IndexedTraversal' i s a -> (i -> a -> r) -> m (Maybe r)
--   
ipreviews :: MonadReader s m => IndexedGetting i (First r) s a -> (i -> a -> r) -> m (Maybe r)

-- | Retrieve the first value targeted by a Fold or Traversal
--   (or Just the result from a Getter or Lens) into
--   the current state.
--   
--   
--   preuse = use . pre
--   
--   
--   
--   preuse :: MonadState s m => Getter s a     -> m (Maybe a)
--   preuse :: MonadState s m => Fold s a       -> m (Maybe a)
--   preuse :: MonadState s m => Lens' s a      -> m (Maybe a)
--   preuse :: MonadState s m => Iso' s a       -> m (Maybe a)
--   preuse :: MonadState s m => Traversal' s a -> m (Maybe a)
--   
preuse :: MonadState s m => Getting (First a) s a -> m (Maybe a)

-- | Retrieve a function of the first value targeted by a Fold or
--   Traversal (or Just the result from a Getter or
--   Lens) into the current state.
--   
--   
--   preuses = uses . pre
--   
--   
--   
--   preuses :: MonadState s m => Getter s a     -> (a -> r) -> m (Maybe r)
--   preuses :: MonadState s m => Fold s a       -> (a -> r) -> m (Maybe r)
--   preuses :: MonadState s m => Lens' s a      -> (a -> r) -> m (Maybe r)
--   preuses :: MonadState s m => Iso' s a       -> (a -> r) -> m (Maybe r)
--   preuses :: MonadState s m => Traversal' s a -> (a -> r) -> m (Maybe r)
--   
preuses :: MonadState s m => Getting (First r) s a -> (a -> r) -> m (Maybe r)

-- | Retrieve the first index and value targeted by an IndexedFold
--   or IndexedTraversal (or Just the index and result from
--   an IndexedGetter or IndexedLens) into the current state.
--   
--   
--   ipreuse = use . ipre
--   
--   
--   
--   ipreuse :: MonadState s m => IndexedGetter i s a     -> m (Maybe (i, a))
--   ipreuse :: MonadState s m => IndexedFold i s a       -> m (Maybe (i, a))
--   ipreuse :: MonadState s m => IndexedLens' i s a      -> m (Maybe (i, a))
--   ipreuse :: MonadState s m => IndexedTraversal' i s a -> m (Maybe (i, a))
--   
ipreuse :: MonadState s m => IndexedGetting i (First (i, a)) s a -> m (Maybe (i, a))

-- | Retrieve a function of the first index and value targeted by an
--   IndexedFold or IndexedTraversal (or a function of
--   Just the index and result from an IndexedGetter or
--   IndexedLens) into the current state.
--   
--   
--   ipreuses = uses . ipre
--   
--   
--   
--   ipreuses :: MonadState s m => IndexedGetter i s a     -> (i -> a -> r) -> m (Maybe r)
--   ipreuses :: MonadState s m => IndexedFold i s a       -> (i -> a -> r) -> m (Maybe r)
--   ipreuses :: MonadState s m => IndexedLens' i s a      -> (i -> a -> r) -> m (Maybe r)
--   ipreuses :: MonadState s m => IndexedTraversal' i s a -> (i -> a -> r) -> m (Maybe r)
--   
ipreuses :: MonadState s m => IndexedGetting i (First r) s a -> (i -> a -> r) -> m (Maybe r)

-- | Check to see if this Fold or Traversal matches 1 or more
--   entries.
--   
--   
--   >>> has (element 0) []
--   False
--   
--   
--   
--   >>> has _Left (Left 12)
--   True
--   
--   
--   
--   >>> has _Right (Left 12)
--   False
--   
--   
--   This will always return True for a Lens or
--   Getter.
--   
--   
--   >>> has _1 ("hello","world")
--   True
--   
--   
--   
--   has :: Getter s a     -> s -> Bool
--   has :: Fold s a       -> s -> Bool
--   has :: Iso' s a       -> s -> Bool
--   has :: Lens' s a      -> s -> Bool
--   has :: Traversal' s a -> s -> Bool
--   
has :: Getting Any s a -> s -> Bool

-- | Check to see if this Fold or Traversal has no matches.
--   
--   
--   >>> hasn't _Left (Right 12)
--   True
--   
--   
--   
--   >>> hasn't _Left (Left 12)
--   False
--   
hasn't :: Getting All s a -> s -> Bool

-- | Obtain a Fold by lifting an operation that returns a
--   Foldable result.
--   
--   This can be useful to lift operations from Data.List and
--   elsewhere into a Fold.
--   
--   
--   >>> [1,2,3,4]^..folding tail
--   [2,3,4]
--   
folding :: (Foldable f, Contravariant g, Applicative g) => (s -> f a) -> LensLike g s t a b

-- | Obtain a Fold from any Foldable.
--   
--   
--   >>> Just 3^..folded
--   [3]
--   
--   
--   
--   >>> Nothing^..folded
--   []
--   
--   
--   
--   >>> [(1,2),(3,4)]^..folded.both
--   [1,2,3,4]
--   
folded :: Foldable f => Fold (f a) a

-- | Build a Fold that unfolds its values from a seed.
--   
--   
--   unfoldr ≡ toListOf . unfolded
--   
--   
--   
--   >>> 10^..unfolded (\b -> if b == 0 then Nothing else Just (b, b-1))
--   [10,9,8,7,6,5,4,3,2,1]
--   
unfolded :: (b -> Maybe (a, b)) -> Fold b a

-- | x ^. iterated f returns an infinite Fold
--   of repeated applications of f to x.
--   
--   
--   toListOf (iterated f) a ≡ iterate f a
--   
iterated :: (a -> a) -> Fold a a

-- | Obtain a Fold that can be composed with to filter another
--   Lens, Iso, Getter, Fold (or
--   Traversal).
--   
--   Note: This is not a legal Traversal, unless you are very
--   careful not to invalidate the predicate on the target.
--   
--   Note: This is also not a legal Prism, unless you are
--   very careful not to inject a value that matches the predicate.
--   
--   As a counter example, consider that given evens = filtered
--   even the second Traversal law is violated:
--   
--   
--   over evens succ . over evens succ /= over evens (succ . succ)
--   
--   
--   So, in order for this to qualify as a legal Traversal you can
--   only use it for actions that preserve the result of the predicate!
--   
--   
--   >>> [1..10]^..folded.filtered even
--   [2,4,6,8,10]
--   
--   
--   This will preserve an index if it is present.
filtered :: (Choice p, Applicative f) => (a -> Bool) -> Overloaded' p f a a

-- | This allows you to traverse the elements of a pretty much any
--   LensLike construction in the opposite order.
--   
--   This will preserve indexes on Indexed types and will give you
--   the elements of a (finite) Fold or Traversal in the
--   opposite order.
--   
--   This has no practical impact on a Getter, Setter,
--   Lens or Iso.
--   
--   NB: To write back through an Iso, you want to use
--   from. Similarly, to write back through an Prism, you
--   want to use re.
backwards :: (Profunctor p, Profunctor q) => Overloading p q (Backwards f) s t a b -> Overloading p q f s t a b

-- | Fold by repeating the input forever.
--   
--   
--   repeat ≡ toListOf repeated
--   
--   
--   
--   >>> timingOut $ 5^..taking 20 repeated
--   [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
--   
repeated :: Fold a a

-- | A Fold that replicates its input n times.
--   
--   
--   replicate n ≡ toListOf (replicated n)
--   
--   
--   
--   >>> 5^..replicated 20
--   [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
--   
replicated :: Int -> Fold a a

-- | Transform a Fold into a Fold that loops over its
--   elements over and over.
--   
--   
--   >>> timingOut $ [1,2,3]^..taking 7 (cycled traverse)
--   [1,2,3,1,2,3,1]
--   
cycled :: (Contravariant f, Applicative f) => LensLike f s t a b -> LensLike f s t a b

-- | Obtain a Fold by taking elements from another Fold,
--   Lens, Iso, Getter or Traversal while a
--   predicate holds.
--   
--   
--   takeWhile p ≡ toListOf (takingWhile p folded)
--   
--   
--   
--   >>> timingOut $ toListOf (takingWhile (<=3) folded) [1..]
--   [1,2,3]
--   
--   
--   
--   takingWhile :: (a -> Bool) -> Fold s a                         -> Fold s a
--   takingWhile :: (a -> Bool) -> Getter s a                       -> Fold s a
--   takingWhile :: (a -> Bool) -> Traversal' s a                   -> Fold s a -- * See note below
--   takingWhile :: (a -> Bool) -> Lens' s a                        -> Fold s a -- * See note below
--   takingWhile :: (a -> Bool) -> Prism' s a                       -> Fold s a -- * See note below
--   takingWhile :: (a -> Bool) -> Iso' s a                         -> Fold s a -- * See note below
--   takingWhile :: (a -> Bool) -> Action m s a                     -> MonadicFold m s a
--   takingWhile :: (a -> Bool) -> MonadicFold m s a                -> MonadicFold m s a
--   takingWhile :: (a -> Bool) -> IndexedTraversal' i s a          -> IndexedFold i s a -- * See note below
--   takingWhile :: (a -> Bool) -> IndexedLens' i s a               -> IndexedFold i s a -- * See note below
--   takingWhile :: (a -> Bool) -> IndexedFold i s a                -> IndexedFold i s a
--   takingWhile :: (a -> Bool) -> IndexedGetter i s a              -> IndexedFold i s a
--   takingWhile :: (a -> Bool) -> IndexedAction i m s a            -> IndexedMonadicFold i m s a
--   takingWhile :: (a -> Bool) -> IndexedMonadicFold i m s a       -> IndexedMonadicFold i m s a
--   
--   
--   Note: When applied to a Traversal, takingWhile
--   yields something that can be used as if it were a Traversal,
--   but which is not a Traversal per the laws, unless you are
--   careful to ensure that you do not invalidate the predicate when
--   writing back through it.
takingWhile :: (Conjoined p, Applicative f) => (a -> Bool) -> Over p (TakingWhile p f a a) s t a a -> Over p f s t a a

-- | Obtain a Fold by dropping elements from another Fold,
--   Lens, Iso, Getter or Traversal while a
--   predicate holds.
--   
--   
--   dropWhile p ≡ toListOf (droppingWhile p folded)
--   
--   
--   
--   >>> toListOf (droppingWhile (<=3) folded) [1..6]
--   [4,5,6]
--   
--   
--   
--   >>> toListOf (droppingWhile (<=3) folded) [1,6,1]
--   [6,1]
--   
--   
--   
--   droppingWhile :: (a -> Bool) -> Fold s a                         -> Fold s a
--   droppingWhile :: (a -> Bool) -> Getter s a                       -> Fold s a
--   droppingWhile :: (a -> Bool) -> Traversal' s a                   -> Fold s a                -- see notes
--   droppingWhile :: (a -> Bool) -> Lens' s a                        -> Fold s a                -- see notes
--   droppingWhile :: (a -> Bool) -> Prism' s a                       -> Fold s a                -- see notes
--   droppingWhile :: (a -> Bool) -> Iso' s a                         -> Fold s a                -- see notes
--   
--   
--   
--   droppingWhile :: (a -> Bool) -> IndexPreservingTraversal' s a    -> IndexPreservingFold s a -- see notes
--   droppingWhile :: (a -> Bool) -> IndexPreservingLens' s a         -> IndexPreservingFold s a -- see notes
--   droppingWhile :: (a -> Bool) -> IndexPreservingGetter s a        -> IndexPreservingFold s a
--   droppingWhile :: (a -> Bool) -> IndexPreservingFold s a          -> IndexPreservingFold s a
--   droppingWhile :: (a -> Bool) -> IndexPreservingAction m s a      -> IndexPreservingFold s a
--   
--   
--   
--   droppingWhile :: (a -> Bool) -> IndexPreservingMonadicFold m s a -> IndexPreservingMonadicFold m s a
--   
--   
--   
--   droppingWhile :: (a -> Bool) -> IndexedTraversal' i s a          -> IndexedFold i s a       -- see notes
--   droppingWhile :: (a -> Bool) -> IndexedLens' i s a               -> IndexedFold i s a       -- see notes
--   droppingWhile :: (a -> Bool) -> IndexedGetter i s a              -> IndexedFold i s a
--   droppingWhile :: (a -> Bool) -> IndexedFold i s a                -> IndexedFold i s a
--   droppingWhile :: (a -> Bool) -> IndexedAction i m s a            -> IndexedFold i s a
--   
--   
--   
--   droppingWhile :: (a -> Bool) -> IndexedMonadicFold i m s a       -> IndexedMonadicFold i m s a
--   
--   
--   Note: Many uses of this combinator will yield something that meets the
--   types, but not the laws of a valid Traversal or
--   IndexedTraversal. The Traversal and
--   IndexedTraversal laws are only satisfied if the new values you
--   assign also pass the predicate! Otherwise subsequent traversals will
--   visit fewer elements and Traversal fusion is not sound.
droppingWhile :: (Conjoined p, Profunctor q, Applicative f) => (a -> Bool) -> Overloading p q (Compose (State Bool) f) s t a a -> Overloading p q f s t a a

-- | 
--   foldMap = foldMapOf folded
--   
--   
--   
--   foldMapOf ≡ views
--   ifoldMapOf l = foldMapOf l . Indexed
--   
--   
--   
--   foldMapOf ::             Getter s a     -> (a -> r) -> s -> r
--   foldMapOf :: Monoid r => Fold s a       -> (a -> r) -> s -> r
--   foldMapOf ::             Lens' s a      -> (a -> r) -> s -> r
--   foldMapOf ::             Iso' s a       -> (a -> r) -> s -> r
--   foldMapOf :: Monoid r => Traversal' s a -> (a -> r) -> s -> r
--   foldMapOf :: Monoid r => Prism' s a     -> (a -> r) -> s -> r
--   
--   
--   
--   foldMapOf :: Getting r s a -> (a -> r) -> s -> r
--   
foldMapOf :: Profunctor p => Accessing p r s a -> p a r -> s -> r

-- | 
--   fold = foldOf folded
--   
--   
--   
--   foldOf ≡ view
--   
--   
--   
--   foldOf ::             Getter s m     -> s -> m
--   foldOf :: Monoid m => Fold s m       -> s -> m
--   foldOf ::             Lens' s m      -> s -> m
--   foldOf ::             Iso' s m       -> s -> m
--   foldOf :: Monoid m => Traversal' s m -> s -> m
--   foldOf :: Monoid m => Prism' s m     -> s -> m
--   
foldOf :: Getting a s a -> s -> a

-- | Right-associative fold of parts of a structure that are viewed through
--   a Lens, Getter, Fold or Traversal.
--   
--   
--   foldr ≡ foldrOf folded
--   
--   
--   
--   foldrOf :: Getter s a     -> (a -> r -> r) -> r -> s -> r
--   foldrOf :: Fold s a       -> (a -> r -> r) -> r -> s -> r
--   foldrOf :: Lens' s a      -> (a -> r -> r) -> r -> s -> r
--   foldrOf :: Iso' s a       -> (a -> r -> r) -> r -> s -> r
--   foldrOf :: Traversal' s a -> (a -> r -> r) -> r -> s -> r
--   foldrOf :: Prism' s a     -> (a -> r -> r) -> r -> s -> r
--   
--   
--   
--   ifoldrOf l ≡ foldrOf l . Indexed
--   
--   
--   
--   foldrOf :: Getting (Endo r) s a -> (a -> r -> r) -> r -> s -> r
--   
foldrOf :: Profunctor p => Accessing p (Endo r) s a -> p a (r -> r) -> r -> s -> r

-- | Left-associative fold of the parts of a structure that are viewed
--   through a Lens, Getter, Fold or Traversal.
--   
--   
--   foldl ≡ foldlOf folded
--   
--   
--   
--   foldlOf :: Getter s a     -> (r -> a -> r) -> r -> s -> r
--   foldlOf :: Fold s a       -> (r -> a -> r) -> r -> s -> r
--   foldlOf :: Lens' s a      -> (r -> a -> r) -> r -> s -> r
--   foldlOf :: Iso' s a       -> (r -> a -> r) -> r -> s -> r
--   foldlOf :: Traversal' s a -> (r -> a -> r) -> r -> s -> r
--   foldlOf :: Prism' s a     -> (r -> a -> r) -> r -> s -> r
--   
foldlOf :: Getting (Dual (Endo r)) s a -> (r -> a -> r) -> r -> s -> r

-- | Extract a list of the targets of a Fold. See also (^..).
--   
--   
--   toList ≡ toListOf folded
--   (^..) ≡ flip toListOf
--   
toListOf :: Getting (Endo [a]) s a -> s -> [a]

-- | Returns True if any target of a Fold satisfies a
--   predicate.
--   
--   
--   >>> anyOf both (=='x') ('x','y')
--   True
--   
--   >>> import Data.Data.Lens
--   
--   >>> anyOf biplate (== "world") (((),2::Int),"hello",("world",11))
--   True
--   
--   
--   
--   any ≡ anyOf folded
--   
--   
--   
--   ianyOf l ≡ allOf l . Indexed
--   
--   
--   
--   anyOf :: Getter s a     -> (a -> Bool) -> s -> Bool
--   anyOf :: Fold s a       -> (a -> Bool) -> s -> Bool
--   anyOf :: Lens' s a      -> (a -> Bool) -> s -> Bool
--   anyOf :: Iso' s a       -> (a -> Bool) -> s -> Bool
--   anyOf :: Traversal' s a -> (a -> Bool) -> s -> Bool
--   anyOf :: Prism' s a     -> (a -> Bool) -> s -> Bool
--   
anyOf :: Profunctor p => Accessing p Any s a -> p a Bool -> s -> Bool

-- | Returns True if every target of a Fold satisfies a
--   predicate.
--   
--   
--   >>> allOf both (>=3) (4,5)
--   True
--   
--   >>> allOf folded (>=2) [1..10]
--   False
--   
--   
--   
--   all ≡ allOf folded
--   
--   
--   
--   iallOf l = allOf l . Indexed
--   
--   
--   
--   allOf :: Getter s a     -> (a -> Bool) -> s -> Bool
--   allOf :: Fold s a       -> (a -> Bool) -> s -> Bool
--   allOf :: Lens' s a      -> (a -> Bool) -> s -> Bool
--   allOf :: Iso' s a       -> (a -> Bool) -> s -> Bool
--   allOf :: Traversal' s a -> (a -> Bool) -> s -> Bool
--   allOf :: Prism' s a     -> (a -> Bool) -> s -> Bool
--   
allOf :: Profunctor p => Accessing p All s a -> p a Bool -> s -> Bool

-- | Returns True if every target of a Fold is True.
--   
--   
--   >>> andOf both (True,False)
--   False
--   
--   >>> andOf both (True,True)
--   True
--   
--   
--   
--   and ≡ andOf folded
--   
--   
--   
--   andOf :: Getter s Bool     -> s -> Bool
--   andOf :: Fold s Bool       -> s -> Bool
--   andOf :: Lens' s Bool      -> s -> Bool
--   andOf :: Iso' s Bool       -> s -> Bool
--   andOf :: Traversal' s Bool -> s -> Bool
--   andOf :: Prism' s Bool     -> s -> Bool
--   
andOf :: Getting All s Bool -> s -> Bool

-- | Returns True if any target of a Fold is True.
--   
--   
--   >>> orOf both (True,False)
--   True
--   
--   >>> orOf both (False,False)
--   False
--   
--   
--   
--   or ≡ orOf folded
--   
--   
--   
--   orOf :: Getter s Bool     -> s -> Bool
--   orOf :: Fold s Bool       -> s -> Bool
--   orOf :: Lens' s Bool      -> s -> Bool
--   orOf :: Iso' s Bool       -> s -> Bool
--   orOf :: Traversal' s Bool -> s -> Bool
--   orOf :: Prism' s Bool     -> s -> Bool
--   
orOf :: Getting Any s Bool -> s -> Bool

-- | Calculate the Product of every number targeted by a
--   Fold.
--   
--   
--   >>> productOf both (4,5)
--   20
--   
--   >>> productOf folded [1,2,3,4,5]
--   120
--   
--   
--   
--   product ≡ productOf folded
--   
productOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a

-- | Calculate the Sum of every number targeted by a Fold.
--   
--   
--   >>> sumOf both (5,6)
--   11
--   
--   >>> sumOf folded [1,2,3,4]
--   10
--   
--   >>> sumOf (folded.both) [(1,2),(3,4)]
--   10
--   
--   >>> import Data.Data.Lens
--   
--   >>> sumOf biplate [(1::Int,[]),(2,[(3::Int,4::Int)])] :: Int
--   10
--   
--   
--   
--   sum ≡ sumOf folded
--   
--   
--   This operation may be more strict than you would expect. If you want a
--   lazier version use ala Sum .
--   foldMapOf
--   
--   
--   sumOf _1 :: Num a => (a, b) -> a
--   sumOf (folded . _1) :: (Foldable f, Num a) => f (a, b) -> a
--   
--   
--   
--   sumOf :: Num a => Getter s a     -> s -> a
--   sumOf :: Num a => Fold s a       -> s -> a
--   sumOf :: Num a => Lens' s a      -> s -> a
--   sumOf :: Num a => Iso' s a       -> s -> a
--   sumOf :: Num a => Traversal' s a -> s -> a
--   sumOf :: Num a => Prism' s a     -> s -> a
--   
sumOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a

-- | Traverse over all of the targets of a Fold (or Getter),
--   computing an Applicative (or Functor)-based answer, but
--   unlike traverseOf do not construct a new structure.
--   traverseOf_ generalizes traverse_ to work over any
--   Fold.
--   
--   When passed a Getter, traverseOf_ can work over any
--   Functor, but when passed a Fold, traverseOf_
--   requires an Applicative.
--   
--   
--   >>> traverseOf_ both putStrLn ("hello","world")
--   hello
--   world
--   
--   
--   
--   traverse_ ≡ traverseOf_ folded
--   
--   
--   
--   traverseOf_ _2 :: Functor f => (c -> f r) -> (d, c) -> f ()
--   traverseOf_ _Left :: Applicative f => (a -> f b) -> Either a c -> f ()
--   
--   
--   
--   itraverseOf_ l ≡ traverseOf_ l . Indexed
--   
--   
--   The rather specific signature of traverseOf_ allows it to be
--   used as if the signature was any of:
--   
--   
--   traverseOf_ :: Functor f     => Getter s a     -> (a -> f r) -> s -> f ()
--   traverseOf_ :: Applicative f => Fold s a       -> (a -> f r) -> s -> f ()
--   traverseOf_ :: Functor f     => Lens' s a      -> (a -> f r) -> s -> f ()
--   traverseOf_ :: Functor f     => Iso' s a       -> (a -> f r) -> s -> f ()
--   traverseOf_ :: Applicative f => Traversal' s a -> (a -> f r) -> s -> f ()
--   traverseOf_ :: Applicative f => Prism' s a     -> (a -> f r) -> s -> f ()
--   
traverseOf_ :: (Profunctor p, Functor f) => Accessing p (Traversed r f) s a -> p a (f r) -> s -> f ()

-- | Traverse over all of the targets of a Fold (or Getter),
--   computing an Applicative (or Functor)-based answer, but
--   unlike forOf do not construct a new structure. forOf_
--   generalizes for_ to work over any Fold.
--   
--   When passed a Getter, forOf_ can work over any
--   Functor, but when passed a Fold, forOf_ requires
--   an Applicative.
--   
--   
--   for_ ≡ forOf_ folded
--   
--   
--   
--   >>> forOf_ both ("hello","world") putStrLn
--   hello
--   world
--   
--   
--   The rather specific signature of forOf_ allows it to be used as
--   if the signature was any of:
--   
--   
--   iforOf_ l s ≡ forOf_ l s . Indexed
--   
--   
--   
--   forOf_ :: Functor f     => Getter s a     -> s -> (a -> f r) -> f ()
--   forOf_ :: Applicative f => Fold s a       -> s -> (a -> f r) -> f ()
--   forOf_ :: Functor f     => Lens' s a      -> s -> (a -> f r) -> f ()
--   forOf_ :: Functor f     => Iso' s a       -> s -> (a -> f r) -> f ()
--   forOf_ :: Applicative f => Traversal' s a -> s -> (a -> f r) -> f ()
--   forOf_ :: Applicative f => Prism' s a     -> s -> (a -> f r) -> f ()
--   
forOf_ :: (Profunctor p, Functor f) => Accessing p (Traversed r f) s a -> s -> p a (f r) -> f ()

-- | Evaluate each action in observed by a Fold on a structure from
--   left to right, ignoring the results.
--   
--   
--   sequenceA_ ≡ sequenceAOf_ folded
--   
--   
--   
--   >>> sequenceAOf_ both (putStrLn "hello",putStrLn "world")
--   hello
--   world
--   
--   
--   
--   sequenceAOf_ :: Functor f     => Getter s (f a)     -> s -> f ()
--   sequenceAOf_ :: Applicative f => Fold s (f a)       -> s -> f ()
--   sequenceAOf_ :: Functor f     => Lens' s (f a)      -> s -> f ()
--   sequenceAOf_ :: Functor f     => Iso' s (f a)       -> s -> f ()
--   sequenceAOf_ :: Applicative f => Traversal' s (f a) -> s -> f ()
--   sequenceAOf_ :: Applicative f => Prism' s (f a)     -> s -> f ()
--   
sequenceAOf_ :: Functor f => Getting (Traversed a f) s (f a) -> s -> f ()

-- | Map each target of a Fold on a structure to a monadic action,
--   evaluate these actions from left to right, and ignore the results.
--   
--   
--   >>> mapMOf_ both putStrLn ("hello","world")
--   hello
--   world
--   
--   
--   
--   mapM_ ≡ mapMOf_ folded
--   
--   
--   
--   mapMOf_ :: Monad m => Getter s a     -> (a -> m r) -> s -> m ()
--   mapMOf_ :: Monad m => Fold s a       -> (a -> m r) -> s -> m ()
--   mapMOf_ :: Monad m => Lens' s a      -> (a -> m r) -> s -> m ()
--   mapMOf_ :: Monad m => Iso' s a       -> (a -> m r) -> s -> m ()
--   mapMOf_ :: Monad m => Traversal' s a -> (a -> m r) -> s -> m ()
--   mapMOf_ :: Monad m => Prism' s a     -> (a -> m r) -> s -> m ()
--   
mapMOf_ :: (Profunctor p, Monad m) => Accessing p (Sequenced r m) s a -> p a (m r) -> s -> m ()

-- | forMOf_ is mapMOf_ with two of its arguments flipped.
--   
--   
--   >>> forMOf_ both ("hello","world") putStrLn
--   hello
--   world
--   
--   
--   
--   forM_ ≡ forMOf_ folded
--   
--   
--   
--   forMOf_ :: Monad m => Getter s a     -> s -> (a -> m r) -> m ()
--   forMOf_ :: Monad m => Fold s a       -> s -> (a -> m r) -> m ()
--   forMOf_ :: Monad m => Lens' s a      -> s -> (a -> m r) -> m ()
--   forMOf_ :: Monad m => Iso' s a       -> s -> (a -> m r) -> m ()
--   forMOf_ :: Monad m => Traversal' s a -> s -> (a -> m r) -> m ()
--   forMOf_ :: Monad m => Prism' s a     -> s -> (a -> m r) -> m ()
--   
forMOf_ :: (Profunctor p, Monad m) => Accessing p (Sequenced r m) s a -> s -> p a (m r) -> m ()

-- | Evaluate each monadic action referenced by a Fold on the
--   structure from left to right, and ignore the results.
--   
--   
--   >>> sequenceOf_ both (putStrLn "hello",putStrLn "world")
--   hello
--   world
--   
--   
--   
--   sequence_ ≡ sequenceOf_ folded
--   
--   
--   
--   sequenceOf_ :: Monad m => Getter s (m a)     -> s -> m ()
--   sequenceOf_ :: Monad m => Fold s (m a)       -> s -> m ()
--   sequenceOf_ :: Monad m => Lens' s (m a)      -> s -> m ()
--   sequenceOf_ :: Monad m => Iso' s (m a)       -> s -> m ()
--   sequenceOf_ :: Monad m => Traversal' s (m a) -> s -> m ()
--   sequenceOf_ :: Monad m => Prism' s (m a)     -> s -> m ()
--   
sequenceOf_ :: Monad m => Getting (Sequenced a m) s (m a) -> s -> m ()

-- | The sum of a collection of actions, generalizing concatOf.
--   
--   
--   >>> asumOf both ("hello","world")
--   "helloworld"
--   
--   
--   
--   >>> asumOf each (Nothing, Just "hello", Nothing)
--   Just "hello"
--   
--   
--   
--   asum ≡ asumOf folded
--   
--   
--   
--   asumOf :: Alternative f => Getter s (f a)     -> s -> f a
--   asumOf :: Alternative f => Fold s (f a)       -> s -> f a
--   asumOf :: Alternative f => Lens' s (f a)      -> s -> f a
--   asumOf :: Alternative f => Iso' s (f a)       -> s -> f a
--   asumOf :: Alternative f => Traversal' s (f a) -> s -> f a
--   asumOf :: Alternative f => Prism' s (f a)     -> s -> f a
--   
asumOf :: Alternative f => Getting (Endo (f a)) s (f a) -> s -> f a

-- | The sum of a collection of actions, generalizing concatOf.
--   
--   
--   >>> msumOf both ("hello","world")
--   "helloworld"
--   
--   
--   
--   >>> msumOf each (Nothing, Just "hello", Nothing)
--   Just "hello"
--   
--   
--   
--   msum ≡ msumOf folded
--   
--   
--   
--   msumOf :: MonadPlus m => Getter s (m a)     -> s -> m a
--   msumOf :: MonadPlus m => Fold s (m a)       -> s -> m a
--   msumOf :: MonadPlus m => Lens' s (m a)      -> s -> m a
--   msumOf :: MonadPlus m => Iso' s (m a)       -> s -> m a
--   msumOf :: MonadPlus m => Traversal' s (m a) -> s -> m a
--   msumOf :: MonadPlus m => Prism' s (m a)     -> s -> m a
--   
msumOf :: MonadPlus m => Getting (Endo (m a)) s (m a) -> s -> m a

-- | Map a function over all the targets of a Fold of a container
--   and concatenate the resulting lists.
--   
--   
--   >>> concatMapOf both (\x -> [x, x + 1]) (1,3)
--   [1,2,3,4]
--   
--   
--   
--   concatMap ≡ concatMapOf folded
--   
--   
--   
--   concatMapOf :: Getter s a     -> (a -> [r]) -> s -> [r]
--   concatMapOf :: Fold s a       -> (a -> [r]) -> s -> [r]
--   concatMapOf :: Lens' s a      -> (a -> [r]) -> s -> [r]
--   concatMapOf :: Iso' s a       -> (a -> [r]) -> s -> [r]
--   concatMapOf :: Traversal' s a -> (a -> [r]) -> s -> [r]
--   
concatMapOf :: Profunctor p => Accessing p [r] s a -> p a [r] -> s -> [r]

-- | Concatenate all of the lists targeted by a Fold into a longer
--   list.
--   
--   
--   >>> concatOf both ("pan","ama")
--   "panama"
--   
--   
--   
--   concat ≡ concatOf folded
--   concatOf ≡ view
--   
--   
--   
--   concatOf :: Getter s [r]     -> s -> [r]
--   concatOf :: Fold s [r]       -> s -> [r]
--   concatOf :: Iso' s [r]       -> s -> [r]
--   concatOf :: Lens' s [r]      -> s -> [r]
--   concatOf :: Traversal' s [r] -> s -> [r]
--   
concatOf :: Getting [r] s [r] -> s -> [r]

-- | Does the element occur anywhere within a given Fold of the
--   structure?
--   
--   
--   >>> elemOf both "hello" ("hello","world")
--   True
--   
--   
--   
--   elem ≡ elemOf folded
--   
--   
--   
--   elemOf :: Eq a => Getter s a     -> a -> s -> Bool
--   elemOf :: Eq a => Fold s a       -> a -> s -> Bool
--   elemOf :: Eq a => Lens' s a      -> a -> s -> Bool
--   elemOf :: Eq a => Iso' s a       -> a -> s -> Bool
--   elemOf :: Eq a => Traversal' s a -> a -> s -> Bool
--   elemOf :: Eq a => Prism' s a     -> a -> s -> Bool
--   
elemOf :: Eq a => Getting Any s a -> a -> s -> Bool

-- | Does the element not occur anywhere within a given Fold of the
--   structure?
--   
--   
--   >>> notElemOf each 'd' ('a','b','c')
--   True
--   
--   
--   
--   >>> notElemOf each 'a' ('a','b','c')
--   False
--   
--   
--   
--   notElem ≡ notElemOf folded
--   
--   
--   
--   notElemOf :: Eq a => Getter s a     -> a -> s -> Bool
--   notElemOf :: Eq a => Fold s a       -> a -> s -> Bool
--   notElemOf :: Eq a => Iso' s a       -> a -> s -> Bool
--   notElemOf :: Eq a => Lens' s a      -> a -> s -> Bool
--   notElemOf :: Eq a => Traversal' s a -> a -> s -> Bool
--   notElemOf :: Eq a => Prism' s a     -> a -> s -> Bool
--   
notElemOf :: Eq a => Getting All s a -> a -> s -> Bool

-- | Calculate the number of targets there are for a Fold in a given
--   container.
--   
--   Note: This can be rather inefficient for large containers and
--   just like length, this will not terminate for infinite folds.
--   
--   
--   length ≡ lengthOf folded
--   
--   
--   
--   >>> lengthOf _1 ("hello",())
--   1
--   
--   
--   
--   >>> lengthOf traverse [1..10]
--   10
--   
--   
--   
--   >>> lengthOf (traverse.traverse) [[1,2],[3,4],[5,6]]
--   6
--   
--   
--   
--   lengthOf (folded . folded) :: (Foldable f, Foldable g) => f (g a) -> Int
--   
--   
--   
--   lengthOf :: Getter s a     -> s -> Int
--   lengthOf :: Fold s a       -> s -> Int
--   lengthOf :: Lens' s a      -> s -> Int
--   lengthOf :: Iso' s a       -> s -> Int
--   lengthOf :: Traversal' s a -> s -> Int
--   
lengthOf :: Getting (Endo (Endo Int)) s a -> s -> Int

-- | Returns True if this Fold or Traversal has no
--   targets in the given container.
--   
--   Note: nullOf on a valid Iso, Lens or
--   Getter should always return False.
--   
--   
--   null ≡ nullOf folded
--   
--   
--   This may be rather inefficient compared to the null check of
--   many containers.
--   
--   
--   >>> nullOf _1 (1,2)
--   False
--   
--   
--   
--   >>> nullOf ignored ()
--   True
--   
--   
--   
--   >>> nullOf traverse []
--   True
--   
--   
--   
--   >>> nullOf (element 20) [1..10]
--   True
--   
--   
--   
--   nullOf (folded . _1 . folded) :: (Foldable f, Foldable g) => f (g a, b) -> Bool
--   
--   
--   
--   nullOf :: Getter s a     -> s -> Bool
--   nullOf :: Fold s a       -> s -> Bool
--   nullOf :: Iso' s a       -> s -> Bool
--   nullOf :: Lens' s a      -> s -> Bool
--   nullOf :: Traversal' s a -> s -> Bool
--   
nullOf :: Getting All s a -> s -> Bool

-- | Returns True if this Fold or Traversal has any
--   targets in the given container.
--   
--   A more "conversational" alias for this combinator is has.
--   
--   Note: notNullOf on a valid Iso, Lens or
--   Getter should always return True.
--   
--   
--   null ≡ notNullOf folded
--   
--   
--   This may be rather inefficient compared to the not .
--   null check of many containers.
--   
--   
--   >>> notNullOf _1 (1,2)
--   True
--   
--   
--   
--   >>> notNullOf traverse [1..10]
--   True
--   
--   
--   
--   >>> notNullOf folded []
--   False
--   
--   
--   
--   >>> notNullOf (element 20) [1..10]
--   False
--   
--   
--   
--   notNullOf (folded . _1 . folded) :: (Foldable f, Foldable g) => f (g a, b) -> Bool
--   
--   
--   
--   notNullOf :: Getter s a     -> s -> Bool
--   notNullOf :: Fold s a       -> s -> Bool
--   notNullOf :: Iso' s a       -> s -> Bool
--   notNullOf :: Lens' s a      -> s -> Bool
--   notNullOf :: Traversal' s a -> s -> Bool
--   
notNullOf :: Getting Any s a -> s -> Bool

-- | Retrieve the First entry of a Fold or Traversal
--   or retrieve Just the result from a Getter or
--   Lens.
--   
--   The answer is computed in a manner that leaks space less than
--   ala First . foldMapOf and gives
--   you back access to the outermost Just constructor more quickly,
--   but may have worse constant factors.
--   
--   
--   >>> firstOf traverse [1..10]
--   Just 1
--   
--   
--   
--   >>> firstOf both (1,2)
--   Just 1
--   
--   
--   
--   >>> firstOf ignored ()
--   Nothing
--   
--   
--   
--   firstOf :: Getter s a     -> s -> Maybe a
--   firstOf :: Fold s a       -> s -> Maybe a
--   firstOf :: Lens' s a      -> s -> Maybe a
--   firstOf :: Iso' s a       -> s -> Maybe a
--   firstOf :: Traversal' s a -> s -> Maybe a
--   
firstOf :: Getting (Leftmost a) s a -> s -> Maybe a

-- | Retrieve the Last entry of a Fold or Traversal or
--   retrieve Just the result from a Getter or Lens.
--   
--   The answer is computed in a manner that leaks space less than
--   ala Last . foldMapOf and gives
--   you back access to the outermost Just constructor more quickly,
--   but may have worse constant factors.
--   
--   
--   >>> lastOf traverse [1..10]
--   Just 10
--   
--   
--   
--   >>> lastOf both (1,2)
--   Just 2
--   
--   
--   
--   >>> lastOf ignored ()
--   Nothing
--   
--   
--   
--   lastOf :: Getter s a     -> s -> Maybe a
--   lastOf :: Fold s a       -> s -> Maybe a
--   lastOf :: Lens' s a      -> s -> Maybe a
--   lastOf :: Iso' s a       -> s -> Maybe a
--   lastOf :: Traversal' s a -> s -> Maybe a
--   
lastOf :: Getting (Rightmost a) s a -> s -> Maybe a

-- | Obtain the maximum element (if any) targeted by a Fold or
--   Traversal safely.
--   
--   Note: maximumOf on a valid Iso, Lens or
--   Getter will always return Just a value.
--   
--   
--   >>> maximumOf traverse [1..10]
--   Just 10
--   
--   
--   
--   >>> maximumOf traverse []
--   Nothing
--   
--   
--   
--   >>> maximumOf (folded.filtered even) [1,4,3,6,7,9,2]
--   Just 6
--   
--   
--   
--   maximum ≡ fromMaybe (error "empty") . maximumOf folded
--   
--   
--   In the interest of efficiency, This operation has semantics more
--   strict than strictly necessary. rmap getMax
--   (foldMapOf l Max) has lazier semantics but could
--   leak memory.
--   
--   
--   maximumOf :: Ord a => Getter s a     -> s -> Maybe a
--   maximumOf :: Ord a => Fold s a       -> s -> Maybe a
--   maximumOf :: Ord a => Iso' s a       -> s -> Maybe a
--   maximumOf :: Ord a => Lens' s a      -> s -> Maybe a
--   maximumOf :: Ord a => Traversal' s a -> s -> Maybe a
--   
maximumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a

-- | Obtain the minimum element (if any) targeted by a Fold or
--   Traversal safely.
--   
--   Note: minimumOf on a valid Iso, Lens or
--   Getter will always return Just a value.
--   
--   
--   >>> minimumOf traverse [1..10]
--   Just 1
--   
--   
--   
--   >>> minimumOf traverse []
--   Nothing
--   
--   
--   
--   >>> minimumOf (folded.filtered even) [1,4,3,6,7,9,2]
--   Just 2
--   
--   
--   
--   minimum ≡ fromMaybe (error "empty") . minimumOf folded
--   
--   
--   In the interest of efficiency, This operation has semantics more
--   strict than strictly necessary. rmap getMin
--   (foldMapOf l Min) has lazier semantics but could
--   leak memory.
--   
--   
--   minimumOf :: Ord a => Getter s a     -> s -> Maybe a
--   minimumOf :: Ord a => Fold s a       -> s -> Maybe a
--   minimumOf :: Ord a => Iso' s a       -> s -> Maybe a
--   minimumOf :: Ord a => Lens' s a      -> s -> Maybe a
--   minimumOf :: Ord a => Traversal' s a -> s -> Maybe a
--   
minimumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a

-- | Obtain the maximum element (if any) targeted by a Fold,
--   Traversal, Lens, Iso, or Getter according
--   to a user supplied Ordering.
--   
--   
--   >>> maximumByOf traverse (compare `on` length) ["mustard","relish","ham"]
--   Just "mustard"
--   
--   
--   In the interest of efficiency, This operation has semantics more
--   strict than strictly necessary.
--   
--   
--   maximumBy cmp ≡ fromMaybe (error "empty") . maximumByOf folded cmp
--   
--   
--   
--   maximumByOf :: Getter s a     -> (a -> a -> Ordering) -> s -> Maybe a
--   maximumByOf :: Fold s a       -> (a -> a -> Ordering) -> s -> Maybe a
--   maximumByOf :: Iso' s a       -> (a -> a -> Ordering) -> s -> Maybe a
--   maximumByOf :: Lens' s a      -> (a -> a -> Ordering) -> s -> Maybe a
--   maximumByOf :: Traversal' s a -> (a -> a -> Ordering) -> s -> Maybe a
--   
maximumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a

-- | Obtain the minimum element (if any) targeted by a Fold,
--   Traversal, Lens, Iso or Getter according
--   to a user supplied Ordering.
--   
--   In the interest of efficiency, This operation has semantics more
--   strict than strictly necessary.
--   
--   
--   >>> minimumByOf traverse (compare `on` length) ["mustard","relish","ham"]
--   Just "ham"
--   
--   
--   
--   minimumBy cmp ≡ fromMaybe (error "empty") . minimumByOf folded cmp
--   
--   
--   
--   minimumByOf :: Getter s a     -> (a -> a -> Ordering) -> s -> Maybe a
--   minimumByOf :: Fold s a       -> (a -> a -> Ordering) -> s -> Maybe a
--   minimumByOf :: Iso' s a       -> (a -> a -> Ordering) -> s -> Maybe a
--   minimumByOf :: Lens' s a      -> (a -> a -> Ordering) -> s -> Maybe a
--   minimumByOf :: Traversal' s a -> (a -> a -> Ordering) -> s -> Maybe a
--   
minimumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a

-- | The findOf function takes a Lens (or Getter,
--   Iso, Fold, or Traversal), a predicate and a
--   structure and returns the leftmost element of the structure matching
--   the predicate, or Nothing if there is no such element.
--   
--   
--   >>> findOf each even (1,3,4,6)
--   Just 4
--   
--   
--   
--   >>> findOf folded even [1,3,5,7]
--   Nothing
--   
--   
--   
--   findOf :: Getter s a     -> (a -> Bool) -> s -> Maybe a
--   findOf :: Fold s a       -> (a -> Bool) -> s -> Maybe a
--   findOf :: Iso' s a       -> (a -> Bool) -> s -> Maybe a
--   findOf :: Lens' s a      -> (a -> Bool) -> s -> Maybe a
--   findOf :: Traversal' s a -> (a -> Bool) -> s -> Maybe a
--   
--   
--   
--   find ≡ findOf folded
--   ifindOf l ≡ findOf l . Indexed
--   
--   
--   A simpler version that didn't permit indexing, would be:
--   
--   
--   findOf :: Getting (Endo (Maybe a)) s a -> (a -> Bool) -> s -> Maybe a
--   findOf l p = foldrOf l (a y -> if p a then Just a else y) Nothing
--   
findOf :: Conjoined p => Accessing p (Endo (Maybe a)) s a -> p a Bool -> s -> Maybe a

-- | Strictly fold right over the elements of a structure.
--   
--   
--   foldr' ≡ foldrOf' folded
--   
--   
--   
--   foldrOf' :: Getter s a     -> (a -> r -> r) -> r -> s -> r
--   foldrOf' :: Fold s a       -> (a -> r -> r) -> r -> s -> r
--   foldrOf' :: Iso' s a       -> (a -> r -> r) -> r -> s -> r
--   foldrOf' :: Lens' s a      -> (a -> r -> r) -> r -> s -> r
--   foldrOf' :: Traversal' s a -> (a -> r -> r) -> r -> s -> r
--   
foldrOf' :: Getting (Dual (Endo (Endo r))) s a -> (a -> r -> r) -> r -> s -> r

-- | Fold over the elements of a structure, associating to the left, but
--   strictly.
--   
--   
--   foldl' ≡ foldlOf' folded
--   
--   
--   
--   foldlOf' :: Getter s a     -> (r -> a -> r) -> r -> s -> r
--   foldlOf' :: Fold s a       -> (r -> a -> r) -> r -> s -> r
--   foldlOf' :: Iso' s a       -> (r -> a -> r) -> r -> s -> r
--   foldlOf' :: Lens' s a      -> (r -> a -> r) -> r -> s -> r
--   foldlOf' :: Traversal' s a -> (r -> a -> r) -> r -> s -> r
--   
foldlOf' :: Getting (Endo (Endo r)) s a -> (r -> a -> r) -> r -> s -> r

-- | A variant of foldrOf that has no base case and thus may only be
--   applied to lenses and structures such that the Lens views at
--   least one element of the structure.
--   
--   
--   >>> foldr1Of each (+) (1,2,3,4)
--   10
--   
--   
--   
--   foldr1Of l f ≡ foldr1 f . toListOf l
--   foldr1 ≡ foldr1Of folded
--   
--   
--   
--   foldr1Of :: Getter s a     -> (a -> a -> a) -> s -> a
--   foldr1Of :: Fold s a       -> (a -> a -> a) -> s -> a
--   foldr1Of :: Iso' s a       -> (a -> a -> a) -> s -> a
--   foldr1Of :: Lens' s a      -> (a -> a -> a) -> s -> a
--   foldr1Of :: Traversal' s a -> (a -> a -> a) -> s -> a
--   
foldr1Of :: Getting (Endo (Maybe a)) s a -> (a -> a -> a) -> s -> a

-- | A variant of foldlOf that has no base case and thus may only be
--   applied to lenses and structures such that the Lens views at
--   least one element of the structure.
--   
--   
--   >>> foldl1Of each (+) (1,2,3,4)
--   10
--   
--   
--   
--   foldl1Of l f ≡ foldl1 f . toListOf l
--   foldl1 ≡ foldl1Of folded
--   
--   
--   
--   foldl1Of :: Getter s a     -> (a -> a -> a) -> s -> a
--   foldl1Of :: Fold s a       -> (a -> a -> a) -> s -> a
--   foldl1Of :: Iso' s a       -> (a -> a -> a) -> s -> a
--   foldl1Of :: Lens' s a      -> (a -> a -> a) -> s -> a
--   foldl1Of :: Traversal' s a -> (a -> a -> a) -> s -> a
--   
foldl1Of :: Getting (Dual (Endo (Maybe a))) s a -> (a -> a -> a) -> s -> a

-- | A variant of foldrOf' that has no base case and thus may only
--   be applied to folds and structures such that the fold views at least
--   one element of the structure.
--   
--   
--   foldr1Of l f ≡ foldr1 f . toListOf l
--   
--   
--   
--   foldr1Of' :: Getter s a     -> (a -> a -> a) -> s -> a
--   foldr1Of' :: Fold s a       -> (a -> a -> a) -> s -> a
--   foldr1Of' :: Iso' s a       -> (a -> a -> a) -> s -> a
--   foldr1Of' :: Lens' s a      -> (a -> a -> a) -> s -> a
--   foldr1Of' :: Traversal' s a -> (a -> a -> a) -> s -> a
--   
foldr1Of' :: Getting (Dual (Endo (Endo (Maybe a)))) s a -> (a -> a -> a) -> s -> a

-- | A variant of foldlOf' that has no base case and thus may only
--   be applied to folds and structures such that the fold views at least
--   one element of the structure.
--   
--   
--   foldl1Of' l f ≡ foldl1' f . toListOf l
--   
--   
--   
--   foldl1Of' :: Getter s a     -> (a -> a -> a) -> s -> a
--   foldl1Of' :: Fold s a       -> (a -> a -> a) -> s -> a
--   foldl1Of' :: Iso' s a       -> (a -> a -> a) -> s -> a
--   foldl1Of' :: Lens' s a      -> (a -> a -> a) -> s -> a
--   foldl1Of' :: Traversal' s a -> (a -> a -> a) -> s -> a
--   
foldl1Of' :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> a) -> s -> a

-- | Monadic fold over the elements of a structure, associating to the
--   right, i.e. from right to left.
--   
--   
--   foldrM ≡ foldrMOf folded
--   
--   
--   
--   foldrMOf :: Monad m => Getter s a     -> (a -> r -> m r) -> r -> s -> m r
--   foldrMOf :: Monad m => Fold s a       -> (a -> r -> m r) -> r -> s -> m r
--   foldrMOf :: Monad m => Iso' s a       -> (a -> r -> m r) -> r -> s -> m r
--   foldrMOf :: Monad m => Lens' s a      -> (a -> r -> m r) -> r -> s -> m r
--   foldrMOf :: Monad m => Traversal' s a -> (a -> r -> m r) -> r -> s -> m r
--   
foldrMOf :: Monad m => Getting (Dual (Endo (r -> m r))) s a -> (a -> r -> m r) -> r -> s -> m r

-- | Monadic fold over the elements of a structure, associating to the
--   left, i.e. from left to right.
--   
--   
--   foldlM ≡ foldlMOf folded
--   
--   
--   
--   foldlMOf :: Monad m => Getter s a     -> (r -> a -> m r) -> r -> s -> m r
--   foldlMOf :: Monad m => Fold s a       -> (r -> a -> m r) -> r -> s -> m r
--   foldlMOf :: Monad m => Iso' s a       -> (r -> a -> m r) -> r -> s -> m r
--   foldlMOf :: Monad m => Lens' s a      -> (r -> a -> m r) -> r -> s -> m r
--   foldlMOf :: Monad m => Traversal' s a -> (r -> a -> m r) -> r -> s -> m r
--   
foldlMOf :: Monad m => Getting (Endo (r -> m r)) s a -> (r -> a -> m r) -> r -> s -> m r

-- | An infix version of itoListOf.
(^@..) :: s -> IndexedGetting i (Endo [(i, a)]) s a -> [(i, a)]

-- | Perform a safe head (with index) of an IndexedFold or
--   IndexedTraversal or retrieve Just the index and result
--   from an IndexedGetter or IndexedLens.
--   
--   When using a IndexedTraversal as a partial IndexedLens,
--   or an IndexedFold as a partial IndexedGetter this can be
--   a convenient way to extract the optional value.
--   
--   
--   (^@?) :: s -> IndexedGetter i s a     -> Maybe (i, a)
--   (^@?) :: s -> IndexedFold i s a       -> Maybe (i, a)
--   (^@?) :: s -> IndexedLens' i s a      -> Maybe (i, a)
--   (^@?) :: s -> IndexedTraversal' i s a -> Maybe (i, a)
--   
(^@?) :: s -> IndexedGetting i (Endo (Maybe (i, a))) s a -> Maybe (i, a)

-- | Perform an *UNSAFE* head (with index) of an IndexedFold
--   or IndexedTraversal assuming that it is there.
--   
--   
--   (^@?!) :: s -> IndexedGetter i s a     -> (i, a)
--   (^@?!) :: s -> IndexedFold i s a       -> (i, a)
--   (^@?!) :: s -> IndexedLens' i s a      -> (i, a)
--   (^@?!) :: s -> IndexedTraversal' i s a -> (i, a)
--   
(^@?!) :: s -> IndexedGetting i (Endo (i, a)) s a -> (i, a)

-- | Fold an IndexedFold or IndexedTraversal by mapping
--   indices and values to an arbitrary Monoid with access to the
--   i.
--   
--   When you don't need access to the index then foldMapOf is more
--   flexible in what it accepts.
--   
--   
--   foldMapOf l ≡ ifoldMapOf l . const
--   
--   
--   
--   ifoldMapOf ::             IndexedGetter i s a     -> (i -> a -> m) -> s -> m
--   ifoldMapOf :: Monoid m => IndexedFold i s a       -> (i -> a -> m) -> s -> m
--   ifoldMapOf ::             IndexedLens' i s a      -> (i -> a -> m) -> s -> m
--   ifoldMapOf :: Monoid m => IndexedTraversal' i s a -> (i -> a -> m) -> s -> m
--   
ifoldMapOf :: IndexedGetting i m s a -> (i -> a -> m) -> s -> m

-- | Right-associative fold of parts of a structure that are viewed through
--   an IndexedFold or IndexedTraversal with access to the
--   i.
--   
--   When you don't need access to the index then foldrOf is more
--   flexible in what it accepts.
--   
--   
--   foldrOf l ≡ ifoldrOf l . const
--   
--   
--   
--   ifoldrOf :: IndexedGetter i s a     -> (i -> a -> r -> r) -> r -> s -> r
--   ifoldrOf :: IndexedFold i s a       -> (i -> a -> r -> r) -> r -> s -> r
--   ifoldrOf :: IndexedLens' i s a      -> (i -> a -> r -> r) -> r -> s -> r
--   ifoldrOf :: IndexedTraversal' i s a -> (i -> a -> r -> r) -> r -> s -> r
--   
ifoldrOf :: IndexedGetting i (Endo r) s a -> (i -> a -> r -> r) -> r -> s -> r

-- | Left-associative fold of the parts of a structure that are viewed
--   through an IndexedFold or IndexedTraversal with access
--   to the i.
--   
--   When you don't need access to the index then foldlOf is more
--   flexible in what it accepts.
--   
--   
--   foldlOf l ≡ ifoldlOf l . const
--   
--   
--   
--   ifoldlOf :: IndexedGetter i s a     -> (i -> r -> a -> r) -> r -> s -> r
--   ifoldlOf :: IndexedFold i s a       -> (i -> r -> a -> r) -> r -> s -> r
--   ifoldlOf :: IndexedLens' i s a      -> (i -> r -> a -> r) -> r -> s -> r
--   ifoldlOf :: IndexedTraversal' i s a -> (i -> r -> a -> r) -> r -> s -> r
--   
ifoldlOf :: IndexedGetting i (Dual (Endo r)) s a -> (i -> r -> a -> r) -> r -> s -> r

-- | Return whether or not any element viewed through an IndexedFold
--   or IndexedTraversal satisfy a predicate, with access to the
--   i.
--   
--   When you don't need access to the index then anyOf is more
--   flexible in what it accepts.
--   
--   
--   anyOf l ≡ ianyOf l . const
--   
--   
--   
--   ianyOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Bool
--   ianyOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Bool
--   ianyOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Bool
--   ianyOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Bool
--   
ianyOf :: IndexedGetting i Any s a -> (i -> a -> Bool) -> s -> Bool

-- | Return whether or not all elements viewed through an
--   IndexedFold or IndexedTraversal satisfy a predicate,
--   with access to the i.
--   
--   When you don't need access to the index then allOf is more
--   flexible in what it accepts.
--   
--   
--   allOf l ≡ iallOf l . const
--   
--   
--   
--   iallOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Bool
--   iallOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Bool
--   iallOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Bool
--   iallOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Bool
--   
iallOf :: IndexedGetting i All s a -> (i -> a -> Bool) -> s -> Bool

-- | Traverse the targets of an IndexedFold or
--   IndexedTraversal with access to the i, discarding the
--   results.
--   
--   When you don't need access to the index then traverseOf_ is
--   more flexible in what it accepts.
--   
--   
--   traverseOf_ l ≡ itraverseOf l . const
--   
--   
--   
--   itraverseOf_ :: Functor f     => IndexedGetter i s a     -> (i -> a -> f r) -> s -> f ()
--   itraverseOf_ :: Applicative f => IndexedFold i s a       -> (i -> a -> f r) -> s -> f ()
--   itraverseOf_ :: Functor f     => IndexedLens' i s a      -> (i -> a -> f r) -> s -> f ()
--   itraverseOf_ :: Applicative f => IndexedTraversal' i s a -> (i -> a -> f r) -> s -> f ()
--   
itraverseOf_ :: Functor f => IndexedGetting i (Traversed r f) s a -> (i -> a -> f r) -> s -> f ()

-- | Traverse the targets of an IndexedFold or
--   IndexedTraversal with access to the index, discarding the
--   results (with the arguments flipped).
--   
--   
--   iforOf_ ≡ flip . itraverseOf_
--   
--   
--   When you don't need access to the index then forOf_ is more
--   flexible in what it accepts.
--   
--   
--   forOf_ l a ≡ iforOf_ l a . const
--   
--   
--   
--   iforOf_ :: Functor f     => IndexedGetter i s a     -> s -> (i -> a -> f r) -> f ()
--   iforOf_ :: Applicative f => IndexedFold i s a       -> s -> (i -> a -> f r) -> f ()
--   iforOf_ :: Functor f     => IndexedLens' i s a      -> s -> (i -> a -> f r) -> f ()
--   iforOf_ :: Applicative f => IndexedTraversal' i s a -> s -> (i -> a -> f r) -> f ()
--   
iforOf_ :: Functor f => IndexedGetting i (Traversed r f) s a -> s -> (i -> a -> f r) -> f ()

-- | Run monadic actions for each target of an IndexedFold or
--   IndexedTraversal with access to the index, discarding the
--   results.
--   
--   When you don't need access to the index then mapMOf_ is more
--   flexible in what it accepts.
--   
--   
--   mapMOf_ l ≡ imapMOf l . const
--   
--   
--   
--   imapMOf_ :: Monad m => IndexedGetter i s a     -> (i -> a -> m r) -> s -> m ()
--   imapMOf_ :: Monad m => IndexedFold i s a       -> (i -> a -> m r) -> s -> m ()
--   imapMOf_ :: Monad m => IndexedLens' i s a      -> (i -> a -> m r) -> s -> m ()
--   imapMOf_ :: Monad m => IndexedTraversal' i s a -> (i -> a -> m r) -> s -> m ()
--   
imapMOf_ :: Monad m => IndexedGetting i (Sequenced r m) s a -> (i -> a -> m r) -> s -> m ()

-- | Run monadic actions for each target of an IndexedFold or
--   IndexedTraversal with access to the index, discarding the
--   results (with the arguments flipped).
--   
--   
--   iforMOf_ ≡ flip . imapMOf_
--   
--   
--   When you don't need access to the index then forMOf_ is more
--   flexible in what it accepts.
--   
--   
--   forMOf_ l a ≡ iforMOf l a . const
--   
--   
--   
--   iforMOf_ :: Monad m => IndexedGetter i s a     -> s -> (i -> a -> m r) -> m ()
--   iforMOf_ :: Monad m => IndexedFold i s a       -> s -> (i -> a -> m r) -> m ()
--   iforMOf_ :: Monad m => IndexedLens' i s a      -> s -> (i -> a -> m r) -> m ()
--   iforMOf_ :: Monad m => IndexedTraversal' i s a -> s -> (i -> a -> m r) -> m ()
--   
iforMOf_ :: Monad m => IndexedGetting i (Sequenced r m) s a -> s -> (i -> a -> m r) -> m ()

-- | Concatenate the results of a function of the elements of an
--   IndexedFold or IndexedTraversal with access to the
--   index.
--   
--   When you don't need access to the index then concatMapOf is
--   more flexible in what it accepts.
--   
--   
--   concatMapOf l ≡ iconcatMapOf l . const
--   iconcatMapOf ≡ ifoldMapOf
--   
--   
--   
--   iconcatMapOf :: IndexedGetter i s a     -> (i -> a -> [r]) -> s -> [r]
--   iconcatMapOf :: IndexedFold i s a       -> (i -> a -> [r]) -> s -> [r]
--   iconcatMapOf :: IndexedLens' i s a      -> (i -> a -> [r]) -> s -> [r]
--   iconcatMapOf :: IndexedTraversal' i s a -> (i -> a -> [r]) -> s -> [r]
--   
iconcatMapOf :: IndexedGetting i [r] s a -> (i -> a -> [r]) -> s -> [r]

-- | The findOf function takes an IndexedFold or
--   IndexedTraversal, a predicate that is also supplied the index,
--   a structure and returns the left-most element of the structure
--   matching the predicate, or Nothing if there is no such element.
--   
--   When you don't need access to the index then findOf is more
--   flexible in what it accepts.
--   
--   
--   findOf l ≡ ifindOf l . const
--   
--   
--   
--   ifindOf :: IndexedGetter i s a     -> (i -> a -> Bool) -> s -> Maybe a
--   ifindOf :: IndexedFold i s a       -> (i -> a -> Bool) -> s -> Maybe a
--   ifindOf :: IndexedLens' i s a      -> (i -> a -> Bool) -> s -> Maybe a
--   ifindOf :: IndexedTraversal' i s a -> (i -> a -> Bool) -> s -> Maybe a
--   
ifindOf :: IndexedGetting i (Endo (Maybe a)) s a -> (i -> a -> Bool) -> s -> Maybe a

-- | Strictly fold right over the elements of a structure with an
--   index.
--   
--   When you don't need access to the index then foldrOf' is more
--   flexible in what it accepts.
--   
--   
--   foldrOf' l ≡ ifoldrOf' l . const
--   
--   
--   
--   ifoldrOf' :: IndexedGetter i s a     -> (i -> a -> r -> r) -> r -> s -> r
--   ifoldrOf' :: IndexedFold i s a       -> (i -> a -> r -> r) -> r -> s -> r
--   ifoldrOf' :: IndexedLens' i s a      -> (i -> a -> r -> r) -> r -> s -> r
--   ifoldrOf' :: IndexedTraversal' i s a -> (i -> a -> r -> r) -> r -> s -> r
--   
ifoldrOf' :: IndexedGetting i (Dual (Endo (r -> r))) s a -> (i -> a -> r -> r) -> r -> s -> r

-- | Fold over the elements of a structure with an index, associating to
--   the left, but strictly.
--   
--   When you don't need access to the index then foldlOf' is more
--   flexible in what it accepts.
--   
--   
--   foldlOf' l ≡ ifoldlOf' l . const
--   
--   
--   
--   ifoldlOf' :: IndexedGetter i s a       -> (i -> r -> a -> r) -> r -> s -> r
--   ifoldlOf' :: IndexedFold i s a         -> (i -> r -> a -> r) -> r -> s -> r
--   ifoldlOf' :: IndexedLens' i s a        -> (i -> r -> a -> r) -> r -> s -> r
--   ifoldlOf' :: IndexedTraversal' i s a   -> (i -> r -> a -> r) -> r -> s -> r
--   
ifoldlOf' :: IndexedGetting i (Endo (r -> r)) s a -> (i -> r -> a -> r) -> r -> s -> r

-- | Monadic fold right over the elements of a structure with an index.
--   
--   When you don't need access to the index then foldrMOf is more
--   flexible in what it accepts.
--   
--   
--   foldrMOf l ≡ ifoldrMOf l . const
--   
--   
--   
--   ifoldrMOf :: Monad m => IndexedGetter i s a     -> (i -> a -> r -> m r) -> r -> s -> m r
--   ifoldrMOf :: Monad m => IndexedFold i s a       -> (i -> a -> r -> m r) -> r -> s -> m r
--   ifoldrMOf :: Monad m => IndexedLens' i s a      -> (i -> a -> r -> m r) -> r -> s -> m r
--   ifoldrMOf :: Monad m => IndexedTraversal' i s a -> (i -> a -> r -> m r) -> r -> s -> m r
--   
ifoldrMOf :: Monad m => IndexedGetting i (Dual (Endo (r -> m r))) s a -> (i -> a -> r -> m r) -> r -> s -> m r

-- | Monadic fold over the elements of a structure with an index,
--   associating to the left.
--   
--   When you don't need access to the index then foldlMOf is more
--   flexible in what it accepts.
--   
--   
--   foldlMOf l ≡ ifoldlMOf l . const
--   
--   
--   
--   ifoldlMOf :: Monad m => IndexedGetter i s a     -> (i -> r -> a -> m r) -> r -> s -> m r
--   ifoldlMOf :: Monad m => IndexedFold i s a       -> (i -> r -> a -> m r) -> r -> s -> m r
--   ifoldlMOf :: Monad m => IndexedLens' i s a      -> (i -> r -> a -> m r) -> r -> s -> m r
--   ifoldlMOf :: Monad m => IndexedTraversal' i s a -> (i -> r -> a -> m r) -> r -> s -> m r
--   
ifoldlMOf :: Monad m => IndexedGetting i (Endo (r -> m r)) s a -> (i -> r -> a -> m r) -> r -> s -> m r

-- | Extract the key-value pairs from a structure.
--   
--   When you don't need access to the indices in the result, then
--   toListOf is more flexible in what it accepts.
--   
--   
--   toListOf l ≡ map fst . itoListOf l
--   
--   
--   
--   itoListOf :: IndexedGetter i s a     -> s -> [(i,a)]
--   itoListOf :: IndexedFold i s a       -> s -> [(i,a)]
--   itoListOf :: IndexedLens' i s a      -> s -> [(i,a)]
--   itoListOf :: IndexedTraversal' i s a -> s -> [(i,a)]
--   
itoListOf :: IndexedGetting i (Endo [(i, a)]) s a -> s -> [(i, a)]

-- | Filter an IndexedFold or IndexedGetter, obtaining an
--   IndexedFold.
--   
--   
--   >>> [0,0,0,5,5,5]^..traversed.ifiltered (\i a -> i <= a)
--   [0,5,5,5]
--   
--   
--   Compose with filtered to filter another IndexedLens,
--   IndexedIso, IndexedGetter, IndexedFold (or
--   IndexedTraversal) with access to both the value and the index.
--   
--   Note: As with filtered, this is not a legal
--   IndexedTraversal, unless you are very careful not to invalidate
--   the predicate on the target!
ifiltered :: (Indexable i p, Applicative f) => (i -> a -> Bool) -> Overloading' p (Indexed i) f a a

-- | Obtain an IndexedFold by taking elements from another
--   IndexedFold, IndexedLens, IndexedGetter or
--   IndexedTraversal while a predicate holds.
--   
--   
--   itakingWhile :: (i -> a -> Bool) -> IndexedFold i s a          -> IndexedFold i s a
--   itakingWhile :: (i -> a -> Bool) -> IndexedTraversal' i s a    -> IndexedFold i s a
--   itakingWhile :: (i -> a -> Bool) -> IndexedLens' i s a         -> IndexedFold i s a
--   itakingWhile :: (i -> a -> Bool) -> IndexedGetter i s a        -> IndexedFold i s a
--   itakingWhile :: (i -> a -> Bool) -> IndexedMonadicFold i m s a -> IndexedMonadicFold i m s a
--   itakingWhile :: (i -> a -> Bool) -> IndexedAction i m s a      -> IndexedMonadicFold i m s a
--   
itakingWhile :: (Indexable i p, Profunctor q, Contravariant f, Applicative f) => (i -> a -> Bool) -> Overloading (Indexed i) q (Accessor (Endo (f s))) s s a a -> Overloading p q f s s a a

-- | Obtain an IndexedFold by dropping elements from another
--   IndexedFold, IndexedLens, IndexedGetter or
--   IndexedTraversal while a predicate holds.
--   
--   
--   idroppingWhile :: (i -> a -> Bool) -> IndexedFold i s a          -> IndexedFold i s a
--   idroppingWhile :: (i -> a -> Bool) -> IndexedTraversal' i s a    -> IndexedFold i s a -- see notes
--   idroppingWhile :: (i -> a -> Bool) -> IndexedLens' i s a         -> IndexedFold i s a -- see notes
--   idroppingWhile :: (i -> a -> Bool) -> IndexedGetter i s a        -> IndexedFold i s a
--   idroppingWhile :: (i -> a -> Bool) -> IndexedMonadicFold i m s a -> IndexedMonadicFold i m s a
--   idroppingWhile :: (i -> a -> Bool) -> IndexedAction i m s a      -> IndexedMonadicFold i m s a
--   
--   
--   Applying idroppingWhile to an IndexedLens or
--   IndexedTraversal will still allow you to use it as a
--   pseudo-IndexedTraversal, but if you change the value of the
--   targets to ones where the predicate returns True, then you will
--   break the Traversal laws and Traversal fusion will no
--   longer be sound.
idroppingWhile :: (Indexable i p, Profunctor q, Applicative f) => (i -> a -> Bool) -> Overloading (Indexed i) q (Compose (State Bool) f) s t a a -> Overloading p q f s t a a

-- | A deprecated alias for firstOf.

-- | Deprecated: headOf will be removed after GHC 7.8 is
--   released. (Use preview or firstOf) 
headOf :: Getting (First a) s a -> s -> Maybe a

-- | Used for preview.
data Leftmost a

-- | Used for lastOf.
data Rightmost a

-- | Used internally by traverseOf_ and the like.
--   
--   The argument a of the result should not be used!
data Traversed a f

-- | Used internally by mapM_ and the like.
--   
--   The argument a of the result should not be used!
data Sequenced a m

-- | This module uses dirty tricks to generate a Handler from an
--   arbitrary Fold.
module Control.Lens.Internal.Exception

-- | Both MonadCatchIO-transformers and Control.Exception
--   provide a Handler type.
--   
--   This lets us write combinators to build handlers that are agnostic
--   about the choice of which of these they use.
class Handleable e (m :: * -> *) (h :: * -> *) | h -> e m where handler_ l = handler l . const
handler :: Handleable e m h => Getting (First a) e a -> (a -> m r) -> h r
handler_ :: Handleable e m h => Getting (First a) e a -> m r -> h r

-- | There was an Exception caused by abusing the internals of a
--   Handler.
data HandlingException
HandlingException :: HandlingException
instance Typeable HandlingException
instance Show HandlingException
instance Reifies s (SomeException -> Maybe a) => Exception (Handling a s m)
instance Show (Handling a s m)
instance Typeable (Handling a s m)
instance Exception HandlingException
instance Handleable SomeException m (Handler m)
instance Handleable SomeException IO Handler

-- | These are general purpose combinators that provide utility for
--   non-lens code
module Control.Lens.Combinators

-- | Passes the result of the left side to the function on the right side
--   (forward pipe operator).
--   
--   This is the flipped version of ($), which is more common in
--   languages like F# as (|>) where it is needed for
--   inference. Here it is supplied for notational convenience and given a
--   precedence that allows it to be nested inside uses of ($).
--   
--   
--   >>> a & f
--   f a
--   
--   
--   
--   >>> "hello" & length & succ
--   6
--   
--   
--   This combinator is commonly used when applying multiple Lens
--   operations in sequence.
--   
--   
--   >>> ("hello","world") & _1.element 0 .~ 'j' & _1.element 4 .~ 'y'
--   ("jelly","world")
--   
--   
--   This reads somewhat similar to:
--   
--   
--   >>> flip execState ("hello","world") $ do _1.element 0 .= 'j'; _1.element 4 .= 'y'
--   ("jelly","world")
--   
(&) :: a -> (a -> b) -> b

-- | Infix flipped fmap.
--   
--   
--   (<&>) = flip fmap
--   
(<&>) :: Functor f => f a -> (a -> b) -> f b

-- | This is convenient to flip argument order of composite
--   functions.
--   
--   
--   >>> over _2 ?? ("hello","world") $ length
--   ("hello",5)
--   
--   
--   
--   >>> over ?? length ?? ("hello","world") $ _2
--   ("hello",5)
--   
(??) :: Functor f => f (a -> b) -> a -> f b

-- | A Lens s t a b is a purely functional reference.
--   
--   While a Traversal could be used for Getting like a valid
--   Fold, it wasn't a valid Getter as Applicative
--   wasn't a superclass of Gettable.
--   
--   Functor, however is the superclass of both.
--   
--   
--   type Lens s t a b = forall f. Functor f => (a -> f b) -> s -> f t
--   
--   
--   Every Lens is a valid Setter.
--   
--   Every Lens can be used for Getting like a Fold
--   that doesn't use the Applicative or Gettable.
--   
--   Every Lens is a valid Traversal that only uses the
--   Functor part of the Applicative it is supplied.
--   
--   Every Lens can be used for Getting like a valid
--   Getter, since Functor is a superclass of
--   Gettable.
--   
--   Since every Lens can be used for Getting like a valid
--   Getter it follows that it must view exactly one element in the
--   structure.
--   
--   The Lens laws follow from this property and the desire for it
--   to act like a Traversable when used as a Traversal.
--   
--   In the examples below, getter and setter are
--   supplied as example getters and setters, and are not actual functions
--   supplied by this package.
module Control.Lens.Lens

-- | A Lens is actually a lens family as described in
--   http://comonad.com/reader/2012/mirrored-lenses/.
--   
--   With great power comes great responsibility and a Lens is
--   subject to the three common sense Lens laws:
--   
--   1) You get back what you put in:
--   
--   
--   view l (set l b a)  ≡ b
--   
--   
--   2) Putting back what you got doesn't change anything:
--   
--   
--   set l (view l a) a  ≡ a
--   
--   
--   3) Setting twice is the same as setting once:
--   
--   
--   set l c (set l b a) ≡ set l c a
--   
--   
--   These laws are strong enough that the 4 type parameters of a
--   Lens cannot vary fully independently. For more on how they
--   interact, read the "Why is it a Lens Family?" section of
--   http://comonad.com/reader/2012/mirrored-lenses/.
--   
--   Every Lens can be used directly as a Setter or
--   Traversal.
--   
--   You can also use a Lens for Getting as if it were a
--   Fold or Getter.
--   
--   Since every Lens is a valid Traversal, the
--   Traversal laws are required of any Lens you create:
--   
--   
--   l pure ≡ pure
--   fmap (l f) . l g ≡ getCompose . l (Compose . fmap f . g)
--   
--   
--   
--   type Lens s t a b = forall f. Functor f => LensLike f s t a b
--   
type Lens s t a b = forall f. Functor f => (a -> f b) -> s -> f t

-- | 
--   type Lens' = Simple Lens
--   
type Lens' s a = Lens s s a a

-- | Every IndexedLens is a valid Lens and a valid
--   IndexedTraversal.
type IndexedLens i s t a b = forall f p. (Indexable i p, Functor f) => p a (f b) -> s -> f t

-- | 
--   type IndexedLens' i = Simple (IndexedLens i)
--   
type IndexedLens' i s a = IndexedLens i s s a a

-- | When you see this as an argument to a function, it expects a
--   Lens.
--   
--   This type can also be used when you need to store a Lens in a
--   container, since it is rank-1. You can turn them back into a
--   Lens with cloneLens, or use it directly with combinators
--   like storing and (^#).
type ALens s t a b = LensLike (Pretext (->) a b) s t a b

-- | 
--   type ALens' = Simple ALens
--   
type ALens' s a = ALens s s a a

-- | When you see this as an argument to a function, it expects an
--   IndexedLens
type AnIndexedLens i s t a b = Overloading (Indexed i) (->) (Pretext (Indexed i) a b) s t a b

-- | 
--   type AnIndexedLens' = Simple (AnIndexedLens i)
--   
type AnIndexedLens' i s a = AnIndexedLens i s s a a

-- | Build a Lens from a getter and a setter.
--   
--   
--   lens :: Functor f => (s -> a) -> (s -> b -> t) -> (a -> f b) -> s -> f t
--   
--   
--   
--   >>> s ^. lens getter setter
--   getter s
--   
--   
--   
--   >>> s & lens getter setter .~ b
--   setter s b
--   
--   
--   
--   >>> s & lens getter setter %~ f
--   setter s (f (getter s))
--   
lens :: (s -> a) -> (s -> b -> t) -> Lens s t a b

-- | Build an IndexedLens from a Getter and a Setter.
ilens :: (s -> (i, a)) -> (s -> b -> t) -> IndexedLens i s t a b

-- | Build an index-preserving Lens from a Getter and a
--   Setter.
--   
--   
--   lens :: (s -> a) -> (s -> b -> t) -> Lens s t a b
--   lens sa sbt afb s = sbt s <$> afb (sa s)
--   
iplens :: (Conjoined p, Functor f) => (s -> a) -> (s -> b -> t) -> Overloaded p f s t a b

-- | (%%~) can be used in one of two scenarios:
--   
--   When applied to a Lens, it can edit the target of the
--   Lens in a structure, extracting a functorial result.
--   
--   When applied to a Traversal, it can edit the targets of the
--   traversals, extracting an applicative summary of its actions.
--   
--   For all that the definition of this combinator is just:
--   
--   
--   (%%~) ≡ id
--   
--   
--   It may be beneficial to think about it as if it had these even more
--   restricted types, however:
--   
--   
--   (%%~) :: Functor f =>     Iso s t a b       -> (a -> f b) -> s -> f t
--   (%%~) :: Functor f =>     Lens s t a b      -> (a -> f b) -> s -> f t
--   (%%~) :: Applicative f => Traversal s t a b -> (a -> f b) -> s -> f t
--   
--   
--   When applied to a Traversal, it can edit the targets of the
--   traversals, extracting a supplemental monoidal summary of its actions,
--   by choosing f = ((,) m)
--   
--   
--   (%%~) ::             Iso s t a b       -> (a -> (r, b)) -> s -> (r, t)
--   (%%~) ::             Lens s t a b      -> (a -> (r, b)) -> s -> (r, t)
--   (%%~) :: Monoid m => Traversal s t a b -> (a -> (m, b)) -> s -> (m, t)
--   
(%%~) :: Overloading p q f s t a b -> p a (f b) -> q s (f t)

-- | Modify the target of a Lens in the current state returning some
--   extra information of type r or modify all targets of a
--   Traversal in the current state, extracting extra information of
--   type r and return a monoidal summary of the changes.
--   
--   
--   >>> runState (_1 %%= \x -> (f x, g x)) (a,b)
--   (f a,(g a,b))
--   
--   
--   
--   (%%=) ≡ (state .)
--   
--   
--   It may be useful to think of (%%=), instead, as having either
--   of the following more restricted type signatures:
--   
--   
--   (%%=) :: MonadState s m             => Iso s s a b       -> (a -> (r, b)) -> m r
--   (%%=) :: MonadState s m             => Lens s s a b      -> (a -> (r, b)) -> m r
--   (%%=) :: (MonadState s m, Monoid r) => Traversal s s a b -> (a -> (r, b)) -> m r
--   
(%%=) :: MonadState s m => Overloading p (->) ((,) r) s s a b -> p a (r, b) -> m r

-- | Adjust the target of an IndexedLens returning a supplementary
--   result, or adjust all of the targets of an IndexedTraversal and
--   return a monoidal summary of the supplementary results and the answer.
--   
--   
--   (%%@~) ≡ withIndex
--   
--   
--   
--   (%%@~) :: Functor f => IndexedLens i s t a b      -> (i -> a -> f b) -> s -> f t
--   (%%@~) :: Applicative f => IndexedTraversal i s t a b -> (i -> a -> f b) -> s -> f t
--   
--   
--   In particular, it is often useful to think of this function as having
--   one of these even more restricted type signatures:
--   
--   
--   (%%@~) ::             IndexedLens i s t a b      -> (i -> a -> (r, b)) -> s -> (r, t)
--   (%%@~) :: Monoid r => IndexedTraversal i s t a b -> (i -> a -> (r, b)) -> s -> (r, t)
--   
(%%@~) :: IndexedLensLike i f s t a b -> (i -> a -> f b) -> s -> f t

-- | Adjust the target of an IndexedLens returning a supplementary
--   result, or adjust all of the targets of an IndexedTraversal
--   within the current state, and return a monoidal summary of the
--   supplementary results.
--   
--   
--   l %%@= f ≡ state (l %%@~ f)
--   
--   
--   
--   (%%@=) :: MonadState s m                 => IndexedLens i s s a b      -> (i -> a -> (r, b)) -> s -> m r
--   (%%@=) :: (MonadState s m, Monoid r) => IndexedTraversal i s s a b -> (i -> a -> (r, b)) -> s -> m r
--   
(%%@=) :: MonadState s m => IndexedLensLike i ((,) r) s s a b -> (i -> a -> (r, b)) -> m r

-- | Adjust the target of an IndexedLens returning the intermediate
--   result, or adjust all of the targets of an IndexedTraversal and
--   return a monoidal summary along with the answer.
--   
--   
--   l <%~ f ≡ l <%@~ const f
--   
--   
--   When you do not need access to the index then (<%~) is more
--   liberal in what it can accept.
--   
--   If you do not need the intermediate result, you can use (%@~)
--   or even (%~).
--   
--   
--   (<%@~) ::             IndexedLens i s t a b      -> (i -> a -> b) -> s -> (b, t)
--   (<%@~) :: Monoid b => IndexedTraversal i s t a b -> (i -> a -> b) -> s -> (b, t)
--   
(<%@~) :: Overloading (Indexed i) q ((,) b) s t a b -> (i -> a -> b) -> q s (b, t)

-- | Adjust the target of an IndexedLens returning the intermediate
--   result, or adjust all of the targets of an IndexedTraversal
--   within the current state, and return a monoidal summary of the
--   intermediate results.
--   
--   
--   (<%@=) :: MonadState s m                 => IndexedLens i s s a b      -> (i -> a -> b) -> m b
--   (<%@=) :: (MonadState s m, Monoid b) => IndexedTraversal i s s a b -> (i -> a -> b) -> m b
--   
(<%@=) :: MonadState s m => IndexedLensLike i ((,) b) s s a b -> (i -> a -> b) -> m b

-- | Adjust the target of an IndexedLens returning the old value, or
--   adjust all of the targets of an IndexedTraversal and return a
--   monoidal summary of the old values along with the answer.
--   
--   
--   (<<%@~) ::             IndexedLens i s t a b      -> (i -> a -> b) -> s -> (a, t)
--   (<<%@~) :: Monoid a => IndexedTraversal i s t a b -> (i -> a -> b) -> s -> (a, t)
--   
(<<%@~) :: Overloading (Indexed i) q ((,) a) s t a b -> (i -> a -> b) -> q s (a, t)

-- | Adjust the target of an IndexedLens returning the old value, or
--   adjust all of the targets of an IndexedTraversal within the
--   current state, and return a monoidal summary of the old values.
--   
--   
--   (<<%@=) :: MonadState s m                 => IndexedLens i s s a b      -> (i -> a -> b) -> m a
--   (<<%@=) :: (MonadState s m, Monoid b) => IndexedTraversal i s s a b -> (i -> a -> b) -> m a
--   
(<<%@=) :: MonadState s m => IndexedLensLike i ((,) a) s s a b -> (i -> a -> b) -> m a

-- | Merge two lenses, getters, setters, folds or traversals.
--   
--   
--   chosen ≡ choosing id id
--   
--   
--   
--   choosing :: Getter s a     -> Getter s' a     -> Getter (Either s s') a
--   choosing :: Fold s a       -> Fold s' a       -> Fold (Either s s') a
--   choosing :: Lens' s a      -> Lens' s' a      -> Lens' (Either s s') a
--   choosing :: Traversal' s a -> Traversal' s' a -> Traversal' (Either s s') a
--   choosing :: Setter' s a    -> Setter' s' a    -> Setter' (Either s s') a
--   
choosing :: Functor f => LensLike f s t a b -> LensLike f s' t' a b -> LensLike f (Either s s') (Either t t') a b

-- | This is a Lens that updates either side of an Either,
--   where both sides have the same type.
--   
--   
--   chosen ≡ choosing id id
--   
--   
--   
--   >>> Left a^.chosen
--   a
--   
--   
--   
--   >>> Right a^.chosen
--   a
--   
--   
--   
--   >>> Right "hello"^.chosen
--   "hello"
--   
--   
--   
--   >>> Right a & chosen *~ b
--   Right (a * b)
--   
--   
--   
--   chosen :: Lens (Either a a) (Either b b) a b
--   chosen f (Left a)  = Left <$> f a
--   chosen f (Right a) = Right <$> f a
--   
chosen :: IndexPreservingLens (Either a a) (Either b b) a b

-- | alongside makes a Lens from two other lenses.
--   
--   
--   >>> (Left a, Right b)^.alongside chosen chosen
--   (a,b)
--   
--   
--   
--   >>> (Left a, Right b) & alongside chosen chosen .~ (c,d)
--   (Left c,Right d)
--   
--   
--   
--   alongside :: Lens s t a b -> Lens s' t' a' b' -> Lens (s,s') (t,t') (a,a') (b,b')
--   
alongside :: ALens s t a b -> ALens s' t' a' b' -> Lens (s, s') (t, t') (a, a') (b, b')

-- | Lift a Lens so it can run under a function.
inside :: ALens s t a b -> Lens (e -> s) (e -> t) (e -> a) (e -> b)

-- | Modify the target of a Lens and return the result.
--   
--   When you do not need the result of the addition, (%~) is more
--   flexible.
--   
--   
--   (<%~) ::             Lens s t a b      -> (a -> b) -> s -> (b, t)
--   (<%~) ::             Iso s t a b       -> (a -> b) -> s -> (b, t)
--   (<%~) :: Monoid b => Traversal s t a b -> (a -> b) -> s -> (b, t)
--   
(<%~) :: Profunctor p => Overloading p q ((,) b) s t a b -> p a b -> q s (b, t)

-- | Increment the target of a numerically valued Lens and return
--   the result.
--   
--   When you do not need the result of the addition, (+~) is more
--   flexible.
--   
--   
--   (<+~) :: Num a => Lens' s a -> a -> s -> (a, s)
--   (<+~) :: Num a => Iso' s a  -> a -> s -> (a, s)
--   
(<+~) :: Num a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)

-- | Decrement the target of a numerically valued Lens and return
--   the result.
--   
--   When you do not need the result of the subtraction, (-~) is
--   more flexible.
--   
--   
--   (<-~) :: Num a => Lens' s a -> a -> s -> (a, s)
--   (<-~) :: Num a => Iso' s a  -> a -> s -> (a, s)
--   
(<-~) :: Num a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)

-- | Multiply the target of a numerically valued Lens and return the
--   result.
--   
--   When you do not need the result of the multiplication, (*~) is
--   more flexible.
--   
--   
--   (<*~) :: Num a => Lens' s a -> a -> s -> (a, s)
--   (<*~) :: Num a => Iso'  s a -> a -> s -> (a, s)
--   
(<*~) :: Num a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)

-- | Divide the target of a fractionally valued Lens and return the
--   result.
--   
--   When you do not need the result of the division, (//~) is more
--   flexible.
--   
--   
--   (<//~) :: Fractional a => Lens' s a -> a -> s -> (a, s)
--   (<//~) :: Fractional a => Iso'  s a -> a -> s -> (a, s)
--   
(<//~) :: Fractional a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)

-- | Raise the target of a numerically valued Lens to a non-negative
--   Integral power and return the result.
--   
--   When you do not need the result of the division, (^~) is more
--   flexible.
--   
--   
--   (<^~) :: (Num a, Integral e) => Lens' s a -> e -> s -> (a, s)
--   (<^~) :: (Num a, Integral e) => Iso' s a -> e -> s -> (a, s)
--   
(<^~) :: (Num a, Integral e) => Overloading (->) q ((,) a) s t a a -> e -> q s (a, t)

-- | Raise the target of a fractionally valued Lens to an
--   Integral power and return the result.
--   
--   When you do not need the result of the division, (^^~) is more
--   flexible.
--   
--   
--   (<^^~) :: (Fractional a, Integral e) => Lens' s a -> e -> s -> (a, s)
--   (<^^~) :: (Fractional a, Integral e) => Iso' s a -> e -> s -> (a, s)
--   
(<^^~) :: (Fractional a, Integral e) => Overloading (->) q ((,) a) s t a a -> e -> q s (a, t)

-- | Raise the target of a floating-point valued Lens to an
--   arbitrary power and return the result.
--   
--   When you do not need the result of the division, (**~) is more
--   flexible.
--   
--   
--   (<**~) :: Floating a => Lens' s a -> a -> s -> (a, s)
--   (<**~) :: Floating a => Iso' s a  -> a -> s -> (a, s)
--   
(<**~) :: Floating a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)

-- | Logically || a Boolean valued Lens and return the
--   result.
--   
--   When you do not need the result of the operation, (||~) is more
--   flexible.
--   
--   
--   (<||~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
--   (<||~) :: Iso' s Bool  -> Bool -> s -> (Bool, s)
--   
(<||~) :: Overloading (->) q ((,) Bool) s t Bool Bool -> Bool -> q s (Bool, t)

-- | Logically && a Boolean valued Lens and return
--   the result.
--   
--   When you do not need the result of the operation, (&&~)
--   is more flexible.
--   
--   
--   (<&&~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
--   (<&&~) :: Iso' s Bool  -> Bool -> s -> (Bool, s)
--   
(<&&~) :: Overloading (->) q ((,) Bool) s t Bool Bool -> Bool -> q s (Bool, t)

-- | mappend a monoidal value onto the end of the target of a
--   Lens and return the result.
--   
--   When you do not need the result of the operation, (<>~)
--   is more flexible.
(<<>~) :: Monoid m => Overloading (->) q ((,) m) s t m m -> m -> q s (m, t)

-- | Modify the target of a Lens, but return the old value.
--   
--   When you do not need the result of the addition, (%~) is more
--   flexible.
--   
--   
--   (<<%~) ::             Lens s t a b      -> (a -> b) -> s -> (a, t)
--   (<<%~) ::             Iso s t a b       -> (a -> b) -> s -> (a, t)
--   (<<%~) :: Monoid a => Traversal s t a b -> (a -> b) -> s -> (a, t)
--   
(<<%~) :: Strong p => Overloading p q ((,) a) s t a b -> p a b -> q s (a, t)

-- | Modify the target of a Lens, but return the old value.
--   
--   When you do not need the old value, (%~) is more flexible.
--   
--   
--   (<<.~) ::             Lens s t a b      -> b -> s -> (a, t)
--   (<<.~) ::             Iso s t a b       -> b -> s -> (a, t)
--   (<<.~) :: Monoid a => Traversal s t a b -> b -> s -> (a, t)
--   
(<<.~) :: Overloading (->) q ((,) a) s t a b -> b -> q s (a, t)

-- | Modify the target of a Lens into your 'Monad'\'s state by a
--   user supplied function and return the result.
--   
--   When applied to a Traversal, it this will return a monoidal
--   summary of all of the intermediate results.
--   
--   When you do not need the result of the operation, (%=) is more
--   flexible.
--   
--   
--   (<%=) :: MonadState s m             => Lens' s a      -> (a -> a) -> m a
--   (<%=) :: MonadState s m             => Iso' s a       -> (a -> a) -> m a
--   (<%=) :: (MonadState s m, Monoid a) => Traversal' s a -> (a -> a) -> m a
--   
(<%=) :: (Profunctor p, MonadState s m) => Overloading p (->) ((,) b) s s a b -> p a b -> m b

-- | Add to the target of a numerically valued Lens into your
--   'Monad'\'s state and return the result.
--   
--   When you do not need the result of the addition, (+=) is more
--   flexible.
--   
--   
--   (<+=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
--   (<+=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a
--   
(<+=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a

-- | Subtract from the target of a numerically valued Lens into your
--   'Monad'\'s state and return the result.
--   
--   When you do not need the result of the subtraction, (-=) is
--   more flexible.
--   
--   
--   (<-=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
--   (<-=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a
--   
(<-=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a

-- | Multiply the target of a numerically valued Lens into your
--   'Monad'\'s state and return the result.
--   
--   When you do not need the result of the multiplication, (*=) is
--   more flexible.
--   
--   
--   (<*=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
--   (<*=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a
--   
(<*=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a

-- | Divide the target of a fractionally valued Lens into your
--   'Monad'\'s state and return the result.
--   
--   When you do not need the result of the division, (//=) is more
--   flexible.
--   
--   
--   (<//=) :: (MonadState s m, Fractional a) => Lens' s a -> a -> m a
--   (<//=) :: (MonadState s m, Fractional a) => Iso' s a -> a -> m a
--   
(<//=) :: (MonadState s m, Fractional a) => LensLike' ((,) a) s a -> a -> m a

-- | Raise the target of a numerically valued Lens into your
--   'Monad'\'s state to a non-negative Integral power and return
--   the result.
--   
--   When you do not need the result of the operation, (**=) is more
--   flexible.
--   
--   
--   (<^=) :: (MonadState s m, Num a, Integral e) => Lens' s a -> e -> m a
--   (<^=) :: (MonadState s m, Num a, Integral e) => Iso' s a -> e -> m a
--   
(<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m a

-- | Raise the target of a fractionally valued Lens into your
--   'Monad'\'s state to an Integral power and return the result.
--   
--   When you do not need the result of the operation, (^^=) is more
--   flexible.
--   
--   
--   (<^^=) :: (MonadState s m, Fractional b, Integral e) => Lens' s a -> e -> m a
--   (<^^=) :: (MonadState s m, Fractional b, Integral e) => Iso' s a  -> e -> m a
--   
(<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m a

-- | Raise the target of a floating-point valued Lens into your
--   'Monad'\'s state to an arbitrary power and return the result.
--   
--   When you do not need the result of the operation, (**=) is more
--   flexible.
--   
--   
--   (<**=) :: (MonadState s m, Floating a) => Lens' s a -> a -> m a
--   (<**=) :: (MonadState s m, Floating a) => Iso' s a -> a -> m a
--   
(<**=) :: (MonadState s m, Floating a) => LensLike' ((,) a) s a -> a -> m a

-- | Logically || a Boolean valued Lens into your 'Monad'\'s
--   state and return the result.
--   
--   When you do not need the result of the operation, (||=) is more
--   flexible.
--   
--   
--   (<||=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
--   (<||=) :: MonadState s m => Iso' s Bool  -> Bool -> m Bool
--   
(<||=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool

-- | Logically && a Boolean valued Lens into your
--   'Monad'\'s state and return the result.
--   
--   When you do not need the result of the operation, (&&=)
--   is more flexible.
--   
--   
--   (<&&=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
--   (<&&=) :: MonadState s m => Iso' s Bool  -> Bool -> m Bool
--   
(<&&=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool

-- | mappend a monoidal value onto the end of the target of a
--   Lens into your 'Monad'\'s state and return the result.
--   
--   When you do not need the result of the operation, (<>=)
--   is more flexible.
(<<>=) :: (MonadState s m, Monoid r) => LensLike' ((,) r) s r -> r -> m r

-- | Modify the target of a Lens into your 'Monad'\'s state by a
--   user supplied function and return the old value that was
--   replaced.
--   
--   When applied to a Traversal, it this will return a monoidal
--   summary of all of the old values present.
--   
--   When you do not need the result of the operation, (%=) is more
--   flexible.
--   
--   
--   (<<%=) :: MonadState s m             => Lens' s a      -> (a -> a) -> m a
--   (<<%=) :: MonadState s m             => Iso' s a       -> (a -> a) -> m a
--   (<<%=) :: (MonadState s m, Monoid b) => Traversal' s a -> (a -> a) -> m a
--   
--   
--   
--   (<<%=) :: MonadState s m => LensLike ((,)a) s s a b -> (a -> b) -> m a
--   
(<<%=) :: (Strong p, MonadState s m) => Overloading p (->) ((,) a) s s a b -> p a b -> m a

-- | Modify the target of a Lens into your 'Monad'\'s state by a
--   user supplied function and return the old value that was
--   replaced.
--   
--   When applied to a Traversal, it this will return a monoidal
--   summary of all of the old values present.
--   
--   When you do not need the result of the operation, (%=) is more
--   flexible.
--   
--   
--   (<<%=) :: MonadState s m             => Lens' s a      -> (a -> a) -> m a
--   (<<%=) :: MonadState s m             => Iso' s a       -> (a -> a) -> m a
--   (<<%=) :: (MonadState s m, Monoid t) => Traversal' s a -> (a -> a) -> m a
--   
(<<.=) :: MonadState s m => LensLike ((,) a) s s a b -> b -> m a

-- | Run a monadic action, and set the target of Lens to its result.
--   
--   
--   (<<~) :: MonadState s m => Iso s s a b   -> m b -> m b
--   (<<~) :: MonadState s m => Lens s s a b  -> m b -> m b
--   
--   
--   NB: This is limited to taking an actual Lens than admitting a
--   Traversal because there are potential loss of state issues
--   otherwise.
(<<~) :: MonadState s m => ALens s s a b -> m b -> m b

-- | Cloning a Lens is one way to make sure you aren't given
--   something weaker, such as a Traversal and can be used as a way
--   to pass around lenses that have to be monomorphic in f.
--   
--   Note: This only accepts a proper Lens.
--   
--   
--   >>> let example l x = set (cloneLens l) (x^.cloneLens l + 1) x in example _2 ("hello",1,"you")
--   ("hello",2,"you")
--   
cloneLens :: ALens s t a b -> Lens s t a b

-- | Clone a Lens as an IndexedPreservingLens that just
--   passes through whatever index is on any IndexedLens,
--   IndexedFold, IndexedGetter or IndexedTraversal it
--   is composed with.
cloneIndexPreservingLens :: ALens s t a b -> IndexPreservingLens s t a b

-- | Clone an IndexedLens as an IndexedLens with the same
--   index.
cloneIndexedLens :: AnIndexedLens i s t a b -> IndexedLens i s t a b

-- | A version of set that works on ALens.
--   
--   
--   >>> storing _2 "world" ("hello","there")
--   ("hello","world")
--   
storing :: ALens s t a b -> b -> s -> t

-- | A version of (^.) that works on ALens.
--   
--   
--   >>> ("hello","world")^#_2
--   "world"
--   
(^#) :: s -> ALens s t a b -> a

-- | A version of (.~) that works on ALens.
--   
--   
--   >>> ("hello","there") & _2 #~ "world"
--   ("hello","world")
--   
(#~) :: ALens s t a b -> b -> s -> t

-- | A version of (%~) that works on ALens.
--   
--   
--   >>> ("hello","world") & _2 #%~ length
--   ("hello",5)
--   
(#%~) :: ALens s t a b -> (a -> b) -> s -> t

-- | A version of (%%~) that works on ALens.
--   
--   
--   >>> ("hello","world") & _2 #%%~ \x -> (length x, x ++ "!")
--   (5,("hello","world!"))
--   
(#%%~) :: Functor f => ALens s t a b -> (a -> f b) -> s -> f t

-- | A version of (<.~) that works on ALens.
--   
--   
--   >>> ("hello","there") & _2 <#~ "world"
--   ("world",("hello","world"))
--   
(<#~) :: ALens s t a b -> b -> s -> (b, t)

-- | A version of (<%~) that works on ALens.
--   
--   
--   >>> ("hello","world") & _2 <#%~ length
--   (5,("hello",5))
--   
(<#%~) :: ALens s t a b -> (a -> b) -> s -> (b, t)

-- | A version of (.=) that works on ALens.
(#=) :: MonadState s m => ALens s s a b -> b -> m ()

-- | A version of (%=) that works on ALens.
(#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m ()

-- | A version of (%%=) that works on ALens.
(#%%=) :: MonadState s m => ALens s s a b -> (a -> (r, b)) -> m r

-- | A version of (<#=) that works on ALens.
(<#=) :: MonadState s m => ALens s s a b -> b -> m b

-- | A version of (<%=) that works on ALens.
(<#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m b

-- | There is a field for every type in the Void. Very zen.
--   
--   
--   >>> [] & mapped.devoid +~ 1
--   []
--   
--   
--   
--   >>> Nothing & mapped.devoid %~ abs
--   Nothing
--   
--   
--   
--   devoid :: Lens' Void a
--   
devoid :: Over p f Void Void a b

-- | We can always retrieve a () from any type.
--   
--   
--   >>> "hello"^.united
--   ()
--   
--   
--   
--   >>> "hello" & united .~ ()
--   "hello"
--   
united :: Lens' a ()

-- | The indexed store can be used to characterize a Lens and is
--   used by clone.
--   
--   Context a b t is isomorphic to newtype
--   Context a b t = Context { runContext :: forall f.
--   Functor f => (a -> f b) -> f t }, and to
--   exists s. (s, Lens s t a b).
--   
--   A Context is like a Lens that has already been applied
--   to a some structure.
data Context a b t
Context :: (b -> t) -> a -> Context a b t

-- | 
--   type Context' a s = Context a a s
--   
type Context' a = Context a a

-- | This Lens lets you view the current pos of
--   any indexed store comonad and seek to a new position. This
--   reduces the API for working these instances to a single Lens.
--   
--   
--   ipos w ≡ w ^. locus
--   iseek s w ≡ w & locus .~ s
--   iseeks f w ≡ w & locus %~ f
--   
--   
--   
--   locus :: Lens' (Context' a s) a
--   locus :: Conjoined p => Lens' (Pretext' p a s) a
--   locus :: Conjoined p => Lens' (PretextT' p g a s) a
--   
locus :: IndexedComonadStore p => Lens (p a c s) (p b c s) a b

-- | This module exports a minimalist API for working with lenses in highly
--   monomorphic settings.
module Control.Lens.Loupe

-- | When you see this as an argument to a function, it expects a
--   Lens.
--   
--   This type can also be used when you need to store a Lens in a
--   container, since it is rank-1. You can turn them back into a
--   Lens with cloneLens, or use it directly with combinators
--   like storing and (^#).
type ALens s t a b = LensLike (Pretext (->) a b) s t a b

-- | 
--   type ALens' = Simple ALens
--   
type ALens' s a = ALens s s a a

-- | Cloning a Lens is one way to make sure you aren't given
--   something weaker, such as a Traversal and can be used as a way
--   to pass around lenses that have to be monomorphic in f.
--   
--   Note: This only accepts a proper Lens.
--   
--   
--   >>> let example l x = set (cloneLens l) (x^.cloneLens l + 1) x in example _2 ("hello",1,"you")
--   ("hello",2,"you")
--   
cloneLens :: ALens s t a b -> Lens s t a b

-- | A version of set that works on ALens.
--   
--   
--   >>> storing _2 "world" ("hello","there")
--   ("hello","world")
--   
storing :: ALens s t a b -> b -> s -> t

-- | A version of (^.) that works on ALens.
--   
--   
--   >>> ("hello","world")^#_2
--   "world"
--   
(^#) :: s -> ALens s t a b -> a

-- | A version of (.~) that works on ALens.
--   
--   
--   >>> ("hello","there") & _2 #~ "world"
--   ("hello","world")
--   
(#~) :: ALens s t a b -> b -> s -> t

-- | A version of (%~) that works on ALens.
--   
--   
--   >>> ("hello","world") & _2 #%~ length
--   ("hello",5)
--   
(#%~) :: ALens s t a b -> (a -> b) -> s -> t

-- | A version of (%%~) that works on ALens.
--   
--   
--   >>> ("hello","world") & _2 #%%~ \x -> (length x, x ++ "!")
--   (5,("hello","world!"))
--   
(#%%~) :: Functor f => ALens s t a b -> (a -> f b) -> s -> f t

-- | A version of (<.~) that works on ALens.
--   
--   
--   >>> ("hello","there") & _2 <#~ "world"
--   ("world",("hello","world"))
--   
(<#~) :: ALens s t a b -> b -> s -> (b, t)

-- | A version of (<%~) that works on ALens.
--   
--   
--   >>> ("hello","world") & _2 <#%~ length
--   (5,("hello",5))
--   
(<#%~) :: ALens s t a b -> (a -> b) -> s -> (b, t)

-- | A version of (.=) that works on ALens.
(#=) :: MonadState s m => ALens s s a b -> b -> m ()

-- | A version of (%=) that works on ALens.
(#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m ()

-- | A version of (%%=) that works on ALens.
(#%%=) :: MonadState s m => ALens s s a b -> (a -> (r, b)) -> m r

-- | A version of (<#=) that works on ALens.
(<#=) :: MonadState s m => ALens s s a b -> b -> m b

-- | A version of (<%=) that works on ALens.
(<#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m b

-- | This is an older alias for a type-restricted form of lens that is able
--   to be passed around in containers monomorphically.
--   
--   Deprecated. This has since been renamed to ALens for
--   consistency.

-- | Deprecated: use ALens 
type Loupe s t a b = LensLike (Pretext (->) a b) s t a b

-- | 
--   type SimpleLoupe = Simple Loupe
--   
--   
--   Deprecated for two reasons. Loupe is now ALens, and we
--   no longer use the verbose SimpleFoo naming convention, this
--   has since been renamed to ALens' for consistency.

-- | Deprecated: use ALens' 
type SimpleLoupe s a = Loupe s s a a

module Control.Lens.Prism

-- | A Prism l is a 0-or-1 target Traversal that can
--   also be turned around with re to obtain a Getter in the
--   opposite direction.
--   
--   There are two laws that a Prism should satisfy:
--   
--   First, if I re or review a value with a Prism and
--   then preview or use (^?), I will get it back:
--   
--   
--   preview l (review l b) ≡ Just b
--   
--   
--   Second, if you can extract a value a using a Prism
--   l from a value s, then the value s is
--   completely described my l and a:
--   
--   If preview l s ≡ Just a then review
--   l a ≡ s
--   
--   These two laws imply that the Traversal laws hold for every
--   Prism and that we traverse at most 1 element:
--   
--   
--   lengthOf l x <= 1
--   
--   
--   It may help to think of this as a Iso that can be partial in
--   one direction.
--   
--   Every Prism is a valid Traversal.
--   
--   Every Iso is a valid Prism.
--   
--   For example, you might have a Prism' Integer
--   Natural allows you to always go from a Natural to
--   an Integer, and provide you with tools to check if an
--   Integer is a Natural and/or to edit one if it is.
--   
--   
--   nat :: Prism' Integer Natural
--   nat = prism toInteger $ \ i ->
--      if i < 0
--      then Left i
--      else Right (fromInteger i)
--   
--   
--   Now we can ask if an Integer is a Natural.
--   
--   
--   >>> 5^?nat
--   Just 5
--   
--   
--   
--   >>> (-5)^?nat
--   Nothing
--   
--   
--   We can update the ones that are:
--   
--   
--   >>> (-3,4) & both.nat *~ 2
--   (-3,8)
--   
--   
--   And we can then convert from a Natural to an Integer.
--   
--   
--   >>> 5 ^. re nat -- :: Natural
--   5
--   
--   
--   Similarly we can use a Prism to traverse the Left
--   half of an Either:
--   
--   
--   >>> Left "hello" & _Left %~ length
--   Left 5
--   
--   
--   or to construct an Either:
--   
--   
--   >>> 5^.re _Left
--   Left 5
--   
--   
--   such that if you query it with the Prism, you will get your
--   original input back.
--   
--   
--   >>> 5^.re _Left ^? _Left
--   Just 5
--   
--   
--   Another interesting way to think of a Prism is as the
--   categorical dual of a Lens -- a co-Lens, so to speak.
--   This is what permits the construction of outside.
--   
--   Note: Composition with a Prism is index-preserving.
type Prism s t a b = forall p f. (Choice p, Applicative f) => p a (f b) -> p s (f t)

-- | A Simple Prism.
type Prism' s a = Prism s s a a

-- | If you see this in a signature for a function, the function is
--   expecting a Prism.
type APrism s t a b = Market a b a (Mutator b) -> Market a b s (Mutator t)

-- | 
--   type APrism' = Simple APrism
--   
type APrism' s a = APrism s s a a

-- | Build a Prism.
--   
--   Either t a is used instead of Maybe a
--   to permit the types of s and t to differ.
prism :: (b -> t) -> (s -> Either t a) -> Prism s t a b

-- | This is usually used to build a Prism', when you have to use an
--   operation like cast which already returns a Maybe.
prism' :: (b -> s) -> (s -> Maybe a) -> Prism s s a b

-- | Clone a Prism so that you can reuse the same monomorphically
--   typed Prism for different purposes.
--   
--   See cloneLens and cloneTraversal for examples of why you
--   might want to do this.
clonePrism :: APrism s t a b -> Prism s t a b

-- | Use a Prism as a kind of first-class pattern.
--   
--   
--   outside :: Prism s t a b -> Lens (t -> r) (s -> r) (b -> r) (a -> r)
--   
outside :: APrism s t a b -> Lens (t -> r) (s -> r) (b -> r) (a -> r)

-- | Use a Prism to work over part of a structure.
aside :: APrism s t a b -> Prism (e, s) (e, t) (e, a) (e, b)

-- | Given a pair of prisms, project sums.
--   
--   Viewing a Prism as a co-Lens, this combinator can be
--   seen to be dual to alongside.
without :: APrism s t a b -> APrism u v c d -> Prism (Either s u) (Either t v) (Either a c) (Either b d)

-- | Check to see if this Prism doesn't match.
--   
--   
--   >>> isn't _Left (Right 12)
--   True
--   
--   
--   
--   >>> isn't _Left (Left 12)
--   False
--   
isn't :: APrism s t a b -> s -> Bool

-- | This Prism provides a Traversal for tweaking the
--   Left half of an Either:
--   
--   
--   >>> over _Left (+1) (Left 2)
--   Left 3
--   
--   
--   
--   >>> over _Left (+1) (Right 2)
--   Right 2
--   
--   
--   
--   >>> Right 42 ^._Left :: String
--   ""
--   
--   
--   
--   >>> Left "hello" ^._Left
--   "hello"
--   
--   
--   It also can be turned around to obtain the embedding into the
--   Left half of an Either:
--   
--   
--   >>> _Left # 5
--   Left 5
--   
--   
--   
--   >>> 5^.re _Left
--   Left 5
--   
_Left :: Prism (Either a c) (Either b c) a b

-- | This Prism provides a Traversal for tweaking the
--   Right half of an Either:
--   
--   
--   >>> over _Right (+1) (Left 2)
--   Left 2
--   
--   
--   
--   >>> over _Right (+1) (Right 2)
--   Right 3
--   
--   
--   
--   >>> Right "hello" ^._Right
--   "hello"
--   
--   
--   
--   >>> Left "hello" ^._Right :: [Double]
--   []
--   
--   
--   It also can be turned around to obtain the embedding into the
--   Right half of an Either:
--   
--   
--   >>> _Right # 5
--   Right 5
--   
--   
--   
--   >>> 5^.re _Right
--   Right 5
--   
_Right :: Prism (Either c a) (Either c b) a b

-- | This Prism provides a Traversal for tweaking the target
--   of the value of Just in a Maybe.
--   
--   
--   >>> over _Just (+1) (Just 2)
--   Just 3
--   
--   
--   Unlike traverse this is a Prism, and so you can use it
--   to inject as well:
--   
--   
--   >>> _Just # 5
--   Just 5
--   
--   
--   
--   >>> 5^.re _Just
--   Just 5
--   
--   
--   Interestingly,
--   
--   
--   m ^? _Just ≡ m
--   
--   
--   
--   >>> Just x ^? _Just
--   Just x
--   
--   
--   
--   >>> Nothing ^? _Just
--   Nothing
--   
_Just :: Prism (Maybe a) (Maybe b) a b

-- | This Prism provides the Traversal of a Nothing in
--   a Maybe.
--   
--   
--   >>> Nothing ^? _Nothing
--   Just ()
--   
--   
--   
--   >>> Just () ^? _Nothing
--   Nothing
--   
--   
--   But you can turn it around and use it to construct Nothing as
--   well:
--   
--   
--   >>> _Nothing # ()
--   Nothing
--   
_Nothing :: Prism' (Maybe a) ()

-- | Void is a logically uninhabited data type.
--   
--   This is a Prism that will always fail to match.
_Void :: Prism s s a Void

-- | This Prism compares for exact equality with a given value.
--   
--   
--   >>> only 4 # ()
--   4
--   
--   
--   
--   >>> 5 ^? only 4
--   Nothing
--   
only :: Eq a => a -> Prism' a ()

-- | The generalization of DownStar of a "costrong" Functor
--   
--   Minimal complete definition: left' or right'
--   
--   Note: We use traverse and extract as approximate
--   costrength as needed.
class Profunctor p => Choice (p :: * -> * -> *)
left' :: Choice p => p a b -> p (Either a c) (Either b c)
right' :: Choice p => p a b -> p (Either c a) (Either c b)

-- | A Traversal s t a b is a generalization of
--   traverse from Traversable. It allows you to
--   traverse over a structure and change out its contents with
--   monadic or Applicative side-effects. Starting from
--   
--   
--   traverse :: (Traversable t, Applicative f) => (a -> f b) -> t a -> f (t b)
--   
--   
--   we monomorphize the contents and result to obtain
--   
--   
--   type Traversal s t a b = forall f. Applicative f => (a -> f b) -> s -> f t
--   
--   
--   While a Traversal isn't quite a Fold, it _can_ be used
--   for Getting like a Fold, because given a Monoid
--   m, we have an Applicative for (Const
--   m). Everything you know how to do with a Traversable
--   container, you can with with a Traversal, and here we provide
--   combinators that generalize the usual Traversable operations.
module Control.Lens.Traversal

-- | A Traversal can be used directly as a Setter or a
--   Fold (but not as a Lens) and provides the ability to
--   both read and update multiple fields, subject to some relatively weak
--   Traversal laws.
--   
--   These have also been known as multilenses, but they have the signature
--   and spirit of
--   
--   
--   traverse :: Traversable f => Traversal (f a) (f b) a b
--   
--   
--   and the more evocative name suggests their application.
--   
--   Most of the time the Traversal you will want to use is just
--   traverse, but you can also pass any Lens or Iso
--   as a Traversal, and composition of a Traversal (or
--   Lens or Iso) with a Traversal (or Lens or
--   Iso) using (.) forms a valid Traversal.
--   
--   The laws for a Traversal t follow from the laws for
--   Traversable as stated in "The Essence of the Iterator Pattern".
--   
--   
--   t pure ≡ pure
--   fmap (t f) . t g ≡ getCompose . t (Compose . fmap f . g)
--   
--   
--   One consequence of this requirement is that a Traversal needs
--   to leave the same number of elements as a candidate for subsequent
--   Traversal that it started with. Another testament to the
--   strength of these laws is that the caveat expressed in section 5.5 of
--   the "Essence of the Iterator Pattern" about exotic Traversable
--   instances that traverse the same entry multiple times was
--   actually already ruled out by the second law in that same paper!
type Traversal s t a b = forall f. Applicative f => (a -> f b) -> s -> f t

-- | 
--   type Traversal' = Simple Traversal
--   
type Traversal' s a = Traversal s s a a

-- | Every IndexedTraversal is a valid Traversal or
--   IndexedFold.
--   
--   The Indexed constraint is used to allow an
--   IndexedTraversal to be used directly as a Traversal.
--   
--   The Traversal laws are still required to hold.
type IndexedTraversal i s t a b = forall p f. (Indexable i p, Applicative f) => p a (f b) -> s -> f t

-- | 
--   type IndexedTraversal' i = Simple (IndexedTraversal i)
--   
type IndexedTraversal' i s a = IndexedTraversal i s s a a

-- | When you see this as an argument to a function, it expects a
--   Traversal.
type ATraversal s t a b = LensLike (Bazaar (->) a b) s t a b

-- | 
--   type ATraversal' = Simple ATraversal
--   
type ATraversal' s a = ATraversal s s a a

-- | When you see this as an argument to a function, it expects an
--   IndexedTraversal.
type AnIndexedTraversal i s t a b = Over (Indexed i) (Bazaar (Indexed i) a b) s t a b

-- | 
--   type AnIndexedTraversal' = Simple (AnIndexedTraversal i)
--   
type AnIndexedTraversal' i s a = AnIndexedTraversal i s s a a

-- | When you see this as an argument to a function, it expects
--   
--   
--   
- to be indexed if p is an instance of Indexed
--   i,
--   
- to be unindexed if p is (->),
--   
- a Traversal if f is Applicative,
--   
- a Getter if f is only Gettable,
--   
- a Lens if p is only a Functor,
--   
- a Fold if f is Gettable and
--   Applicative.
--   
type Traversing p f s t a b = Over p (BazaarT p f a b) s t a b

-- | 
--   type Traversing' f = Simple (Traversing f)
--   
type Traversing' p f s a = Traversing p f s s a a

-- | Map each element of a structure targeted by a Lens or
--   Traversal, evaluate these actions from left to right, and
--   collect the results.
--   
--   This function is only provided for consistency, id is strictly
--   more general.
--   
--   
--   >>> traverseOf each print (1,2,3)
--   1
--   2
--   3
--   ((),(),())
--   
--   
--   
--   traverseOf ≡ id
--   itraverseOf l ≡ traverseOf l . Indexed
--   
--   
--   This yields the obvious law:
--   
--   
--   traverse ≡ traverseOf traverse
--   
--   
--   
--   traverseOf :: Functor f => Iso s t a b       -> (a -> f b) -> s -> f t
--   traverseOf :: Functor f => Lens s t a b      -> (a -> f b) -> s -> f t
--   traverseOf :: Applicative f => Traversal s t a b -> (a -> f b) -> s -> f t
--   
traverseOf :: Over p f s t a b -> p a (f b) -> s -> f t

-- | A version of traverseOf with the arguments flipped, such that:
--   
--   
--   >>> forOf each (1,2,3) print
--   1
--   2
--   3
--   ((),(),())
--   
--   
--   This function is only provided for consistency, flip is
--   strictly more general.
--   
--   
--   forOf ≡ flip
--   forOf ≡ flip . traverseOf
--   
--   
--   
--   for ≡ forOf traverse
--   ifor l s ≡ for l s . Indexed
--   
--   
--   
--   forOf :: Functor f => Iso s t a b -> s -> (a -> f b) -> f t
--   forOf :: Functor f => Lens s t a b -> s -> (a -> f b) -> f t
--   forOf :: Applicative f => Traversal s t a b -> s -> (a -> f b) -> f t
--   
forOf :: Over p f s t a b -> s -> p a (f b) -> f t

-- | Evaluate each action in the structure from left to right, and collect
--   the results.
--   
--   
--   >>> sequenceAOf both ([1,2],[3,4])
--   [(1,3),(1,4),(2,3),(2,4)]
--   
--   
--   
--   sequenceA ≡ sequenceAOf traverse ≡ traverse id
--   sequenceAOf l ≡ traverseOf l id ≡ l id
--   
--   
--   
--   sequenceAOf :: Functor f => Iso s t (f b) b       -> s -> f t
--   sequenceAOf :: Functor f => Lens s t (f b) b      -> s -> f t
--   sequenceAOf :: Applicative f => Traversal s t (f b) b -> s -> f t
--   
sequenceAOf :: LensLike f s t (f b) b -> s -> f t

-- | Map each element of a structure targeted by a Lens to a monadic
--   action, evaluate these actions from left to right, and collect the
--   results.
--   
--   
--   >>> mapMOf both (\x -> [x, x + 1]) (1,3)
--   [(1,3),(1,4),(2,3),(2,4)]
--   
--   
--   
--   mapM ≡ mapMOf traverse
--   imapMOf l ≡ forM l . Indexed
--   
--   
--   
--   mapMOf :: Monad m => Iso s t a b       -> (a -> m b) -> s -> m t
--   mapMOf :: Monad m => Lens s t a b      -> (a -> m b) -> s -> m t
--   mapMOf :: Monad m => Traversal s t a b -> (a -> m b) -> s -> m t
--   
mapMOf :: Profunctor p => Over p (WrappedMonad m) s t a b -> p a (m b) -> s -> m t

-- | forMOf is a flipped version of mapMOf, consistent with
--   the definition of forM.
--   
--   
--   >>> forMOf both (1,3) $ \x -> [x, x + 1]
--   [(1,3),(1,4),(2,3),(2,4)]
--   
--   
--   
--   forM ≡ forMOf traverse
--   forMOf l ≡ flip (mapMOf l)
--   iforMOf l s ≡ forM l s . Indexed
--   
--   
--   
--   forMOf :: Monad m => Iso s t a b       -> s -> (a -> m b) -> m t
--   forMOf :: Monad m => Lens s t a b      -> s -> (a -> m b) -> m t
--   forMOf :: Monad m => Traversal s t a b -> s -> (a -> m b) -> m t
--   
forMOf :: Profunctor p => Over p (WrappedMonad m) s t a b -> s -> p a (m b) -> m t

-- | Sequence the (monadic) effects targeted by a Lens in a
--   container from left to right.
--   
--   
--   >>> sequenceOf each ([1,2],[3,4],[5,6])
--   [(1,3,5),(1,3,6),(1,4,5),(1,4,6),(2,3,5),(2,3,6),(2,4,5),(2,4,6)]
--   
--   
--   
--   sequence ≡ sequenceOf traverse
--   sequenceOf l ≡ mapMOf l id
--   sequenceOf l ≡ unwrapMonad . l WrapMonad
--   
--   
--   
--   sequenceOf :: Monad m => Iso s t (m b) b       -> s -> m t
--   sequenceOf :: Monad m => Lens s t (m b) b      -> s -> m t
--   sequenceOf :: Monad m => Traversal s t (m b) b -> s -> m t
--   
sequenceOf :: LensLike (WrappedMonad m) s t (m b) b -> s -> m t

-- | This generalizes transpose to an arbitrary Traversal.
--   
--   Note: transpose handles ragged inputs more intelligently, but
--   for non-ragged inputs:
--   
--   
--   >>> transposeOf traverse [[1,2,3],[4,5,6]]
--   [[1,4],[2,5],[3,6]]
--   
--   
--   
--   transpose ≡ transposeOf traverse
--   
--   
--   Since every Lens is a Traversal, we can use this as a
--   form of monadic strength as well:
--   
--   
--   transposeOf _2 :: (b, [a]) -> [(b, a)]
--   
transposeOf :: LensLike ZipList s t [a] a -> s -> [t]

-- | This generalizes mapAccumL to an arbitrary Traversal.
--   
--   
--   mapAccumL ≡ mapAccumLOf traverse
--   
--   
--   mapAccumLOf accumulates State from left to right.
--   
--   
--   mapAccumLOf :: Iso s t a b       -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   mapAccumLOf :: Lens s t a b      -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   mapAccumLOf :: Traversal s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   
--   
--   
--   mapAccumLOf :: LensLike (State acc) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   mapAccumLOf l f acc0 s = swap (runState (l (a -> state (acc -> swap (f acc a))) s) acc0)
--   
mapAccumLOf :: Conjoined p => Over p (State acc) s t a b -> p acc (a -> (acc, b)) -> acc -> s -> (acc, t)

-- | This generalizes mapAccumR to an arbitrary Traversal.
--   
--   
--   mapAccumR ≡ mapAccumROf traverse
--   
--   
--   mapAccumROf accumulates State from right to left.
--   
--   
--   mapAccumROf :: Iso s t a b       -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   mapAccumROf :: Lens s t a b      -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   mapAccumROf :: Traversal s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   
--   
--   
--   mapAccumROf :: LensLike (Backwards (State acc)) s t a b -> (acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   
mapAccumROf :: Conjoined p => Over p (Backwards (State acc)) s t a b -> p acc (a -> (acc, b)) -> acc -> s -> (acc, t)

-- | This permits the use of scanr1 over an arbitrary
--   Traversal or Lens.
--   
--   
--   scanr1 ≡ scanr1Of traverse
--   
--   
--   
--   scanr1Of :: Iso s t a a       -> (a -> a -> a) -> s -> t
--   scanr1Of :: Lens s t a a      -> (a -> a -> a) -> s -> t
--   scanr1Of :: Traversal s t a a -> (a -> a -> a) -> s -> t
--   
scanr1Of :: LensLike (Backwards (State (Maybe a))) s t a a -> (a -> a -> a) -> s -> t

-- | This permits the use of scanl1 over an arbitrary
--   Traversal or Lens.
--   
--   
--   scanl1 ≡ scanl1Of traverse
--   
--   
--   
--   scanl1Of :: Iso s t a a       -> (a -> a -> a) -> s -> t
--   scanl1Of :: Lens s t a a      -> (a -> a -> a) -> s -> t
--   scanl1Of :: Traversal s t a a -> (a -> a -> a) -> s -> t
--   
scanl1Of :: LensLike (State (Maybe a)) s t a a -> (a -> a -> a) -> s -> t

-- | Try to map a function over this Traversal, failing if the
--   Traversal has no targets.
--   
--   
--   >>> failover (element 3) (*2) [1,2] :: Maybe [Int]
--   Nothing
--   
--   
--   
--   >>> failover _Left (*2) (Right 4) :: Maybe (Either Int Int)
--   Nothing
--   
--   
--   
--   >>> failover _Right (*2) (Right 4) :: Maybe (Either Int Int)
--   Just (Right 8)
--   
failover :: MonadPlus m => LensLike ((,) Any) s t a b -> (a -> b) -> s -> m t

-- | A Traversal is completely characterized by its behavior on a
--   Bazaar.
--   
--   Cloning a Traversal is one way to make sure you aren't given
--   something weaker, such as a Fold and can be used as a way to
--   pass around traversals that have to be monomorphic in f.
--   
--   Note: This only accepts a proper Traversal (or Lens). To
--   clone a Lens as such, use cloneLens.
--   
--   Note: It is usually better to use ReifiedTraversal and
--   reflectTraversal than to cloneTraversal. The former can
--   execute at full speed, while the latter needs to round trip through
--   the Bazaar.
--   
--   
--   >>> let foo l a = (view (coerced (cloneTraversal l)) a, set (cloneTraversal l) 10 a)
--   
--   >>> foo both ("hello","world")
--   ("helloworld",(10,10))
--   
--   
--   
--   cloneTraversal :: LensLike (Bazaar (->) a b) s t a b -> Traversal s t a b
--   
cloneTraversal :: ATraversal s t a b -> Traversal s t a b

-- | Clone a Traversal yielding an IndexPreservingTraversal
--   that passes through whatever index it is composed with.
cloneIndexPreservingTraversal :: ATraversal s t a b -> IndexPreservingTraversal s t a b

-- | Clone an IndexedTraversal yielding an IndexedTraversal
--   with the same index.
cloneIndexedTraversal :: AnIndexedTraversal i s t a b -> IndexedTraversal i s t a b

-- | partsOf turns a Traversal into a Lens that
--   resembles an early version of the uniplate (or biplate)
--   type.
--   
--   Note: You should really try to maintain the invariant of the
--   number of children in the list.
--   
--   Any extras will be lost. If you do not supply enough, then the
--   remainder will come from the original structure.
--   
--   So technically, this is only a Lens if you do not change the
--   number of results it returns.
--   
--   When applied to a Fold the result is merely a Getter.
--   
--   
--   partsOf :: Iso' s a       -> Lens' s [a]
--   partsOf :: Lens' s a      -> Lens' s [a]
--   partsOf :: Traversal' s a -> Lens' s [a]
--   partsOf :: Fold s a       -> Getter s [a]
--   partsOf :: Getter s a     -> Getter s [a]
--   
partsOf :: Functor f => Traversing (->) f s t a a -> LensLike f s t [a] [a]

-- | A type-restricted version of partsOf that can only be used with
--   a Traversal.
partsOf' :: ATraversal s t a a -> Lens s t [a] [a]

-- | unsafePartsOf turns a Traversal into a uniplate
--   (or biplate) family.
--   
--   If you do not need the types of s and t to be
--   different, it is recommended that you use partsOf.
--   
--   It is generally safer to traverse with the Bazaar rather than
--   use this combinator. However, it is sometimes convenient.
--   
--   This is unsafe because if you don't supply at least as many
--   b's as you were given a's, then the reconstruction
--   of t will result in an error!
--   
--   When applied to a Fold the result is merely a Getter
--   (and becomes safe).
--   
--   
--   unsafePartsOf :: Iso s t a b       -> Lens s t [a] [b]
--   unsafePartsOf :: Lens s t a b      -> Lens s t [a] [b]
--   unsafePartsOf :: Traversal s t a b -> Lens s t [a] [b]
--   unsafePartsOf :: Fold s a          -> Getter s [a]
--   unsafePartsOf :: Getter s a        -> Getter s [a]
--   
unsafePartsOf :: Functor f => Traversing (->) f s t a b -> LensLike f s t [a] [b]
unsafePartsOf' :: ATraversal s t a b -> Lens s t [a] [b]

-- | The one-level version of contextsOf. This extracts a list of
--   the immediate children according to a given Traversal as
--   editable contexts.
--   
--   Given a context you can use pos to see the values, peek
--   at what the structure would be like with an edited result, or simply
--   extract the original structure.
--   
--   
--   propChildren l x = childrenOf l x == map pos (holesOf l x)
--   propId l x = all (== x) [extract w | w <- holesOf l x]
--   
--   
--   
--   holesOf :: Iso' s a                -> s -> [Pretext' (->) a s]
--   holesOf :: Lens' s a               -> s -> [Pretext' (->) a s]
--   holesOf :: Traversal' s a          -> s -> [Pretext' (->) a s]
--   holesOf :: IndexedLens' i s a      -> s -> [Pretext' (Indexed i) a s]
--   holesOf :: IndexedTraversal' i s a -> s -> [Pretext' (Indexed i) a s]
--   
holesOf :: Conjoined p => Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t]

-- | This converts a Traversal that you "know" will target one or
--   more elements to a Lens. It can also be used to transform a
--   non-empty Fold into a Getter or a non-empty
--   MonadicFold into an Action.
--   
--   The resulting Lens, Getter, or Action will be
--   partial if the supplied Traversal returns no results.
--   
--   
--   singular :: Traversal s t a a          -> Lens s t a a
--   singular :: Fold s a                   -> Getter s a
--   singular :: MonadicFold m s a          -> Action m s a
--   singular :: IndexedTraversal i s t a a -> IndexedLens i s t a a
--   singular :: IndexedFold i s a          -> IndexedGetter i s a
--   singular :: IndexedMonadicFold i m s a -> IndexedAction i m s a
--   
singular :: (Conjoined p, Functor f) => Over p (BazaarT p f a a) s t a a -> Over p f s t a a

-- | This converts a Traversal that you "know" will target only one
--   element to a Lens. It can also be used to transform a
--   Fold into a Getter or a MonadicFold into an
--   Action.
--   
--   The resulting Lens, Getter, or Action will be
--   partial if the Traversal targets nothing or more than one
--   element.
--   
--   
--   unsafeSingular :: Traversal s t a b          -> Lens s t a b
--   unsafeSingular :: Fold s a                   -> Getter s a
--   unsafeSingular :: MonadicFold m s a          -> Action m s a
--   unsafeSingular :: IndexedTraversal i s t a b -> IndexedLens i s t a b
--   unsafeSingular :: IndexedFold i s a          -> IndexedGetter i s a
--   unsafeSingular :: IndexedMonadicFold i m s a -> IndexedAction i m s a
--   
unsafeSingular :: (Conjoined p, Functor f) => Over p (BazaarT p f a b) s t a b -> Over p f s t a b

-- | Functors representing data structures that can be traversed from left
--   to right.
--   
--   Minimal complete definition: traverse or sequenceA.
--   
--   Instances are similar to Functor, e.g. given a data type
--   
--   
--   data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
--   
--   
--   a suitable instance would be
--   
--   
--   instance Traversable Tree where
--      traverse f Empty = pure Empty
--      traverse f (Leaf x) = Leaf <$> f x
--      traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r
--   
--   
--   This is suitable even for abstract types, as the laws for
--   <*> imply a form of associativity.
--   
--   The superclass instances should satisfy the following:
--   
--   
--   
- In the Functor instance, fmap should be equivalent
--   to traversal with the identity applicative functor
--   (fmapDefault).
--   
- In the Foldable instance, foldMap should be
--   equivalent to traversal with a constant applicative functor
--   (foldMapDefault).
--   
class (Functor t, Foldable t) => Traversable (t :: * -> *)
traverse :: (Traversable t, Applicative f) => (a -> f b) -> t a -> f (t b)

-- | Traverse both parts of a tuple with matching types.
--   
--   
--   >>> both *~ 10 $ (1,2)
--   (10,20)
--   
--   
--   
--   >>> over both length ("hello","world")
--   (5,5)
--   
--   
--   
--   >>> ("hello","world")^.both
--   "helloworld"
--   
both :: Traversal (a, a) (b, b) a b

-- | Apply a different Traversal or Fold to each side of a
--   tuple.
--   
--   
--   beside :: Traversal s t a b                -> Traversal s' t' a b                -> Traversal (s,s') (t,t') a b
--   beside :: Lens s t a b                     -> Lens s' t' a b                     -> Traversal (s,s') (t,t') a b
--   beside :: Fold s a                         -> Fold s' a                          -> Fold (s,s') a
--   beside :: Getter s a                       -> Getter s' a                        -> Fold (s,s') a
--   beside :: Action m s a                     -> Action m s' a                      -> MonadicFold m (s,s') a
--   beside :: MonadicFold m s a                -> MonadicFold m s' a                 -> MonadicFold m (s,s') a
--   
--   
--   
--   beside :: IndexedTraversal i s t a b       -> IndexedTraversal i s' t' a b       -> IndexedTraversal i (s,s') (t,t') a b
--   beside :: IndexedLens i s t a b            -> IndexedLens i s' t' a b            -> IndexedTraversal i (s,s') (t,t') a b
--   beside :: IndexedFold i s a                -> IndexedFold i s' a                 -> IndexedFold i (s,s') a
--   beside :: IndexedGetter i s a              -> IndexedGetter i s' a               -> IndexedFold i (s,s') a
--   beside :: IndexedAction i m s a            -> IndexedAction i m s' a             -> IndexedMonadicFold i m (s,s') a
--   beside :: IndexedMonadicFold i m s a       -> IndexedMonadicFold i m s' a        -> IndexedMonadicFold i m (s,s') a
--   
--   
--   
--   beside :: IndexPreservingTraversal s t a b -> IndexPreservingTraversal s' t' a b -> IndexPreservingTraversal (s,s') (t,t') a b
--   beside :: IndexPreservingLens s t a b      -> IndexPreservingLens s' t' a b      -> IndexPreservingTraversal (s,s') (t,t') a b
--   beside :: IndexPreservingFold s a          -> IndexPreservingFold s' a           -> IndexPreservingFold (s,s') a
--   beside :: IndexPreservingGetter s a        -> IndexPreservingGetter s' a         -> IndexPreservingFold (s,s') a
--   beside :: IndexPreservingAction m s a      -> IndexPreservingAction m s' a       -> IndexPreservingMonadicFold m (s,s') a
--   beside :: IndexPreservingMonadicFold m s a -> IndexPreservingMonadicFold m s' a  -> IndexPreservingMonadicFold m (s,s') a
--   
--   
--   
--   >>> ("hello",["world","!!!"])^..beside id traverse
--   ["hello","world","!!!"]
--   
beside :: (Representable q, Applicative (Rep q), Applicative f) => Overloading p q f s t a b -> Overloading p q f s' t' a b -> Overloading p q f (s, s') (t, t') a b

-- | Visit the first n targets of a Traversal, Fold,
--   Getter or Lens.
--   
--   
--   >>> [("hello","world"),("!!!","!!!")]^.. taking 2 (traverse.both)
--   ["hello","world"]
--   
--   
--   
--   >>> timingOut $ [1..] ^.. taking 3 traverse
--   [1,2,3]
--   
--   
--   
--   >>> over (taking 5 traverse) succ "hello world"
--   "ifmmp world"
--   
--   
--   
--   taking :: Int -> Traversal' s a                   -> Traversal' s a
--   taking :: Int -> Lens' s a                        -> Traversal' s a
--   taking :: Int -> Iso' s a                         -> Traversal' s a
--   taking :: Int -> Prism' s a                       -> Traversal' s a
--   taking :: Int -> Getter s a                       -> Fold s a
--   taking :: Int -> Fold s a                         -> Fold s a
--   taking :: Int -> Action m s a                     -> MonadicFold m s a
--   taking :: Int -> MonadicFold m s a                -> MonadicFold m s a
--   taking :: Int -> IndexedTraversal' i s a          -> IndexedTraversal' i s a
--   taking :: Int -> IndexedLens' i s a               -> IndexedTraversal' i s a
--   taking :: Int -> IndexedGetter i s a              -> IndexedFold i s a
--   taking :: Int -> IndexedFold i s a                -> IndexedFold i s a
--   taking :: Int -> IndexedAction i m s a            -> IndexedMonadicFold i m s a
--   taking :: Int -> IndexedMonadicFold i m s a       -> IndexedMonadicFold i m s a
--   
taking :: (Conjoined p, Applicative f) => Int -> Over p (BazaarT p f a a) s t a a -> Over p f s t a a

-- | Visit all but the first n targets of a Traversal,
--   Fold, Getter or Lens.
--   
--   
--   >>> ("hello","world") ^? dropping 1 both
--   Just "world"
--   
--   
--   Dropping works on infinite traversals as well:
--   
--   
--   >>> [1..] ^? dropping 1 folded
--   Just 2
--   
--   
--   
--   dropping :: Int -> Traversal' s a                   -> Traversal' s a
--   dropping :: Int -> Lens' s a                        -> Traversal' s a
--   dropping :: Int -> Iso' s a                         -> Traversal' s a
--   dropping :: Int -> Prism' s a                       -> Traversal' s a
--   dropping :: Int -> Getter s a                       -> Fold s a
--   dropping :: Int -> Fold s a                         -> Fold s a
--   dropping :: Int -> Action m s a                     -> MonadicFold m s a
--   dropping :: Int -> MonadicFold m s a                -> MonadicFold m s a
--   dropping :: Int -> IndexedTraversal' i s a          -> IndexedTraversal' i s a
--   dropping :: Int -> IndexedLens' i s a               -> IndexedTraversal' i s a
--   dropping :: Int -> IndexedGetter i s a              -> IndexedFold i s a
--   dropping :: Int -> IndexedFold i s a                -> IndexedFold i s a
--   dropping :: Int -> IndexedAction i m s a            -> IndexedMonadicFold i m s a
--   dropping :: Int -> IndexedMonadicFold i m s a       -> IndexedMonadicFold i m s a
--   
dropping :: (Conjoined p, Applicative f) => Int -> Over p (Indexing f) s t a a -> Over p f s t a a

-- | This is the trivial empty Traversal.
--   
--   
--   ignored :: IndexedTraversal i s s a b
--   
--   
--   
--   ignored ≡ const pure
--   
--   
--   
--   >>> 6 & ignored %~ absurd
--   6
--   
ignored :: Applicative f => pafb -> s -> f s

-- | Allows IndexedTraversal the value at the smallest index.
class Ord k => TraverseMin k m | m -> k
traverseMin :: TraverseMin k m => IndexedTraversal' k (m v) v

-- | Allows IndexedTraversal of the value at the largest index.
class Ord k => TraverseMax k m | m -> k
traverseMax :: TraverseMax k m => IndexedTraversal' k (m v) v

-- | Traverse any Traversable container. This is an
--   IndexedTraversal that is indexed by ordinal position.
traversed :: Traversable f => IndexedTraversal Int (f a) (f b) a b

-- | Traverse any Traversable container. This is an
--   IndexedTraversal that is indexed by ordinal position.
traversed64 :: Traversable f => IndexedTraversal Int64 (f a) (f b) a b

-- | Traverse the nth element elementOf a Traversal,
--   Lens or Iso if it exists.
--   
--   
--   >>> [[1],[3,4]] & elementOf (traverse.traverse) 1 .~ 5
--   [[1],[5,4]]
--   
--   
--   
--   >>> [[1],[3,4]] ^? elementOf (folded.folded) 1
--   Just 3
--   
--   
--   
--   >>> timingOut $ ['a'..] ^?! elementOf folded 5
--   'f'
--   
--   
--   
--   >>> timingOut $ take 10 $ elementOf traverse 3 .~ 16 $ [0..]
--   [0,1,2,16,4,5,6,7,8,9]
--   
--   
--   
--   elementOf :: Traversal' s a -> Int -> IndexedTraversal' Int s a
--   elementOf :: Fold s a       -> Int -> IndexedFold Int s a
--   
elementOf :: Applicative f => LensLike (Indexing f) s t a a -> Int -> IndexedLensLike Int f s t a a

-- | Traverse the nth element of a Traversable container.
--   
--   
--   element ≡ elementOf traverse
--   
element :: Traversable t => Int -> IndexedTraversal' Int (t a) a

-- | Traverse (or fold) selected elements of a Traversal (or
--   Fold) where their ordinal positions match a predicate.
--   
--   
--   elementsOf :: Traversal' s a -> (Int -> Bool) -> IndexedTraversal' Int s a
--   elementsOf :: Fold s a       -> (Int -> Bool) -> IndexedFold Int s a
--   
elementsOf :: Applicative f => LensLike (Indexing f) s t a a -> (Int -> Bool) -> IndexedLensLike Int f s t a a

-- | Traverse elements of a Traversable container where their
--   ordinal positions matches a predicate.
--   
--   
--   elements ≡ elementsOf traverse
--   
elements :: Traversable t => (Int -> Bool) -> IndexedTraversal' Int (t a) a

-- | An indexed version of partsOf that receives the entire list of
--   indices as its index.
ipartsOf :: (Indexable [i] p, Functor f) => Traversing (Indexed i) f s t a a -> Over p f s t [a] [a]

-- | A type-restricted version of ipartsOf that can only be used
--   with an IndexedTraversal.
ipartsOf' :: (Indexable [i] p, Functor f) => Over (Indexed i) (Bazaar' (Indexed i) a) s t a a -> Over p f s t [a] [a]

-- | An indexed version of unsafePartsOf that receives the entire
--   list of indices as its index.
iunsafePartsOf :: (Indexable [i] p, Functor f) => Traversing (Indexed i) f s t a b -> Over p f s t [a] [b]
iunsafePartsOf' :: Over (Indexed i) (Bazaar (Indexed i) a b) s t a b -> IndexedLens [i] s t [a] [b]

-- | Traversal with an index.
--   
--   NB: When you don't need access to the index then you can just
--   apply your IndexedTraversal directly as a function!
--   
--   
--   itraverseOf ≡ withIndex
--   traverseOf l = itraverseOf l . const = id
--   
--   
--   
--   itraverseOf :: Functor f     => IndexedLens i s t a b      -> (i -> a -> f b) -> s -> f t
--   itraverseOf :: Applicative f => IndexedTraversal i s t a b -> (i -> a -> f b) -> s -> f t
--   
itraverseOf :: (Indexed i a (f b) -> s -> f t) -> (i -> a -> f b) -> s -> f t

-- | Traverse with an index (and the arguments flipped).
--   
--   
--   forOf l a ≡ iforOf l a . const
--   iforOf ≡ flip . itraverseOf
--   
--   
--   
--   iforOf :: Functor f => IndexedLens i s t a b      -> s -> (i -> a -> f b) -> f t
--   iforOf :: Applicative f => IndexedTraversal i s t a b -> s -> (i -> a -> f b) -> f t
--   
iforOf :: (Indexed i a (f b) -> s -> f t) -> s -> (i -> a -> f b) -> f t

-- | Map each element of a structure targeted by a Lens to a monadic
--   action, evaluate these actions from left to right, and collect the
--   results, with access its position.
--   
--   When you don't need access to the index mapMOf is more liberal
--   in what it can accept.
--   
--   
--   mapMOf l ≡ imapMOf l . const
--   
--   
--   
--   imapMOf :: Monad m => IndexedLens      i s t a b -> (i -> a -> m b) -> s -> m t
--   imapMOf :: Monad m => IndexedTraversal i s t a b -> (i -> a -> m b) -> s -> m t
--   
imapMOf :: (Indexed i a (WrappedMonad m b) -> s -> WrappedMonad m t) -> (i -> a -> m b) -> s -> m t

-- | Map each element of a structure targeted by a Lens to a monadic
--   action, evaluate these actions from left to right, and collect the
--   results, with access its position (and the arguments flipped).
--   
--   
--   forMOf l a ≡ iforMOf l a . const
--   iforMOf ≡ flip . imapMOf
--   
--   
--   
--   iforMOf :: Monad m => IndexedLens i s t a b      -> s -> (i -> a -> m b) -> m t
--   iforMOf :: Monad m => IndexedTraversal i s t a b -> s -> (i -> a -> m b) -> m t
--   
iforMOf :: (Indexed i a (WrappedMonad m b) -> s -> WrappedMonad m t) -> s -> (i -> a -> m b) -> m t

-- | Generalizes mapAccumR to an arbitrary IndexedTraversal
--   with access to the index.
--   
--   imapAccumROf accumulates state from right to left.
--   
--   
--   mapAccumROf l ≡ imapAccumROf l . const
--   
--   
--   
--   imapAccumROf :: IndexedLens i s t a b      -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   imapAccumROf :: IndexedTraversal i s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   
imapAccumROf :: Over (Indexed i) (Backwards (State acc)) s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)

-- | Generalizes mapAccumL to an arbitrary IndexedTraversal
--   with access to the index.
--   
--   imapAccumLOf accumulates state from left to right.
--   
--   
--   mapAccumLOf l ≡ imapAccumLOf l . const
--   
--   
--   
--   imapAccumLOf :: IndexedLens i s t a b      -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   imapAccumLOf :: IndexedTraversal i s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)
--   
imapAccumLOf :: Over (Indexed i) (State acc) s t a b -> (i -> acc -> a -> (acc, b)) -> acc -> s -> (acc, t)

-- | This is used to characterize a Traversal.
--   
--   a.k.a. indexed Cartesian store comonad, indexed Kleene store comonad,
--   or an indexed FunList.
--   
--   http://twanvl.nl/blog/haskell/non-regular1
--   
--   A Bazaar is like a Traversal that has already been
--   applied to some structure.
--   
--   Where a Context a b t holds an a and a
--   function from b to t, a Bazaar a b t
--   holds N as and a function from N
--   bs to t, (where N might be infinite).
--   
--   Mnemonically, a Bazaar holds many stores and you can easily add
--   more.
--   
--   This is a final encoding of Bazaar.
newtype Bazaar p a b t
Bazaar :: (forall f. Applicative f => p a (f b) -> f t) -> Bazaar p a b t
runBazaar :: Bazaar p a b t -> forall f. Applicative f => p a (f b) -> f t

-- | This alias is helpful when it comes to reducing repetition in type
--   signatures.
--   
--   
--   type Bazaar' p a t = Bazaar p a a t
--   
type Bazaar' p a = Bazaar p a a

-- | This Traversal allows you to traverse the individual
--   stores in a Bazaar.
loci :: Traversal (Bazaar (->) a c s) (Bazaar (->) b c s) a b

-- | This IndexedTraversal allows you to traverse the
--   individual stores in a Bazaar with access to their indices.
iloci :: IndexedTraversal i (Bazaar (Indexed i) a c s) (Bazaar (Indexed i) b c s) a b
instance Ord k => TraverseMax k (Map k)
instance TraverseMax Int IntMap
instance Ord k => TraverseMin k (Map k)
instance TraverseMin Int IntMap

-- | (The classes in here need to be defined together for
--   DefaultSignatures to work.)
module Control.Lens.Indexed

-- | This class permits overloading of function application for things that
--   also admit a notion of a key or index.
class Conjoined p => Indexable i p
indexed :: Indexable i p => p a b -> i -> a -> b

-- | This is a Profunctor that is both Corepresentable by
--   f and Representable by g such that f
--   is left adjoint to g. From this you can derive a lot of
--   structure due to the preservation of limits and colimits.
class (Choice p, Corepresentable p, Comonad (Corep p), Traversable (Corep p), Strong p, Representable p, Monad (Rep p), MonadFix (Rep p), Distributive (Rep p), ArrowLoop p, ArrowApply p, ArrowChoice p) => Conjoined p where distrib = tabulate . collect . rep conjoined _ r = r
distrib :: (Conjoined p, Functor f) => p a b -> p (f a) (f b)
conjoined :: Conjoined p => (p ~ (->) => q (a -> b) r) -> q (p a b) r -> q (p a b) r

-- | A function with access to a index. This constructor may be useful when
--   you need to store an Indexable in a container to avoid
--   ImpredicativeTypes.
--   
--   
--   index :: Indexed i a b -> i -> a -> b
--   
newtype Indexed i a b
Indexed :: (i -> a -> b) -> Indexed i a b
runIndexed :: Indexed i a b -> i -> a -> b

-- | Compose an Indexed function with a non-indexed function.
--   
--   Mnemonically, the < points to the indexing we want to
--   preserve.
(<.) :: Indexable i p => (Indexed i s t -> r) -> ((a -> b) -> s -> t) -> p a b -> r

-- | Composition of Indexed functions.
--   
--   Mnemonically, the < and > points to the fact
--   that we want to preserve the indices.
(<.>) :: Indexable (i, j) p => (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> p a b -> r

-- | Compose a non-indexed function with an Indexed function.
--   
--   Mnemonically, the > points to the indexing we want to
--   preserve.
--   
--   This is the same as (.).
--   
--   f . g (and f .> g) gives you the
--   index of g unless g is index-preserving, like a
--   Prism, Iso or Equality, in which case it'll pass
--   through the index of f.
(.>) :: (st -> r) -> (kab -> st) -> kab -> r

-- | Remap the index.
reindexed :: Indexable j p => (i -> j) -> (Indexed i a b -> r) -> p a b -> r

-- | Composition of Indexed functions with a user supplied function
--   for combining indices.
icompose :: Indexable p c => (i -> j -> p) -> (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> c a b -> r

-- | Transform a Traversal into an IndexedTraversal or a
--   Fold into an IndexedFold, etc.
--   
--   
--   indexing :: Traversal s t a b -> IndexedTraversal Int s t a b
--   indexing :: Prism s t a b     -> IndexedTraversal Int s t a b
--   indexing :: Lens s t a b      -> IndexedLens Int  s t a b
--   indexing :: Iso s t a b       -> IndexedLens Int s t a b
--   indexing :: Fold s a          -> IndexedFold Int s a
--   indexing :: Getter s a        -> IndexedGetter Int s a
--   
--   
--   
--   indexing :: Indexable Int p => LensLike (Indexing f) s t a b -> Overloading p (->) f s t a b
--   
indexing :: Indexable Int p => ((a -> Indexing f b) -> s -> Indexing f t) -> p a (f b) -> s -> f t

-- | Transform a Traversal into an IndexedTraversal or a
--   Fold into an IndexedFold, etc.
--   
--   This combinator is like indexing except that it handles large
--   traversals and folds gracefully.
--   
--   
--   indexing64 :: Traversal s t a b -> IndexedTraversal Int64 s t a b
--   indexing64 :: Prism s t a b     -> IndexedTraversal Int64 s t a b
--   indexing64 :: Lens s t a b      -> IndexedLens Int64 s t a b
--   indexing64 :: Iso s t a b       -> IndexedLens Int64 s t a b
--   indexing64 :: Fold s a          -> IndexedFold Int64 s a
--   indexing64 :: Getter s a        -> IndexedGetter Int64 s a
--   
--   
--   
--   indexing64 :: Indexable Int64 p => LensLike (Indexing64 f) s t a b -> Overloading p (->) f s t a b
--   
indexing64 :: Indexable Int64 p => ((a -> Indexing64 f b) -> s -> Indexing64 f t) -> p a (f b) -> s -> f t

-- | A Functor with an additional index.
--   
--   Instances must satisfy a modified form of the Functor laws:
--   
--   
--   imap f . imap g ≡ imap (\i -> f i . g i)
--   imap (\_ a -> a) ≡ id
--   
class Functor f => FunctorWithIndex i f | f -> i where imap = iover itraversed imapped = conjoined mapped (isets imap)
imap :: FunctorWithIndex i f => (i -> a -> b) -> f a -> f b
imapped :: (FunctorWithIndex i f, FunctorWithIndex i f) => IndexedSetter i (f a) (f b) a b

-- | A container that supports folding with an additional index.
class Foldable f => FoldableWithIndex i f | f -> i where ifoldMap = ifoldMapOf itraversed ifolded = conjoined folded $ \ f -> coerce . getFolding . ifoldMap (\ i -> Folding #. indexed f i) ifoldr f z t = appEndo (ifoldMap (\ i -> Endo #. f i) t) z ifoldl f z t = appEndo (getDual (ifoldMap (\ i -> Dual #. Endo #. flip (f i)) t)) z ifoldr' f z0 xs = ifoldl f' id xs z0 where f' i k x z = k $! f i x z ifoldl' f z0 xs = ifoldr f' id xs z0 where f' i x k z = k $! f i z x
ifoldMap :: (FoldableWithIndex i f, Monoid m) => (i -> a -> m) -> f a -> m
ifolded :: FoldableWithIndex i f => IndexedFold i (f a) a
ifoldr :: FoldableWithIndex i f => (i -> a -> b -> b) -> b -> f a -> b
ifoldl :: FoldableWithIndex i f => (i -> b -> a -> b) -> b -> f a -> b
ifoldr' :: FoldableWithIndex i f => (i -> a -> b -> b) -> b -> f a -> b
ifoldl' :: FoldableWithIndex i f => (i -> b -> a -> b) -> b -> f a -> b

-- | Obtain a Fold by lifting an operation that returns a
--   Foldable result.
--   
--   This can be useful to lift operations from List and
--   elsewhere into a Fold.
ifolding :: FoldableWithIndex i f => (s -> f a) -> IndexedFold i s a

-- | Return whether or not any element in a container satisfies a
--   predicate, with access to the index i.
--   
--   When you don't need access to the index then any is more
--   flexible in what it accepts.
--   
--   
--   any ≡ iany . const
--   
iany :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool

-- | Return whether or not all elements in a container satisfy a predicate,
--   with access to the index i.
--   
--   When you don't need access to the index then all is more
--   flexible in what it accepts.
--   
--   
--   all ≡ iall . const
--   
iall :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool

-- | Traverse elements with access to the index i, discarding the
--   results.
--   
--   When you don't need access to the index then traverse_ is more
--   flexible in what it accepts.
--   
--   
--   traverse_ l = itraverse . const
--   
itraverse_ :: (FoldableWithIndex i t, Applicative f) => (i -> a -> f b) -> t a -> f ()

-- | Traverse elements with access to the index i, discarding the
--   results (with the arguments flipped).
--   
--   
--   ifor_ ≡ flip itraverse_
--   
--   
--   When you don't need access to the index then for_ is more
--   flexible in what it accepts.
--   
--   
--   for_ a ≡ ifor_ a . const
--   
ifor_ :: (FoldableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f ()

-- | Run monadic actions for each target of an IndexedFold or
--   IndexedTraversal with access to the index, discarding the
--   results.
--   
--   When you don't need access to the index then mapMOf_ is more
--   flexible in what it accepts.
--   
--   
--   mapM_ ≡ imapM . const
--   
imapM_ :: (FoldableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m ()

-- | Run monadic actions for each target of an IndexedFold or
--   IndexedTraversal with access to the index, discarding the
--   results (with the arguments flipped).
--   
--   
--   iforM_ ≡ flip imapM_
--   
--   
--   When you don't need access to the index then forMOf_ is more
--   flexible in what it accepts.
--   
--   
--   forMOf_ l a ≡ iforMOf l a . const
--   
iforM_ :: (FoldableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m ()

-- | Concatenate the results of a function of the elements of an indexed
--   container with access to the index.
--   
--   When you don't need access to the index then concatMap is more
--   flexible in what it accepts.
--   
--   
--   concatMap ≡ iconcatMap . const
--   iconcatMap ≡ ifoldMap
--   
iconcatMap :: FoldableWithIndex i f => (i -> a -> [b]) -> f a -> [b]

-- | Searches a container with a predicate that is also supplied the index,
--   returning the left-most element of the structure matching the
--   predicate, or Nothing if there is no such element.
--   
--   When you don't need access to the index then find is more
--   flexible in what it accepts.
--   
--   
--   find ≡ ifind . const
--   
ifind :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Maybe (i, a)

-- | Monadic fold right over the elements of a structure with an index.
--   
--   When you don't need access to the index then foldrM is more
--   flexible in what it accepts.
--   
--   
--   foldrM ≡ ifoldrM . const
--   
ifoldrM :: (FoldableWithIndex i f, Monad m) => (i -> a -> b -> m b) -> b -> f a -> m b

-- | Monadic fold over the elements of a structure with an index,
--   associating to the left.
--   
--   When you don't need access to the index then foldlM is more
--   flexible in what it accepts.
--   
--   
--   foldlM ≡ ifoldlM . const
--   
ifoldlM :: (FoldableWithIndex i f, Monad m) => (i -> b -> a -> m b) -> b -> f a -> m b

-- | Extract the key-value pairs from a structure.
--   
--   When you don't need access to the indices in the result, then
--   toList is more flexible in what it accepts.
--   
--   
--   toList ≡ map fst . itoList
--   
itoList :: FoldableWithIndex i f => f a -> [(i, a)]

-- | Fold a container with indices returning both the indices and the
--   values.
--   
--   The result is only valid to compose in a Traversal, if you
--   don't edit the index as edits to the index have no effect.
withIndex :: (Indexable i p, Functor f) => Overloading p (Indexed i) f s t (i, s) (j, t)

-- | When composed with an IndexedFold or IndexedTraversal
--   this yields an (Indexed) Fold of the indices.
asIndex :: (Indexable i p, Contravariant f, Functor f) => Overloading' p (Indexed i) f s i

-- | This allows you to filter an IndexedFold, IndexedGetter,
--   IndexedTraversal or IndexedLens based on a predicate on
--   the indices.
--   
--   
--   >>> ["hello","the","world","!!!"]^..traversed.indices even
--   ["hello","world"]
--   
--   
--   
--   >>> over (traversed.indices (>0)) Prelude.reverse $ ["He","was","stressed","o_O"]
--   ["He","saw","desserts","O_o"]
--   
indices :: (Indexable i p, Applicative f) => (i -> Bool) -> Overloading' p (Indexed i) f a a

-- | This allows you to filter an IndexedFold, IndexedGetter,
--   IndexedTraversal or IndexedLens based on an index.
--   
--   
--   >>> ["hello","the","world","!!!"]^?traversed.index 2
--   Just "world"
--   
index :: (Indexable i p, Eq i, Applicative f) => i -> Overloading' p (Indexed i) f a a

-- | A Traversable with an additional index.
--   
--   An instance must satisfy a (modified) form of the Traversable
--   laws:
--   
--   
--   itraverse (const Identity) ≡ Identity
--   fmap (itraverse f) . itraverse g ≡ getCompose . itraverse (\i -> Compose . fmap (f i) . g i)
--   
class (FunctorWithIndex i t, FoldableWithIndex i t, Traversable t) => TraversableWithIndex i t | t -> i where itraverse = traversed .# Indexed itraversed = conjoined traverse (itraverse . indexed)
itraverse :: (TraversableWithIndex i t, Applicative f) => (i -> a -> f b) -> t a -> f (t b)
itraversed :: TraversableWithIndex i t => IndexedTraversal i (t a) (t b) a b

-- | Traverse with an index (and the arguments flipped).
--   
--   
--   for a ≡ ifor a . const
--   ifor ≡ flip itraverse
--   
ifor :: (TraversableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f (t b)

-- | Map each element of a structure to a monadic action, evaluate these
--   actions from left to right, and collect the results, with access the
--   index.
--   
--   When you don't need access to the index mapM is more liberal in
--   what it can accept.
--   
--   
--   mapM ≡ imapM . const
--   
imapM :: (TraversableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m (t b)

-- | Map each element of a structure to a monadic action, evaluate these
--   actions from left to right, and collect the results, with access its
--   position (and the arguments flipped).
--   
--   
--   forM a ≡ iforM a . const
--   iforM ≡ flip imapM
--   
iforM :: (TraversableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m (t b)

-- | Generalizes mapAccumR to add access to the index.
--   
--   imapAccumROf accumulates state from right to left.
--   
--   
--   mapAccumR ≡ imapAccumR . const
--   
imapAccumR :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b)

-- | Generalizes mapAccumL to add access to the index.
--   
--   imapAccumLOf accumulates state from left to right.
--   
--   
--   mapAccumLOf ≡ imapAccumL . const
--   
imapAccumL :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b)
instance TraversableWithIndex i (Magma i t b)
instance FoldableWithIndex i (Magma i t b)
instance FunctorWithIndex i (Magma i t b)
instance TraversableWithIndex i (Level i)
instance FoldableWithIndex i (Level i)
instance FunctorWithIndex i (Level i)
instance FunctorWithIndex r ((->) r)
instance (Eq k, Hashable k) => TraversableWithIndex k (HashMap k)
instance (Eq k, Hashable k) => FoldableWithIndex k (HashMap k)
instance (Eq k, Hashable k) => FunctorWithIndex k (HashMap k)
instance TraversableWithIndex k (Map k)
instance FoldableWithIndex k (Map k)
instance FunctorWithIndex k (Map k)
instance TraversableWithIndex Int IntMap
instance FoldableWithIndex Int IntMap
instance FunctorWithIndex Int IntMap
instance TraversableWithIndex Int Vector
instance FoldableWithIndex Int Vector
instance FunctorWithIndex Int Vector
instance TraversableWithIndex Int Seq
instance FoldableWithIndex Int Seq
instance FunctorWithIndex Int Seq
instance TraversableWithIndex () Maybe
instance FoldableWithIndex () Maybe
instance FunctorWithIndex () Maybe
instance TraversableWithIndex Int []
instance FoldableWithIndex Int []
instance FunctorWithIndex Int []
instance TraversableWithIndex k ((,) k)
instance FoldableWithIndex k ((,) k)
instance FunctorWithIndex k ((,) k)
instance TraversableWithIndex () Identity
instance FoldableWithIndex () Identity
instance FunctorWithIndex () Identity
instance TraversableWithIndex i f => TraversableWithIndex i (Reverse f)
instance FoldableWithIndex i f => FoldableWithIndex i (Reverse f)
instance FunctorWithIndex i f => FunctorWithIndex i (Reverse f)
instance TraversableWithIndex i f => TraversableWithIndex i (Backwards f)
instance FoldableWithIndex i f => FoldableWithIndex i (Backwards f)
instance FunctorWithIndex i f => FunctorWithIndex i (Backwards f)

module Control.Lens.Tuple

-- | Provides access to 1st field of a tuple.
class Field1 s t a b | s -> a, t -> b, s b -> t, t a -> s
_1 :: Field1 s t a b => IndexedLens Int s t a b

-- | Provides access to the 2nd field of a tuple.
class Field2 s t a b | s -> a, t -> b, s b -> t, t a -> s
_2 :: Field2 s t a b => IndexedLens Int s t a b

-- | Provides access to the 3rd field of a tuple.
class Field3 s t a b | s -> a, t -> b, s b -> t, t a -> s
_3 :: Field3 s t a b => IndexedLens Int s t a b

-- | Provide access to the 4th field of a tuple.
class Field4 s t a b | s -> a, t -> b, s b -> t, t a -> s
_4 :: Field4 s t a b => IndexedLens Int s t a b

-- | Provides access to the 5th field of a tuple.
class Field5 s t a b | s -> a, t -> b, s b -> t, t a -> s
_5 :: Field5 s t a b => IndexedLens Int s t a b

-- | Provides access to the 6th element of a tuple.
class Field6 s t a b | s -> a, t -> b, s b -> t, t a -> s
_6 :: Field6 s t a b => IndexedLens Int s t a b

-- | Provide access to the 7th field of a tuple.
class Field7 s t a b | s -> a, t -> b, s b -> t, t a -> s
_7 :: Field7 s t a b => IndexedLens Int s t a b

-- | Provide access to the 8th field of a tuple.
class Field8 s t a b | s -> a, t -> b, s b -> t, t a -> s
_8 :: Field8 s t a b => IndexedLens Int s t a b

-- | Provides access to the 9th field of a tuple.
class Field9 s t a b | s -> a, t -> b, s b -> t, t a -> s
_9 :: Field9 s t a b => IndexedLens Int s t a b
instance Field9 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g, h, i') i i'
instance Field8 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g, h', i) h h'
instance Field8 (a, b, c, d, e, f, g, h) (a, b, c, d, e, f, g, h') h h'
instance Field7 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f, g', h, i) g g'
instance Field7 (a, b, c, d, e, f, g, h) (a, b, c, d, e, f, g', h) g g'
instance Field7 (a, b, c, d, e, f, g) (a, b, c, d, e, f, g') g g'
instance Field6 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e, f', g, h, i) f f'
instance Field6 (a, b, c, d, e, f, g, h) (a, b, c, d, e, f', g, h) f f'
instance Field6 (a, b, c, d, e, f, g) (a, b, c, d, e, f', g) f f'
instance Field6 (a, b, c, d, e, f) (a, b, c, d, e, f') f f'
instance Field5 (a, b, c, d, e, f, g, h, i) (a, b, c, d, e', f, g, h, i) e e'
instance Field5 (a, b, c, d, e, f, g, h) (a, b, c, d, e', f, g, h) e e'
instance Field5 (a, b, c, d, e, f, g) (a, b, c, d, e', f, g) e e'
instance Field5 (a, b, c, d, e, f) (a, b, c, d, e', f) e e'
instance Field5 (a, b, c, d, e) (a, b, c, d, e') e e'
instance Field4 (a, b, c, d, e, f, g, h, i) (a, b, c, d', e, f, g, h, i) d d'
instance Field4 (a, b, c, d, e, f, g, h) (a, b, c, d', e, f, g, h) d d'
instance Field4 (a, b, c, d, e, f, g) (a, b, c, d', e, f, g) d d'
instance Field4 (a, b, c, d, e, f) (a, b, c, d', e, f) d d'
instance Field4 (a, b, c, d, e) (a, b, c, d', e) d d'
instance Field4 (a, b, c, d) (a, b, c, d') d d'
instance Field3 (a, b, c, d, e, f, g, h, i) (a, b, c', d, e, f, g, h, i) c c'
instance Field3 (a, b, c, d, e, f, g, h) (a, b, c', d, e, f, g, h) c c'
instance Field3 (a, b, c, d, e, f, g) (a, b, c', d, e, f, g) c c'
instance Field3 (a, b, c, d, e, f) (a, b, c', d, e, f) c c'
instance Field3 (a, b, c, d, e) (a, b, c', d, e) c c'
instance Field3 (a, b, c, d) (a, b, c', d) c c'
instance Field3 (a, b, c) (a, b, c') c c'
instance Field2 (a, b, c, d, e, f, g, h, i) (a, b', c, d, e, f, g, h, i) b b'
instance Field2 (a, b, c, d, e, f, g, h) (a, b', c, d, e, f, g, h) b b'
instance Field2 (a, b, c, d, e, f, g) (a, b', c, d, e, f, g) b b'
instance Field2 (a, b, c, d, e, f) (a, b', c, d, e, f) b b'
instance Field2 (a, b, c, d, e) (a, b', c, d, e) b b'
instance Field2 (a, b, c, d) (a, b', c, d) b b'
instance Field2 (a, b, c) (a, b', c) b b'
instance Field2 (a, b) (a, b') b b'
instance Field1 (a, b, c, d, e, f, g, h, i) (a', b, c, d, e, f, g, h, i) a a'
instance Field1 (a, b, c, d, e, f, g, h) (a', b, c, d, e, f, g, h) a a'
instance Field1 (a, b, c, d, e, f, g) (a', b, c, d, e, f, g) a a'
instance Field1 (a, b, c, d, e, f) (a', b, c, d, e, f) a a'
instance Field1 (a, b, c, d, e) (a', b, c, d, e) a a'
instance Field1 (a, b, c, d) (a', b, c, d) a a'
instance Field1 (a, b, c) (a', b, c) a a'
instance Field1 (a, b) (a', b) a a'
instance Field1 (Identity a) (Identity b) a b

module Control.Lens.Cons

-- | This class provides a way to attach or detach elements on the left
--   side of a structure in a flexible manner.
class (Profunctor p, Functor f) => Cons p f s t a b | s -> a, t -> b, s b -> t, t a -> s
_Cons :: Cons p f s t a b => Overloaded p f s t (a, s) (b, t)

-- | cons an element onto a container.
--   
--   This is an infix alias for cons.
(<|) :: Cons Reviewed Identity s s a a => a -> s -> s

-- | cons an element onto a container.
cons :: Cons Reviewed Identity s s a a => a -> s -> s

-- | Attempt to extract the left-most element from a container, and a
--   version of the container without that element.
uncons :: Cons (->) (Accessor (First (a, s))) s s a a => s -> Maybe (a, s)

-- | A Traversal reading and writing to the head of a
--   non-empty container.
--   
--   
--   >>> [a,b,c]^? _head
--   Just a
--   
--   
--   
--   >>> [a,b,c] & _head .~ d
--   [d,b,c]
--   
--   
--   
--   >>> [a,b,c] & _head %~ f
--   [f a,b,c]
--   
--   
--   
--   >>> [] & _head %~ f
--   []
--   
--   
--   
--   >>> [1,2,3]^?!_head
--   1
--   
--   
--   
--   >>> []^?_head
--   Nothing
--   
--   
--   
--   >>> [1,2]^?_head
--   Just 1
--   
--   
--   
--   >>> [] & _head .~ 1
--   []
--   
--   
--   
--   >>> [0] & _head .~ 2
--   [2]
--   
--   
--   
--   >>> [0,1] & _head .~ 2
--   [2,1]
--   
--   
--   This isn't limited to lists.
--   
--   For instance you can also traverse the head of a Seq:
--   
--   
--   >>> Seq.fromList [a,b,c,d] & _head %~ f
--   fromList [f a,b,c,d]
--   
--   
--   
--   >>> Seq.fromList [] ^? _head
--   Nothing
--   
--   
--   
--   >>> Seq.fromList [a,b,c,d] ^? _head
--   Just a
--   
--   
--   
--   _head :: Traversal' [a] a
--   _head :: Traversal' (Seq a) a
--   _head :: Traversal' (Vector a) a
--   
_head :: Cons (->) f s s a a => LensLike' f s a

-- | A Traversal reading and writing to the tail of a
--   non-empty container.
--   
--   
--   >>> [a,b] & _tail .~ [c,d,e]
--   [a,c,d,e]
--   
--   
--   
--   >>> [] & _tail .~ [a,b]
--   []
--   
--   
--   
--   >>> [a,b,c,d,e] & _tail.traverse %~ f
--   [a,f b,f c,f d,f e]
--   
--   
--   
--   >>> [1,2] & _tail .~ [3,4,5]
--   [1,3,4,5]
--   
--   
--   
--   >>> [] & _tail .~ [1,2]
--   []
--   
--   
--   
--   >>> [a,b,c]^?_tail
--   Just [b,c]
--   
--   
--   
--   >>> [1,2]^?!_tail
--   [2]
--   
--   
--   
--   >>> "hello"^._tail
--   "ello"
--   
--   
--   
--   >>> ""^._tail
--   ""
--   
--   
--   This isn't limited to lists. For instance you can also traverse
--   the tail of a Seq.
--   
--   
--   >>> Seq.fromList [a,b] & _tail .~ Seq.fromList [c,d,e]
--   fromList [a,c,d,e]
--   
--   
--   
--   >>> Seq.fromList [a,b,c] ^? _tail
--   Just (fromList [b,c])
--   
--   
--   
--   >>> Seq.fromList [] ^? _tail
--   Nothing
--   
--   
--   
--   _tail :: Traversal' [a] [a]
--   _tail :: Traversal' (Seq a) (Seq a)
--   _tail :: Traversal' (Vector a) (Vector a)
--   
_tail :: Cons (->) f s s a a => LensLike' f s s

-- | This class provides a way to attach or detach elements on the right
--   side of a structure in a flexible manner.
class (Profunctor p, Functor f) => Snoc p f s t a b | s -> a, t -> b, s b -> t, t a -> s
_Snoc :: Snoc p f s t a b => Overloaded p f s t (s, a) (t, b)

-- | snoc an element onto the end of a container.
--   
--   This is an infix alias for snoc.
(|>) :: Snoc Reviewed Identity s s a a => s -> a -> s

-- | snoc an element onto the end of a container.
snoc :: Snoc Reviewed Identity s s a a => s -> a -> s

-- | Attempt to extract the right-most element from a container, and a
--   version of the container without that element.
unsnoc :: Snoc (->) (Accessor (First (s, a))) s s a a => s -> Maybe (s, a)

-- | A Traversal reading and replacing all but the a last element of
--   a non-empty container.
--   
--   
--   >>> [a,b,c,d]^?_init
--   Just [a,b,c]
--   
--   
--   
--   >>> []^?_init
--   Nothing
--   
--   
--   
--   >>> [a,b] & _init .~ [c,d,e]
--   [c,d,e,b]
--   
--   
--   
--   >>> [] & _init .~ [a,b]
--   []
--   
--   
--   
--   >>> [a,b,c,d] & _init.traverse %~ f
--   [f a,f b,f c,d]
--   
--   
--   
--   >>> [1,2,3]^?_init
--   Just [1,2]
--   
--   
--   
--   >>> [1,2,3,4]^?!_init
--   [1,2,3]
--   
--   
--   
--   >>> "hello"^._init
--   "hell"
--   
--   
--   
--   >>> ""^._init
--   ""
--   
--   
--   
--   _init :: Traversal' [a] [a]
--   _init :: Traversal' (Seq a) (Seq a)
--   _init :: Traversal' (Vector a) (Vector a)
--   
_init :: Snoc (->) f s s a a => LensLike' f s s

-- | A Traversal reading and writing to the last element of a
--   non-empty container.
--   
--   
--   >>> [a,b,c]^?!_last
--   c
--   
--   
--   
--   >>> []^?_last
--   Nothing
--   
--   
--   
--   >>> [a,b,c] & _last %~ f
--   [a,b,f c]
--   
--   
--   
--   >>> [1,2]^?_last
--   Just 2
--   
--   
--   
--   >>> [] & _last .~ 1
--   []
--   
--   
--   
--   >>> [0] & _last .~ 2
--   [2]
--   
--   
--   
--   >>> [0,1] & _last .~ 2
--   [0,2]
--   
--   
--   This Traversal is not limited to lists, however. We can also
--   work with other containers, such as a Vector.
--   
--   
--   >>> Vector.fromList "abcde" ^? _last
--   Just 'e'
--   
--   
--   
--   >>> Vector.empty ^? _last
--   Nothing
--   
--   
--   
--   >>> Vector.fromList "abcde" & _last .~ 'Q'
--   fromList "abcdQ"
--   
--   
--   
--   _last :: Traversal' [a] a
--   _last :: Traversal' (Seq a) a
--   _last :: Traversal' (Vector a) a
--   
_last :: Snoc (->) f s s a a => LensLike' f s a
instance (Choice p, Applicative f) => Snoc p f Text Text Char Char
instance (Choice p, Applicative f) => Snoc p f Text Text Char Char
instance (Choice p, Applicative f) => Snoc p f ByteString ByteString Word8 Word8
instance (Choice p, Applicative f) => Snoc p f ByteString ByteString Word8 Word8
instance (Choice p, Applicative f, Unbox a, Unbox b) => Snoc p f (Vector a) (Vector b) a b
instance (Choice p, Applicative f, Storable a, Storable b) => Snoc p f (Vector a) (Vector b) a b
instance (Choice p, Applicative f, Prim a, Prim b) => Snoc p f (Vector a) (Vector b) a b
instance (Choice p, Applicative f) => Snoc p f (Vector a) (Vector b) a b
instance (Choice p, Applicative f) => Snoc p f (Seq a) (Seq b) a b
instance (Choice p, Applicative f) => Snoc p f [a] [b] a b
instance (Choice p, Applicative f, Unbox a, Unbox b) => Cons p f (Vector a) (Vector b) a b
instance (Choice p, Applicative f, Storable a, Storable b) => Cons p f (Vector a) (Vector b) a b
instance (Choice p, Applicative f, Prim a, Prim b) => Cons p f (Vector a) (Vector b) a b
instance (Choice p, Applicative f) => Cons p f (Vector a) (Vector b) a b
instance (Choice p, Applicative f) => Cons p f Text Text Char Char
instance (Choice p, Applicative f) => Cons p f Text Text Char Char
instance (Choice p, Applicative f) => Cons p f ByteString ByteString Word8 Word8
instance (Choice p, Applicative f) => Cons p f ByteString ByteString Word8 Word8
instance (Choice p, Applicative f) => Cons p f (Seq a) (Seq b) a b
instance (Choice p, Applicative f) => Cons p f [a] [b] a b

-- | This module provides combinators for breadth-first searching within
--   arbitrary traversals.
module Control.Lens.Level

-- | This data type represents a path-compressed copy of one level of a
--   source data structure. We can safely use path-compression because we
--   know the depth of the tree.
--   
--   Path compression is performed by viewing a Level as a PATRICIA
--   trie of the paths into the structure to leaves at a given depth,
--   similar in many ways to a IntMap, but unlike a regular PATRICIA
--   trie we do not need to store the mask bits merely the depth of the
--   fork.
--   
--   One invariant of this structure is that underneath a Two node
--   you will not find any Zero nodes, so Zero can only occur
--   at the root.
data Level i a

-- | This provides a breadth-first Traversal of the individual
--   levels of any other Traversal via iterative deepening
--   depth-first search. The levels are returned to you in a compressed
--   format.
--   
--   This can permit us to extract the levels directly:
--   
--   
--   >>> ["hello","world"]^..levels (traverse.traverse)
--   [Zero,Zero,One () 'h',Two 0 (One () 'e') (One () 'w'),Two 0 (One () 'l') (One () 'o'),Two 0 (One () 'l') (One () 'r'),Two 0 (One () 'o') (One () 'l'),One () 'd']
--   
--   
--   But we can also traverse them in turn:
--   
--   
--   >>> ["hello","world"]^..levels (traverse.traverse).traverse
--   "hewlolrold"
--   
--   
--   We can use this to traverse to a fixed depth in the tree of
--   (<*>) used in the Traversal:
--   
--   
--   >>> ["hello","world"] & taking 4 (levels (traverse.traverse)).traverse %~ toUpper
--   ["HEllo","World"]
--   
--   
--   Or we can use it to traverse the first n elements in found in
--   that Traversal regardless of the depth at which they were
--   found.
--   
--   
--   >>> ["hello","world"] & taking 4 (levels (traverse.traverse).traverse) %~ toUpper
--   ["HELlo","World"]
--   
--   
--   The resulting Traversal of the levels which is indexed
--   by the depth of each Level.
--   
--   
--   >>> ["dog","cat"]^@..levels (traverse.traverse) <. traverse
--   [(2,'d'),(3,'o'),(3,'c'),(4,'g'),(4,'a'),(5,'t')]
--   
--   
--   Note: Internally this is implemented by using an illegal
--   Applicative, as it extracts information in an order that
--   violates the Applicative laws.
levels :: ATraversal s t a b -> IndexedTraversal Int s t (Level () a) (Level () b)

-- | This provides a breadth-first Traversal of the individual
--   levels of any other Traversal via iterative deepening
--   depth-first search. The levels are returned to you in a compressed
--   format.
--   
--   This is similar to levels, but retains the index of the
--   original IndexedTraversal, so you can access it when traversing
--   the levels later on.
--   
--   
--   >>> ["dog","cat"]^@..ilevels (traversed<.>traversed).itraversed
--   [((0,0),'d'),((0,1),'o'),((1,0),'c'),((0,2),'g'),((1,1),'a'),((1,2),'t')]
--   
--   
--   The resulting Traversal of the levels which is indexed by the
--   depth of each Level.
--   
--   
--   >>> ["dog","cat"]^@..ilevels (traversed<.>traversed)<.>itraversed
--   [((2,(0,0)),'d'),((3,(0,1)),'o'),((3,(1,0)),'c'),((4,(0,2)),'g'),((4,(1,1)),'a'),((5,(1,2)),'t')]
--   
--   
--   Note: Internally this is implemented by using an illegal
--   Applicative, as it extracts information in an order that
--   violates the Applicative laws.
ilevels :: AnIndexedTraversal i s t a b -> IndexedTraversal Int s t (Level i a) (Level j b)

-- | This module provides internal types and functions used in the
--   implementation of Control.Lens.Zipper. You shouldn't need to
--   import it directly, and the exported types can be used to break
--   Zipper invariants.
module Control.Lens.Internal.Zipper

-- | A Jacket is used to store the contents of a Traversal in
--   a way that we do not have to re-asocciate the elements. This enables
--   us to more gracefully deal with infinite traversals.
data Jacket i a
Ap :: Int -> Bool -> Bool -> (Last i) -> (Jacket i a) -> (Jacket i a) -> Jacket i a
Leaf :: i -> a -> Jacket i a
Pure :: Jacket i a

-- | Return the number of children in a jacket
size :: Jacket i a -> Int

-- | This is an internal function used to check from left-to-right if a
--   Jacket has any Leaf nots or not.
nullLeft :: Jacket i a -> Bool

-- | This is an internal function used to check from right-to-left if a
--   Jacket has any Leaf nots or not.
nullRight :: Jacket i a -> Bool

-- | This is used to extract the maximal key from a Jacket. This is
--   used by moveTo and moveToward to seek specific keys,
--   borrowing the asympotic guarantees of the original structure in many
--   cases!
maximal :: Jacket i a -> Last i

-- | Construct a Jacket from a Bazaar
jacketIns :: Bazaar (Indexed i) a b t -> Jacket i a

-- | Once we've updated a Zipper we need to put the values back into
--   the original shape. Flow is an illegal Applicative that
--   is used to put the values back.
newtype Flow i b a
Flow :: (Jacket i b -> a) -> Flow i b a
runFlow :: Flow i b a -> Jacket i b -> a

-- | Given a Bazaar and a Jacket build from that
--   Bazaar with jacketIns, refill the Bazaar with its
--   new contents.
jacketOuts :: Bazaar (Indexed i) a b t -> Jacket j b -> t

-- | This is only a valid Lens if you don't change the shape of the
--   Jacket!
jacket :: AnIndexedTraversal i s t a b -> Lens s t (Jacket i a) (Jacket j b)

-- | A Path into a Jacket that ends at a Leaf.
data Path i a
ApL :: Int -> Bool -> Bool -> (Last i) -> !(Path i a) -> !(Jacket i a) -> Path i a
ApR :: Int -> Bool -> Bool -> (Last i) -> !(Jacket i a) -> !(Path i a) -> Path i a
Start :: Path i a

-- | Calculate the absolute position of the Leaf targeted by a
--   Path.
--   
--   This can be quite expensive for right-biased traversals such as you
--   receive from a list.
offset :: Path i a -> Int

-- | Return the total number of children in the Jacket by walking
--   the Path to the root.
pathsize :: Path i a -> Int

-- | Reconstruct a Jacket from a Path.
recompress :: Path i a -> i -> a -> Jacket i a

-- | Walk down the tree to the leftmost child.
startl :: Path i a -> Jacket i a -> r -> (Path i a -> i -> a -> r) -> r

-- | Walk down the tree to the rightmost child.
startr :: Path i a -> Jacket i a -> r -> (Path i a -> i -> a -> r) -> r

-- | Move left one Leaf.
movel :: Path i a -> Jacket i a -> r -> (Path i a -> i -> a -> r) -> r

-- | Move right one Leaf.
mover :: Path i a -> Jacket i a -> r -> (Path i a -> i -> a -> r) -> r

-- | This is used to represent the Top of the Zipper.
--   
--   Every Zipper starts with Top.
--   
--   e.g. Top :>> a is the type of the
--   trivial Zipper.
data Top

-- | This is the type of a Zipper. It visually resembles a
--   "breadcrumb trail" as used in website navigation. Each breadcrumb in
--   the trail represents a level you can move up to.
--   
--   This type operator associates to the left, so you can use a type like
--   
--   
--   Top :>> (String,Double) :>> String :>> Char
--   
--   
--   to represent a Zipper from
--   (String,Double) down to Char that has an
--   intermediate crumb for the String containing the Char.
--   
--   You can construct a Zipper into *any* data structure with
--   zipper.
--   
--   You can repackage up the contents of a Zipper with
--   rezip.
--   
--   
--   >>> rezip $ zipper 42
--   42
--   
--   
--   The combinators in this module provide lot of things you can do to the
--   Zipper while you have it open.
--   
--   Note that a value of type h :> s :> a
--   doesn't actually contain a value of type h :> s --
--   as we descend into a level, the previous level is unpacked and stored
--   in Coil form. Only one value of type _ :> _
--   exists at any particular time for any particular Zipper.
data Zipper h i a
Zipper :: !(Coil h i a) -> Int -> !Int -> !(Path i a) -> i -> a -> Zipper h i a

-- | An empty data type, used to represent the pairing of a position in a
--   Zipper with an index. See :>.
data (:@) a i

-- | This type family represents a Zipper with the p
--   variable abstracting over the position and the index, in terms of
--   :@. You can visually see it in type signatures as:
--   
--   
--   h :> (a :@ i) = Zipper h i a
--   

-- | Many zippers are indexed by Int keys. This type alias is convenient
--   for reducing syntactic noise for talking about these boring indices.
type (:>>) h a = Zipper h Int a

-- | This represents the type a Zipper will have when it is fully
--   Zipped back up.

-- | A Coil is a linked list of the levels above the current one.
--   The length of a Coil is known at compile time.
--   
--   This is part of the internal structure of a Zipper. You
--   shouldn't need to manipulate this directly.
data Coil t i a
Coil :: Coil Top Int a
Snoc :: !(Coil h j s) -> AnIndexedTraversal' i s a -> Int -> !Int -> !(Path j s) -> j -> (Jacket i a -> s) -> Coil (Zipper h j s) i a

-- | This Lens views the current target of the Zipper.
focus :: IndexedLens' i (Zipper h i a) a

-- | Construct a Zipper that can explore anything, and start it at
--   the Top.
zipper :: a -> Top :>> a

-- | Return the index of the focus.
focalPoint :: Zipper h i a -> i

-- | Return the index into the current Traversal within the current
--   level of the Zipper.
--   
--   
--   jerkTo (tooth l) l = Just
--   
--   
--   Mnemonically, zippers have a number of teeth within each level.
--   This is which tooth you are currently at.
--   
--   This is based on ordinal position regardless of the underlying index
--   type. It may be excessively expensive for a list.
--   
--   focalPoint may be much cheaper if you have a Traversal
--   indexed by ordinal position!
tooth :: Zipper h i a -> Int

-- | Move the Zipper upward, closing the current level and
--   focusing on the parent element.
--   
--   NB: Attempts to move upward from the Top of the Zipper
--   will fail to typecheck.
upward :: Ord j => (h :> (s :@ j)) :> (a :@ i) -> h :> (s :@ j)

-- | Jerk the Zipper one tooth to the rightward within
--   the current Lens or Traversal.
--   
--   Attempts to move past the start of the current Traversal (or
--   trivially, the current Lens) will return Nothing.
--   
--   
--   >>> isNothing $ zipper "hello" & rightward
--   True
--   
--   
--   
--   >>> zipper "hello" & fromWithin traverse & rightward <&> view focus
--   'e'
--   
--   
--   
--   >>> zipper "hello" & fromWithin traverse & rightward <&> focus .~ 'u' <&> rezip
--   "hullo"
--   
--   
--   
--   >>> rezip $ zipper (1,2) & fromWithin both & tug rightward & focus .~ 3
--   (1,3)
--   
rightward :: MonadPlus m => h :> (a :@ i) -> m (h :> (a :@ i))

-- | Jerk the Zipper leftward one tooth within the
--   current Lens or Traversal.
--   
--   Attempts to move past the end of the current Traversal (or
--   trivially, the current Lens) will return Nothing.
--   
--   
--   >>> isNothing $ zipper "hello" & leftward
--   True
--   
leftward :: MonadPlus m => h :> (a :@ i) -> m (h :> (a :@ i))

-- | Move to the leftmost position of the current Traversal.
--   
--   This is just a convenient alias for farthest
--   leftward.
--   
--   
--   >>> zipper "hello" & fromWithin traverse & leftmost & focus .~ 'a' & rezip
--   "aello"
--   
leftmost :: a :> (b :@ i) -> a :> (b :@ i)

-- | Move to the rightmost position of the current Traversal.
--   
--   This is just a convenient alias for farthest
--   rightward.
--   
--   
--   >>> zipper "hello" & fromWithin traverse & rightmost & focus .~ 'y' & leftmost & focus .~ 'j' & rezip
--   "jelly"
--   
rightmost :: a :> (b :@ i) -> a :> (b :@ i)

-- | This allows you to safely tug leftward or tug
--   rightward on a Zipper. This will attempt the move, and
--   stay where it was if it fails.
--   
--   The more general signature allows its use in other circumstances,
--   however.
--   
--   
--   tug f x ≡ fromMaybe a (f a)
--   
--   
--   
--   >>> fmap rezip $ zipper "hello" & within traverse <&> tug leftward <&> focus .~ 'j'
--   "jello"
--   
--   
--   
--   >>> fmap rezip $ zipper "hello" & within traverse <&> tug rightward <&> focus .~ 'u'
--   "hullo"
--   
tug :: (a -> Maybe a) -> a -> a

-- | This allows you to safely tug leftward or
--   tug rightward multiple times on a
--   Zipper, moving multiple steps in a given direction and stopping
--   at the last place you couldn't move from. This lets you safely move a
--   Zipper, because it will stop at either end.
--   
--   
--   >>> fmap rezip $ zipper "stale" & within traverse <&> tugs rightward 2 <&> focus .~ 'y'
--   "style"
--   
--   
--   
--   >>> rezip $ zipper "want" & fromWithin traverse & tugs rightward 2 & focus .~ 'r' & tugs leftward 100 & focus .~ 'c'
--   "cart"
--   
tugs :: (a -> Maybe a) -> Int -> a -> a

-- | Move in a direction as far as you can go, then stop there.
--   
--   This repeatedly applies a function until it returns Nothing,
--   and then returns the last answer.
--   
--   
--   >>> fmap rezip $ zipper ("hello","world") & downward _1 & within traverse <&> rightmost <&> focus .~ 'a'
--   ("hella","world")
--   
--   
--   
--   >>> rezip $ zipper ("hello","there") & fromWithin (both.traverse) & rightmost & focus .~ 'm'
--   ("hello","therm")
--   
farthest :: (a -> Maybe a) -> a -> a

-- | This allows for you to repeatedly pull a Zipper in a given
--   direction, failing if it falls off the end.
--   
--   
--   >>> isNothing $ zipper "hello" & within traverse >>= jerks rightward 10
--   True
--   
--   
--   
--   >>> fmap rezip $ zipper "silly" & within traverse >>= jerks rightward 3 <&> focus .~ 'k'
--   "silky"
--   
jerks :: Monad m => (a -> m a) -> Int -> a -> m a

-- | Returns the number of siblings at the current level in the
--   Zipper.
--   
--   
--   teeth z >= 1
--   
--   
--   NB: If the current Traversal targets an infinite number
--   of elements then this may not terminate.
--   
--   This is also a particularly expensive operation to perform on an
--   unbalanced tree.
--   
--   
--   >>> zipper ("hello","world") & teeth
--   1
--   
--   
--   
--   >>> zipper ("hello","world") & fromWithin both & teeth
--   2
--   
--   
--   
--   >>> zipper ("hello","world") & downward _1 & teeth
--   1
--   
--   
--   
--   >>> zipper ("hello","world") & downward _1 & fromWithin traverse & teeth
--   5
--   
--   
--   
--   >>> zipper ("hello","world") & fromWithin (_1.traverse) & teeth
--   5
--   
--   
--   
--   >>> zipper ("hello","world") & fromWithin (both.traverse) & teeth
--   10
--   
teeth :: h :> (a :@ i) -> Int

-- | Move the Zipper horizontally to the element in the nth
--   position in the current level, absolutely indexed, starting with the
--   farthest leftward as 0.
--   
--   This returns Nothing if the target element doesn't exist.
--   
--   
--   jerkTo n ≡ jerks rightward n . farthest leftward
--   
--   
--   
--   >>> isNothing $ zipper "not working." & jerkTo 20
--   True
--   
jerkTo :: MonadPlus m => Int -> (h :> (a :@ i)) -> m (h :> (a :@ i))

-- | Move the Zipper horizontally to the element in the nth
--   position of the current level, absolutely indexed, starting with the
--   farthest leftward as 0.
--   
--   If the element at that position doesn't exist, then this will clamp to
--   the range 0 <= n < teeth.
--   
--   
--   tugTo n ≡ tugs rightward n . farthest leftward
--   
--   
--   
--   >>> rezip $ zipper "not working." & fromWithin traverse & tugTo 100 & focus .~ '!' & tugTo 1 & focus .~ 'u'
--   "nut working!"
--   
tugTo :: Int -> h :> (a :@ i) -> h :> (a :@ i)

-- | Move towards a particular index in the current Traversal.
moveToward :: i -> h :> (a :@ i) -> h :> (a :@ i)

-- | Move horizontally to a particular index i in the current
--   Traversal. In the case of simple zippers, the index is
--   Int and we can move between traversals fairly easily:
--   
--   
--   >>> zipper (42, 32) & fromWithin both & moveTo 0 <&> view focus
--   42
--   
--   
--   
--   >>> zipper (42, 32) & fromWithin both & moveTo 1 <&> view focus
--   32
--   
moveTo :: MonadPlus m => i -> h :> (a :@ i) -> m (h :> (a :@ i))

-- | Construct an IndexedLens from ALens where the index is
--   fixed to 0.
lensed :: ALens' s a -> IndexedLens' Int s a

-- | Step down into a Lens. This is a constrained form of
--   fromWithin for when you know there is precisely one target that
--   can never fail.
--   
--   
--   downward :: Lens' s a -> (h :> s) -> h :> s :> a
--   downward :: Iso' s a  -> (h :> s) -> h :> s :> a
--   
downward :: ALens' s a -> h :> (s :@ j) -> (h :> (s :@ j)) :>> a

-- | Step down into a IndexedLens. This is a constrained form of
--   ifromWithin for when you know there is precisely one target
--   that can never fail.
--   
--   
--   idownward :: IndexedLens' i s a -> (h :> s:@j) -> h :> s:@j :> a:@i
--   
idownward :: Ord i => AnIndexedLens' i s a -> h :> (s :@ j) -> (h :> (s :@ j)) :> (a :@ i)

-- | Step down into the leftmost entry of a Traversal.
--   
--   
--   within :: Traversal' s a -> (h :> s:@j) -> Maybe (h :> s:@j :>> a)
--   within :: Prism' s a     -> (h :> s:@j) -> Maybe (h :> s:@j :>> a)
--   within :: Lens' s a      -> (h :> s:@j) -> Maybe (h :> s:@j :>> a)
--   within :: Iso' s a       -> (h :> s:@j) -> Maybe (h :> s:@j :>> a)
--   
--   
--   
--   within :: MonadPlus m => ATraversal' s a -> (h :> s:@j) -> m (h :> s:@j :>> a)
--   
within :: MonadPlus m => LensLike' (Indexing (Bazaar' (Indexed Int) a)) s a -> (h :> (s :@ j)) -> m ((h :> (s :@ j)) :>> a)

-- | Step down into the leftmost entry of an
--   IndexedTraversal.
--   
--   Note: The index is assumed to be ordered and must increase
--   monotonically or else you cannot (safely) moveTo or
--   moveToward or use tapes.
--   
--   
--   iwithin :: IndexedTraversal' i s a -> (h :> s:@j) -> Maybe (h :> s:@j :> a:@i)
--   iwithin :: IndexedLens' i s a      -> (h :> s:@j) -> Maybe (h :> s:@j :> a:@i)
--   
--   
--   
--   iwithin :: MonadPlus m => ATraversal' s a -> (h :> s:@j) -> m (h :> s:@j :>> a)
--   
iwithin :: (MonadPlus m, Ord i) => AnIndexedTraversal' i s a -> (h :> (s :@ j)) -> m ((h :> (s :@ j)) :> (a :@ i))

-- | Step down into every entry of a Traversal simultaneously.
--   
--   
--   >>> zipper ("hello","world") & withins both >>= leftward >>= withins traverse >>= rightward <&> focus %~ toUpper <&> rezip :: [(String,String)]
--   [("hEllo","world"),("heLlo","world"),("helLo","world"),("hellO","world")]
--   
--   
--   
--   withins :: Traversal' s a -> (h :> s:@j) -> [h :> s:@j :>> a]
--   withins :: Lens' s a      -> (h :> s:@j) -> [h :> s:@j :>> a]
--   withins :: Iso' s a       -> (h :> s:@j) -> [h :> s:@j :>> a]
--   
withins :: MonadPlus m => LensLike' (Indexing (Bazaar' (Indexed Int) a)) s a -> (h :> (s :@ j)) -> m ((h :> (s :@ j)) :>> a)

-- | Step down into every entry of an IndexedTraversal
--   simultaneously.
--   
--   Note: The index is assumed to be ordered and must increase
--   monotonically or else you cannot (safely) moveTo or
--   moveToward or use tapes.
--   
--   
--   iwithins :: IndexedTraversal' i s a -> (h :> s:@j) -> [h :> s:@j :> a:@i]
--   iwithins :: IndexedLens' i s a      -> (h :> s:@j) -> [h :> s:@j :> a:@i]
--   
iwithins :: (MonadPlus m, Ord i) => AnIndexedTraversal' i s a -> (h :> (s :@ j)) -> m ((h :> (s :@ j)) :> (a :@ i))

-- | Unsafely step down into a Traversal that is assumed to
--   be non-empty.
--   
--   If this invariant is not met then this will usually result in an
--   error!
--   
--   
--   fromWithin :: Traversal' s a -> (h :> s:@j) -> h :> s:@j :>> a
--   fromWithin :: Lens' s a      -> (h :> s:@j) -> h :> s:@j :>> a
--   fromWithin :: Iso' s a       -> (h :> s:@j) -> h :> s:@j :>> a
--   
--   
--   You can reason about this function as if the definition was:
--   
--   
--   fromWithin l ≡ fromJust . within l
--   
fromWithin :: LensLike' (Indexing (Bazaar' (Indexed Int) a)) s a -> (h :> (s :@ j)) -> (h :> (s :@ j)) :>> a

-- | Unsafey step down into an IndexedTraversal that is
--   assumed to be non-empty
--   
--   If this invariant is not met then this will usually result in an
--   error!
--   
--   
--   ifromWithin :: IndexedTraversal' i s a -> (h :> s:@j) -> h :> s:@j :> a:@i
--   ifromWithin :: IndexedLens' i s a      -> (h :> s:@j) -> h :> s:@j :> a:@i
--   
--   
--   You can reason about this function as if the definition was:
--   
--   
--   fromWithin l ≡ fromJust . within l
--   
ifromWithin :: Ord i => AnIndexedTraversal' i s a -> (h :> (s :@ j)) -> (h :> (s :@ j)) :> (a :@ i)

-- | This enables us to pull the Zipper back up to the Top.
class Zipping h a
recoil :: Zipping h a => Coil h i a -> Jacket i a -> Zipped h a

-- | Close something back up that you opened as a Zipper.
rezip :: Zipping h a => (h :> (a :@ i)) -> Zipped h a

-- | Extract the current focus from a Zipper as a
--   Pretext, with access to the current index.
focusedContext :: (Indexable i p, Zipping h a) => (h :> (a :@ i)) -> Pretext p a a (Zipped h a)

-- | A Tape is a recorded path through the (indexed)
--   Traversal chain of a Zipper.
data Tape h i a
Tape :: Track h i a -> i -> Tape h i a

-- | Save the current path as as a Tape we can play back later.
saveTape :: Zipper h i a -> Tape h i a

-- | Restore ourselves to a previously recorded position precisely.
--   
--   If the position does not exist, then fail.
restoreTape :: MonadPlus m => Tape h i a -> Zipped h a -> m (Zipper h i a)

-- | Restore ourselves to a location near our previously recorded position.
--   
--   When moving left to right through a Traversal, if this will
--   clamp at each level to the range 0 <= k <
--   teeth, so the only failures will occur when one of the
--   sequence of downward traversals find no targets.
restoreNearTape :: MonadPlus m => Tape h i a -> Zipped h a -> m (Zipper h i a)

-- | Restore ourselves to a previously recorded position.
--   
--   This *assumes* that nothing has been done in the meantime to affect
--   the existence of anything on the entire path.
--   
--   Motions leftward or rightward are clamped, but all
--   traversals included on the Tape are assumed to be non-empty.
--   
--   Violate these assumptions at your own risk!
unsafelyRestoreTape :: Tape h i a -> Zipped h a -> Zipper h i a

-- | This is used to peel off the path information from a Coil for
--   use when saving the current path for later replay.
peel :: Coil h i a -> Track h i a

-- | The Track forms the bulk of a Tape.
data Track t i a
Track :: Track Top Int a
Fork :: Track h j s -> j -> AnIndexedTraversal' i s a -> Track (Zipper h j s) i a

-- | Restore ourselves to a previously recorded position precisely.
--   
--   If the position does not exist, then fail.
restoreTrack :: MonadPlus m => Track h i a -> Zipped h a -> m (Zipper h i a)

-- | Restore ourselves to a location near our previously recorded position.
--   
--   When moving leftward to rightward through a
--   Traversal, if this will clamp at each level to the range 0
--   <= k < teeth, so the only failures
--   will occur when one of the sequence of downward traversals find no
--   targets.
restoreNearTrack :: MonadPlus m => Track h i a -> Zipped h a -> m (Zipper h i a)

-- | Restore ourselves to a previously recorded position.
--   
--   This *assumes* that nothing has been done in the meantime to affect
--   the existence of anything on the entire Path.
--   
--   Motions leftward or rightward are clamped, but all
--   traversals included on the Tape are assumed to be non-empty.
--   
--   Violate these assumptions at your own risk!
unsafelyRestoreTrack :: Track h i a -> Zipped h a -> Zipper h i a
instance (Show i, Show a) => Show (Jacket i a)
instance (Show i, Show a) => Show (Path i a)
instance Zipping h s => Zipping (Zipper h i s) a
instance Zipping Top a
instance Functor (Path i)
instance Applicative (Flow i b)
instance Apply (Flow i b)
instance Functor (Flow i b)
instance Monoid (Jacket i a)
instance TraversableWithIndex i (Jacket i)
instance FoldableWithIndex i (Jacket i)
instance FunctorWithIndex i (Jacket i)
instance Traversable (Jacket i)
instance Foldable (Jacket i)
instance Functor (Jacket i)

-- | This module provides a Zipper with fairly strong type checking
--   guarantees.
--   
--   The code here is inspired by Brandon Simmons' zippo package,
--   but uses a different approach to represent the Zipper that
--   makes the whole thing look like his breadcrumb trail, and can move
--   side-to-side through traversals.
--   
--   Some examples types:
--   
--   
--   
- Top :>> a represents a trivial
--   Zipper with its focus at the root.
--   
- Top :>> Tree a :>>
--   a represents a Zipper that starts with a Tree
--   and descends in a single step to values of type a.
--   
- Top :>> Tree a :>>
--   Tree a :>> Tree a represents a
--   Zipper into a Tree with an intermediate bookmarked
--   Tree, focusing in yet another Tree.
--   
--   
--   Since individual levels of a Zipper are managed by an arbitrary
--   IndexedTraversal, you can move left and right through the
--   IndexedTraversal selecting neighboring elements.
--   
--   
--   >>> zipper ("hello","world") & downward _1 & fromWithin traverse & focus .~ 'J' & rightmost & focus .~ 'y' & rezip
--   ("Jelly","world")
--   
--   
--   This is particularly powerful when compiled with plate,
--   uniplate or biplate for walking down into self-similar
--   children in syntax trees and other structures.
--   
--   Given keys in ascending order you can jump directly to a given key
--   with moveTo. When used with traversals for balanced tree-like
--   structures such as an IntMap or Map, searching for a key
--   with moveTo can be done in logarithmic time.
module Control.Lens.Zipper

-- | This is used to represent the Top of the Zipper.
--   
--   Every Zipper starts with Top.
--   
--   e.g. Top :>> a is the type of the
--   trivial Zipper.
data Top

-- | This type family represents a Zipper with the p
--   variable abstracting over the position and the index, in terms of
--   :@. You can visually see it in type signatures as:
--   
--   
--   h :> (a :@ i) = Zipper h i a
--   

-- | Many zippers are indexed by Int keys. This type alias is convenient
--   for reducing syntactic noise for talking about these boring indices.
type (:>>) h a = Zipper h Int a

-- | An empty data type, used to represent the pairing of a position in a
--   Zipper with an index. See :>.
data (:@) a i

-- | This is the type of a Zipper. It visually resembles a
--   "breadcrumb trail" as used in website navigation. Each breadcrumb in
--   the trail represents a level you can move up to.
--   
--   This type operator associates to the left, so you can use a type like
--   
--   
--   Top :>> (String,Double) :>> String :>> Char
--   
--   
--   to represent a Zipper from
--   (String,Double) down to Char that has an
--   intermediate crumb for the String containing the Char.
--   
--   You can construct a Zipper into *any* data structure with
--   zipper.
--   
--   You can repackage up the contents of a Zipper with
--   rezip.
--   
--   
--   >>> rezip $ zipper 42
--   42
--   
--   
--   The combinators in this module provide lot of things you can do to the
--   Zipper while you have it open.
--   
--   Note that a value of type h :> s :> a
--   doesn't actually contain a value of type h :> s --
--   as we descend into a level, the previous level is unpacked and stored
--   in Coil form. Only one value of type _ :> _
--   exists at any particular time for any particular Zipper.
data Zipper h i a

-- | Construct a Zipper that can explore anything, and start it at
--   the Top.
zipper :: a -> Top :>> a

-- | This Lens views the current target of the Zipper.
focus :: IndexedLens' i (Zipper h i a) a

-- | Extract the current focus from a Zipper as a
--   Pretext, with access to the current index.
focusedContext :: (Indexable i p, Zipping h a) => (h :> (a :@ i)) -> Pretext p a a (Zipped h a)

-- | Move the Zipper upward, closing the current level and
--   focusing on the parent element.
--   
--   NB: Attempts to move upward from the Top of the Zipper
--   will fail to typecheck.
upward :: Ord j => (h :> (s :@ j)) :> (a :@ i) -> h :> (s :@ j)

-- | Step down into a Lens. This is a constrained form of
--   fromWithin for when you know there is precisely one target that
--   can never fail.
--   
--   
--   downward :: Lens' s a -> (h :> s) -> h :> s :> a
--   downward :: Iso' s a  -> (h :> s) -> h :> s :> a
--   
downward :: ALens' s a -> h :> (s :@ j) -> (h :> (s :@ j)) :>> a

-- | Step down into a IndexedLens. This is a constrained form of
--   ifromWithin for when you know there is precisely one target
--   that can never fail.
--   
--   
--   idownward :: IndexedLens' i s a -> (h :> s:@j) -> h :> s:@j :> a:@i
--   
idownward :: Ord i => AnIndexedLens' i s a -> h :> (s :@ j) -> (h :> (s :@ j)) :> (a :@ i)

-- | Step down into the leftmost entry of a Traversal.
--   
--   
--   within :: Traversal' s a -> (h :> s:@j) -> Maybe (h :> s:@j :>> a)
--   within :: Prism' s a     -> (h :> s:@j) -> Maybe (h :> s:@j :>> a)
--   within :: Lens' s a      -> (h :> s:@j) -> Maybe (h :> s:@j :>> a)
--   within :: Iso' s a       -> (h :> s:@j) -> Maybe (h :> s:@j :>> a)
--   
--   
--   
--   within :: MonadPlus m => ATraversal' s a -> (h :> s:@j) -> m (h :> s:@j :>> a)
--   
within :: MonadPlus m => LensLike' (Indexing (Bazaar' (Indexed Int) a)) s a -> (h :> (s :@ j)) -> m ((h :> (s :@ j)) :>> a)

-- | Step down into the leftmost entry of an
--   IndexedTraversal.
--   
--   Note: The index is assumed to be ordered and must increase
--   monotonically or else you cannot (safely) moveTo or
--   moveToward or use tapes.
--   
--   
--   iwithin :: IndexedTraversal' i s a -> (h :> s:@j) -> Maybe (h :> s:@j :> a:@i)
--   iwithin :: IndexedLens' i s a      -> (h :> s:@j) -> Maybe (h :> s:@j :> a:@i)
--   
--   
--   
--   iwithin :: MonadPlus m => ATraversal' s a -> (h :> s:@j) -> m (h :> s:@j :>> a)
--   
iwithin :: (MonadPlus m, Ord i) => AnIndexedTraversal' i s a -> (h :> (s :@ j)) -> m ((h :> (s :@ j)) :> (a :@ i))

-- | Step down into every entry of a Traversal simultaneously.
--   
--   
--   >>> zipper ("hello","world") & withins both >>= leftward >>= withins traverse >>= rightward <&> focus %~ toUpper <&> rezip :: [(String,String)]
--   [("hEllo","world"),("heLlo","world"),("helLo","world"),("hellO","world")]
--   
--   
--   
--   withins :: Traversal' s a -> (h :> s:@j) -> [h :> s:@j :>> a]
--   withins :: Lens' s a      -> (h :> s:@j) -> [h :> s:@j :>> a]
--   withins :: Iso' s a       -> (h :> s:@j) -> [h :> s:@j :>> a]
--   
withins :: MonadPlus m => LensLike' (Indexing (Bazaar' (Indexed Int) a)) s a -> (h :> (s :@ j)) -> m ((h :> (s :@ j)) :>> a)

-- | Step down into every entry of an IndexedTraversal
--   simultaneously.
--   
--   Note: The index is assumed to be ordered and must increase
--   monotonically or else you cannot (safely) moveTo or
--   moveToward or use tapes.
--   
--   
--   iwithins :: IndexedTraversal' i s a -> (h :> s:@j) -> [h :> s:@j :> a:@i]
--   iwithins :: IndexedLens' i s a      -> (h :> s:@j) -> [h :> s:@j :> a:@i]
--   
iwithins :: (MonadPlus m, Ord i) => AnIndexedTraversal' i s a -> (h :> (s :@ j)) -> m ((h :> (s :@ j)) :> (a :@ i))

-- | Jerk the Zipper leftward one tooth within the
--   current Lens or Traversal.
--   
--   Attempts to move past the end of the current Traversal (or
--   trivially, the current Lens) will return Nothing.
--   
--   
--   >>> isNothing $ zipper "hello" & leftward
--   True
--   
leftward :: MonadPlus m => h :> (a :@ i) -> m (h :> (a :@ i))

-- | Jerk the Zipper one tooth to the rightward within
--   the current Lens or Traversal.
--   
--   Attempts to move past the start of the current Traversal (or
--   trivially, the current Lens) will return Nothing.
--   
--   
--   >>> isNothing $ zipper "hello" & rightward
--   True
--   
--   
--   
--   >>> zipper "hello" & fromWithin traverse & rightward <&> view focus
--   'e'
--   
--   
--   
--   >>> zipper "hello" & fromWithin traverse & rightward <&> focus .~ 'u' <&> rezip
--   "hullo"
--   
--   
--   
--   >>> rezip $ zipper (1,2) & fromWithin both & tug rightward & focus .~ 3
--   (1,3)
--   
rightward :: MonadPlus m => h :> (a :@ i) -> m (h :> (a :@ i))

-- | Move to the leftmost position of the current Traversal.
--   
--   This is just a convenient alias for farthest
--   leftward.
--   
--   
--   >>> zipper "hello" & fromWithin traverse & leftmost & focus .~ 'a' & rezip
--   "aello"
--   
leftmost :: a :> (b :@ i) -> a :> (b :@ i)

-- | Move to the rightmost position of the current Traversal.
--   
--   This is just a convenient alias for farthest
--   rightward.
--   
--   
--   >>> zipper "hello" & fromWithin traverse & rightmost & focus .~ 'y' & leftmost & focus .~ 'j' & rezip
--   "jelly"
--   
rightmost :: a :> (b :@ i) -> a :> (b :@ i)

-- | This allows you to safely tug leftward or tug
--   rightward on a Zipper. This will attempt the move, and
--   stay where it was if it fails.
--   
--   The more general signature allows its use in other circumstances,
--   however.
--   
--   
--   tug f x ≡ fromMaybe a (f a)
--   
--   
--   
--   >>> fmap rezip $ zipper "hello" & within traverse <&> tug leftward <&> focus .~ 'j'
--   "jello"
--   
--   
--   
--   >>> fmap rezip $ zipper "hello" & within traverse <&> tug rightward <&> focus .~ 'u'
--   "hullo"
--   
tug :: (a -> Maybe a) -> a -> a

-- | This allows you to safely tug leftward or
--   tug rightward multiple times on a
--   Zipper, moving multiple steps in a given direction and stopping
--   at the last place you couldn't move from. This lets you safely move a
--   Zipper, because it will stop at either end.
--   
--   
--   >>> fmap rezip $ zipper "stale" & within traverse <&> tugs rightward 2 <&> focus .~ 'y'
--   "style"
--   
--   
--   
--   >>> rezip $ zipper "want" & fromWithin traverse & tugs rightward 2 & focus .~ 'r' & tugs leftward 100 & focus .~ 'c'
--   "cart"
--   
tugs :: (a -> Maybe a) -> Int -> a -> a

-- | This allows for you to repeatedly pull a Zipper in a given
--   direction, failing if it falls off the end.
--   
--   
--   >>> isNothing $ zipper "hello" & within traverse >>= jerks rightward 10
--   True
--   
--   
--   
--   >>> fmap rezip $ zipper "silly" & within traverse >>= jerks rightward 3 <&> focus .~ 'k'
--   "silky"
--   
jerks :: Monad m => (a -> m a) -> Int -> a -> m a

-- | Move in a direction as far as you can go, then stop there.
--   
--   This repeatedly applies a function until it returns Nothing,
--   and then returns the last answer.
--   
--   
--   >>> fmap rezip $ zipper ("hello","world") & downward _1 & within traverse <&> rightmost <&> focus .~ 'a'
--   ("hella","world")
--   
--   
--   
--   >>> rezip $ zipper ("hello","there") & fromWithin (both.traverse) & rightmost & focus .~ 'm'
--   ("hello","therm")
--   
farthest :: (a -> Maybe a) -> a -> a

-- | Return the index into the current Traversal within the current
--   level of the Zipper.
--   
--   
--   jerkTo (tooth l) l = Just
--   
--   
--   Mnemonically, zippers have a number of teeth within each level.
--   This is which tooth you are currently at.
--   
--   This is based on ordinal position regardless of the underlying index
--   type. It may be excessively expensive for a list.
--   
--   focalPoint may be much cheaper if you have a Traversal
--   indexed by ordinal position!
tooth :: Zipper h i a -> Int

-- | Returns the number of siblings at the current level in the
--   Zipper.
--   
--   
--   teeth z >= 1
--   
--   
--   NB: If the current Traversal targets an infinite number
--   of elements then this may not terminate.
--   
--   This is also a particularly expensive operation to perform on an
--   unbalanced tree.
--   
--   
--   >>> zipper ("hello","world") & teeth
--   1
--   
--   
--   
--   >>> zipper ("hello","world") & fromWithin both & teeth
--   2
--   
--   
--   
--   >>> zipper ("hello","world") & downward _1 & teeth
--   1
--   
--   
--   
--   >>> zipper ("hello","world") & downward _1 & fromWithin traverse & teeth
--   5
--   
--   
--   
--   >>> zipper ("hello","world") & fromWithin (_1.traverse) & teeth
--   5
--   
--   
--   
--   >>> zipper ("hello","world") & fromWithin (both.traverse) & teeth
--   10
--   
teeth :: h :> (a :@ i) -> Int

-- | Move the Zipper horizontally to the element in the nth
--   position in the current level, absolutely indexed, starting with the
--   farthest leftward as 0.
--   
--   This returns Nothing if the target element doesn't exist.
--   
--   
--   jerkTo n ≡ jerks rightward n . farthest leftward
--   
--   
--   
--   >>> isNothing $ zipper "not working." & jerkTo 20
--   True
--   
jerkTo :: MonadPlus m => Int -> (h :> (a :@ i)) -> m (h :> (a :@ i))

-- | Move the Zipper horizontally to the element in the nth
--   position of the current level, absolutely indexed, starting with the
--   farthest leftward as 0.
--   
--   If the element at that position doesn't exist, then this will clamp to
--   the range 0 <= n < teeth.
--   
--   
--   tugTo n ≡ tugs rightward n . farthest leftward
--   
--   
--   
--   >>> rezip $ zipper "not working." & fromWithin traverse & tugTo 100 & focus .~ '!' & tugTo 1 & focus .~ 'u'
--   "nut working!"
--   
tugTo :: Int -> h :> (a :@ i) -> h :> (a :@ i)

-- | Move horizontally to a particular index i in the current
--   Traversal. In the case of simple zippers, the index is
--   Int and we can move between traversals fairly easily:
--   
--   
--   >>> zipper (42, 32) & fromWithin both & moveTo 0 <&> view focus
--   42
--   
--   
--   
--   >>> zipper (42, 32) & fromWithin both & moveTo 1 <&> view focus
--   32
--   
moveTo :: MonadPlus m => i -> h :> (a :@ i) -> m (h :> (a :@ i))

-- | Move towards a particular index in the current Traversal.
moveToward :: i -> h :> (a :@ i) -> h :> (a :@ i)

-- | Close something back up that you opened as a Zipper.
rezip :: Zipping h a => (h :> (a :@ i)) -> Zipped h a

-- | This represents the type a Zipper will have when it is fully
--   Zipped back up.

-- | This enables us to pull the Zipper back up to the Top.
class Zipping h a

-- | A Tape is a recorded path through the (indexed)
--   Traversal chain of a Zipper.
data Tape h i a

-- | Save the current path as as a Tape we can play back later.
saveTape :: Zipper h i a -> Tape h i a

-- | Restore ourselves to a previously recorded position precisely.
--   
--   If the position does not exist, then fail.
restoreTape :: MonadPlus m => Tape h i a -> Zipped h a -> m (Zipper h i a)

-- | Restore ourselves to a location near our previously recorded position.
--   
--   When moving left to right through a Traversal, if this will
--   clamp at each level to the range 0 <= k <
--   teeth, so the only failures will occur when one of the
--   sequence of downward traversals find no targets.
restoreNearTape :: MonadPlus m => Tape h i a -> Zipped h a -> m (Zipper h i a)

-- | Unsafely step down into a Traversal that is assumed to
--   be non-empty.
--   
--   If this invariant is not met then this will usually result in an
--   error!
--   
--   
--   fromWithin :: Traversal' s a -> (h :> s:@j) -> h :> s:@j :>> a
--   fromWithin :: Lens' s a      -> (h :> s:@j) -> h :> s:@j :>> a
--   fromWithin :: Iso' s a       -> (h :> s:@j) -> h :> s:@j :>> a
--   
--   
--   You can reason about this function as if the definition was:
--   
--   
--   fromWithin l ≡ fromJust . within l
--   
fromWithin :: LensLike' (Indexing (Bazaar' (Indexed Int) a)) s a -> (h :> (s :@ j)) -> (h :> (s :@ j)) :>> a

-- | Unsafey step down into an IndexedTraversal that is
--   assumed to be non-empty
--   
--   If this invariant is not met then this will usually result in an
--   error!
--   
--   
--   ifromWithin :: IndexedTraversal' i s a -> (h :> s:@j) -> h :> s:@j :> a:@i
--   ifromWithin :: IndexedLens' i s a      -> (h :> s:@j) -> h :> s:@j :> a:@i
--   
--   
--   You can reason about this function as if the definition was:
--   
--   
--   fromWithin l ≡ fromJust . within l
--   
ifromWithin :: Ord i => AnIndexedTraversal' i s a -> (h :> (s :@ j)) -> (h :> (s :@ j)) :> (a :@ i)

-- | Restore ourselves to a previously recorded position.
--   
--   This *assumes* that nothing has been done in the meantime to affect
--   the existence of anything on the entire path.
--   
--   Motions leftward or rightward are clamped, but all
--   traversals included on the Tape are assumed to be non-empty.
--   
--   Violate these assumptions at your own risk!
unsafelyRestoreTape :: Tape h i a -> Zipped h a -> Zipper h i a

-- | This module is designed to be imported qualified.
module Control.Lens.Internal.Deque

-- | A Banker's deque based on Chris Okasaki's "Purely Functional Data
--   Structures"
data Deque a
BD :: !Int -> [a] -> !Int -> [a] -> Deque a

-- | O(1). Calculate the size of a Deque
--   
--   
--   >>> size (fromList [1,4,6])
--   3
--   
size :: Deque a -> Int

-- | O(n) amortized. Construct a Deque from a list of values.
--   
--   
--   >>> fromList [1,2]
--   BD 1 [1] 1 [2]
--   
fromList :: [a] -> Deque a

-- | O(1). Determine of a Deque is empty.
--   
--   
--   >>> null empty
--   True
--   
--   
--   
--   >>> null (singleton 1)
--   False
--   
null :: Deque a -> Bool

-- | O(1). Generate a singleton Deque
--   
--   
--   >>> singleton 1
--   BD 1 [1] 0 []
--   
singleton :: a -> Deque a
instance Show a => Show (Deque a)
instance (Choice p, Applicative f) => Snoc p f (Deque a) (Deque b) a b
instance (Choice p, Applicative f) => Cons p f (Deque a) (Deque b) a b
instance Monoid (Deque a)
instance Semigroup (Deque a)
instance TraversableWithIndex Int Deque
instance Traversable Deque
instance FoldableWithIndex Int Deque
instance Foldable Deque
instance MonadPlus Deque
instance Monad Deque
instance Bind Deque
instance Reversing (Deque a)
instance Alternative Deque
instance Plus Deque
instance Alt Deque
instance Applicative Deque
instance Apply Deque
instance FunctorWithIndex Int Deque
instance Functor Deque
instance Ord a => Ord (Deque a)
instance Eq a => Eq (Deque a)

module Control.Lens.Each

-- | This is a common Index type shared by Each, At,
--   Contains and Ixed.

-- | Extract each element of a (potentially monomorphic) container.
--   
--   Notably, when applied to a tuple, this generalizes both to
--   arbitrary homogeneous tuples.
--   
--   
--   >>> (1,2,3) & each *~ 10
--   (10,20,30)
--   
--   
--   It can also be used on monomorphic containers like Text or
--   ByteString.
--   
--   
--   >>> over each Char.toUpper ("hello"^.Text.packed)
--   "HELLO"
--   
--   
--   each is an IndexedTraversal, so it can be used to access
--   keys in many containers:
--   
--   
--   >>> itoListOf each $ Map.fromList [("hello",2),("world",4)]
--   [("hello",2),("world",4)]
--   
--   
--   
--   >>> ("hello","world") & each.each %~ Char.toUpper
--   ("HELLO","WORLD")
--   
class (Functor f, Index s ~ Index t) => Each f s t a b | s -> a, t -> b, s b -> t, t a -> s where each = traversed
each :: Each f s t a b => IndexedLensLike (Index s) f s t a b
instance Settable f => Each f (i -> a) (i -> b) a b
instance (Applicative f, Ix i, IArray UArray a, IArray UArray b) => Each f (UArray i a) (UArray i b) a b
instance (Applicative f, Ix i) => Each f (Array i a) (Array i b) a b
instance Applicative f => Each f ByteString ByteString Word8 Word8
instance Applicative f => Each f ByteString ByteString Word8 Word8
instance Applicative f => Each f Text Text Char Char
instance Applicative f => Each f Text Text Char Char
instance (Applicative f, Unbox a, Unbox b) => Each f (Vector a) (Vector b) a b
instance (Applicative f, Storable a, Storable b) => Each f (Vector a) (Vector b) a b
instance (Applicative f, Prim a, Prim b) => Each f (Vector a) (Vector b) a b
instance Applicative f => Each f (Vector a) (Vector b) a b
instance Applicative f => Each f (Tree a) (Tree b) a b
instance Applicative f => Each f (Seq a) (Seq b) a b
instance Applicative f => Each f (Maybe a) (Maybe b) a b
instance Functor f => Each f (Identity a) (Identity b) a b
instance Applicative f => Each f [a] [b] a b
instance Applicative f => Each f (HashMap c a) (HashMap c b) a b
instance Applicative f => Each f (IntMap a) (IntMap b) a b
instance Applicative f => Each f (Map c a) (Map c b) a b
instance Applicative f => Each f (Complex a) (Complex b) a b
instance (Applicative f, a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7, a ~ a8, a ~ a9, b ~ b2, b ~ b3, b ~ b4, b ~ b5, b ~ b6, b ~ b7, b ~ b8, b ~ b9) => Each f (a, a2, a3, a4, a5, a6, a7, a8, a9) (b, b2, b3, b4, b5, b6, b7, b8, b9) a b
instance (Applicative f, a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7, a ~ a8, b ~ b2, b ~ b3, b ~ b4, b ~ b5, b ~ b6, b ~ b7, b ~ b8) => Each f (a, a2, a3, a4, a5, a6, a7, a8) (b, b2, b3, b4, b5, b6, b7, b8) a b
instance (Applicative f, a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, a ~ a7, b ~ b2, b ~ b3, b ~ b4, b ~ b5, b ~ b6, b ~ b7) => Each f (a, a2, a3, a4, a5, a6, a7) (b, b2, b3, b4, b5, b6, b7) a b
instance (Applicative f, a ~ a2, a ~ a3, a ~ a4, a ~ a5, a ~ a6, b ~ b2, b ~ b3, b ~ b4, b ~ b5, b ~ b6) => Each f (a, a2, a3, a4, a5, a6) (b, b2, b3, b4, b5, b6) a b
instance (Applicative f, a ~ a2, a ~ a3, a ~ a4, a ~ a5, b ~ b2, b ~ b3, b ~ b4, b ~ b5) => Each f (a, a2, a3, a4, a5) (b, b2, b3, b4, b5) a b
instance (Applicative f, a ~ a2, a ~ a3, a ~ a4, b ~ b2, b ~ b3, b ~ b4) => Each f (a, a2, a3, a4) (b, b2, b3, b4) a b
instance (Applicative f, a ~ a2, a ~ a3, b ~ b2, b ~ b3) => Each f (a, a2, a3) (b, b2, b3) a b
instance (Applicative f, a ~ a', b ~ b') => Each f (a, a') (b, b') a b

-- | This module exists for users who like to work with qualified imports
--   but want access to the operators from Lens.
--   
--   
--   import qualified Control.Lens as L
--   import Control.Lens.Operators
--   
module Control.Lens.Operators

-- | Passes the result of the left side to the function on the right side
--   (forward pipe operator).
--   
--   This is the flipped version of ($), which is more common in
--   languages like F# as (|>) where it is needed for
--   inference. Here it is supplied for notational convenience and given a
--   precedence that allows it to be nested inside uses of ($).
--   
--   
--   >>> a & f
--   f a
--   
--   
--   
--   >>> "hello" & length & succ
--   6
--   
--   
--   This combinator is commonly used when applying multiple Lens
--   operations in sequence.
--   
--   
--   >>> ("hello","world") & _1.element 0 .~ 'j' & _1.element 4 .~ 'y'
--   ("jelly","world")
--   
--   
--   This reads somewhat similar to:
--   
--   
--   >>> flip execState ("hello","world") $ do _1.element 0 .= 'j'; _1.element 4 .= 'y'
--   ("jelly","world")
--   
(&) :: a -> (a -> b) -> b

-- | Infix flipped fmap.
--   
--   
--   (<&>) = flip fmap
--   
(<&>) :: Functor f => f a -> (a -> b) -> f b

-- | This is convenient to flip argument order of composite
--   functions.
--   
--   
--   >>> over _2 ?? ("hello","world") $ length
--   ("hello",5)
--   
--   
--   
--   >>> over ?? length ?? ("hello","world") $ _2
--   ("hello",5)
--   
(??) :: Functor f => f (a -> b) -> a -> f b

-- | View the value pointed to by a Getter or Lens or the
--   result of folding over all the results of a Fold or
--   Traversal that points at a monoidal values.
--   
--   This is the same operation as view with the arguments flipped.
--   
--   The fixity and semantics are such that subsequent field accesses can
--   be performed with (.).
--   
--   
--   >>> (a,b)^._2
--   b
--   
--   
--   
--   >>> ("hello","world")^._2
--   "world"
--   
--   
--   
--   >>> import Data.Complex
--   
--   >>> ((0, 1 :+ 2), 3)^._1._2.to magnitude
--   2.23606797749979
--   
--   
--   
--   (^.) ::             s -> Getter s a     -> a
--   (^.) :: Monoid m => s -> Fold s m       -> m
--   (^.) ::             s -> Iso' s a       -> a
--   (^.) ::             s -> Lens' s a      -> a
--   (^.) :: Monoid m => s -> Traversal' s m -> m
--   
(^.) :: s -> Getting a s a -> a

-- | View the value pointed to by a Getter or Lens.
--   
--   This is the same operation as iview with the arguments flipped.
--   
--   The fixity and semantics are such that subsequent field accesses can
--   be performed with (.).
--   
--   
--   >>> (a,b,c,d)^@._2
--   (1,b)
--   
--   
--   
--   >>> ("hello","world","!!!")^@._2
--   (1,"world")
--   
--   
--   
--   (^@.) :: s -> IndexedGetter i s a -> (i, a)
--   (^@.) :: s -> IndexedLens' i s a  -> (i, a)
--   
--   
--   The result probably doesn't have much meaning when applied to an
--   IndexedFold.
(^@.) :: s -> IndexedGetting i (i, a) s a -> (i, a)

-- | A version of (^.) that works on ALens.
--   
--   
--   >>> ("hello","world")^#_2
--   "world"
--   
(^#) :: s -> ALens s t a b -> a

-- | Perform an Action.
--   
--   
--   >>> ["hello","world"]^!folded.act putStrLn
--   hello
--   world
--   
(^!) :: Monad m => s -> Acting m a s t a b -> m a

-- | Perform an IndexedAction.
(^@!) :: Monad m => s -> IndexedActing i m (i, a) s t a b -> m (i, a)

-- | Perform a MonadicFold and collect all of the results in a list.
--   
--   
--   >>> ["ab","cd","ef"]^!!folded.acts
--   ["ace","acf","ade","adf","bce","bcf","bde","bdf"]
--   
(^!!) :: Monad m => s -> Acting m [a] s t a b -> m [a]

-- | Obtain a list of all of the results of an IndexedMonadicFold.
(^@!!) :: Monad m => s -> IndexedActing i m [(i, a)] s t a b -> m [(i, a)]

-- | Perform a MonadicFold and collect the leftmost result.
--   
--   Note: this still causes all effects for all elements.
--   
--   
--   >>> [Just 1, Just 2, Just 3]^!?folded.acts
--   Just (Just 1)
--   
--   >>> [Just 1, Nothing]^!?folded.acts
--   Nothing
--   
(^!?) :: Monad m => s -> Acting m (Leftmost a) s t a b -> m (Maybe a)

-- | Perform an IndexedMonadicFold and collect the Leftmost
--   result.
--   
--   Note: this still causes all effects for all elements.
(^@!?) :: Monad m => s -> IndexedActing i m (Leftmost (i, a)) s t a b -> m (Maybe (i, a))

-- | A convenient infix (flipped) version of toListOf.
--   
--   
--   >>> [[1,2],[3]]^..traverse.traverse
--   [1,2,3]
--   
--   
--   
--   >>> (1,2)^..both
--   [1,2]
--   
--   
--   
--   toList xs ≡ xs ^.. folded
--   (^..) ≡ flip toListOf
--   
--   
--   
--   (^..) :: s -> Getter s a     -> [a]
--   (^..) :: s -> Fold s a       -> [a]
--   (^..) :: s -> Lens' s a      -> [a]
--   (^..) :: s -> Iso' s a       -> [a]
--   (^..) :: s -> Traversal' s a -> [a]
--   (^..) :: s -> Prism' s a     -> [a]
--   
(^..) :: s -> Getting (Endo [a]) s a -> [a]

-- | An infix version of itoListOf.
(^@..) :: s -> IndexedGetting i (Endo [(i, a)]) s a -> [(i, a)]

-- | Perform a safe head of a Fold or Traversal or
--   retrieve Just the result from a Getter or Lens.
--   
--   When using a Traversal as a partial Lens, or a
--   Fold as a partial Getter this can be a convenient way to
--   extract the optional value.
--   
--   Note: if you get stack overflows due to this, you may want to use
--   firstOf instead, which can deal more gracefully with heavily
--   left-biased trees.
--   
--   
--   >>> Left 4 ^?_Left
--   Just 4
--   
--   
--   
--   >>> Right 4 ^?_Left
--   Nothing
--   
--   
--   
--   >>> "world" ^? ix 3
--   Just 'l'
--   
--   
--   
--   >>> "world" ^? ix 20
--   Nothing
--   
--   
--   
--   (^?) ≡ flip preview
--   
--   
--   
--   (^?) :: s -> Getter s a     -> Maybe a
--   (^?) :: s -> Fold s a       -> Maybe a
--   (^?) :: s -> Lens' s a      -> Maybe a
--   (^?) :: s -> Iso' s a       -> Maybe a
--   (^?) :: s -> Traversal' s a -> Maybe a
--   
(^?) :: s -> Getting (First a) s a -> Maybe a

-- | Perform a safe head (with index) of an IndexedFold or
--   IndexedTraversal or retrieve Just the index and result
--   from an IndexedGetter or IndexedLens.
--   
--   When using a IndexedTraversal as a partial IndexedLens,
--   or an IndexedFold as a partial IndexedGetter this can be
--   a convenient way to extract the optional value.
--   
--   
--   (^@?) :: s -> IndexedGetter i s a     -> Maybe (i, a)
--   (^@?) :: s -> IndexedFold i s a       -> Maybe (i, a)
--   (^@?) :: s -> IndexedLens' i s a      -> Maybe (i, a)
--   (^@?) :: s -> IndexedTraversal' i s a -> Maybe (i, a)
--   
(^@?) :: s -> IndexedGetting i (Endo (Maybe (i, a))) s a -> Maybe (i, a)

-- | Perform an *UNSAFE* head of a Fold or Traversal
--   assuming that it is there.
--   
--   
--   >>> Left 4 ^?! _Left
--   4
--   
--   
--   
--   >>> "world" ^?! ix 3
--   'l'
--   
--   
--   
--   (^?!) :: s -> Getter s a     -> a
--   (^?!) :: s -> Fold s a       -> a
--   (^?!) :: s -> Lens' s a      -> a
--   (^?!) :: s -> Iso' s a       -> a
--   (^?!) :: s -> Traversal' s a -> a
--   
(^?!) :: s -> Getting (Endo a) s a -> a

-- | Perform an *UNSAFE* head (with index) of an IndexedFold
--   or IndexedTraversal assuming that it is there.
--   
--   
--   (^@?!) :: s -> IndexedGetter i s a     -> (i, a)
--   (^@?!) :: s -> IndexedFold i s a       -> (i, a)
--   (^@?!) :: s -> IndexedLens' i s a      -> (i, a)
--   (^@?!) :: s -> IndexedTraversal' i s a -> (i, a)
--   
(^@?!) :: s -> IndexedGetting i (Endo (i, a)) s a -> (i, a)

-- | An infix alias for review.
--   
--   
--   unto f # x ≡ f x
--   l # x ≡ x ^. re l
--   
--   
--   This is commonly used when using a Prism as a smart
--   constructor.
--   
--   
--   >>> _Left # 4
--   Left 4
--   
--   
--   But it can be used for any Prism
--   
--   
--   >>> base 16 # 123
--   "7b"
--   
--   
--   
--   (#) :: Iso'      s a -> a -> s
--   (#) :: Prism'    s a -> a -> s
--   (#) :: Review'   s a -> a -> s
--   (#) :: Equality' s a -> a -> s
--   
(#) :: AReview s t a b -> b -> t

-- | Replace the target of a Lens or all of the targets of a
--   Setter or Traversal with a constant value.
--   
--   This is an infix version of set, provided for consistency with
--   (.=).
--   
--   
--   f <$ a ≡ mapped .~ f $ a
--   
--   
--   
--   >>> (a,b,c,d) & _4 .~ e
--   (a,b,c,e)
--   
--   
--   
--   >>> (42,"world") & _1 .~ "hello"
--   ("hello","world")
--   
--   
--   
--   >>> (a,b) & both .~ c
--   (c,c)
--   
--   
--   
--   (.~) :: Setter s t a b    -> b -> s -> t
--   (.~) :: Iso s t a b       -> b -> s -> t
--   (.~) :: Lens s t a b      -> b -> s -> t
--   (.~) :: Traversal s t a b -> b -> s -> t
--   
(.~) :: ASetter s t a b -> b -> s -> t

-- | Replace the target of a Lens or all of the targets of a
--   Setter or Traversal in our monadic state with a new
--   value, irrespective of the old.
--   
--   This is an infix version of assign.
--   
--   
--   >>> execState (do _1 .= c; _2 .= d) (a,b)
--   (c,d)
--   
--   
--   
--   >>> execState (both .= c) (a,b)
--   (c,c)
--   
--   
--   
--   (.=) :: MonadState s m => Iso' s a       -> a -> m ()
--   (.=) :: MonadState s m => Lens' s a      -> a -> m ()
--   (.=) :: MonadState s m => Traversal' s a -> a -> m ()
--   (.=) :: MonadState s m => Setter' s a    -> a -> m ()
--   
--   
--   It puts the state in the monad or it gets the hose again.
(.=) :: MonadState s m => ASetter s s a b -> b -> m ()

-- | Set with pass-through.
--   
--   This is mostly present for consistency, but may be useful for for
--   chaining assignments.
--   
--   If you do not need a copy of the intermediate result, then using l
--   .~ t directly is a good idea.
--   
--   
--   >>> (a,b) & _1 <.~ c
--   (c,(c,b))
--   
--   
--   
--   >>> ("good","morning","vietnam") & _3 <.~ "world"
--   ("world",("good","morning","world"))
--   
--   
--   
--   >>> (42,Map.fromList [("goodnight","gracie")]) & _2.at "hello" <.~ Just "world"
--   (Just "world",(42,fromList [("goodnight","gracie"),("hello","world")]))
--   
--   
--   
--   (<.~) :: Setter s t a b    -> b -> s -> (b, t)
--   (<.~) :: Iso s t a b       -> b -> s -> (b, t)
--   (<.~) :: Lens s t a b      -> b -> s -> (b, t)
--   (<.~) :: Traversal s t a b -> b -> s -> (b, t)
--   
(<.~) :: ASetter s t a b -> b -> s -> (b, t)

-- | Set with pass-through
--   
--   This is useful for chaining assignment without round-tripping through
--   your Monad stack.
--   
--   
--   do x <- _2 <.= ninety_nine_bottles_of_beer_on_the_wall
--   
--   
--   If you do not need a copy of the intermediate result, then using l
--   .= d will avoid unused binding warnings.
--   
--   
--   (<.=) :: MonadState s m => Setter s s a b    -> b -> m b
--   (<.=) :: MonadState s m => Iso s s a b       -> b -> m b
--   (<.=) :: MonadState s m => Lens s s a b      -> b -> m b
--   (<.=) :: MonadState s m => Traversal s s a b -> b -> m b
--   
(<.=) :: MonadState s m => ASetter s s a b -> b -> m b

-- | Modify the target of a Lens, but return the old value.
--   
--   When you do not need the old value, (%~) is more flexible.
--   
--   
--   (<<.~) ::             Lens s t a b      -> b -> s -> (a, t)
--   (<<.~) ::             Iso s t a b       -> b -> s -> (a, t)
--   (<<.~) :: Monoid a => Traversal s t a b -> b -> s -> (a, t)
--   
(<<.~) :: Overloading (->) q ((,) a) s t a b -> b -> q s (a, t)

-- | Modify the target of a Lens into your 'Monad'\'s state by a
--   user supplied function and return the old value that was
--   replaced.
--   
--   When applied to a Traversal, it this will return a monoidal
--   summary of all of the old values present.
--   
--   When you do not need the result of the operation, (%=) is more
--   flexible.
--   
--   
--   (<<%=) :: MonadState s m             => Lens' s a      -> (a -> a) -> m a
--   (<<%=) :: MonadState s m             => Iso' s a       -> (a -> a) -> m a
--   (<<%=) :: (MonadState s m, Monoid t) => Traversal' s a -> (a -> a) -> m a
--   
(<<.=) :: MonadState s m => LensLike ((,) a) s s a b -> b -> m a

-- | A version of (.~) that works on ALens.
--   
--   
--   >>> ("hello","there") & _2 #~ "world"
--   ("hello","world")
--   
(#~) :: ALens s t a b -> b -> s -> t

-- | A version of (.=) that works on ALens.
(#=) :: MonadState s m => ALens s s a b -> b -> m ()

-- | A version of (<.~) that works on ALens.
--   
--   
--   >>> ("hello","there") & _2 <#~ "world"
--   ("world",("hello","world"))
--   
(<#~) :: ALens s t a b -> b -> s -> (b, t)

-- | A version of (<#=) that works on ALens.
(<#=) :: MonadState s m => ALens s s a b -> b -> m b

-- | Set the target of a Lens, Traversal or Setter to
--   Just a value.
--   
--   
--   l ?~ t ≡ set l (Just t)
--   
--   
--   
--   >>> Nothing & id ?~ a
--   Just a
--   
--   
--   
--   >>> Map.empty & at 3 ?~ x
--   fromList [(3,x)]
--   
--   
--   
--   (?~) :: Setter s t a (Maybe b)    -> b -> s -> t
--   (?~) :: Iso s t a (Maybe b)       -> b -> s -> t
--   (?~) :: Lens s t a (Maybe b)      -> b -> s -> t
--   (?~) :: Traversal s t a (Maybe b) -> b -> s -> t
--   
(?~) :: ASetter s t a (Maybe b) -> b -> s -> t

-- | Replace the target of a Lens or all of the targets of a
--   Setter or Traversal in our monadic state with
--   Just a new value, irrespective of the old.
--   
--   
--   >>> execState (do at 1 ?= a; at 2 ?= b) Map.empty
--   fromList [(1,a),(2,b)]
--   
--   
--   
--   >>> execState (do _1 ?= b; _2 ?= c) (Just a, Nothing)
--   (Just b,Just c)
--   
--   
--   
--   (?=) :: MonadState s m => Iso' s (Maybe a)       -> a -> m ()
--   (?=) :: MonadState s m => Lens' s (Maybe a)      -> a -> m ()
--   (?=) :: MonadState s m => Traversal' s (Maybe a) -> a -> m ()
--   (?=) :: MonadState s m => Setter' s (Maybe a)    -> a -> m ()
--   
(?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m ()

-- | Set to Just a value with pass-through.
--   
--   This is mostly present for consistency, but may be useful for for
--   chaining assignments.
--   
--   If you do not need a copy of the intermediate result, then using l
--   ?~ d directly is a good idea.
--   
--   
--   >>> import Data.Map as Map
--   
--   >>> _2.at "hello" <?~ "world" $ (42,Map.fromList [("goodnight","gracie")])
--   ("world",(42,fromList [("goodnight","gracie"),("hello","world")]))
--   
--   
--   
--   (<?~) :: Setter s t a (Maybe b)    -> b -> s -> (b, t)
--   (<?~) :: Iso s t a (Maybe b)       -> b -> s -> (b, t)
--   (<?~) :: Lens s t a (Maybe b)      -> b -> s -> (b, t)
--   (<?~) :: Traversal s t a (Maybe b) -> b -> s -> (b, t)
--   
(<?~) :: ASetter s t a (Maybe b) -> b -> s -> (b, t)

-- | Set Just a value with pass-through
--   
--   This is useful for chaining assignment without round-tripping through
--   your Monad stack.
--   
--   
--   do x <- at foo <?= ninety_nine_bottles_of_beer_on_the_wall
--   
--   
--   If you do not need a copy of the intermediate result, then using l
--   ?= d will avoid unused binding warnings.
--   
--   
--   (<?=) :: MonadState s m => Setter s s a (Maybe b)    -> b -> m b
--   (<?=) :: MonadState s m => Iso s s a (Maybe b)       -> b -> m b
--   (<?=) :: MonadState s m => Lens s s a (Maybe b)      -> b -> m b
--   (<?=) :: MonadState s m => Traversal s s a (Maybe b) -> b -> m b
--   
(<?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m b

-- | Modifies the target of a Lens or all of the targets of a
--   Setter or Traversal with a user supplied function.
--   
--   This is an infix version of over.
--   
--   
--   fmap f ≡ mapped %~ f
--   fmapDefault f ≡ traverse %~ f
--   
--   
--   
--   >>> (a,b,c) & _3 %~ f
--   (a,b,f c)
--   
--   
--   
--   >>> (a,b) & both %~ f
--   (f a,f b)
--   
--   
--   
--   >>> _2 %~ length $ (1,"hello")
--   (1,5)
--   
--   
--   
--   >>> traverse %~ f $ [a,b,c]
--   [f a,f b,f c]
--   
--   
--   
--   >>> traverse %~ even $ [1,2,3]
--   [False,True,False]
--   
--   
--   
--   >>> traverse.traverse %~ length $ [["hello","world"],["!!!"]]
--   [[5,5],[3]]
--   
--   
--   
--   (%~) :: Setter s t a b    -> (a -> b) -> s -> t
--   (%~) :: Iso s t a b       -> (a -> b) -> s -> t
--   (%~) :: Lens s t a b      -> (a -> b) -> s -> t
--   (%~) :: Traversal s t a b -> (a -> b) -> s -> t
--   
(%~) :: Profunctor p => Setting p s t a b -> p a b -> s -> t

-- | Map over the target of a Lens or all of the targets of a
--   Setter or Traversal in our monadic state.
--   
--   
--   >>> execState (do _1 %= f;_2 %= g) (a,b)
--   (f a,g b)
--   
--   
--   
--   >>> execState (do both %= f) (a,b)
--   (f a,f b)
--   
--   
--   
--   (%=) :: MonadState s m => Iso' s a       -> (a -> a) -> m ()
--   (%=) :: MonadState s m => Lens' s a      -> (a -> a) -> m ()
--   (%=) :: MonadState s m => Traversal' s a -> (a -> a) -> m ()
--   (%=) :: MonadState s m => Setter' s a    -> (a -> a) -> m ()
--   
--   
--   
--   (%=) :: MonadState s m => ASetter s s a b -> (a -> b) -> m ()
--   
(%=) :: (Profunctor p, MonadState s m) => Setting p s s a b -> p a b -> m ()

-- | Modify the target of a Lens and return the result.
--   
--   When you do not need the result of the addition, (%~) is more
--   flexible.
--   
--   
--   (<%~) ::             Lens s t a b      -> (a -> b) -> s -> (b, t)
--   (<%~) ::             Iso s t a b       -> (a -> b) -> s -> (b, t)
--   (<%~) :: Monoid b => Traversal s t a b -> (a -> b) -> s -> (b, t)
--   
(<%~) :: Profunctor p => Overloading p q ((,) b) s t a b -> p a b -> q s (b, t)

-- | Modify the target of a Lens into your 'Monad'\'s state by a
--   user supplied function and return the result.
--   
--   When applied to a Traversal, it this will return a monoidal
--   summary of all of the intermediate results.
--   
--   When you do not need the result of the operation, (%=) is more
--   flexible.
--   
--   
--   (<%=) :: MonadState s m             => Lens' s a      -> (a -> a) -> m a
--   (<%=) :: MonadState s m             => Iso' s a       -> (a -> a) -> m a
--   (<%=) :: (MonadState s m, Monoid a) => Traversal' s a -> (a -> a) -> m a
--   
(<%=) :: (Profunctor p, MonadState s m) => Overloading p (->) ((,) b) s s a b -> p a b -> m b

-- | Modify the target of a Lens, but return the old value.
--   
--   When you do not need the result of the addition, (%~) is more
--   flexible.
--   
--   
--   (<<%~) ::             Lens s t a b      -> (a -> b) -> s -> (a, t)
--   (<<%~) ::             Iso s t a b       -> (a -> b) -> s -> (a, t)
--   (<<%~) :: Monoid a => Traversal s t a b -> (a -> b) -> s -> (a, t)
--   
(<<%~) :: Strong p => Overloading p q ((,) a) s t a b -> p a b -> q s (a, t)

-- | Modify the target of a Lens into your 'Monad'\'s state by a
--   user supplied function and return the old value that was
--   replaced.
--   
--   When applied to a Traversal, it this will return a monoidal
--   summary of all of the old values present.
--   
--   When you do not need the result of the operation, (%=) is more
--   flexible.
--   
--   
--   (<<%=) :: MonadState s m             => Lens' s a      -> (a -> a) -> m a
--   (<<%=) :: MonadState s m             => Iso' s a       -> (a -> a) -> m a
--   (<<%=) :: (MonadState s m, Monoid b) => Traversal' s a -> (a -> a) -> m a
--   
--   
--   
--   (<<%=) :: MonadState s m => LensLike ((,)a) s s a b -> (a -> b) -> m a
--   
(<<%=) :: (Strong p, MonadState s m) => Overloading p (->) ((,) a) s s a b -> p a b -> m a

-- | A version of (%~) that works on ALens.
--   
--   
--   >>> ("hello","world") & _2 #%~ length
--   ("hello",5)
--   
(#%~) :: ALens s t a b -> (a -> b) -> s -> t

-- | A version of (%=) that works on ALens.
(#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m ()

-- | A version of (<%~) that works on ALens.
--   
--   
--   >>> ("hello","world") & _2 <#%~ length
--   (5,("hello",5))
--   
(<#%~) :: ALens s t a b -> (a -> b) -> s -> (b, t)

-- | A version of (<%=) that works on ALens.
(<#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m b

-- | Adjust every target of an IndexedSetter, IndexedLens or
--   IndexedTraversal with access to the index.
--   
--   
--   (%@~) ≡ imapOf
--   
--   
--   When you do not need access to the index then (%@~) is more
--   liberal in what it can accept.
--   
--   
--   l %~ f ≡ l %@~ const f
--   
--   
--   
--   (%@~) :: IndexedSetter i s t a b    -> (i -> a -> b) -> s -> t
--   (%@~) :: IndexedLens i s t a b      -> (i -> a -> b) -> s -> t
--   (%@~) :: IndexedTraversal i s t a b -> (i -> a -> b) -> s -> t
--   
(%@~) :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t

-- | Adjust every target in the current state of an IndexedSetter,
--   IndexedLens or IndexedTraversal with access to the
--   index.
--   
--   When you do not need access to the index then (%=) is more
--   liberal in what it can accept.
--   
--   
--   l %= f ≡ l %@= const f
--   
--   
--   
--   (%@=) :: MonadState s m => IndexedSetter i s s a b    -> (i -> a -> b) -> m ()
--   (%@=) :: MonadState s m => IndexedLens i s s a b      -> (i -> a -> b) -> m ()
--   (%@=) :: MonadState s m => IndexedTraversal i s t a b -> (i -> a -> b) -> m ()
--   
(%@=) :: MonadState s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m ()

-- | Adjust the target of an IndexedLens returning the intermediate
--   result, or adjust all of the targets of an IndexedTraversal and
--   return a monoidal summary along with the answer.
--   
--   
--   l <%~ f ≡ l <%@~ const f
--   
--   
--   When you do not need access to the index then (<%~) is more
--   liberal in what it can accept.
--   
--   If you do not need the intermediate result, you can use (%@~)
--   or even (%~).
--   
--   
--   (<%@~) ::             IndexedLens i s t a b      -> (i -> a -> b) -> s -> (b, t)
--   (<%@~) :: Monoid b => IndexedTraversal i s t a b -> (i -> a -> b) -> s -> (b, t)
--   
(<%@~) :: Overloading (Indexed i) q ((,) b) s t a b -> (i -> a -> b) -> q s (b, t)

-- | Adjust the target of an IndexedLens returning the intermediate
--   result, or adjust all of the targets of an IndexedTraversal
--   within the current state, and return a monoidal summary of the
--   intermediate results.
--   
--   
--   (<%@=) :: MonadState s m                 => IndexedLens i s s a b      -> (i -> a -> b) -> m b
--   (<%@=) :: (MonadState s m, Monoid b) => IndexedTraversal i s s a b -> (i -> a -> b) -> m b
--   
(<%@=) :: MonadState s m => IndexedLensLike i ((,) b) s s a b -> (i -> a -> b) -> m b

-- | Adjust the target of an IndexedLens returning the old value, or
--   adjust all of the targets of an IndexedTraversal and return a
--   monoidal summary of the old values along with the answer.
--   
--   
--   (<<%@~) ::             IndexedLens i s t a b      -> (i -> a -> b) -> s -> (a, t)
--   (<<%@~) :: Monoid a => IndexedTraversal i s t a b -> (i -> a -> b) -> s -> (a, t)
--   
(<<%@~) :: Overloading (Indexed i) q ((,) a) s t a b -> (i -> a -> b) -> q s (a, t)

-- | Adjust the target of an IndexedLens returning the old value, or
--   adjust all of the targets of an IndexedTraversal within the
--   current state, and return a monoidal summary of the old values.
--   
--   
--   (<<%@=) :: MonadState s m                 => IndexedLens i s s a b      -> (i -> a -> b) -> m a
--   (<<%@=) :: (MonadState s m, Monoid b) => IndexedTraversal i s s a b -> (i -> a -> b) -> m a
--   
(<<%@=) :: MonadState s m => IndexedLensLike i ((,) a) s s a b -> (i -> a -> b) -> m a

-- | (%%~) can be used in one of two scenarios:
--   
--   When applied to a Lens, it can edit the target of the
--   Lens in a structure, extracting a functorial result.
--   
--   When applied to a Traversal, it can edit the targets of the
--   traversals, extracting an applicative summary of its actions.
--   
--   For all that the definition of this combinator is just:
--   
--   
--   (%%~) ≡ id
--   
--   
--   It may be beneficial to think about it as if it had these even more
--   restricted types, however:
--   
--   
--   (%%~) :: Functor f =>     Iso s t a b       -> (a -> f b) -> s -> f t
--   (%%~) :: Functor f =>     Lens s t a b      -> (a -> f b) -> s -> f t
--   (%%~) :: Applicative f => Traversal s t a b -> (a -> f b) -> s -> f t
--   
--   
--   When applied to a Traversal, it can edit the targets of the
--   traversals, extracting a supplemental monoidal summary of its actions,
--   by choosing f = ((,) m)
--   
--   
--   (%%~) ::             Iso s t a b       -> (a -> (r, b)) -> s -> (r, t)
--   (%%~) ::             Lens s t a b      -> (a -> (r, b)) -> s -> (r, t)
--   (%%~) :: Monoid m => Traversal s t a b -> (a -> (m, b)) -> s -> (m, t)
--   
(%%~) :: Overloading p q f s t a b -> p a (f b) -> q s (f t)

-- | Modify the target of a Lens in the current state returning some
--   extra information of type r or modify all targets of a
--   Traversal in the current state, extracting extra information of
--   type r and return a monoidal summary of the changes.
--   
--   
--   >>> runState (_1 %%= \x -> (f x, g x)) (a,b)
--   (f a,(g a,b))
--   
--   
--   
--   (%%=) ≡ (state .)
--   
--   
--   It may be useful to think of (%%=), instead, as having either
--   of the following more restricted type signatures:
--   
--   
--   (%%=) :: MonadState s m             => Iso s s a b       -> (a -> (r, b)) -> m r
--   (%%=) :: MonadState s m             => Lens s s a b      -> (a -> (r, b)) -> m r
--   (%%=) :: (MonadState s m, Monoid r) => Traversal s s a b -> (a -> (r, b)) -> m r
--   
(%%=) :: MonadState s m => Overloading p (->) ((,) r) s s a b -> p a (r, b) -> m r

-- | A version of (%%~) that works on ALens.
--   
--   
--   >>> ("hello","world") & _2 #%%~ \x -> (length x, x ++ "!")
--   (5,("hello","world!"))
--   
(#%%~) :: Functor f => ALens s t a b -> (a -> f b) -> s -> f t

-- | A version of (%%=) that works on ALens.
(#%%=) :: MonadState s m => ALens s s a b -> (a -> (r, b)) -> m r

-- | Adjust the target of an IndexedLens returning a supplementary
--   result, or adjust all of the targets of an IndexedTraversal and
--   return a monoidal summary of the supplementary results and the answer.
--   
--   
--   (%%@~) ≡ withIndex
--   
--   
--   
--   (%%@~) :: Functor f => IndexedLens i s t a b      -> (i -> a -> f b) -> s -> f t
--   (%%@~) :: Applicative f => IndexedTraversal i s t a b -> (i -> a -> f b) -> s -> f t
--   
--   
--   In particular, it is often useful to think of this function as having
--   one of these even more restricted type signatures:
--   
--   
--   (%%@~) ::             IndexedLens i s t a b      -> (i -> a -> (r, b)) -> s -> (r, t)
--   (%%@~) :: Monoid r => IndexedTraversal i s t a b -> (i -> a -> (r, b)) -> s -> (r, t)
--   
(%%@~) :: IndexedLensLike i f s t a b -> (i -> a -> f b) -> s -> f t

-- | Adjust the target of an IndexedLens returning a supplementary
--   result, or adjust all of the targets of an IndexedTraversal
--   within the current state, and return a monoidal summary of the
--   supplementary results.
--   
--   
--   l %%@= f ≡ state (l %%@~ f)
--   
--   
--   
--   (%%@=) :: MonadState s m                 => IndexedLens i s s a b      -> (i -> a -> (r, b)) -> s -> m r
--   (%%@=) :: (MonadState s m, Monoid r) => IndexedTraversal i s s a b -> (i -> a -> (r, b)) -> s -> m r
--   
(%%@=) :: MonadState s m => IndexedLensLike i ((,) r) s s a b -> (i -> a -> (r, b)) -> m r

-- | Increment the target(s) of a numerically valued Lens,
--   Setter or Traversal.
--   
--   
--   >>> (a,b) & _1 +~ c
--   (a + c,b)
--   
--   
--   
--   >>> (a,b) & both +~ c
--   (a + c,b + c)
--   
--   
--   
--   >>> (1,2) & _2 +~ 1
--   (1,3)
--   
--   
--   
--   >>> [(a,b),(c,d)] & traverse.both +~ e
--   [(a + e,b + e),(c + e,d + e)]
--   
--   
--   
--   (+~) :: Num a => Setter' s a    -> a -> s -> s
--   (+~) :: Num a => Iso' s a       -> a -> s -> s
--   (+~) :: Num a => Lens' s a      -> a -> s -> s
--   (+~) :: Num a => Traversal' s a -> a -> s -> s
--   
(+~) :: Num a => ASetter s t a a -> a -> s -> t

-- | Modify the target(s) of a Lens', Iso, Setter or
--   Traversal by adding a value.
--   
--   Example:
--   
--   
--   fresh :: MonadState Int m => m Int
--   fresh = do
--     id += 1
--     use id
--   
--   
--   
--   >>> execState (do _1 += c; _2 += d) (a,b)
--   (a + c,b + d)
--   
--   
--   
--   >>> execState (do _1.at 1.non 0 += 10) (Map.fromList [(2,100)],"hello")
--   (fromList [(1,10),(2,100)],"hello")
--   
--   
--   
--   (+=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
--   (+=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
--   (+=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
--   (+=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()
--   
(+=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m ()

-- | Increment the target of a numerically valued Lens and return
--   the result.
--   
--   When you do not need the result of the addition, (+~) is more
--   flexible.
--   
--   
--   (<+~) :: Num a => Lens' s a -> a -> s -> (a, s)
--   (<+~) :: Num a => Iso' s a  -> a -> s -> (a, s)
--   
(<+~) :: Num a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)

-- | Add to the target of a numerically valued Lens into your
--   'Monad'\'s state and return the result.
--   
--   When you do not need the result of the addition, (+=) is more
--   flexible.
--   
--   
--   (<+=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
--   (<+=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a
--   
(<+=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a

-- | Decrement the target(s) of a numerically valued Lens,
--   Iso, Setter or Traversal.
--   
--   
--   >>> (a,b) & _1 -~ c
--   (a - c,b)
--   
--   
--   
--   >>> (a,b) & both -~ c
--   (a - c,b - c)
--   
--   
--   
--   >>> _1 -~ 2 $ (1,2)
--   (-1,2)
--   
--   
--   
--   >>> mapped.mapped -~ 1 $ [[4,5],[6,7]]
--   [[3,4],[5,6]]
--   
--   
--   
--   (-~) :: Num a => Setter' s a    -> a -> s -> s
--   (-~) :: Num a => Iso' s a       -> a -> s -> s
--   (-~) :: Num a => Lens' s a      -> a -> s -> s
--   (-~) :: Num a => Traversal' s a -> a -> s -> s
--   
(-~) :: Num a => ASetter s t a a -> a -> s -> t

-- | Modify the target(s) of a Lens', Iso, Setter or
--   Traversal by subtracting a value.
--   
--   
--   >>> execState (do _1 -= c; _2 -= d) (a,b)
--   (a - c,b - d)
--   
--   
--   
--   (-=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
--   (-=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
--   (-=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
--   (-=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()
--   
(-=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m ()

-- | Decrement the target of a numerically valued Lens and return
--   the result.
--   
--   When you do not need the result of the subtraction, (-~) is
--   more flexible.
--   
--   
--   (<-~) :: Num a => Lens' s a -> a -> s -> (a, s)
--   (<-~) :: Num a => Iso' s a  -> a -> s -> (a, s)
--   
(<-~) :: Num a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)

-- | Subtract from the target of a numerically valued Lens into your
--   'Monad'\'s state and return the result.
--   
--   When you do not need the result of the subtraction, (-=) is
--   more flexible.
--   
--   
--   (<-=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
--   (<-=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a
--   
(<-=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a

-- | Multiply the target(s) of a numerically valued Lens,
--   Iso, Setter or Traversal.
--   
--   
--   >>> (a,b) & _1 *~ c
--   (a * c,b)
--   
--   
--   
--   >>> (a,b) & both *~ c
--   (a * c,b * c)
--   
--   
--   
--   >>> (1,2) & _2 *~ 4
--   (1,8)
--   
--   
--   
--   >>> Just 24 & mapped *~ 2
--   Just 48
--   
--   
--   
--   (*~) :: Num a => Setter' s a    -> a -> s -> s
--   (*~) :: Num a => Iso' s a       -> a -> s -> s
--   (*~) :: Num a => Lens' s a      -> a -> s -> s
--   (*~) :: Num a => Traversal' s a -> a -> s -> s
--   
(*~) :: Num a => ASetter s t a a -> a -> s -> t

-- | Modify the target(s) of a Lens', Iso, Setter or
--   Traversal by multiplying by value.
--   
--   
--   >>> execState (do _1 *= c; _2 *= d) (a,b)
--   (a * c,b * d)
--   
--   
--   
--   (*=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
--   (*=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
--   (*=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
--   (*=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()
--   
(*=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m ()

-- | Multiply the target of a numerically valued Lens and return the
--   result.
--   
--   When you do not need the result of the multiplication, (*~) is
--   more flexible.
--   
--   
--   (<*~) :: Num a => Lens' s a -> a -> s -> (a, s)
--   (<*~) :: Num a => Iso'  s a -> a -> s -> (a, s)
--   
(<*~) :: Num a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)

-- | Multiply the target of a numerically valued Lens into your
--   'Monad'\'s state and return the result.
--   
--   When you do not need the result of the multiplication, (*=) is
--   more flexible.
--   
--   
--   (<*=) :: (MonadState s m, Num a) => Lens' s a -> a -> m a
--   (<*=) :: (MonadState s m, Num a) => Iso' s a -> a -> m a
--   
(<*=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a

-- | Divide the target(s) of a numerically valued Lens, Iso,
--   Setter or Traversal.
--   
--   
--   >>> (a,b) & _1 //~ c
--   (a / c,b)
--   
--   
--   
--   >>> (a,b) & both //~ c
--   (a / c,b / c)
--   
--   
--   
--   >>> ("Hawaii",10) & _2 //~ 2
--   ("Hawaii",5.0)
--   
--   
--   
--   (//~) :: Fractional a => Setter' s a    -> a -> s -> s
--   (//~) :: Fractional a => Iso' s a       -> a -> s -> s
--   (//~) :: Fractional a => Lens' s a      -> a -> s -> s
--   (//~) :: Fractional a => Traversal' s a -> a -> s -> s
--   
(//~) :: Fractional a => ASetter s t a a -> a -> s -> t

-- | Modify the target(s) of a Lens', Iso, Setter or
--   Traversal by dividing by a value.
--   
--   
--   >>> execState (do _1 //= c; _2 //= d) (a,b)
--   (a / c,b / d)
--   
--   
--   
--   (//=) :: (MonadState s m, Fractional a) => Setter' s a    -> a -> m ()
--   (//=) :: (MonadState s m, Fractional a) => Iso' s a       -> a -> m ()
--   (//=) :: (MonadState s m, Fractional a) => Lens' s a      -> a -> m ()
--   (//=) :: (MonadState s m, Fractional a) => Traversal' s a -> a -> m ()
--   
(//=) :: (MonadState s m, Fractional a) => ASetter' s a -> a -> m ()

-- | Divide the target of a fractionally valued Lens and return the
--   result.
--   
--   When you do not need the result of the division, (//~) is more
--   flexible.
--   
--   
--   (<//~) :: Fractional a => Lens' s a -> a -> s -> (a, s)
--   (<//~) :: Fractional a => Iso'  s a -> a -> s -> (a, s)
--   
(<//~) :: Fractional a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)

-- | Divide the target of a fractionally valued Lens into your
--   'Monad'\'s state and return the result.
--   
--   When you do not need the result of the division, (//=) is more
--   flexible.
--   
--   
--   (<//=) :: (MonadState s m, Fractional a) => Lens' s a -> a -> m a
--   (<//=) :: (MonadState s m, Fractional a) => Iso' s a -> a -> m a
--   
(<//=) :: (MonadState s m, Fractional a) => LensLike' ((,) a) s a -> a -> m a

-- | Raise the target(s) of a numerically valued Lens, Setter
--   or Traversal to a non-negative integral power.
--   
--   
--   >>> (1,3) & _2 ^~ 2
--   (1,9)
--   
--   
--   
--   (^~) :: (Num a, Integral e) => Setter' s a    -> e -> s -> s
--   (^~) :: (Num a, Integral e) => Iso' s a       -> e -> s -> s
--   (^~) :: (Num a, Integral e) => Lens' s a      -> e -> s -> s
--   (^~) :: (Num a, Integral e) => Traversal' s a -> e -> s -> s
--   
(^~) :: (Num a, Integral e) => ASetter s t a a -> e -> s -> t

-- | Raise the target(s) of a numerically valued Lens, Setter
--   or Traversal to a non-negative integral power.
--   
--   
--   (^=) ::  (MonadState s m, Num a, Integral e) => Setter' s a    -> e -> m ()
--   (^=) ::  (MonadState s m, Num a, Integral e) => Iso' s a       -> e -> m ()
--   (^=) ::  (MonadState s m, Num a, Integral e) => Lens' s a      -> e -> m ()
--   (^=) ::  (MonadState s m, Num a, Integral e) => Traversal' s a -> e -> m ()
--   
(^=) :: (MonadState s m, Num a, Integral e) => ASetter' s a -> e -> m ()

-- | Raise the target of a numerically valued Lens to a non-negative
--   Integral power and return the result.
--   
--   When you do not need the result of the division, (^~) is more
--   flexible.
--   
--   
--   (<^~) :: (Num a, Integral e) => Lens' s a -> e -> s -> (a, s)
--   (<^~) :: (Num a, Integral e) => Iso' s a -> e -> s -> (a, s)
--   
(<^~) :: (Num a, Integral e) => Overloading (->) q ((,) a) s t a a -> e -> q s (a, t)

-- | Raise the target of a numerically valued Lens into your
--   'Monad'\'s state to a non-negative Integral power and return
--   the result.
--   
--   When you do not need the result of the operation, (**=) is more
--   flexible.
--   
--   
--   (<^=) :: (MonadState s m, Num a, Integral e) => Lens' s a -> e -> m a
--   (<^=) :: (MonadState s m, Num a, Integral e) => Iso' s a -> e -> m a
--   
(<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m a

-- | Raise the target(s) of a fractionally valued Lens,
--   Setter or Traversal to an integral power.
--   
--   
--   >>> (1,2) & _2 ^^~ (-1)
--   (1,0.5)
--   
--   
--   
--   (^^~) :: (Fractional a, Integral e) => Setter' s a    -> e -> s -> s
--   (^^~) :: (Fractional a, Integral e) => Iso' s a       -> e -> s -> s
--   (^^~) :: (Fractional a, Integral e) => Lens' s a      -> e -> s -> s
--   (^^~) :: (Fractional a, Integral e) => Traversal' s a -> e -> s -> s
--   
(^^~) :: (Fractional a, Integral e) => ASetter s t a a -> e -> s -> t

-- | Raise the target(s) of a numerically valued Lens, Setter
--   or Traversal to an integral power.
--   
--   
--   (^^=) ::  (MonadState s m, Fractional a, Integral e) => Setter' s a    -> e -> m ()
--   (^^=) ::  (MonadState s m, Fractional a, Integral e) => Iso' s a       -> e -> m ()
--   (^^=) ::  (MonadState s m, Fractional a, Integral e) => Lens' s a      -> e -> m ()
--   (^^=) ::  (MonadState s m, Fractional a, Integral e) => Traversal' s a -> e -> m ()
--   
(^^=) :: (MonadState s m, Fractional a, Integral e) => ASetter' s a -> e -> m ()

-- | Raise the target of a fractionally valued Lens to an
--   Integral power and return the result.
--   
--   When you do not need the result of the division, (^^~) is more
--   flexible.
--   
--   
--   (<^^~) :: (Fractional a, Integral e) => Lens' s a -> e -> s -> (a, s)
--   (<^^~) :: (Fractional a, Integral e) => Iso' s a -> e -> s -> (a, s)
--   
(<^^~) :: (Fractional a, Integral e) => Overloading (->) q ((,) a) s t a a -> e -> q s (a, t)

-- | Raise the target of a fractionally valued Lens into your
--   'Monad'\'s state to an Integral power and return the result.
--   
--   When you do not need the result of the operation, (^^=) is more
--   flexible.
--   
--   
--   (<^^=) :: (MonadState s m, Fractional b, Integral e) => Lens' s a -> e -> m a
--   (<^^=) :: (MonadState s m, Fractional b, Integral e) => Iso' s a  -> e -> m a
--   
(<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m a

-- | Raise the target(s) of a floating-point valued Lens,
--   Setter or Traversal to an arbitrary power.
--   
--   
--   >>> (a,b) & _1 **~ c
--   (a**c,b)
--   
--   
--   
--   >>> (a,b) & both **~ c
--   (a**c,b**c)
--   
--   
--   
--   >>> _2 **~ 10 $ (3,2)
--   (3,1024.0)
--   
--   
--   
--   (**~) :: Floating a => Setter' s a    -> a -> s -> s
--   (**~) :: Floating a => Iso' s a       -> a -> s -> s
--   (**~) :: Floating a => Lens' s a      -> a -> s -> s
--   (**~) :: Floating a => Traversal' s a -> a -> s -> s
--   
(**~) :: Floating a => ASetter s t a a -> a -> s -> t

-- | Raise the target(s) of a numerically valued Lens, Setter
--   or Traversal to an arbitrary power
--   
--   
--   >>> execState (do _1 **= c; _2 **= d) (a,b)
--   (a**c,b**d)
--   
--   
--   
--   (**=) ::  (MonadState s m, Floating a) => Setter' s a    -> a -> m ()
--   (**=) ::  (MonadState s m, Floating a) => Iso' s a       -> a -> m ()
--   (**=) ::  (MonadState s m, Floating a) => Lens' s a      -> a -> m ()
--   (**=) ::  (MonadState s m, Floating a) => Traversal' s a -> a -> m ()
--   
(**=) :: (MonadState s m, Floating a) => ASetter' s a -> a -> m ()

-- | Raise the target of a floating-point valued Lens to an
--   arbitrary power and return the result.
--   
--   When you do not need the result of the division, (**~) is more
--   flexible.
--   
--   
--   (<**~) :: Floating a => Lens' s a -> a -> s -> (a, s)
--   (<**~) :: Floating a => Iso' s a  -> a -> s -> (a, s)
--   
(<**~) :: Floating a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)

-- | Raise the target of a floating-point valued Lens into your
--   'Monad'\'s state to an arbitrary power and return the result.
--   
--   When you do not need the result of the operation, (**=) is more
--   flexible.
--   
--   
--   (<**=) :: (MonadState s m, Floating a) => Lens' s a -> a -> m a
--   (<**=) :: (MonadState s m, Floating a) => Iso' s a -> a -> m a
--   
(<**=) :: (MonadState s m, Floating a) => LensLike' ((,) a) s a -> a -> m a

-- | Logically || the target(s) of a Bool-valued Lens
--   or Setter.
--   
--   
--   >>> both ||~ True $ (False,True)
--   (True,True)
--   
--   
--   
--   >>> both ||~ False $ (False,True)
--   (False,True)
--   
--   
--   
--   (||~) :: Setter' s Bool    -> Bool -> s -> s
--   (||~) :: Iso' s Bool       -> Bool -> s -> s
--   (||~) :: Lens' s Bool      -> Bool -> s -> s
--   (||~) :: Traversal' s Bool -> Bool -> s -> s
--   
(||~) :: ASetter s t Bool Bool -> Bool -> s -> t

-- | Modify the target(s) of a Lens', 'Iso, Setter or
--   Traversal by taking their logical || with a value.
--   
--   
--   >>> execState (do _1 ||= True; _2 ||= False; _3 ||= True; _4 ||= False) (True,True,False,False)
--   (True,True,True,False)
--   
--   
--   
--   (||=) :: MonadState s m => Setter' s Bool    -> Bool -> m ()
--   (||=) :: MonadState s m => Iso' s Bool       -> Bool -> m ()
--   (||=) :: MonadState s m => Lens' s Bool      -> Bool -> m ()
--   (||=) :: MonadState s m => Traversal' s Bool -> Bool -> m ()
--   
(||=) :: MonadState s m => ASetter' s Bool -> Bool -> m ()

-- | Logically || a Boolean valued Lens and return the
--   result.
--   
--   When you do not need the result of the operation, (||~) is more
--   flexible.
--   
--   
--   (<||~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
--   (<||~) :: Iso' s Bool  -> Bool -> s -> (Bool, s)
--   
(<||~) :: Overloading (->) q ((,) Bool) s t Bool Bool -> Bool -> q s (Bool, t)

-- | Logically || a Boolean valued Lens into your 'Monad'\'s
--   state and return the result.
--   
--   When you do not need the result of the operation, (||=) is more
--   flexible.
--   
--   
--   (<||=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
--   (<||=) :: MonadState s m => Iso' s Bool  -> Bool -> m Bool
--   
(<||=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool

-- | Logically && the target(s) of a Bool-valued
--   Lens or Setter.
--   
--   
--   >>> both &&~ True $ (False, True)
--   (False,True)
--   
--   
--   
--   >>> both &&~ False $ (False, True)
--   (False,False)
--   
--   
--   
--   (&&~) :: Setter' s Bool    -> Bool -> s -> s
--   (&&~) :: Iso' s Bool       -> Bool -> s -> s
--   (&&~) :: Lens' s Bool      -> Bool -> s -> s
--   (&&~) :: Traversal' s Bool -> Bool -> s -> s
--   
(&&~) :: ASetter s t Bool Bool -> Bool -> s -> t

-- | Modify the target(s) of a Lens', Iso, Setter or
--   Traversal by taking their logical && with a
--   value.
--   
--   
--   >>> execState (do _1 &&= True; _2 &&= False; _3 &&= True; _4 &&= False) (True,True,False,False)
--   (True,False,False,False)
--   
--   
--   
--   (&&=) :: MonadState s m => Setter' s Bool    -> Bool -> m ()
--   (&&=) :: MonadState s m => Iso' s Bool       -> Bool -> m ()
--   (&&=) :: MonadState s m => Lens' s Bool      -> Bool -> m ()
--   (&&=) :: MonadState s m => Traversal' s Bool -> Bool -> m ()
--   
(&&=) :: MonadState s m => ASetter' s Bool -> Bool -> m ()

-- | Logically && a Boolean valued Lens and return
--   the result.
--   
--   When you do not need the result of the operation, (&&~)
--   is more flexible.
--   
--   
--   (<&&~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
--   (<&&~) :: Iso' s Bool  -> Bool -> s -> (Bool, s)
--   
(<&&~) :: Overloading (->) q ((,) Bool) s t Bool Bool -> Bool -> q s (Bool, t)

-- | Logically && a Boolean valued Lens into your
--   'Monad'\'s state and return the result.
--   
--   When you do not need the result of the operation, (&&=)
--   is more flexible.
--   
--   
--   (<&&=) :: MonadState s m => Lens' s Bool -> Bool -> m Bool
--   (<&&=) :: MonadState s m => Iso' s Bool  -> Bool -> m Bool
--   
(<&&=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool

-- | Modify the target of a monoidally valued by mappending another
--   value.
--   
--   
--   >>> (Sum a,b) & _1 <>~ Sum c
--   (Sum {getSum = a + c},b)
--   
--   
--   
--   >>> (Sum a,Sum b) & both <>~ Sum c
--   (Sum {getSum = a + c},Sum {getSum = b + c})
--   
--   
--   
--   >>> both <>~ "!!!" $ ("hello","world")
--   ("hello!!!","world!!!")
--   
--   
--   
--   (<>~) :: Monoid a => Setter s t a a    -> a -> s -> t
--   (<>~) :: Monoid a => Iso s t a a       -> a -> s -> t
--   (<>~) :: Monoid a => Lens s t a a      -> a -> s -> t
--   (<>~) :: Monoid a => Traversal s t a a -> a -> s -> t
--   
(<>~) :: Monoid a => ASetter s t a a -> a -> s -> t

-- | Modify the target(s) of a Lens', Iso, Setter or
--   Traversal by mappending a value.
--   
--   
--   >>> execState (do _1 <>= Sum c; _2 <>= Product d) (Sum a,Product b)
--   (Sum {getSum = a + c},Product {getProduct = b * d})
--   
--   
--   
--   >>> execState (both <>= "!!!") ("hello","world")
--   ("hello!!!","world!!!")
--   
--   
--   
--   (<>=) :: (MonadState s m, Monoid a) => Setter' s a -> a -> m ()
--   (<>=) :: (MonadState s m, Monoid a) => Iso' s a -> a -> m ()
--   (<>=) :: (MonadState s m, Monoid a) => Lens' s a -> a -> m ()
--   (<>=) :: (MonadState s m, Monoid a) => Traversal' s a -> a -> m ()
--   
(<>=) :: (MonadState s m, Monoid a) => ASetter' s a -> a -> m ()

-- | mappend a monoidal value onto the end of the target of a
--   Lens and return the result.
--   
--   When you do not need the result of the operation, (<>~)
--   is more flexible.
(<<>~) :: Monoid m => Overloading (->) q ((,) m) s t m m -> m -> q s (m, t)

-- | mappend a monoidal value onto the end of the target of a
--   Lens into your 'Monad'\'s state and return the result.
--   
--   When you do not need the result of the operation, (<>=)
--   is more flexible.
(<<>=) :: (MonadState s m, Monoid r) => LensLike' ((,) r) s r -> r -> m r

-- | Composition of Indexed functions.
--   
--   Mnemonically, the < and > points to the fact
--   that we want to preserve the indices.
(<.>) :: Indexable (i, j) p => (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> p a b -> r

-- | Compose an Indexed function with a non-indexed function.
--   
--   Mnemonically, the < points to the indexing we want to
--   preserve.
(<.) :: Indexable i p => (Indexed i s t -> r) -> ((a -> b) -> s -> t) -> p a b -> r

-- | Compose a non-indexed function with an Indexed function.
--   
--   Mnemonically, the > points to the indexing we want to
--   preserve.
--   
--   This is the same as (.).
--   
--   f . g (and f .> g) gives you the
--   index of g unless g is index-preserving, like a
--   Prism, Iso or Equality, in which case it'll pass
--   through the index of f.
(.>) :: (st -> r) -> (kab -> st) -> kab -> r

-- | Run a monadic action, and set all of the targets of a Lens,
--   Setter or Traversal to its result.
--   
--   
--   (<~) :: MonadState s m => Iso s s a b       -> m b -> m ()
--   (<~) :: MonadState s m => Lens s s a b      -> m b -> m ()
--   (<~) :: MonadState s m => Traversal s s a b -> m b -> m ()
--   (<~) :: MonadState s m => Setter s s a b    -> m b -> m ()
--   
--   
--   As a reasonable mnemonic, this lets you store the result of a monadic
--   action in a Lens rather than in a local variable.
--   
--   
--   do foo <- bar
--      ...
--   
--   
--   will store the result in a variable, while
--   
--   
--   do foo <~ bar
--      ...
--   
--   
--   will store the result in a Lens, Setter, or
--   Traversal.
(<~) :: MonadState s m => ASetter s s a b -> m b -> m ()

-- | Run a monadic action, and set the target of Lens to its result.
--   
--   
--   (<<~) :: MonadState s m => Iso s s a b   -> m b -> m b
--   (<<~) :: MonadState s m => Lens s s a b  -> m b -> m b
--   
--   
--   NB: This is limited to taking an actual Lens than admitting a
--   Traversal because there are potential loss of state issues
--   otherwise.
(<<~) :: MonadState s m => ALens s s a b -> m b -> m b

-- | This type family represents a Zipper with the p
--   variable abstracting over the position and the index, in terms of
--   :@. You can visually see it in type signatures as:
--   
--   
--   h :> (a :@ i) = Zipper h i a
--   

-- | Many zippers are indexed by Int keys. This type alias is convenient
--   for reducing syntactic noise for talking about these boring indices.
type (:>>) h a = Zipper h Int a

-- | cons an element onto a container.
--   
--   This is an infix alias for cons.
(<|) :: Cons Reviewed Identity s s a a => a -> s -> s

-- | snoc an element onto the end of a container.
--   
--   This is an infix alias for snoc.
(|>) :: Snoc Reviewed Identity s s a a => s -> a -> s

-- | Smart and naïve generic traversals given Data instances.
--   
--   template, uniplate, and biplate each build up
--   information about what types can be contained within another type to
--   speed up Traversal.
module Data.Data.Lens

-- | Find every occurrence of a given type a recursively that
--   doesn't require passing through something of type a using
--   Data, while avoiding traversal of areas that cannot contain a
--   value of type a.
--   
--   This is uniplate with a more liberal signature.
template :: (Data s, Typeable a) => Traversal' s a

-- | Naïve Traversal using Data. This does not attempt to
--   optimize the traversal.
--   
--   This is primarily useful when the children are immediately obvious,
--   and for benchmarking.
tinplate :: (Data s, Typeable a) => Traversal' s a

-- | Find descendants of type a non-transitively, while avoiding
--   computation of areas that cannot contain values of type a
--   using Data.
--   
--   uniplate is a useful default definition for plate
uniplate :: Data a => Traversal' a a

-- | biplate performs like template, except when s ~
--   a, it returns itself and nothing else.
biplate :: (Data s, Typeable a) => Traversal' s a

-- | This automatically constructs a Traversal' from an function.
--   
--   
--   >>> (2,4) & upon fst *~ 5
--   (10,4)
--   
--   
--   There are however, caveats on how this function can be used!
--   
--   First, the user supplied function must access only one field of the
--   specified type. That is to say the target must be a single element
--   that would be visited by holesOnOf template
--   uniplate
--   
--   Note: this even permits a number of functions to be used directly.
--   
--   
--   >>> [1,2,3,4] & upon head .~ 0
--   [0,2,3,4]
--   
--   
--   
--   >>> [1,2,3,4] & upon last .~ 5
--   [1,2,3,5]
--   
--   
--   
--   >>> [1,2,3,4] ^? upon tail
--   Just [2,3,4]
--   
--   
--   
--   >>> "" ^? upon tail
--   Nothing
--   
--   
--   Accessing parents on the way down to children is okay:
--   
--   
--   >>> [1,2,3,4] & upon (tail.tail) .~ [10,20]
--   [1,2,10,20]
--   
--   
--   Second, the structure must not contain strict or unboxed fields of the
--   same type that will be visited by Data
--   
--   
--   upon :: (Data s, Data a) => (s -> a) -> IndexedTraversal' [Int] s a
--   
upon :: (Indexable [Int] p, Applicative f, Data s, Data a) => (s -> a) -> p a (f a) -> s -> f s

-- | The design of onceUpon' doesn't allow it to search inside of
--   values of type a for other values of type a.
--   upon' provides this additional recursion.
--   
--   Like onceUpon', upon' trusts the user supplied function
--   more than upon using it directly as the accessor. This enables
--   reading from the resulting Lens to be considerably faster at
--   the risk of generating an illegal lens.
--   
--   
--   >>> upon' (tail.tail) .~ [10,20] $ [1,2,3,4]
--   [1,2,10,20]
--   
upon' :: (Data s, Data a) => (s -> a) -> IndexedLens' [Int] s a

-- | This automatically constructs a Traversal' from a field
--   accessor.
--   
--   The index of the Traversal can be used as an offset into
--   elementOf (indexing template) or into
--   the list returned by holesOf template.
--   
--   The design of onceUpon doesn't allow it to search inside of
--   values of type a for other values of type a.
--   upon provides this additional recursion, but at the expense of
--   performance.
--   
--   
--   >>> onceUpon (tail.tail) .~ [10,20] $ [1,2,3,4] -- BAD
--   [1,10,20]
--   
--   
--   
--   >>> upon (tail.tail) .~ [10,20] $ [1,2,3,4] -- GOOD
--   [1,2,10,20]
--   
--   
--   When in doubt, use upon instead.
onceUpon :: (Data s, Typeable a) => (s -> a) -> IndexedTraversal' Int s a

-- | This more trusting version of upon uses your function directly
--   as the getter for a Lens.
--   
--   This means that reading from upon' is considerably faster than
--   upon.
--   
--   However, you pay for faster access in two ways:
--   
--   
--   
- When passed an illegal field accessor, upon' will give you
--   a Lens that quietly violates the laws, unlike upon,
--   which will give you a legal Traversal that avoids modifying the
--   target.
--   
- Modifying with the lens is slightly slower, since it has to go
--   back and calculate the index after the fact.
--   
--   
--   When given a legal field accessor, the index of the Lens can be
--   used as an offset into elementOf (indexed
--   template) or into the list returned by holesOf
--   template.
--   
--   When in doubt, use upon' instead.
onceUpon' :: (Data s, Typeable a) => (s -> a) -> IndexedLens' Int s a

-- | A generic applicative transformation that maps over the immediate
--   subterms.
--   
--   gtraverse is to traverse what gmapM is to
--   mapM
--   
--   This really belongs in Data.Data.
gtraverse :: (Applicative f, Data a) => (forall d. Data d => d -> f d) -> a -> f a
instance Typeable1 FieldException
instance Eq a => Eq (Answer a)
instance Ord a => Ord (Answer a)
instance Show a => Show (Answer a)
instance Read a => Read (Answer a)
instance Functor Oracle
instance Functor Answer
instance Typeable a => Exception (FieldException a)
instance Show (FieldException a)

-- | The name "plate" stems originally from "boilerplate", which was the
--   term used by the "Scrap Your Boilerplate" papers, and later inherited
--   by Neil Mitchell's "Uniplate".
--   
--   http://community.haskell.org/~ndm/uniplate/
--   
--   The combinators in here are designed to be compatible with and subsume
--   the uniplate API with the notion of a Traversal
--   replacing a uniplate or biplate.
--   
--   By implementing these combinators in terms of plate instead of
--   uniplate additional type safety is gained, as the user is no
--   longer responsible for maintaining invariants such as the number of
--   children they received.
--   
--   Note: The Biplate is deliberately excluded from the
--   API here, with the intention that you replace them with either
--   explicit traversals, or by using the On variants of the
--   combinators below with biplate from Data.Data.Lens. As
--   a design, it forced the user into too many situations where they had
--   to choose between correctness and ease of use, and it was brittle in
--   the face of competing imports.
--   
--   The sensible use of these combinators makes some simple assumptions.
--   Notably, any of the On combinators are expecting a
--   Traversal, Setter or Fold to play the role of the
--   biplate combinator, and so when the types of the contents and
--   the container match, they should be the id Traversal,
--   Setter or Fold.
--   
--   It is often beneficial to use the combinators in this module with the
--   combinators from Data.Data.Lens or GHC.Generics.Lens
--   to make it easier to automatically derive definitions for
--   plate, or to derive custom traversals.
module Control.Lens.Plated

-- | A Plated type is one where we know how to extract its immediate
--   self-similar children.
--   
--   Example 1:
--   
--   
--   import Control.Applicative
--   import Control.Lens
--   import Control.Lens.Plated
--   import Data.Data
--   import Data.Data.Lens (uniplate)
--   
--   
--   
--   data Expr
--     = Val Int
--     | Neg Expr
--     | Add Expr Expr
--     deriving (Eq,Ord,Show,Read,Data,Typeable)
--   
--   
--   
--   instance Plated Expr where
--     plate f (Neg e) = Neg <$> f e
--     plate f (Add a b) = Add <$> f a <*> f b
--     plate _ a = pure a
--   
--   
--   or
--   
--   
--   instance Plated Expr where
--     plate = uniplate
--   
--   
--   Example 2:
--   
--   
--   import Control.Applicative
--   import Control.Lens
--   import Control.Lens.Plated
--   import Data.Data
--   import Data.Data.Lens (uniplate)
--   
--   
--   
--   data Tree a
--     = Bin (Tree a) (Tree a)
--     | Tip a
--     deriving (Eq,Ord,Show,Read,Data,Typeable)
--   
--   
--   
--   instance Plated (Tree a) where
--     plate f (Bin l r) = Bin <$> f l <*> f r
--     plate _ t = pure t
--   
--   
--   or
--   
--   
--   instance Data a => Plated (Tree a) where
--     plate = uniplate
--   
--   
--   Note the big distinction between these two implementations.
--   
--   The former will only treat children directly in this tree as
--   descendents, the latter will treat trees contained in the values under
--   the tips also as descendants!
--   
--   When in doubt, pick a Traversal and just use the various
--   ...Of combinators rather than pollute Plated with
--   orphan instances!
--   
--   If you want to find something unplated and non-recursive with
--   biplate use the ...OnOf variant with ignored,
--   though those usecases are much better served in most cases by using
--   the existing Lens combinators! e.g.
--   
--   
--   toListOf biplate ≡ universeOnOf biplate ignored
--   
--   
--   This same ability to explicitly pass the Traversal in question
--   is why there is no analogue to uniplate's Biplate.
--   
--   Moreover, since we can allow custom traversals, we implement
--   reasonable defaults for polymorphic data types, that only
--   traverse into themselves, and not their polymorphic
--   arguments.
class Plated a where plate = uniplate
plate :: Plated a => Traversal' a a

-- | Extract the immediate descendants of a Plated container.
--   
--   
--   children ≡ toListOf plate
--   
children :: Plated a => a -> [a]

-- | Rewrite by applying a rule everywhere you can. Ensures that the rule
--   cannot be applied anywhere in the result:
--   
--   
--   propRewrite r x = all (isNothing . r) (universe (rewrite r x))
--   
--   
--   Usually transform is more appropriate, but rewrite can
--   give better compositionality. Given two single transformations
--   f and g, you can construct a -> f a
--   mplus g a which performs both rewrites until a fixed
--   point.
rewrite :: Plated a => (a -> Maybe a) -> a -> a

-- | Rewrite by applying a rule everywhere you can. Ensures that the rule
--   cannot be applied anywhere in the result:
--   
--   
--   propRewriteOf l r x = all (isNothing . r) (universeOf l (rewriteOf l r x))
--   
--   
--   Usually transformOf is more appropriate, but rewriteOf
--   can give better compositionality. Given two single transformations
--   f and g, you can construct a -> f a
--   mplus g a which performs both rewrites until a fixed
--   point.
--   
--   
--   rewriteOf :: Iso' a a       -> (a -> Maybe a) -> a -> a
--   rewriteOf :: Lens' a a      -> (a -> Maybe a) -> a -> a
--   rewriteOf :: Traversal' a a -> (a -> Maybe a) -> a -> a
--   rewriteOf :: Setter' a a    -> (a -> Maybe a) -> a -> a
--   
rewriteOf :: ASetter' a a -> (a -> Maybe a) -> a -> a

-- | Rewrite recursively over part of a larger structure.
--   
--   
--   rewriteOn :: Plated a => Iso' s a       -> (a -> Maybe a) -> s -> s
--   rewriteOn :: Plated a => Lens' s a      -> (a -> Maybe a) -> s -> s
--   rewriteOn :: Plated a => Traversal' s a -> (a -> Maybe a) -> s -> s
--   rewriteOn :: Plated a => ASetter' s a   -> (a -> Maybe a) -> s -> s
--   
rewriteOn :: Plated a => ASetter s t a a -> (a -> Maybe a) -> s -> t

-- | Rewrite recursively over part of a larger structure using a specified
--   Setter.
--   
--   
--   rewriteOnOf :: Plated a => Iso' s a       -> Iso' a a       -> (a -> Maybe a) -> s -> s
--   rewriteOnOf :: Plated a => Lens' s a      -> Lens' a a      -> (a -> Maybe a) -> s -> s
--   rewriteOnOf :: Plated a => Traversal' s a -> Traversal' a a -> (a -> Maybe a) -> s -> s
--   rewriteOnOf :: Plated a => Setter' s a    -> Setter' a a    -> (a -> Maybe a) -> s -> s
--   
rewriteOnOf :: ASetter s t a a -> ASetter' a a -> (a -> Maybe a) -> s -> t

-- | Rewrite by applying a monadic rule everywhere you can. Ensures that
--   the rule cannot be applied anywhere in the result.
rewriteM :: (Monad m, Plated a) => (a -> m (Maybe a)) -> a -> m a

-- | Rewrite by applying a monadic rule everywhere you recursing with a
--   user-specified Traversal. Ensures that the rule cannot be
--   applied anywhere in the result.
rewriteMOf :: Monad m => LensLike' (WrappedMonad m) a a -> (a -> m (Maybe a)) -> a -> m a

-- | Rewrite by applying a monadic rule everywhere inside of a structure
--   located by a user-specified Traversal. Ensures that the rule
--   cannot be applied anywhere in the result.
rewriteMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m (Maybe a)) -> s -> m t

-- | Rewrite by applying a monadic rule everywhere inside of a structure
--   located by a user-specified Traversal, using a user-specified
--   Traversal for recursion. Ensures that the rule cannot be
--   applied anywhere in the result.
rewriteMOnOf :: Monad m => LensLike (WrappedMonad m) s t a a -> LensLike' (WrappedMonad m) a a -> (a -> m (Maybe a)) -> s -> m t

-- | Retrieve all of the transitive descendants of a Plated
--   container, including itself.
universe :: Plated a => a -> [a]

-- | Given a Fold that knows how to locate immediate children,
--   retrieve all of the transitive descendants of a node, including
--   itself.
--   
--   
--   universeOf :: Fold a a -> a -> [a]
--   
universeOf :: Getting [a] a a -> a -> [a]

-- | Given a Fold that knows how to find Plated parts of a
--   container retrieve them and all of their descendants, recursively.
universeOn :: Plated a => Getting [a] s a -> s -> [a]

-- | Given a Fold that knows how to locate immediate children,
--   retrieve all of the transitive descendants of a node, including itself
--   that lie in a region indicated by another Fold.
--   
--   
--   toListOf l ≡ universeOnOf l ignored
--   
universeOnOf :: Getting [a] s a -> Getting [a] a a -> s -> [a]

-- | Transform every element in the tree, in a bottom-up manner.
--   
--   For example, replacing negative literals with literals:
--   
--   
--   negLits = transform $ \x -> case x of
--     Neg (Lit i) -> Lit (negate i)
--     _           -> x
--   
transform :: Plated a => (a -> a) -> a -> a

-- | Transform every element by recursively applying a given Setter
--   in a bottom-up manner.
--   
--   
--   transformOf :: Traversal' a a -> (a -> a) -> a -> a
--   transformOf :: Setter' a a    -> (a -> a) -> a -> a
--   
transformOf :: ASetter' a a -> (a -> a) -> a -> a

-- | Transform every element in the tree in a bottom-up manner over a
--   region indicated by a Setter.
--   
--   
--   transformOn :: Plated a => Traversal' s a -> (a -> a) -> s -> s
--   transformOn :: Plated a => Setter' s a    -> (a -> a) -> s -> s
--   
transformOn :: Plated a => ASetter s t a a -> (a -> a) -> s -> t

-- | Transform every element in a region indicated by a Setter by
--   recursively applying another Setter in a bottom-up manner.
--   
--   
--   transformOnOf :: Setter' s a -> Traversal' a a -> (a -> a) -> s -> s
--   transformOnOf :: Setter' s a -> Setter' a a    -> (a -> a) -> s -> s
--   
transformOnOf :: ASetter s t a a -> ASetter' a a -> (a -> a) -> s -> t

-- | Transform every element in the tree, in a bottom-up manner,
--   monadically.
transformM :: (Monad m, Plated a) => (a -> m a) -> a -> m a

-- | Transform every element in a tree using a user supplied
--   Traversal in a bottom-up manner with a monadic effect.
--   
--   
--   transformMOf :: Monad m => Traversal' a a -> (a -> m a) -> a -> m a
--   
transformMOf :: Monad m => LensLike' (WrappedMonad m) a a -> (a -> m a) -> a -> m a

-- | Transform every element in the tree in a region indicated by a
--   supplied Traversal, in a bottom-up manner, monadically.
--   
--   
--   transformMOn :: (Monad m, Plated a) => Traversal' s a -> (a -> m a) -> s -> m s
--   
transformMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m a) -> s -> m t

-- | Transform every element in a tree that lies in a region indicated by a
--   supplied Traversal, walking with a user supplied
--   Traversal in a bottom-up manner with a monadic effect.
--   
--   
--   transformMOnOf :: Monad m => Traversal' s a -> Traversal' a a -> (a -> m a) -> s -> m s
--   
transformMOnOf :: Monad m => LensLike (WrappedMonad m) s t a a -> LensLike' (WrappedMonad m) a a -> (a -> m a) -> s -> m t

-- | Return a list of all of the editable contexts for every location in
--   the structure, recursively.
--   
--   
--   propUniverse x = universe x == map pos (contexts x)
--   propId x = all (== x) [extract w | w <- contexts x]
--   
--   
--   
--   contexts ≡ contextsOf plate
--   
contexts :: Plated a => a -> [Context a a a]

-- | Return a list of all of the editable contexts for every location in
--   the structure, recursively, using a user-specified Traversal to
--   walk each layer.
--   
--   
--   propUniverse l x = universeOf l x == map pos (contextsOf l x)
--   propId l x = all (== x) [extract w | w <- contextsOf l x]
--   
--   
--   
--   contextsOf :: Traversal' a a -> a -> [Context a a a]
--   
contextsOf :: ATraversal' a a -> a -> [Context a a a]

-- | Return a list of all of the editable contexts for every location in
--   the structure in an areas indicated by a user supplied
--   Traversal, recursively using plate.
--   
--   
--   contextsOn b ≡ contextsOnOf b plate
--   
--   
--   
--   contextsOn :: Plated a => Traversal' s a -> s -> [Context a a s]
--   
contextsOn :: Plated a => ATraversal s t a a -> s -> [Context a a t]

-- | Return a list of all of the editable contexts for every location in
--   the structure in an areas indicated by a user supplied
--   Traversal, recursively using another user-supplied
--   Traversal to walk each layer.
--   
--   
--   contextsOnOf :: Traversal' s a -> Traversal' a a -> s -> [Context a a s]
--   
contextsOnOf :: ATraversal s t a a -> ATraversal' a a -> s -> [Context a a t]

-- | The one-level version of context. This extracts a list of the
--   immediate children as editable contexts.
--   
--   Given a context you can use pos to see the values, peek
--   at what the structure would be like with an edited result, or simply
--   extract the original structure.
--   
--   
--   propChildren x = children l x == map pos (holes l x)
--   propId x = all (== x) [extract w | w <- holes l x]
--   
--   
--   
--   holes = holesOf plate
--   
holes :: Plated a => a -> [Pretext (->) a a a]

-- | An alias for holesOf, provided for consistency with the other
--   combinators.
--   
--   
--   holesOn ≡ holesOf
--   
--   
--   
--   holesOn :: Iso' s a                -> s -> [Pretext (->) a a s]
--   holesOn :: Lens' s a               -> s -> [Pretext (->) a a s]
--   holesOn :: Traversal' s a          -> s -> [Pretext (->) a a s]
--   holesOn :: IndexedLens' i s a      -> s -> [Pretext (Indexed i) a a s]
--   holesOn :: IndexedTraversal' i s a -> s -> [Pretext (Indexed i) a a s]
--   
holesOn :: Conjoined p => Overloading p (->) (Bazaar p a a) s t a a -> s -> [Pretext p a a t]

-- | Extract one level of holes from a container in a region
--   specified by one Traversal, using another.
--   
--   
--   holesOnOf b l ≡ holesOf (b . l)
--   
--   
--   
--   holesOnOf :: Iso' s a       -> Iso' a a                -> s -> [Pretext (->) a a s]
--   holesOnOf :: Lens' s a      -> Lens' a a               -> s -> [Pretext (->) a a s]
--   holesOnOf :: Traversal' s a -> Traversal' a a          -> s -> [Pretext (->) a a s]
--   holesOnOf :: Lens' s a      -> IndexedLens' i a a      -> s -> [Pretext (Indexed i) a a s]
--   holesOnOf :: Traversal' s a -> IndexedTraversal' i a a -> s -> [Pretext (Indexed i) a a s]
--   
holesOnOf :: Conjoined p => LensLike (Bazaar p r r) s t a b -> Overloading p (->) (Bazaar p r r) a b r r -> s -> [Pretext p r r t]

-- | Perform a fold-like computation on each value, technically a
--   paramorphism.
--   
--   
--   para ≡ paraOf plate
--   
para :: Plated a => (a -> [r] -> r) -> a -> r

-- | Perform a fold-like computation on each value, technically a
--   paramorphism.
--   
--   
--   paraOf :: Fold a a -> (a -> [r] -> r) -> a -> r
--   
paraOf :: Getting (Endo [a]) a a -> (a -> [r] -> r) -> a -> r

-- | Fold the immediate children of a Plated container.
--   
--   
--   composOpFold z c f = foldrOf plate (c . f) z
--   
composOpFold :: Plated a => b -> (b -> b -> b) -> (a -> b) -> a -> b

-- | The original uniplate combinator, implemented in terms of
--   Plated as a Lens.
--   
--   
--   parts ≡ partsOf plate
--   
--   
--   The resulting Lens is safer to use as it ignores
--   'over-application' and deals gracefully with under-application, but it
--   is only a proper Lens if you don't change the list
--   length!
parts :: Plated a => Lens' a [a]
instance Plated Pat
instance Plated Stmt
instance Plated Type
instance Plated Con
instance Plated Dec
instance Plated Exp
instance Plated (Tree a)
instance Plated [a]

module Control.Lens.At

-- | At provides a Lens that can be used to read, write or
--   delete the value associated with a key in a Map-like container
--   on an ad hoc basis.
--   
--   An instance of At should satisfy:
--   
--   
--   ix k ≡ at k <. traverse
--   
class At m
at :: At m => Index m -> IndexedLens' (Index m) m (Maybe (IxValue m))
sans :: At m => Index m -> m -> m

-- | This provides a common notion of a value at an index that is shared by
--   both Ixed and At.

-- | This simple IndexedTraversal lets you traverse the value
--   at a given key in a Map or element at an ordinal position in a
--   list or Seq.
class Functor f => Ixed f m where ix = ixAt
ix :: Ixed f m => Index m -> IndexedLensLike' (Index m) f m (IxValue m)

-- | A definition of ix for types with an At instance. This
--   is the default if you don't specify a definition for ix.
ixAt :: (Applicative f, At m) => Index m -> IndexedLensLike' (Index m) f m (IxValue m)

-- | A definition of ix for types with an Each instance.
ixEach :: (Applicative f, Eq (Index m), Each f m m (IxValue m) (IxValue m)) => Index m -> IndexedLensLike' (Index m) f m (IxValue m)

-- | This class provides a simple IndexedFold (or
--   IndexedTraversal) that lets you view (and modify) information
--   about whether or not a container contains a given Index.
class Functor f => Contains f m where contains = containsAt
contains :: Contains f m => Index m -> IndexedLensLike' (Index m) f m Bool

-- | A definition of contains for types with an Ix instance.
containsIx :: (Contravariant f, Functor f, Ixed (Accessor Any) m) => Index m -> IndexedLensLike' (Index m) f m Bool

-- | A definition of ix for types with an At instance. This
--   is the default if you don't specify a definition for contains
--   and you are on GHC >= 7.0.2
containsAt :: (Contravariant f, Functor f, At m) => Index m -> IndexedLensLike' (Index m) f m Bool

-- | Construct a contains check based on some notion of
--   length for the container.
containsLength :: (Ord i, Num i) => (s -> i) -> i -> IndexedGetter i s Bool

-- | Construct a contains check for a fixed number of elements.
containsN :: Int -> Int -> IndexedGetter Int s Bool

-- | Construct a contains check that uses an arbitrary test.
containsTest :: (i -> s -> Bool) -> i -> IndexedGetter i s Bool

-- | Construct a contains check that uses an arbitrary lookup
--   function.
containsLookup :: (i -> s -> Maybe a) -> i -> IndexedGetter i s Bool

-- | Deprecated aliases for ix.

-- | Deprecated: use ix. This function will be removed after GHC
--   7.8 is released. 
_at :: Ixed f m => Index m -> IndexedLensLike' (Index m) f m (IxValue m)

-- | Deprecated aliases for ix.

-- | Deprecated: use ix. This function will be removed after GHC
--   7.8 is released. 
resultAt :: Ixed f m => Index m -> IndexedLensLike' (Index m) f m (IxValue m)
instance (Eq k, Hashable k) => At (HashMap k a)
instance Ord k => At (Map k a)
instance At (IntMap a)
instance (Applicative f, a ~ b, b ~ c, c ~ d, d ~ e, e ~ f', f' ~ g, g ~ h, h ~ i) => Ixed f (a, b, c, d, e, f', g, h, i)
instance (Applicative f, a ~ b, b ~ c, c ~ d, d ~ e, e ~ f', f' ~ g, g ~ h) => Ixed f (a, b, c, d, e, f', g, h)
instance (Applicative f, a ~ b, b ~ c, c ~ d, d ~ e, e ~ f', f' ~ g) => Ixed f (a, b, c, d, e, f', g)
instance (Applicative f, a ~ b, b ~ c, c ~ d, d ~ e, e ~ f') => Ixed f (a, b, c, d, e, f')
instance (Applicative f, a ~ b, b ~ c, c ~ d, d ~ e) => Ixed f (a, b, c, d, e)
instance (Applicative f, a ~ b, b ~ c, c ~ d) => Ixed f (a, b, c, d)
instance (Applicative f, a ~ b, b ~ c) => Ixed f (a, b, c)
instance (Applicative f, a ~ b) => Ixed f (a, b)
instance Applicative f => Ixed f (Complex a)
instance (Functor f, Eq k) => Ixed f (k -> a)
instance Applicative f => Ixed f ByteString
instance Applicative f => Ixed f ByteString
instance Applicative f => Ixed f Text
instance Applicative f => Ixed f Text
instance (Applicative f, Unbox a) => Ixed f (Vector a)
instance (Applicative f, Storable a) => Ixed f (Vector a)
instance (Applicative f, Prim a) => Ixed f (Vector a)
instance Applicative f => Ixed f (Vector a)
instance (Applicative f, IArray UArray e, Ix i) => Ixed f (UArray i e)
instance (Applicative f, Ix i) => Ixed f (Array i e)
instance (Applicative f, Eq k, Hashable k) => Ixed f (HashMap k a)
instance (Applicative f, Ord k) => Ixed f (Map k a)
instance Applicative f => Ixed f (IntMap a)
instance Applicative f => Ixed f (Seq a)
instance Applicative f => Ixed f (Tree a)
instance Functor f => Ixed f (Identity a)
instance Applicative f => Ixed f [a]
instance (Contravariant f, Functor f) => Contains f ByteString
instance (Contravariant f, Functor f) => Contains f ByteString
instance (Contravariant f, Functor f) => Contains f Text
instance (Contravariant f, Functor f) => Contains f Text
instance (Contravariant f, Functor f, Unbox a) => Contains f (Vector a)
instance (Contravariant f, Functor f, Storable a) => Contains f (Vector a)
instance (Contravariant f, Functor f, Prim a) => Contains f (Vector a)
instance (Contravariant f, Functor f) => Contains f (Vector a)
instance (Contravariant f, Functor f, IArray UArray e, Ix i) => Contains f (UArray i e)
instance (Contravariant f, Functor f, Ix i) => Contains f (Array i e)
instance (Contravariant f, Functor f, Eq k, Hashable k) => Contains f (HashMap k a)
instance (Contravariant f, Functor f, Ord k) => Contains f (Map k a)
instance (Contravariant k, Functor k) => Contains k (IntMap a)
instance (Contravariant k, Functor k) => Contains k (a, b, c, d, e, f, g, h, i)
instance (Contravariant k, Functor k) => Contains k (a, b, c, d, e, f, g, h)
instance (Contravariant k, Functor k) => Contains k (a, b, c, d, e, f, g)
instance (Contravariant k, Functor k) => Contains k (a, b, c, d, e, f)
instance (Contravariant k, Functor k) => Contains k (a, b, c, d, e)
instance (Contravariant k, Functor k) => Contains k (a, b, c, d)
instance (Contravariant k, Functor k) => Contains k (a, b, c)
instance (Contravariant k, Functor k) => Contains k (a, b)
instance (Contravariant k, Functor k) => Contains k (Identity a)
instance (Contravariant f, Functor f) => Contains f (Tree a)
instance (Contravariant f, Functor f) => Contains f (Complex a)
instance (Contravariant f, Functor f) => Contains f (Seq a)
instance (Contravariant f, Functor f) => Contains f [a]
instance (Functor f, Eq a, Hashable a) => Contains f (HashSet a)
instance (Functor f, Ord a) => Contains f (Set a)
instance Functor f => Contains f IntSet
instance (Functor f, Contravariant f) => Contains f (e -> a)

-- | Lenses and Traversals for working with Template Haskell
module Language.Haskell.TH.Lens

-- | Has a Name
class HasName t
name :: HasName t => Lens' t Name

-- | Provides for the extraction of free type variables, and alpha
--   renaming.
class HasTypeVars t
typeVarsEx :: HasTypeVars t => Set Name -> Traversal' t Name

-- | Provides substitution for types
class SubstType t
substType :: SubstType t => Map Name Type -> t -> t

-- | Traverse free type variables
typeVars :: HasTypeVars t => Traversal' t Name

-- | Substitute using a map of names in for free type variables
substTypeVars :: HasTypeVars t => Map Name Name -> t -> t

-- | Provides a Traversal of the types of each field of a
--   constructor.
conFields :: Traversal' Con StrictType

-- | Traversal of the types of the named fields of a
--   constructor.
conNamedFields :: Traversal' Con VarStrictType
instance SubstType Pred
instance SubstType t => SubstType [t]
instance SubstType Type
instance HasTypeVars t => HasTypeVars [t]
instance HasTypeVars Con
instance HasTypeVars Pred
instance HasTypeVars Type
instance HasTypeVars Name
instance HasTypeVars TyVarBndr
instance HasName Con
instance HasName Name
instance HasName TyVarBndr

module Control.Lens.TH

-- | Build lenses (and traversals) with a sensible default configuration.
--   
--   
--   makeLenses = makeLensesWith lensRules
--   
makeLenses :: Name -> Q [Dec]

-- | Derive lenses and traversals, specifying explicit pairings of
--   (fieldName, lensName).
--   
--   If you map multiple names to the same label, and it is present in the
--   same constructor then this will generate a Traversal.
--   
--   e.g.
--   
--   
--   makeLensesFor [("_foo", "fooLens"), ("baz", "lbaz")] ''Foo
--   makeLensesFor [("_barX", "bar"), ("_barY", "bar")] ''Bar
--   
makeLensesFor :: [(String, String)] -> Name -> Q [Dec]

-- | Make lenses and traversals for a type, and create a class when the
--   type has no arguments.
--   
--   e.g.
--   
--   
--   data Foo = Foo { _fooX, _fooY :: Int }
--   makeClassy ''Foo
--   
--   
--   will create
--   
--   
--   class HasFoo t where
--     foo :: Simple Lens t Foo
--   instance HasFoo Foo where foo = id
--   fooX, fooY :: HasFoo t => Simple Lens t Int
--   
--   
--   
--   makeClassy = makeLensesWith classyRules
--   
makeClassy :: Name -> Q [Dec]

-- | Derive lenses and traversals, using a named wrapper class, and
--   specifying explicit pairings of (fieldName, traversalName).
--   
--   Example usage:
--   
--   
--   makeClassyFor "HasFoo" "foo" [("_foo", "fooLens"), ("bar", "lbar")] ''Foo
--   
makeClassyFor :: String -> String -> [(String, String)] -> Name -> Q [Dec]

-- | Make a top level isomorphism injecting into the type.
--   
--   The supplied name is required to be for a type with a single
--   constructor that has a single argument.
--   
--   e.g.
--   
--   
--   newtype List a = List [a]
--   makeIso ''List
--   
--   
--   will create
--   
--   
--   list :: Iso [a] [b] (List a) (List b)
--   
--   
--   
--   makeIso = makeLensesWith isoRules
--   
makeIso :: Name -> Q [Dec]

-- | Generate a Prism for each constructor of a data type.
makePrisms :: Name -> Q [Dec]

-- | Build Wrapped instance for a given newtype
makeWrapped :: Name -> DecsQ

-- | 
--   makeFields = makeFieldsWith defaultFieldRules
--   
makeFields :: Name -> Q [Dec]

-- | Build lenses with a custom configuration.
makeLensesWith :: LensRules -> Name -> Q [Dec]

-- | Make fields with the specified FieldRules.
makeFieldsWith :: FieldRules -> Name -> Q [Dec]

-- | Default LensRules.
defaultRules :: LensRules

-- | 
--   defaultFieldRules = camelCaseFields
--   
defaultFieldRules :: FieldRules

-- | Field rules for fields in the form  prefixFieldname 
camelCaseFields :: FieldRules

-- | Field rules for fields in the form  _prefix_fieldname 
underscoreFields :: FieldRules

-- | This configuration describes the options we'll be using to make
--   isomorphisms or lenses.
data LensRules
LensRules :: (String -> Maybe String) -> (String -> Maybe String) -> (String -> Maybe (String, String)) -> Set LensFlag -> LensRules
data FieldRules
FieldRules :: (String -> Maybe String) -> (String -> String) -> (String -> Maybe String) -> (String -> Maybe String) -> FieldRules

-- | Rules for making fairly simple partial lenses, ignoring the special
--   cases for isomorphisms and traversals, and not making any classes.
lensRules :: LensRules

-- | Rules for making lenses and traversals that precompose another
--   Lens.
classyRules :: LensRules

-- | Rules for making an isomorphism from a data type.
isoRules :: LensRules

-- | Lens' to access the convention for naming top level
--   isomorphisms in our LensRules.
--   
--   Defaults to lowercasing the first letter of the constructor.
lensIso :: Lens' LensRules (String -> Maybe String)

-- | Lens' to access the convention for naming fields in our
--   LensRules.
--   
--   Defaults to stripping the _ off of the field name, lowercasing the
--   name, and rejecting the field if it doesn't start with an '_'.
lensField :: Lens' LensRules (String -> Maybe String)

-- | Retrieve options such as the name of the class and method to put in it
--   to build a class around monomorphic data types.
lensClass :: Lens' LensRules (String -> Maybe (String, String))

-- | Retrieve options such as the name of the class and method to put in it
--   to build a class around monomorphic data types.
lensFlags :: Lens' LensRules (Set LensFlag)

-- | Flags for Lens construction
data LensFlag
SimpleLenses :: LensFlag
PartialLenses :: LensFlag
BuildTraversals :: LensFlag
SingletonAndField :: LensFlag
SingletonIso :: LensFlag
HandleSingletons :: LensFlag
SingletonRequired :: LensFlag
CreateClass :: LensFlag
CreateInstance :: LensFlag
ClassRequired :: LensFlag
GenerateSignatures :: LensFlag

-- | Only Generate valid Simple lenses.
simpleLenses :: Lens' LensRules Bool

-- | Enables the generation of partial lenses, generating runtime errors
--   for every constructor that does not have a valid definition for the
--   Lens. This occurs when the constructor lacks the field, or has
--   multiple fields mapped to the same Lens.
partialLenses :: Lens' LensRules Bool

-- | In the situations that a Lens would be partial, when
--   partialLenses is used, this flag instead causes traversals to
--   be generated. Only one can be used, and if neither are, then
--   compile-time errors are generated.
buildTraversals :: Lens' LensRules Bool

-- | Handle singleton constructors specially.
handleSingletons :: Lens' LensRules Bool

-- | Use Iso for singleton constructors.
singletonIso :: Lens' LensRules Bool

-- | Expect a single constructor, single field newtype or data type.
singletonRequired :: Lens' LensRules Bool

-- | Create the class if the constructor is Simple and the
--   lensClass rule matches.
createClass :: Lens' LensRules Bool

-- | Create the instance if the constructor is Simple and the
--   lensClass rule matches.
createInstance :: Lens' LensRules Bool

-- | Die if the lensClass fails to match.
classRequired :: Lens' LensRules Bool

-- | When building a singleton Iso (or Lens) for a record
--   constructor, build both the Iso (or Lens) for the record
--   and the one for the field.
singletonAndField :: Lens' LensRules Bool

-- | Indicate whether or not to supply the signatures for the generated
--   lenses.
--   
--   Disabling this can be useful if you want to provide a more restricted
--   type signature or if you want to supply hand-written haddocks.
generateSignatures :: Lens' LensRules Bool
instance Eq LensFlag
instance Ord LensFlag
instance Show LensFlag
instance Read LensFlag

-- | Usage:
--   
--   You can derive lenses automatically for many data types:
--   
--   
--   import Control.Lens
--   data Foo a = Foo { _fooArgs :: [String], _fooValue :: a }
--   makeLenses ''Foo
--   
--   
--   This defines the following lenses:
--   
--   
--   fooArgs :: Lens' (Foo a) [String]
--   fooValue :: Lens (Foo a) (Foo b) a b
--   
--   
--   You can then access the value with (^.) and set the value of
--   the field with (.~) and can use almost any other combinator
--   that is re-exported here on those fields.
--   
--   The combinators here have unusually specific type signatures, so for
--   particularly tricky ones, the simpler type signatures you might want
--   to pretend the combinators have are specified as well.
--   
--   More information on how to use lenses is available on the lens wiki:
--   
--   http://github.com/ekmett/lens/wiki
--   
module Control.Lens

-- | Note: Generics.Deriving exports a number of names that
--   collide with Control.Lens.
--   
--   You can use hiding or imports to mitigate this to an extent, and the
--   following imports, represent a fair compromise for user code:
--   
--   
--   import Control.Lens hiding (Rep)
--   import Generics.Deriving hiding (from, to)
--   
--   
--   You can use generic to replace from and to from
--   Generics.Deriving, and probably won't be explicitly
--   referencing Rep from Control.Lens in code that uses
--   generics.
module Generics.Deriving.Lens

-- | Convert from the data type to its representation (or back)
--   
--   
--   >>> "hello"^.generic.from generic :: String
--   "hello"
--   
generic :: Generic a => Iso' a (Rep a b)

-- | Convert from the data type to its representation (or back)
generic1 :: Generic1 f => Iso' (f a) (Rep1 f a)

-- | A Generic Traversal that visits every occurrence of
--   something Typeable anywhere in a container.
--   
--   
--   >>> allOf tinplate (=="Hello") (1::Int,2::Double,(),"Hello",["Hello"])
--   True
--   
--   
--   
--   >>> mapMOf_ tinplate putStrLn ("hello",[(2 :: Int, "world!")])
--   hello
--   world!
--   
tinplate :: (Generic a, GTraversal (Rep a), Typeable b) => Traversal' a b

-- | Used to traverse Generic data by uniplate.
class GTraversal f
instance (Traversable f, GTraversal g) => GTraversal (f :.: g)
instance GTraversal a => GTraversal (M1 i c a)
instance (GTraversal f, GTraversal g) => GTraversal (f :+: g)
instance (GTraversal f, GTraversal g) => GTraversal (f :*: g)
instance GTraversal U1
instance (Generic a, GTraversal (Rep a), Typeable a) => GTraversal (K1 i a)

-- | Note: GHC.Generics exports a number of names that collide
--   with Control.Lens.
--   
--   You can use hiding or imports to mitigate this to an extent, and the
--   following imports, represent a fair compromise for user code:
--   
--   
--   import Control.Lens hiding (Rep)
--   import GHC.Generics hiding (from, to)
--   
--   
--   You can use generic to replace from and to from
--   GHC.Generics, and probably won't be explicitly referencing
--   Rep from Control.Lens in code that uses generics.
--   
--   This module provides compatibility with older GHC versions by using
--   the generic-deriving package.
module GHC.Generics.Lens

-- | Control.Exception provides an example of a large open
--   hierarchy that we can model with prisms and isomorphisms.
--   
--   Additional combinators for working with IOException results can
--   be found in System.IO.Error.Lens.
--   
--   The combinators in this module have been generalized to work with
--   MonadCatchIO instead of just IO. This enables them to be
--   used more easily in Monad transformer stacks.
module Control.Exception.Lens

-- | Catch exceptions that match a given Prism (or any
--   Getter, really).
--   
--   
--   >>> catching _AssertionFailed (assert False (return "uncaught")) $ \ _ -> return "caught"
--   "caught"
--   
--   
--   
--   catching :: MonadCatchIO m => Prism' SomeException a     -> m r -> (a -> m r) -> m r
--   catching :: MonadCatchIO m => Lens' SomeException a      -> m r -> (a -> m r) -> m r
--   catching :: MonadCatchIO m => Traversal' SomeException a -> m r -> (a -> m r) -> m r
--   catching :: MonadCatchIO m => Iso' SomeException a       -> m r -> (a -> m r) -> m r
--   catching :: MonadCatchIO m => Getter SomeException a     -> m r -> (a -> m r) -> m r
--   catching :: MonadCatchIO m => Fold SomeException a       -> m r -> (a -> m r) -> m r
--   
catching :: MonadCatchIO m => Getting (First a) SomeException a -> m r -> (a -> m r) -> m r

-- | Catch exceptions that match a given Prism (or any
--   Getter), discarding the information about the match. This is
--   particuarly useful when you have a Prism' e () where
--   the result of the Prism or Fold isn't particularly
--   valuable, just the fact that it matches.
--   
--   
--   >>> catching_ _AssertionFailed (assert False (return "uncaught")) $ return "caught"
--   "caught"
--   
--   
--   
--   catching_ :: MonadCatchIO m => Prism' SomeException a     -> m r -> m r -> m r
--   catching_ :: MonadCatchIO m => Lens' SomeException a      -> m r -> m r -> m r
--   catching_ :: MonadCatchIO m => Traversal' SomeException a -> m r -> m r -> m r
--   catching_ :: MonadCatchIO m => Iso' SomeException a       -> m r -> m r -> m r
--   catching_ :: MonadCatchIO m => Getter SomeException a     -> m r -> m r -> m r
--   catching_ :: MonadCatchIO m => Fold SomeException a       -> m r -> m r -> m r
--   
catching_ :: MonadCatchIO m => Getting (First a) SomeException a -> m r -> m r -> m r

-- | A version of catching with the arguments swapped around; useful
--   in situations where the code for the handler is shorter.
--   
--   
--   >>> handling _NonTermination (\_ -> return "caught") $ throwIO NonTermination
--   "caught"
--   
--   
--   
--   handling :: MonadCatchIO m => Prism' SomeException a     -> (a -> m r) -> m r -> m r
--   handling :: MonadCatchIO m => Lens' SomeException a      -> (a -> m r) -> m r -> m r
--   handling :: MonadCatchIO m => Traversal' SomeException a -> (a -> m r) -> m r -> m r
--   handling :: MonadCatchIO m => Iso' SomeException a       -> (a -> m r) -> m r -> m r
--   handling :: MonadCatchIO m => Fold SomeException a       -> (a -> m r) -> m r -> m r
--   handling :: MonadCatchIO m => Getter SomeException a     -> (a -> m r) -> m r -> m r
--   
handling :: MonadCatchIO m => Getting (First a) SomeException a -> (a -> m r) -> m r -> m r

-- | A version of catching_ with the arguments swapped around;
--   useful in situations where the code for the handler is shorter.
--   
--   
--   >>> handling_ _NonTermination (return "caught") $ throwIO NonTermination
--   "caught"
--   
--   
--   
--   handling_ :: MonadCatchIO m => Prism' SomeException a     -> m r -> m r -> m r
--   handling_ :: MonadCatchIO m => Lens' SomeException a      -> m r -> m r -> m r
--   handling_ :: MonadCatchIO m => Traversal' SomeException a -> m r -> m r -> m r
--   handling_ :: MonadCatchIO m => Iso' SomeException a       -> m r -> m r -> m r
--   handling_ :: MonadCatchIO m => Getter SomeException a     -> m r -> m r -> m r
--   handling_ :: MonadCatchIO m => Fold SomeException a       -> m r -> m r -> m r
--   
handling_ :: MonadCatchIO m => Getting (First a) SomeException a -> m r -> m r -> m r

-- | A variant of try that takes a Prism (or any
--   Getter) to select which exceptions are caught (c.f.
--   tryJust, catchJust). If the Exception does not
--   match the predicate, it is re-thrown.
--   
--   
--   trying :: MonadCatchIO m => Prism'     SomeException a -> m r -> m (Either a r)
--   trying :: MonadCatchIO m => Lens'      SomeException a -> m r -> m (Either a r)
--   trying :: MonadCatchIO m => Traversal' SomeException a -> m r -> m (Either a r)
--   trying :: MonadCatchIO m => Iso'       SomeException a -> m r -> m (Either a r)
--   trying :: MonadCatchIO m => Getter     SomeException a -> m r -> m (Either a r)
--   trying :: MonadCatchIO m => Fold       SomeException a -> m r -> m (Either a r)
--   
trying :: MonadCatchIO m => Getting (First a) SomeException a -> m r -> m (Either a r)

-- | Throw an Exception described by a Prism. Exceptions may
--   be thrown from purely functional code, but may only be caught within
--   the IO Monad.
--   
--   
--   throwing l ≡ reviews l throw
--   
--   
--   
--   throwing :: Prism' SomeException t -> t -> r
--   throwing :: Iso' SomeException t   -> t -> r
--   
throwing :: AReview s SomeException a b -> b -> r

-- | A variant of throwing that can only be used within the
--   IO Monad (or any other MonadCatchIO instance) to
--   throw an Exception described by a Prism.
--   
--   Although throwingM has a type that is a specialization of the
--   type of throwing, the two functions are subtly different:
--   
--   
--   throwing l e `seq` x  ≡ throwing e
--   throwingM l e `seq` x ≡ x
--   
--   
--   The first example will cause the Exception e to be
--   raised, whereas the second one won't. In fact, throwingM will
--   only cause an Exception to be raised when it is used within the
--   MonadCatchIO instance. The throwingM variant should be
--   used in preference to throwing to raise an Exception
--   within the Monad because it guarantees ordering with respect to
--   other monadic operations, whereas throwing does not.
--   
--   
--   throwingM l ≡ reviews l throw
--   
--   
--   
--   throwingM :: MonadIO m => Prism' SomeException t -> t -> m r
--   throwingM :: MonadIO m => Iso' SomeException t   -> t -> m r
--   
throwingM :: MonadIO m => AReview s SomeException a b -> b -> m r

-- | throwingTo raises an Exception specified by a
--   Prism in the target thread.
--   
--   
--   throwingTo thread l ≡ reviews l (throwTo thread)
--   
--   
--   
--   throwingTo :: ThreadId -> Prism' SomeException t -> t -> m a
--   throwingTo :: ThreadId -> Iso' SomeException t   -> t -> m a
--   
throwingTo :: MonadIO m => ThreadId -> AReview s SomeException a b -> b -> m ()

-- | Traverse the strongly typed Exception contained in
--   SomeException where the type of your function matches the
--   desired Exception.
--   
--   
--   exception :: (Applicative f, Exception a)
--             => (a -> f a) -> SomeException -> f SomeException
--   
exception :: Exception a => Prism' SomeException a

-- | Both MonadCatchIO-transformers and Control.Exception
--   provide a Handler type.
--   
--   This lets us write combinators to build handlers that are agnostic
--   about the choice of which of these they use.
class Handleable e (m :: * -> *) (h :: * -> *) | h -> e m where handler_ l = handler l . const
handler :: Handleable e m h => Getting (First a) e a -> (a -> m r) -> h r
handler_ :: Handleable e m h => Getting (First a) e a -> m r -> h r

-- | Exceptions that occur in the IO Monad. An
--   IOException records a more specific error type, a descriptive
--   string and maybe the handle that was used when the error was flagged.
--   
--   Due to their richer structure relative to other exceptions, these have
--   a more carefully overloaded signature.
class AsIOException p f t
_IOException :: AsIOException p f t => Overloaded' p f t IOException

-- | Arithmetic exceptions.
class AsArithException p f t
_ArithException :: AsArithException p f t => Overloaded' p f t ArithException

-- | Handle arithmetic _Overflow.
--   
--   
--   _Overflow ≡ _ArithException . _Overflow
--   
--   
--   
--   _Overflow :: Prism' ArithException ArithException
--   _Overflow :: Prism' SomeException  ArithException
--   
_Overflow :: (AsArithException p f t, Choice p, Applicative f) => Overloaded' p f t ()

-- | Handle arithmetic _Underflow.
--   
--   
--   _Underflow ≡ _ArithException . _Underflow
--   
--   
--   
--   _Underflow :: Prism' ArithException ArithException
--   _Underflow :: Prism' SomeException  ArithException
--   
_Underflow :: (AsArithException p f t, Choice p, Applicative f) => Overloaded' p f t ()

-- | Handle arithmetic loss of precision.
--   
--   
--   _LossOfPrecision ≡ _ArithException . _LossOfPrecision
--   
--   
--   
--   _LossOfPrecision :: Prism' ArithException ArithException
--   _LossOfPrecision :: Prism' SomeException  ArithException
--   
_LossOfPrecision :: (AsArithException p f t, Choice p, Applicative f) => Overloaded' p f t ()

-- | Handle division by zero.
--   
--   
--   _DivideByZero ≡ _ArithException . _DivideByZero
--   
--   
--   
--   _DivideByZero :: Prism' ArithException ArithException
--   _DivideByZero :: Prism' SomeException  ArithException
--   
_DivideByZero :: (AsArithException p f t, Choice p, Applicative f) => Overloaded' p f t ()

-- | Handle exceptional _Denormalized floating point.
--   
--   
--   _Denormal ≡ _ArithException . _Denormal
--   
--   
--   
--   _Denormal :: Prism' ArithException ArithException
--   _Denormal :: Prism' SomeException  ArithException
--   
_Denormal :: (AsArithException p f t, Choice p, Applicative f) => Overloaded' p f t ()

-- | Added in base 4.6 in response to this libraries discussion:
--   
--   
--   http://haskell.1045720.n5.nabble.com/Data-Ratio-and-exceptions-td5711246.html
--   
--   
--   _RatioZeroDenominator ≡ _ArithException . _RatioZeroDenominator
--   
--   
--   
--   _RatioZeroDenominator :: Prism' ArithException ArithException
--   _RatioZeroDenominator :: Prism' SomeException  ArithException
--   
_RatioZeroDenominator :: (AsArithException p f t, Choice p, Applicative f) => Overloaded' p f t ()

-- | Exceptions generated by array operations.
class AsArrayException p f t
_ArrayException :: AsArrayException p f t => Overloaded' p f t ArrayException

-- | An attempt was made to index an array outside its declared bounds.
--   
--   
--   _IndexOutOfBounds ≡ _ArrayException . _IndexOutOfBounds
--   
--   
--   
--   _IndexOutOfBounds :: Prism' ArrayException String
--   _IndexOutOfBounds :: Prism' SomeException  String
--   
_IndexOutOfBounds :: (AsArrayException p f t, Choice p, Applicative f) => Overloaded' p f t String

-- | An attempt was made to evaluate an element of an array that had not
--   been initialized.
--   
--   
--   _UndefinedElement ≡ _ArrayException . _UndefinedElement
--   
--   
--   
--   _UndefinedElement :: Prism' ArrayException String
--   _UndefinedElement :: Prism' SomeException  String
--   
_UndefinedElement :: (AsArrayException p f t, Choice p, Applicative f) => Overloaded' p f t String

-- | assert was applied to False.
class AsAssertionFailed p f t
_AssertionFailed :: AsAssertionFailed p f t => Overloaded' p f t String

-- | Asynchronous exceptions.
class AsAsyncException p f t
_AsyncException :: AsAsyncException p f t => Overloaded' p f t AsyncException

-- | The current thread's stack exceeded its limit. Since an
--   Exception has been raised, the thread's stack will certainly be
--   below its limit again, but the programmer should take remedial action
--   immediately.
--   
--   
--   _StackOverflow :: Prism' AsyncException ()
--   _StackOverflow :: Prism' SomeException  ()
--   
_StackOverflow :: (AsAsyncException p f t, Choice p, Applicative f) => Overloaded' p f t ()

-- | The program's heap is reaching its limit, and the program should take
--   action to reduce the amount of live data it has.
--   
--   Notes:
--   
--   
--   
- It is undefined which thread receives this Exception.
--   
- GHC currently does not throw HeapOverflow exceptions.
--   
--   
--   
--   _HeapOverflow :: Prism' AsyncException ()
--   _HeapOverflow :: Prism' SomeException  ()
--   
_HeapOverflow :: (AsAsyncException p f t, Choice p, Applicative f) => Overloaded' p f t ()

-- | This Exception is raised by another thread calling
--   killThread, or by the system if it needs to terminate the
--   thread for some reason.
--   
--   
--   _ThreadKilled :: Prism' AsyncException ()
--   _ThreadKilled :: Prism' SomeException  ()
--   
_ThreadKilled :: (AsAsyncException p f t, Choice p, Applicative f) => Overloaded' p f t ()

-- | This Exception is raised by default in the main thread of the
--   program when the user requests to terminate the program via the usual
--   mechanism(s) (e.g. Control-C in the console).
--   
--   
--   _UserInterrupt :: Prism' AsyncException ()
--   _UserInterrupt :: Prism' SomeException  ()
--   
_UserInterrupt :: (AsAsyncException p f t, Choice p, Applicative f) => Overloaded' p f t ()

-- | Thrown when the runtime system detects that the computation is
--   guaranteed not to terminate. Note that there is no guarantee that the
--   runtime system will notice whether any given computation is guaranteed
--   to terminate or not.
class (Profunctor p, Functor f) => AsNonTermination p f t
_NonTermination :: AsNonTermination p f t => Overloaded' p f t ()

-- | Thrown when the program attempts to call atomically, from the
--   STM package, inside another call to atomically.
class (Profunctor p, Functor f) => AsNestedAtomically p f t
_NestedAtomically :: AsNestedAtomically p f t => Overloaded' p f t ()

-- | The thread is blocked on an MVar, but there are no other
--   references to the MVar so it can't ever continue.
class (Profunctor p, Functor f) => AsBlockedIndefinitelyOnMVar p f t
_BlockedIndefinitelyOnMVar :: AsBlockedIndefinitelyOnMVar p f t => Overloaded' p f t ()

-- | The thread is waiting to retry an STM transaction, but there
--   are no other references to any TVars involved, so it can't ever
--   continue.
class (Profunctor p, Functor f) => AsBlockedIndefinitelyOnSTM p f t
_BlockedIndefinitelyOnSTM :: AsBlockedIndefinitelyOnSTM p f t => Overloaded' p f t ()

-- | There are no runnable threads, so the program is deadlocked. The
--   Deadlock Exception is raised in the main thread only.
class (Profunctor p, Functor f) => AsDeadlock p f t
_Deadlock :: AsDeadlock p f t => Overloaded' p f t ()

-- | A class method without a definition (neither a default definition, nor
--   a definition in the appropriate instance) was called.
class (Profunctor p, Functor f) => AsNoMethodError p f t
_NoMethodError :: AsNoMethodError p f t => Overloaded' p f t String

-- | A pattern match failed.
class (Profunctor p, Functor f) => AsPatternMatchFail p f t
_PatternMatchFail :: AsPatternMatchFail p f t => Overloaded' p f t String

-- | An uninitialised record field was used.
class (Profunctor p, Functor f) => AsRecConError p f t
_RecConError :: AsRecConError p f t => Overloaded' p f t String

-- | A record selector was applied to a constructor without the appropriate
--   field. This can only happen with a datatype with multiple
--   constructors, where some fields are in one constructor but not
--   another.
class (Profunctor p, Functor f) => AsRecSelError p f t
_RecSelError :: AsRecSelError p f t => Overloaded' p f t String

-- | A record update was performed on a constructor without the appropriate
--   field. This can only happen with a datatype with multiple
--   constructors, where some fields are in one constructor but not
--   another.
class (Profunctor p, Functor f) => AsRecUpdError p f t
_RecUpdError :: AsRecUpdError p f t => Overloaded' p f t String

-- | This is thrown when the user calls error.
class (Profunctor p, Functor f) => AsErrorCall p f t
_ErrorCall :: AsErrorCall p f t => Overloaded' p f t String

-- | This Exception is thrown by lens when the user somehow
--   manages to rethrow an internal HandlingException.
class (Profunctor p, Functor f) => AsHandlingException p f t
_HandlingException :: AsHandlingException p f t => Overloaded' p f t ()
instance (Choice p, Applicative f) => AsHandlingException p f SomeException
instance (Profunctor p, Functor f) => AsHandlingException p f HandlingException
instance (Choice p, Applicative f) => AsErrorCall p f SomeException
instance (Profunctor p, Functor f) => AsErrorCall p f ErrorCall
instance (Choice p, Applicative f) => AsRecUpdError p f SomeException
instance (Profunctor p, Functor f) => AsRecUpdError p f RecUpdError
instance (Choice p, Applicative f) => AsRecSelError p f SomeException
instance (Profunctor p, Functor f) => AsRecSelError p f RecSelError
instance (Choice p, Applicative f) => AsRecConError p f SomeException
instance (Profunctor p, Functor f) => AsRecConError p f RecConError
instance (Choice p, Applicative f) => AsPatternMatchFail p f SomeException
instance (Profunctor p, Functor f) => AsPatternMatchFail p f PatternMatchFail
instance (Choice p, Applicative f) => AsNoMethodError p f SomeException
instance (Profunctor p, Functor f) => AsNoMethodError p f NoMethodError
instance (Choice p, Applicative f) => AsDeadlock p f SomeException
instance (Profunctor p, Functor f) => AsDeadlock p f Deadlock
instance (Choice p, Applicative f) => AsBlockedIndefinitelyOnSTM p f SomeException
instance (Profunctor p, Functor f) => AsBlockedIndefinitelyOnSTM p f BlockedIndefinitelyOnSTM
instance (Choice p, Applicative f) => AsBlockedIndefinitelyOnMVar p f SomeException
instance (Profunctor p, Functor f) => AsBlockedIndefinitelyOnMVar p f BlockedIndefinitelyOnMVar
instance (Choice p, Applicative f) => AsNestedAtomically p f SomeException
instance (Profunctor p, Functor f) => AsNestedAtomically p f NestedAtomically
instance (Choice p, Applicative f) => AsNonTermination p f SomeException
instance (Profunctor p, Functor f) => AsNonTermination p f NonTermination
instance (Choice p, Applicative f) => AsAsyncException p f SomeException
instance AsAsyncException p f AsyncException
instance (Choice p, Applicative f) => AsAssertionFailed p f SomeException
instance (Profunctor p, Functor f) => AsAssertionFailed p f AssertionFailed
instance (Choice p, Applicative f) => AsArrayException p f SomeException
instance AsArrayException p f ArrayException
instance (Choice p, Applicative f) => AsArithException p f SomeException
instance AsArithException p f ArithException
instance (Choice p, Applicative f) => AsIOException p f SomeException
instance AsIOException p f IOException

module System.IO.Error.Lens

-- | Where the error happened.
--   
--   
--   location :: Lens'      IOException   String
--   location :: Traversal' SomeException String
--   
location :: (AsIOException (->) f t, Functor f) => LensLike' f t String

-- | Error type specific information.
--   
--   
--   description :: Lens'      IOException   String
--   description :: Traversal' SomeException String
--   
description :: (AsIOException (->) f t, Functor f) => LensLike' f t String

-- | The handle used by the action flagging this error.
--   
--   
--   handle :: Lens'      IOException   (Maybe Handle)
--   handle :: Traversal' SomeException (Maybe Handle)
--   
handle :: (AsIOException (->) f t, Functor f) => LensLike' f t (Maybe Handle)

-- | fileName the error is related to.
--   
--   
--   fileName :: Lens'      IOException   (Maybe FilePath)
--   fileName :: Traversal' SomeException (Maybe FilePath)
--   
fileName :: (AsIOException (->) f t, Functor f) => LensLike' f t (Maybe FilePath)

-- | errno leading to this error, if any.
--   
--   
--   errno :: Lens'      IOException   (Maybe FilePath)
--   errno :: Traversal' SomeException (Maybe FilePath)
--   
errno :: (AsIOException (->) f t, Functor f) => LensLike' f t (Maybe CInt)

-- | What type of error it is
--   
--   
--   errorType :: Lens'      IOException   IOErrorType
--   errorType :: Traversal' SomeException IOErrorType
--   
errorType :: (AsIOException (->) f t, Functor f) => LensLike' f t IOErrorType
_Interrupted :: Prism' IOErrorType ()
_ResourceVanished :: Prism' IOErrorType ()
_TimeExpired :: Prism' IOErrorType ()
_UnsupportedOperation :: Prism' IOErrorType ()
_HardwareFault :: Prism' IOErrorType ()
_InappropriateType :: Prism' IOErrorType ()
_InvalidArgument :: Prism' IOErrorType ()
_OtherError :: Prism' IOErrorType ()
_ProtocolError :: Prism' IOErrorType ()
_SystemError :: Prism' IOErrorType ()
_UnsatisfiedConstraints :: Prism' IOErrorType ()
_UserError :: Prism' IOErrorType ()
_PermissionDenied :: Prism' IOErrorType ()
_IllegalOperation :: Prism' IOErrorType ()
_EOF :: Prism' IOErrorType ()
_ResourceExhausted :: Prism' IOErrorType ()
_ResourceBusy :: Prism' IOErrorType ()
_NoSuchThing :: Prism' IOErrorType ()
_AlreadyExists :: Prism' IOErrorType ()

-- | This module spends a lot of time fiddling around with
--   ByteString internals to work around
--   http://hackage.haskell.org/trac/ghc/ticket/7556 on older
--   Haskell Platforms and to improve constant and asymptotic factors in
--   our performance.
module Control.Lens.Internal.ByteString

-- | Unpack a strict Bytestring
unpackStrict :: ByteString -> [Word8]

-- | Traverse a strict ByteString from left to right in a biased
--   fashion.
traversedStrict :: Int -> IndexedTraversal' Int ByteString Word8

-- | Traverse a strict ByteString in a relatively balanced fashion,
--   as a balanced tree with biased runs of elements at the leaves.
traversedStrictTree :: Int -> IndexedTraversal' Int ByteString Word8

-- | Unpack a strict Bytestring, pretending the bytes are chars.
unpackStrict8 :: ByteString -> String

-- | Traverse a strict ByteString from left to right in a biased
--   fashion pretending the bytes are characters.
traversedStrict8 :: Int -> IndexedTraversal' Int ByteString Char

-- | Traverse a strict ByteString in a relatively balanced fashion,
--   as a balanced tree with biased runs of elements at the leaves,
--   pretending the bytes are chars.
traversedStrictTree8 :: Int -> IndexedTraversal' Int ByteString Char

-- | Unpack a lazy Bytestring
unpackLazy :: ByteString -> [Word8]

-- | An IndexedTraversal of the individual bytes in a lazy
--   ByteString
traversedLazy :: IndexedTraversal' Int64 ByteString Word8

-- | Unpack a lazy ByteString pretending the bytes are chars.
unpackLazy8 :: ByteString -> String

-- | An IndexedTraversal of the individual bytes in a lazy
--   ByteString pretending the bytes are chars.
traversedLazy8 :: IndexedTraversal' Int64 ByteString Char

module Control.Monad.Error.Lens

-- | Catch exceptions that match a given Prism (or any
--   Getter, really).
--   
--   
--   catching :: MonadError e m => Prism' e a     -> m r -> (a -> m r) -> m r
--   catching :: MonadError e m => Lens' e a      -> m r -> (a -> m r) -> m r
--   catching :: MonadError e m => Traversal' e a -> m r -> (a -> m r) -> m r
--   catching :: MonadError e m => Iso' e a       -> m r -> (a -> m r) -> m r
--   catching :: MonadError e m => Getter e a     -> m r -> (a -> m r) -> m r
--   catching :: MonadError e m => Fold e a       -> m r -> (a -> m r) -> m r
--   
catching :: MonadError e m => Getting (First a) e a -> m r -> (a -> m r) -> m r

-- | Catch exceptions that match a given Prism (or any
--   Getter), discarding the information about the match. This is
--   particuarly useful when you have a Prism' e () where
--   the result of the Prism or Fold isn't particularly
--   valuable, just the fact that it matches.
--   
--   
--   catching_ :: MonadError e m => Prism' e a     -> m r -> m r -> m r
--   catching_ :: MonadError e m => Lens' e a      -> m r -> m r -> m r
--   catching_ :: MonadError e m => Traversal' e a -> m r -> m r -> m r
--   catching_ :: MonadError e m => Iso' e a       -> m r -> m r -> m r
--   catching_ :: MonadError e m => Getter e a     -> m r -> m r -> m r
--   catching_ :: MonadError e m => Fold e a       -> m r -> m r -> m r
--   
catching_ :: MonadError e m => Getting (First a) e a -> m r -> m r -> m r

-- | A version of catching with the arguments swapped around; useful
--   in situations where the code for the handler is shorter.
--   
--   
--   handling :: MonadError e m => Prism' e a     -> (a -> m r) -> m r -> m r
--   handling :: MonadError e m => Lens' e a      -> (a -> m r) -> m r -> m r
--   handling :: MonadError e m => Traversal' e a -> (a -> m r) -> m r -> m r
--   handling :: MonadError e m => Iso' e a       -> (a -> m r) -> m r -> m r
--   handling :: MonadError e m => Fold e a       -> (a -> m r) -> m r -> m r
--   handling :: MonadError e m => Getter e a     -> (a -> m r) -> m r -> m r
--   
handling :: MonadError e m => Getting (First a) e a -> (a -> m r) -> m r -> m r

-- | A version of catching_ with the arguments swapped around;
--   useful in situations where the code for the handler is shorter.
--   
--   
--   handling_ :: MonadError e m => Prism' e a     -> m r -> m r -> m r
--   handling_ :: MonadError e m => Lens' e a      -> m r -> m r -> m r
--   handling_ :: MonadError e m => Traversal' e a -> m r -> m r -> m r
--   handling_ :: MonadError e m => Iso' e a       -> m r -> m r -> m r
--   handling_ :: MonadError e m => Getter e a     -> m r -> m r -> m r
--   handling_ :: MonadError e m => Fold e a       -> m r -> m r -> m r
--   
handling_ :: MonadError e m => Getting (First a) e a -> m r -> m r -> m r

-- | trying takes a Prism (or any Getter) to select
--   which exceptions are caught If the Exception does not match
--   the predicate, it is re-thrown.
--   
--   
--   trying :: MonadError e m => Prism' e a     -> m r -> m (Either a r)
--   trying :: MonadError e m => Lens' e a      -> m r -> m (Either a r)
--   trying :: MonadError e m => Traversal' e a -> m r -> m (Either a r)
--   trying :: MonadError e m => Iso' e a       -> m r -> m (Either a r)
--   trying :: MonadError e m => Getter e a     -> m r -> m (Either a r)
--   trying :: MonadError e m => Fold e a       -> m r -> m (Either a r)
--   
trying :: MonadError e m => Getting (First a) e a -> m r -> m (Either a r)

-- | This function exists to remedy a gap between the functionality of
--   Control.Exception and Control.Monad.Error.
--   Control.Exception supplies catches and a notion of
--   Handler, which we duplicate here in a form suitable for working
--   with any MonadError instance.
--   
--   Sometimes you want to catch two different sorts of error. You could do
--   something like
--   
--   
--   f = handling _Foo handleFoo (handling _Bar handleBar expr)
--   
--   
--   However, there are a couple of problems with this approach. The first
--   is that having two exception handlers is inefficient. However, the
--   more serious issue is that the second exception handler will catch
--   exceptions in the first, e.g. in the example above, if
--   handleFoo uses throwError then the second exception
--   handler will catch it.
--   
--   Instead, we provide a function catches, which would be used
--   thus:
--   
--   
--   f = catches expr [ handler _Foo handleFoo
--                    , handler _Bar handleBar
--                    ]
--   
catches :: MonadError e m => m a -> [Handler e m a] -> m a

-- | You need this when using catches.
data Handler e m r
Handler :: (e -> Maybe a) -> (a -> m r) -> Handler e m r

-- | Both MonadCatchIO-transformers and Control.Exception
--   provide a Handler type.
--   
--   This lets us write combinators to build handlers that are agnostic
--   about the choice of which of these they use.
class Handleable e (m :: * -> *) (h :: * -> *) | h -> e m where handler_ l = handler l . const
handler :: Handleable e m h => Getting (First a) e a -> (a -> m r) -> h r
handler_ :: Handleable e m h => Getting (First a) e a -> m r -> h r

-- | Throw an Exception described by a Prism.
--   
--   
--   throwing l ≡ reviews l throwError
--   
--   
--   
--   throwing :: MonadError e m => Prism' e t -> t -> a
--   throwing :: MonadError e m => Iso' e t   -> t -> a
--   
throwing :: MonadError e m => AReview e e t t -> t -> m x
instance Handleable e m (Handler e m)
instance Monad m => Monoid (Handler e m a)
instance Monad m => Plus (Handler e m)
instance Monad m => Alt (Handler e m)
instance Monad m => Semigroup (Handler e m a)
instance Monad m => Functor (Handler e m)

-- | A Lens or Traversal can be used to take the role of
--   Traversable in Control.Parallel.Strategies, enabling
--   those combinators to work with monomorphic containers.
module Control.Parallel.Strategies.Lens

-- | Evaluate the targets of a Lens or Traversal into a data
--   structure according to the given Strategy.
--   
--   
--   evalTraversable = evalOf traverse = traverse
--   evalOf = id
--   
--   
--   
--   evalOf :: Lens' s a -> Strategy a -> Strategy s
--   evalOf :: Traversal' s a -> Strategy a -> Strategy s
--   evalOf :: (a -> Eval a) -> s -> Eval s) -> Strategy a -> Strategy s
--   
evalOf :: LensLike' Eval s a -> Strategy a -> Strategy s

-- | Evaluate the targets of a Lens or Traversal according
--   into a data structure according to a given Strategy in
--   parallel.
--   
--   
--   parTraversable = parOf traverse
--   
--   
--   
--   parOf :: Lens' s a -> Strategy a -> Strategy s
--   parOf :: Traversal' s a -> Strategy a -> Strategy s
--   parOf :: ((a -> Eval a) -> s -> Eval s) -> Strategy a -> Strategy s
--   
parOf :: LensLike' Eval s a -> Strategy a -> Strategy s

-- | Transform a Lens, Fold, Getter, Setter or
--   Traversal to first evaluates its argument according to a given
--   Strategy before proceeding.
--   
--   
--   after rdeepseq traverse :: Traversable t => Strategy a -> Strategy [a]
--   
after :: Strategy s -> LensLike f s t a b -> LensLike f s t a b

-- | Transform a Lens, Fold, Getter, Setter or
--   Traversal to evaluate its argument according to a given
--   Strategy in parallel with evaluating.
--   
--   
--   throughout rdeepseq traverse :: Traversable t => Strategy a -> Strategy [a]
--   
throughout :: Strategy s -> LensLike f s t a b -> LensLike f s t a b

-- | A Fold can be used to take the role of Foldable in
--   Control.Seq.
module Control.Seq.Lens

-- | Evaluate the elements targeted by a Lens, Traversal,
--   Iso, Getter or Fold according to the given
--   strategy.
--   
--   
--   seqFoldable = seqOf folded
--   
seqOf :: Getting (Endo [a]) s a -> Strategy a -> Strategy s

module Data.Array.Lens

-- | This setter can be used to derive a new IArray from an
--   old IAarray by applying a function to each of the indices to
--   look it up in the old IArray.
--   
--   This is a contravariant Setter.
--   
--   
--   ixmap ≡ over . ixmapped
--   ixmapped ≡ setting . ixmap
--   over (ixmapped b) f arr ! i ≡ arr ! f i
--   bounds (over (ixmapped b) f arr) ≡ b
--   
ixmapped :: (IArray a e, Ix i, Ix j) => (i, i) -> IndexPreservingSetter (a j e) (a i e) i j

module Data.Bits.Lens

-- | Bitwise .|. the target(s) of a Lens or Setter.
--   
--   
--   >>> _2 .|.~ 6 $ ("hello",3)
--   ("hello",7)
--   
--   
--   
--   (.|.~) :: Bits a             => Setter s t a a    -> a -> s -> t
--   (.|.~) :: Bits a             => Iso s t a a       -> a -> s -> t
--   (.|.~) :: Bits a             => Lens s t a a      -> a -> s -> t
--   (.|.~) :: (Monoid a, Bits a) => Traversal s t a a -> a -> s -> t
--   
(.|.~) :: Bits a => ASetter s t a a -> a -> s -> t

-- | Bitwise .&. the target(s) of a Lens or
--   Setter.
--   
--   
--   >>> _2 .&.~ 7 $ ("hello",254)
--   ("hello",6)
--   
--   
--   
--   (.&.~) :: Bits a             => Setter s t a a    -> a -> s -> t
--   (.&.~) :: Bits a             => Iso s t a a       -> a -> s -> t
--   (.&.~) :: Bits a             => Lens s t a a      -> a -> s -> t
--   (.&.~) :: (Monoid a, Bits a) => Traversal s t a a -> a -> s -> t
--   
(.&.~) :: Bits a => ASetter s t a a -> a -> s -> t

-- | Bitwise .|. the target(s) of a Lens (or
--   Traversal), returning the result (or a monoidal summary of all
--   of the results).
--   
--   
--   >>> _2 <.|.~ 6 $ ("hello",3)
--   (7,("hello",7))
--   
--   
--   
--   (<.|.~) :: Bits a             => Iso s t a a       -> a -> s -> (a, t)
--   (<.|.~) :: Bits a             => Lens s t a a      -> a -> s -> (a, t)
--   (<.|.~) :: (Bits a, Monoid a) => Traversal s t a a -> a -> s -> (a, t)
--   
(<.|.~) :: Bits a => LensLike ((,) a) s t a a -> a -> s -> (a, t)

-- | Bitwise .&. the target(s) of a Lens or
--   Traversal, returning the result (or a monoidal summary of all
--   of the results).
--   
--   
--   >>> _2 <.&.~ 7 $ ("hello",254)
--   (6,("hello",6))
--   
--   
--   
--   (<.&.~) :: Bits a             => Iso       s t a a -> a -> s -> (a, t)
--   (<.&.~) :: Bits a             => Lens      s t a a -> a -> s -> (a, t)
--   (<.&.~) :: (Bits a, Monoid a) => Traversal s t a a -> a -> s -> (a, t)
--   
(<.&.~) :: Bits a => LensLike ((,) a) s t a a -> a -> s -> (a, t)

-- | Modify the target(s) of a Lens', Setter or
--   Traversal by computing its bitwise .|. with another
--   value.
--   
--   
--   >>> execState (do _1 .|.= 15; _2 .|.= 3) (7,7)
--   (15,7)
--   
--   
--   
--   (.|.=) :: (MonadState s m, Bits a) => Setter' s a    -> a -> m ()
--   (.|.=) :: (MonadState s m, Bits a) => Iso' s a       -> a -> m ()
--   (.|.=) :: (MonadState s m, Bits a) => Lens' s a      -> a -> m ()
--   (.|.=) :: (MonadState s m, Bits a) => Traversal' s a -> a -> m ()
--   
(.|.=) :: (MonadState s m, Bits a) => ASetter' s a -> a -> m ()

-- | Modify the target(s) of a Lens', Setter' or
--   Traversal' by computing its bitwise .&. with another
--   value.
--   
--   
--   >>> execState (do _1 .&.= 15; _2 .&.= 3) (7,7)
--   (7,3)
--   
--   
--   
--   (.&.=) :: (MonadState s m, Bits a) => Setter' s a    -> a -> m ()
--   (.&.=) :: (MonadState s m, Bits a) => Iso' s a       -> a -> m ()
--   (.&.=) :: (MonadState s m, Bits a) => Lens' s a      -> a -> m ()
--   (.&.=) :: (MonadState s m, Bits a) => Traversal' s a -> a -> m ()
--   
(.&.=) :: (MonadState s m, Bits a) => ASetter' s a -> a -> m ()

-- | Modify the target(s) of a Lens', (or Traversal) by
--   computing its bitwise .|. with another value, returning the
--   result (or a monoidal summary of all of the results traversed).
--   
--   
--   >>> runState (_1 <.|.= 7) (28,0)
--   (31,(31,0))
--   
--   
--   
--   (<.|.=) :: (MonadState s m, Bits a)           => Lens' s a      -> a -> m a
--   (<.|.=) :: (MonadState s m, Bits a, Monoid a) => Traversal' s a -> a -> m a
--   
(<.|.=) :: (MonadState s m, Bits a) => LensLike' ((,) a) s a -> a -> m a

-- | Modify the target(s) of a Lens' (or Traversal') by
--   computing its bitwise .&. with another value, returning the
--   result (or a monoidal summary of all of the results traversed).
--   
--   
--   >>> runState (_1 <.&.= 15) (31,0)
--   (15,(15,0))
--   
--   
--   
--   (<.&.=) :: (MonadState s m, Bits a)           => Lens' s a      -> a -> m a
--   (<.&.=) :: (MonadState s m, Bits a, Monoid a) => Traversal' s a -> a -> m a
--   
(<.&.=) :: (MonadState s m, Bits a) => LensLike' ((,) a) s a -> a -> m a

-- | This Lens can be used to access the value of the nth bit in a
--   number.
--   
--   bitAt n is only a legal Lens into b if
--   0 <= n < bitSize (undefined ::
--   b).
--   
--   
--   >>> 16^.bitAt 4
--   True
--   
--   
--   
--   >>> 15^.bitAt 4
--   False
--   
--   
--   
--   >>> 15 & bitAt 4 .~ True
--   31
--   
--   
--   
--   >>> 16 & bitAt 4 .~ False
--   0
--   
bitAt :: Bits b => Int -> IndexedLens' Int b Bool

-- | Traverse over all bits in a numeric type.
--   
--   The bit position is available as the index.
--   
--   
--   >>> toListOf bits (5 :: Word8)
--   [True,False,True,False,False,False,False,False]
--   
--   
--   If you supply this an Integer, the result will be an infinite
--   Traversal, which can be productively consumed, but not
--   reassembled.
bits :: (Num b, Bits b) => IndexedTraversal' Int b Bool

-- | Get the nth byte, counting from the low end.
--   
--   byteAt n is a legal Lens into b iff
--   0 <= n < div (bitSize
--   (undefined :: b)) 8
--   
--   
--   >>> (0xff00 :: Word16)^.byteAt 0
--   0
--   
--   
--   
--   >>> (0xff00 :: Word16)^.byteAt 1
--   255
--   
--   
--   
--   >>> byteAt 1 .~ 0 $ 0xff00 :: Word16
--   0
--   
--   
--   
--   >>> byteAt 0 .~ 0xff $ 0 :: Word16
--   255
--   
byteAt :: (Integral b, Bits b) => Int -> IndexedLens' Int b Word8

module Data.ByteString.Strict.Lens

-- | pack (or unpack) a list of bytes into a
--   ByteString
--   
--   
--   packedBytes ≡ from unpackedBytes
--   pack x ≡  x ^. packedBytes
--   unpack x ≡ x ^. from packedBytes
--   
--   
--   
--   >>> [104,101,108,108,111]^.packedBytes
--   "hello"
--   
packedBytes :: Iso' [Word8] ByteString

-- | unpack (or pack) a ByteString into a list of
--   bytes
--   
--   
--   unpackedBytes ≡ from packedBytes
--   unpack x ≡ x ^. unpackedBytes
--   pack x ≡  x ^. from unpackedBytes
--   
--   
--   
--   >>> "hello"^.packedChars.unpackedBytes
--   [104,101,108,108,111]
--   
unpackedBytes :: Iso' ByteString [Word8]

-- | Traverse each Word8 in a ByteString.
--   
--   This Traversal walks the ByteString in a tree-like
--   fashion enable zippers to seek to locations in logarithmic time and
--   accelerating many monoidal queries, but up to associativity (and
--   constant factors) it is equivalent to the much slower:
--   
--   
--   bytes ≡ unpackedBytes . traversed
--   
--   
--   
--   >>> anyOf bytes (== 0x80) (Char8.pack "hello")
--   False
--   
bytes :: IndexedTraversal' Int ByteString Word8

-- | pack (or unpack) a list of characters into a
--   ByteString
--   
--   When writing back to the ByteString it is assumed that every
--   Char lies between '\x00' and '\xff'.
--   
--   
--   packedChars ≡ from unpackedChars
--   pack x ≡ x ^. packedChars
--   unpack x ≡ x ^. from packedChars
--   
--   
--   
--   >>> "hello"^.packedChars.each.re (base 16 . enum).to (\x -> if Prelude.length x == 1 then '0':x else x)
--   "68656c6c6f"
--   
packedChars :: Iso' String ByteString

-- | unpack (or pack) a list of characters into a
--   ByteString
--   
--   When writing back to the ByteString it is assumed that every
--   Char lies between '\x00' and '\xff'.
--   
--   
--   unpackedChars ≡ from packedChars
--   unpack x ≡ x ^. unpackedChars
--   pack x ≡ x ^. from unpackedChars
--   
--   
--   
--   >>> [104,101,108,108,111]^.packedBytes.unpackedChars
--   "hello"
--   
unpackedChars :: Iso' ByteString String

-- | Traverse the individual bytes in a ByteString as characters.
--   
--   When writing back to the ByteString it is assumed that every
--   Char lies between '\x00' and '\xff'.
--   
--   This Traversal walks the ByteString in a tree-like
--   fashion enable zippers to seek to locations in logarithmic time and
--   accelerating many monoidal queries, but up to associativity (and
--   constant factors) it is equivalent to the much slower:
--   
--   
--   chars = unpackedChars . traverse
--   
--   
--   
--   >>> anyOf chars (== 'h') "hello"
--   True
--   
chars :: IndexedTraversal' Int ByteString Char

-- | Lazy ByteString lenses.
module Data.ByteString.Lazy.Lens

-- | pack (or unpack) a list of bytes into a
--   ByteString.
--   
--   
--   packedBytes ≡ from unpackedBytes
--   pack x ≡  x ^. packedBytes
--   unpack x ≡ x ^. from packedBytes
--   
--   
--   
--   >>> [104,101,108,108,111]^.packedBytes == Char8.pack "hello"
--   True
--   
packedBytes :: Iso' [Word8] ByteString

-- | unpack (or pack) a ByteString into a list of
--   bytes
--   
--   
--   unpackedBytes ≡ from packedBytes
--   unpack x ≡ x ^. unpackedBytes
--   pack x ≡  x ^. from unpackedBytes
--   
--   
--   
--   >>> "hello"^.packedChars.unpackedBytes
--   [104,101,108,108,111]
--   
unpackedBytes :: Iso' ByteString [Word8]

-- | Traverse the individual bytes in a ByteString.
--   
--   This Traversal walks each strict ByteString chunk in a
--   tree-like fashion enable zippers to seek to locations more quickly and
--   accelerate many monoidal queries, but up to associativity (and
--   constant factors) it is equivalent to the much slower:
--   
--   
--   bytes ≡ unpackedBytes . traversed
--   
--   
--   
--   >>> anyOf bytes (== 0x80) (Char8.pack "hello")
--   False
--   
bytes :: IndexedTraversal' Int64 ByteString Word8

-- | pack (or unpack) a list of characters into a
--   ByteString.
--   
--   When writing back to the ByteString it is assumed that every
--   Char lies between '\x00' and '\xff'.
--   
--   
--   packedChars ≡ from unpackedChars
--   pack x ≡ x ^. packedChars
--   unpack x ≡ x ^. from packedChars
--   
--   
--   
--   >>> "hello"^.packedChars.each.re (base 16 . enum).to (\x -> if Prelude.length x == 1 then '0':x else x)
--   "68656c6c6f"
--   
packedChars :: Iso' String ByteString

-- | unpack (or pack) a list of characters into a
--   ByteString
--   
--   When writing back to the ByteString it is assumed that every
--   Char lies between '\x00' and '\xff'.
--   
--   
--   unpackedChars ≡ from packedChars
--   unpack x ≡ x ^. unpackedChars
--   pack x ≡ x ^. from unpackedChars
--   
--   
--   
--   >>> [104,101,108,108,111]^.packedBytes.unpackedChars
--   "hello"
--   
unpackedChars :: Iso' ByteString String

-- | Traverse the individual bytes in a ByteString as characters.
--   
--   When writing back to the ByteString it is assumed that every
--   Char lies between '\x00' and '\xff'.
--   
--   This Traversal walks each strict ByteString chunk in a
--   tree-like fashion enable zippers to seek to locations more quickly and
--   accelerate many monoidal queries, but up to associativity (and
--   constant factors) it is equivalent to:
--   
--   
--   chars = unpackedChars . traversed
--   
--   
--   
--   >>> anyOf chars (== 'h') "hello"
--   True
--   
chars :: IndexedTraversal' Int64 ByteString Char

module Data.ByteString.Lens

-- | Traversals for ByteStrings.
class IsByteString t where bytes = from packedBytes . traversed chars = from packedChars . traversed
packedBytes :: IsByteString t => Iso' [Word8] t
packedChars :: IsByteString t => Iso' String t
bytes :: IsByteString t => IndexedTraversal' Int t Word8
chars :: IsByteString t => IndexedTraversal' Int t Char

-- | unpack (or pack) a ByteString into a list of
--   bytes
--   
--   
--   unpackedBytes ≡ from packedBytes
--   unpack x ≡ x ^. unpackedBytes
--   pack x ≡  x ^. from unpackedBytes
--   
--   
--   
--   unpackedBytes :: Iso' ByteString [Word8]
--   unpackedBytes :: Iso' ByteString [Word8]
--   
unpackedBytes :: IsByteString t => Iso' t [Word8]

-- | unpack (or pack) a list of characters into a strict (or
--   lazy) ByteString
--   
--   When writing back to the ByteString it is assumed that every
--   Char lies between '\x00' and '\xff'.
--   
--   
--   unpackedChars ≡ from packedChars
--   unpack x ≡ x ^. unpackedChars
--   pack x ≡ x ^. from unpackedChars
--   
--   
--   
--   unpackedChars :: Iso' ByteString String
--   unpackedChars :: Iso' ByteString String
--   
unpackedChars :: IsByteString t => Iso' t String
instance IsByteString ByteString
instance IsByteString ByteString

-- | Lenses and traversals for complex numbers
module Data.Complex.Lens

-- | Access the realPart of a Complex number.
--   
--   
--   >>> (a :+ b)^._realPart
--   a
--   
--   
--   
--   >>> a :+ b & _realPart *~ 2
--   a * 2 :+ b
--   
--   
--   
--   _realPart :: Functor f => (a -> f a) -> Complex a -> f (Complex a)
--   
_realPart :: Lens' (Complex a) a

-- | Access the imagPart of a Complex number.
--   
--   
--   >>> (a :+ b)^._imagPart
--   b
--   
--   
--   
--   >>> a :+ b & _imagPart *~ 2
--   a :+ b * 2
--   
--   
--   
--   _imagPart :: Functor f => (a -> f a) -> Complex a -> f (Complex a)
--   
_imagPart :: Lens' (Complex a) a

-- | This isn't quite a legal Lens. Notably the
--   
--   
--   view l (set l b a) = b
--   
--   
--   law is violated when you set a polar value with 0
--   magnitude and non-zero phase as the phase
--   information is lost, or with a negative magnitude which flips
--   the phase and retains a positive magnitude. So don't do
--   that!
--   
--   Otherwise, this is a perfectly cromulent Lens.
_polar :: RealFloat a => Iso' (Complex a) (a, a)

-- | Access the magnitude of a Complex number.
--   
--   
--   >>> (10.0 :+ 20.0) & _magnitude *~ 2
--   20.0 :+ 40.0
--   
--   
--   This isn't quite a legal Lens. Notably the
--   
--   
--   view l (set l b a) = b
--   
--   
--   law is violated when you set a negative magnitude. This flips
--   the phase and retains a positive magnitude. So don't do
--   that!
--   
--   Otherwise, this is a perfectly cromulent Lens.
--   
--   Setting the magnitude of a zero Complex number assumes
--   the phase is 0.
_magnitude :: RealFloat a => Lens' (Complex a) a

-- | Access the phase of a Complex number.
--   
--   
--   >>> (mkPolar 10 (2-pi) & _phase +~ pi & view _phase) ~~ 2
--   True
--   
--   
--   This isn't quite a legal Lens. Notably the
--   
--   
--   view l (set l b a) = b
--   
--   
--   law is violated when you set a phase outside the range
--   (-pi, pi]. The phase is always in that range
--   when queried. So don't do that!
--   
--   Otherwise, this is a perfectly cromulent Lens.
_phase :: RealFloat a => Lens' (Complex a) a

-- | Access the conjugate of a Complex number.
--   
--   
--   >>> (2.0 :+ 3.0) & _conjugate . _imagPart -~ 1
--   2.0 :+ 4.0
--   
--   
--   
--   >>> (mkPolar 10.0 2.0 ^. _conjugate . _phase) ~~ (-2.0)
--   True
--   
_conjugate :: RealFloat a => Iso' (Complex a) (Complex a)

module Data.Dynamic.Lens

-- | Any Dynamic can be thrown as an Exception
class AsDynamic t
_Dynamic :: (AsDynamic t, Typeable a) => Prism' t a
instance AsDynamic SomeException
instance AsDynamic Dynamic

module Data.IntSet.Lens

-- | IntSet isn't Foldable, but this Fold can be used to access the
--   members of an IntSet.
--   
--   
--   >>> sumOf members $ setOf folded [1,2,3,4]
--   10
--   
members :: Fold IntSet Int

-- | This Setter can be used to change the contents of an
--   IntSet by mapping the elements to new values.
--   
--   Sadly, you can't create a valid Traversal for a Set,
--   because the number of elements might change but you can manipulate it
--   by reading using folded and reindexing it via setmapped.
--   
--   
--   >>> over setmapped (+1) (fromList [1,2,3,4])
--   fromList [2,3,4,5]
--   
setmapped :: IndexPreservingSetter' IntSet Int

-- | Construct an IntSet from a Getter, Fold,
--   Traversal, Lens or Iso.
--   
--   
--   >>> setOf folded [1,2,3,4]
--   fromList [1,2,3,4]
--   
--   
--   
--   >>> setOf (folded._2) [("hello",1),("world",2),("!!!",3)]
--   fromList [1,2,3]
--   
--   
--   
--   setOf :: Getter s Int     -> s -> IntSet
--   setOf :: Fold s Int       -> s -> IntSet
--   setOf :: Iso' s Int       -> s -> IntSet
--   setOf :: Lens' s Int      -> s -> IntSet
--   setOf :: Traversal' s Int -> s -> IntSet
--   
setOf :: Getting IntSet s Int -> s -> IntSet

-- | Traversals for manipulating parts of a list.
module Data.List.Lens

-- | A Prism stripping a prefix from a list when used as a
--   Traversal, or prepending that prefix when run backwards:
--   
--   
--   >>> "preview" ^? prefixed "pre"
--   Just "view"
--   
--   
--   
--   >>> "review" ^? prefixed "pre"
--   Nothing
--   
--   
--   
--   >>> prefixed "pre" # "amble"
--   "preamble"
--   
prefixed :: Eq a => [a] -> Prism' [a] [a]

-- | A Prism stripping a suffix from a list when used as a
--   Traversal, or prepending that prefix when run backwards:
--   
--   
--   >>> "review" ^? suffixed "view"
--   Just "re"
--   
--   
--   
--   >>> "review" ^? suffixed "tire"
--   Nothing
--   
--   
--   
--   >>> suffixed ".o" # "hello"
--   "hello.o"
--   
suffixed :: Eq a => [a] -> Prism' [a] [a]
stripSuffix :: Eq a => [a] -> [a] -> Maybe [a]

-- | This is a deprecated alias for prefixed.

-- | Deprecated: Use prefixed. 
strippingPrefix :: Eq a => [a] -> Prism' [a] [a]

-- | This is a deprecated alias for suffixed.

-- | Deprecated: Use suffixed. 
strippingSuffix :: Eq a => [a] -> Prism' [a] [a]

-- | Lenses for working with Data.List.Split
module Data.List.Split.Lens

-- | Obtain a Fold by splitting another Fold, Lens,
--   Getter or Traversal according to the given splitting
--   strategy.
--   
--   
--   splitting :: Splitter a -> Fold s a -> Fold s [a]
--   
splitting :: Splitter a -> Getting (Endo [a]) s a -> Fold s [a]

-- | Obtain a Fold by splitting another Fold, Lens,
--   Getter or Traversal on the given delimiter.
--   
--   Equivalent to splitting . dropDelims .
--   onSublist.
--   
--   
--   splittingOn :: Eq a => [a] -> Fold s a -> Fold s [a]
--   
splittingOn :: Eq a => [a] -> Getting (Endo [a]) s a -> Fold s [a]

-- | Obtain a Fold by splitting another Fold, Lens,
--   Getter or Traversal on any of the given elements.
--   
--   Equivalent to splitting . dropDelims .
--   oneOf.
--   
--   
--   splittingOn :: Eq a => [a] -> Fold s a -> Fold s [a]
--   
splittingOneOf :: Eq a => [a] -> Getting (Endo [a]) s a -> Fold s [a]

-- | Obtain a Fold by splitting another Fold, Lens,
--   Getter or Traversal on elements satisfying the given
--   predicate.
--   
--   Equivalent to splitting . dropDelims .
--   whenElt.
--   
--   
--   splittingWhen :: (a -> Bool) -> Fold s a -> Fold s [a]
--   
splittingWhen :: (a -> Bool) -> Getting (Endo [a]) s a -> Fold s [a]

-- | Obtain a Fold by splitting another Fold, Lens,
--   Getter or Traversal into chunks terminated by the given
--   delimiter.
--   
--   Equivalent to splitting . dropDelims .
--   onSublist.
--   
--   
--   endingBy :: Eq a => [a] -> Fold s a -> Fold s [a]
--   
endingBy :: Eq a => [a] -> Getting (Endo [a]) s a -> Fold s [a]

-- | Obtain a Fold by splitting another Fold, Lens,
--   Getter or Traversal into chunks terminated by any of the
--   given elements.
--   
--   Equivalent to splitting . dropFinalBlank
--   . dropDelims . oneOf.
--   
--   
--   endingByOneOf :: Eq a => [a] -> Fold s a -> Fold s [a]
--   
endingByOneOf :: Eq a => [a] -> Getting (Endo [a]) s a -> Fold s [a]

-- | Obtain a Fold by splitting another Fold, Lens,
--   Getter or Traversal into words, with word
--   boundaries indicated by the given predicate.
--   
--   Equivalent to splitting . dropBlanks .
--   dropDelims . whenElt.
--   
--   
--   wordingBy :: (a -> Bool) -> Fold s a -> Fold s [a]
--   
wordingBy :: (a -> Bool) -> Getting (Endo [a]) s a -> Fold s [a]

-- | Obtain a Fold by splitting another Fold, Lens,
--   Getter or Traversal into lines, with line
--   boundaries indicated by the given predicate.
--   
--   Equivalent to splitting . dropFinalBlank
--   . dropDelims . whenElt.
--   
--   
--   liningBy :: (a -> Bool) -> Fold s a -> Fold s [a]
--   
liningBy :: (a -> Bool) -> Getting (Endo [a]) s a -> Fold s [a]

-- | Obtain a Fold by splitting another Fold, Lens,
--   Getter or Traversal into length-n pieces.
--   
--   
--   chunking :: Int -> Fold s a -> Fold s [a]
--   
chunking :: Int -> Getting (Endo [a]) s a -> Fold s [a]

-- | Obtain a Fold by splitting another Fold, Lens,
--   Getter or Traversal into chunks of the given lengths, .
--   
--   
--   splittingPlaces :: Integral n => [n] -> Fold s a -> Fold s [a]
--   
splittingPlaces :: Integral n => [n] -> Getting (Endo [a]) s a -> Fold s [a]

-- | Obtain a Fold by splitting another Fold, Lens,
--   Getter or Traversal into chunks of the given lengths.
--   Unlike splittingPlaces, the output Fold will always be
--   the same length as the first input argument.
--   
--   
--   splittingPlacesBlanks :: Integral n => [n] -> Fold s a -> Fold s [a]
--   
splittingPlacesBlanks :: Integral n => [n] -> Getting (Endo [a]) s a -> Fold s [a]

-- | Modify or retrieve the list of delimiters for a Splitter.
delimiters :: Lens (Splitter a) (Splitter b) [a -> Bool] [b -> Bool]

-- | Modify or retrieve the policy for what a Splitter to do with
--   delimiters.
delimiting :: Lens' (Splitter a) DelimPolicy

-- | Modify or retrieve the policy for what a Splitter should about
--   consecutive delimiters.
condensing :: Lens' (Splitter a) CondensePolicy

-- | Modify or retrieve the policy for whether a Splitter should
--   drop an initial blank.
keepInitialBlanks :: Lens' (Splitter a) Bool

-- | Modify or retrieve the policy for whether a Splitter should
--   drop a final blank.
keepFinalBlanks :: Lens' (Splitter a) Bool

module Data.Sequence.Lens

-- | A Seq is isomorphic to a ViewL
--   
--   
--   viewl m ≡ m ^. viewL
--   
--   
--   
--   >>> Seq.fromList [a,b,c] ^. viewL
--   a :< fromList [b,c]
--   
--   
--   
--   >>> Seq.empty ^. viewL
--   EmptyL
--   
--   
--   
--   >>> EmptyL ^. from viewL
--   fromList []
--   
--   
--   
--   >>> review viewL $ a :< fromList [b,c]
--   fromList [a,b,c]
--   
viewL :: Iso (Seq a) (Seq b) (ViewL a) (ViewL b)

-- | A Seq is isomorphic to a ViewR
--   
--   
--   viewr m ≡ m ^. viewR
--   
--   
--   
--   >>> Seq.fromList [a,b,c] ^. viewR
--   fromList [a,b] :> c
--   
--   
--   
--   >>> Seq.empty ^. viewR
--   EmptyR
--   
--   
--   
--   >>> EmptyR ^. from viewR
--   fromList []
--   
--   
--   
--   >>> review viewR $ fromList [a,b] :> c
--   fromList [a,b,c]
--   
viewR :: Iso (Seq a) (Seq b) (ViewR a) (ViewR b)

-- | Traverse all the elements numbered from i to j of a
--   Seq
--   
--   
--   >>> fromList [a,b,c,d,e] & sliced 1 3 %~ f
--   fromList [a,f b,f c,d,e]
--   
sliced :: Int -> Int -> IndexedTraversal' Int (Seq a) a

-- | Traverse the first n elements of a Seq
--   
--   
--   >>> fromList [a,b,c,d,e] ^.. slicedTo 2
--   [a,b]
--   
--   
--   
--   >>> fromList [a,b,c,d,e] & slicedTo 2 %~ f
--   fromList [f a,f b,c,d,e]
--   
--   
--   
--   >>> fromList [a,b,c,d,e] & slicedTo 10 .~ x
--   fromList [x,x,x,x,x]
--   
slicedTo :: Int -> IndexedTraversal' Int (Seq a) a

-- | Traverse all but the first n elements of a Seq
--   
--   
--   >>> fromList [a,b,c,d,e] ^.. slicedFrom 2
--   [c,d,e]
--   
--   
--   
--   >>> fromList [a,b,c,d,e] & slicedFrom 2 %~ f
--   fromList [a,b,f c,f d,f e]
--   
--   
--   
--   >>> fromList [a,b,c,d,e] & slicedFrom 10 .~ x
--   fromList [a,b,c,d,e]
--   
slicedFrom :: Int -> IndexedTraversal' Int (Seq a) a

module Data.Text.Strict.Lens

-- | This isomorphism can be used to pack (or unpack) strict
--   Text.
--   
--   
--   >>> "hello"^.packed -- :: Text
--   "hello"
--   
--   
--   
--   pack x ≡ x ^. packed
--   unpack x ≡ x ^. from packed
--   packed ≡ from unpacked
--   packed ≡ iso pack unpack
--   
packed :: Iso' String Text

-- | This isomorphism can be used to unpack (or pack) lazy
--   Text.
--   
--   
--   >>> "hello"^.unpacked -- :: String
--   "hello"
--   
--   
--   This Iso is provided for notational convenience rather than out
--   of great need, since
--   
--   
--   unpacked ≡ from packed
--   
--   
--   
--   pack x ≡ x ^. from unpacked
--   unpack x ≡ x ^. packed
--   unpacked ≡ iso unpack pack
--   
unpacked :: Iso' Text String

-- | Convert between strict Text and Builder .
--   
--   
--   fromText x ≡ x ^. builder
--   toStrict (toLazyText x) ≡ x ^. from builder
--   
builder :: Iso' Text Builder

-- | Traverse the individual characters in strict Text.
--   
--   
--   >>> anyOf text (=='o') "hello"
--   True
--   
--   
--   When the type is unambiguous, you can also use the more general
--   each.
--   
--   
--   text ≡ unpacked . traversed
--   text ≡ each
--   
text :: IndexedTraversal' Int Text Char

module Data.Text.Lazy.Lens

-- | This isomorphism can be used to pack (or unpack) lazy
--   Text.
--   
--   
--   >>> "hello"^.packed -- :: Text
--   "hello"
--   
--   
--   
--   pack x ≡ x ^. packed
--   unpack x ≡ x ^. from packed
--   packed ≡ from unpacked
--   
packed :: Iso' String Text

-- | This isomorphism can be used to unpack (or pack) lazy
--   Text.
--   
--   
--   >>> "hello"^.unpacked -- :: String
--   "hello"
--   
--   
--   
--   pack x ≡ x ^. from unpacked
--   unpack x ≡ x ^. packed
--   
--   
--   This Iso is provided for notational convenience rather than out
--   of great need, since
--   
--   
--   unpacked ≡ from packed
--   
unpacked :: Iso' Text String

-- | Traverse the individual characters in a Text.
--   
--   
--   >>> anyOf text (=='c') "chello"
--   True
--   
--   
--   
--   text = unpacked . traversed
--   
--   
--   When the type is unambiguous, you can also use the more general
--   each.
--   
--   
--   text ≡ each
--   
text :: IndexedTraversal' Int Text Char

-- | Convert between lazy Text and Builder .
--   
--   
--   fromLazyText x ≡ x ^. builder
--   toLazyText x ≡ x ^. from builder
--   
builder :: Iso' Text Builder

module Data.Text.Lens

-- | Traversals for strict or lazy Text
class IsText t where text = unpacked . traversed
packed :: IsText t => Iso' String t
builder :: IsText t => Iso' t Builder
text :: IsText t => IndexedTraversal' Int t Char

-- | This isomorphism can be used to unpack (or pack) both
--   strict or lazy Text.
--   
--   
--   unpack x ≡ x ^. unpacked
--   pack x ≡ x ^. from unpacked
--   
--   
--   This Iso is provided for notational convenience rather than out
--   of great need, since
--   
--   
--   unpacked ≡ from packed
--   
unpacked :: IsText t => Iso' t String
instance IsText Text
instance IsText Text

module Data.Tree.Lens

-- | A Lens that focuses on the root of a Tree.
--   
--   
--   >>> view root $ Node 42 []
--   42
--   
root :: Lens' (Tree a) a

-- | A Lens returning the direct descendants of the root of a
--   Tree
--   
--   
--   view branches ≡ subForest
--   
branches :: Lens' (Tree a) [Tree a]

module Data.Typeable.Lens

-- | A Traversal' for working with a cast of a
--   Typeable value.
_cast :: (Typeable s, Typeable a) => Traversal' s a

-- | A Traversal' for working with a gcast of a
--   Typeable value.
_gcast :: (Typeable s, Typeable a) => Traversal' (c s) (c a)

-- | This module provides lenses and traversals for working with generic
--   vectors.
module Data.Vector.Lens

-- | Similar to toListOf, but returning a Vector.
--   
--   
--   >>> toVectorOf both (8,15)
--   fromList [8,15]
--   
toVectorOf :: Getting (Endo [a]) s a -> s -> Vector a

-- | Convert a list to a Vector (or back)
--   
--   
--   >>> [1,2,3] ^. vector
--   fromList [1,2,3]
--   
--   
--   
--   >>> [1,2,3] ^. vector . from vector
--   [1,2,3]
--   
--   
--   
--   >>> Vector.fromList [0,8,15] ^. from vector . vector
--   fromList [0,8,15]
--   
vector :: Iso [a] [b] (Vector a) (Vector b)

-- | Convert a Vector to a version that doesn't retain any extra
--   memory.
forced :: Iso (Vector a) (Vector b) (Vector a) (Vector b)

-- | sliced i n provides a Lens that edits the n
--   elements starting at index i from a Lens.
--   
--   This is only a valid Lens if you do not change the length of
--   the resulting Vector.
--   
--   Attempting to return a longer or shorter vector will result in
--   violations of the Lens laws.
--   
--   
--   >>> Vector.fromList [1..10] ^. sliced 2 5
--   fromList [3,4,5,6,7]
--   
--   
--   
--   >>> Vector.fromList [1..10] & sliced 2 5 . mapped .~ 0
--   fromList [1,2,0,0,0,0,0,8,9,10]
--   
sliced :: Int -> Int -> Lens' (Vector a) (Vector a)

-- | This Traversal will ignore any duplicates in the supplied list
--   of indices.
--   
--   
--   >>> toListOf (ordinals [1,3,2,5,9,10]) $ Vector.fromList [2,4..40]
--   [4,8,6,12,20,22]
--   
ordinals :: [Int] -> IndexedTraversal' Int (Vector a) a

-- | This module provides lenses and traversals for working with generic
--   vectors.
module Data.Vector.Generic.Lens

-- | Similar to toListOf, but returning a Vector.
--   
--   
--   >>> toVectorOf both (8,15) :: Vector.Vector Int
--   fromList [8,15]
--   
toVectorOf :: Vector v a => Getting (Endo [a]) s a -> s -> v a

-- | Convert a Vector to a version that doesn't retain any extra
--   memory.
forced :: Vector v a => Iso' (v a) (v a)

-- | Convert a list to a Vector (or back.)
--   
--   
--   >>> [1,2,3] ^. vector :: Vector.Vector Int
--   fromList [1,2,3]
--   
--   
--   
--   >>> Vector.fromList [0,8,15] ^. from vector
--   [0,8,15]
--   
vector :: Vector v a => Iso' [a] (v a)

-- | Convert a Vector to a finite Stream (or back.)
asStream :: Vector v a => Iso' (v a) (Stream a)

-- | Convert a Vector to a finite Stream from right to left
--   (or back.)
asStreamR :: Vector v a => Iso' (v a) (Stream a)

-- | Convert a Vector back and forth to an initializer that when run
--   produces a copy of the Vector.
cloned :: Vector v a => Iso' (v a) (New v a)

-- | sliced i n provides a Lens that edits the n
--   elements starting at index i from a Lens.
--   
--   This is only a valid Lens if you do not change the length of
--   the resulting Vector.
--   
--   Attempting to return a longer or shorter vector will result in
--   violations of the Lens laws.
--   
--   
--   >>> Vector.fromList [1..10] ^. sliced 2 5
--   fromList [3,4,5,6,7]
--   
--   
--   
--   >>> Vector.fromList [1..10] & sliced 2 5 . mapped .~ 0
--   fromList [1,2,0,0,0,0,0,8,9,10]
--   
sliced :: Vector v a => Int -> Int -> Lens' (v a) (v a)

-- | This Traversal will ignore any duplicates in the supplied list
--   of indices.
--   
--   
--   >>> toListOf (ordinals [1,3,2,5,9,10]) $ Vector.fromList [2,4..40]
--   [4,8,6,12,20,22]
--   
ordinals :: Vector v a => [Int] -> IndexedTraversal' Int (v a) a

-- | These prisms can be used with the combinators in
--   Control.Exception.Lens.
module System.Exit.Lens

-- | Exit codes that a program can return with:
class AsExitCode p f t
_ExitCode :: AsExitCode p f t => Overloaded' p f t ExitCode

-- | indicates program failure with an exit code. The exact interpretation
--   of the code is operating-system dependent. In particular, some values
--   may be prohibited (e.g. 0 on a POSIX-compliant system).
--   
--   
--   _ExitFailure :: Prism' ExitCode      Int
--   _ExitFailure :: Prism' SomeException Int
--   
_ExitFailure :: (AsExitCode p f t, Choice p, Applicative f) => Overloaded' p f t Int

-- | indicates successful termination;
--   
--   
--   _ExitSuccess :: Prism' ExitCode      ()
--   _ExitSuccess :: Prism' SomeException ()
--   
_ExitSuccess :: (AsExitCode p f t, Choice p, Applicative f) => Overloaded' p f t ()
instance (Choice p, Applicative f) => AsExitCode p f SomeException
instance AsExitCode p f ExitCode

module System.FilePath.Lens

-- | Modify the path by adding another path.
--   
--   
--   >>> both </>~ "bin" $ ("hello","world")
--   ("hello/bin","world/bin")
--   
--   
--   
--   (</>~) :: Setter s a FilePath FilePath -> FilePath -> s -> a
--   (</>~) :: Iso s a FilePath FilePath -> FilePath -> s -> a
--   (</>~) :: Lens s a FilePath FilePath -> FilePath -> s -> a
--   (</>~) :: Traversal s a FilePath FilePath -> FilePath -> s -> a
--   
(</>~) :: ASetter s t FilePath FilePath -> FilePath -> s -> t

-- | Add a path onto the end of the target of a Lens and return the
--   result
--   
--   When you do not need the result of the operation, (</>~)
--   is more flexible.
(<</>~) :: LensLike ((,) FilePath) s a FilePath FilePath -> FilePath -> s -> (FilePath, a)

-- | Modify the path by adding extension.
--   
--   
--   >>> both <.>~ "txt" $ ("hello","world")
--   ("hello.txt","world.txt")
--   
--   
--   
--   (<.>~) :: Setter s a FilePath FilePath -> String -> s -> a
--   (<.>~) :: Iso s a FilePath FilePath -> String -> s -> a
--   (<.>~) :: Lens s a FilePath FilePath -> String -> s -> a
--   (<.>~) :: Traversal s a FilePath FilePath -> String -> s -> a
--   
(<.>~) :: ASetter s a FilePath FilePath -> String -> s -> a

-- | Add an extension onto the end of the target of a Lens and
--   return the result
--   
--   
--   >>> _1 <<.>~ "txt" $ ("hello","world")
--   ("hello.txt",("hello.txt","world"))
--   
--   
--   When you do not need the result of the operation, (<.>~)
--   is more flexible.
(<<.>~) :: LensLike ((,) FilePath) s a FilePath FilePath -> String -> s -> (FilePath, a)

-- | Modify the target(s) of a Simple Lens, Iso,
--   Setter or Traversal by adding a path.
--   
--   
--   >>> execState (both </>= "bin") ("hello","world")
--   ("hello/bin","world/bin")
--   
--   
--   
--   (</>=) :: MonadState s m => Setter' s FilePath -> FilePath -> m ()
--   (</>=) :: MonadState s m => Iso' s FilePath -> FilePath -> m ()
--   (</>=) :: MonadState s m => Lens' s FilePath -> FilePath -> m ()
--   (</>=) :: MonadState s m => Traversal' s FilePath -> FilePath -> m ()
--   
(</>=) :: MonadState s m => ASetter' s FilePath -> FilePath -> m ()

-- | Add a path onto the end of the target of a Lens into your
--   monad's state and return the result.
--   
--   When you do not need the result of the operation, (</>=)
--   is more flexible.
(<</>=) :: MonadState s m => LensLike' ((,) FilePath) s FilePath -> FilePath -> m FilePath

-- | Modify the target(s) of a Simple Lens, Iso,
--   Setter or Traversal by adding an extension.
--   
--   
--   >>> execState (both <.>= "txt") ("hello","world")
--   ("hello.txt","world.txt")
--   
--   
--   
--   (<.>=) :: MonadState s m => Setter' s FilePath -> String -> m ()
--   (<.>=) :: MonadState s m => Iso' s FilePath -> String -> m ()
--   (<.>=) :: MonadState s m => Lens' s FilePath -> String -> m ()
--   (<.>=) :: MonadState s m => Traversal' s FilePath -> String -> m ()
--   
(<.>=) :: MonadState s m => ASetter' s FilePath -> String -> m ()

-- | Add an extension onto the end of the target of a Lens into your
--   monad's state and return the result.
--   
--   
--   >>> evalState (_1 <<.>= "txt") $("hello","world")
--   "hello.txt"
--   
--   
--   When you do not need the result of the operation, (<.>=)
--   is more flexible.
(<<.>=) :: MonadState s m => LensLike' ((,) FilePath) s FilePath -> String -> m FilePath

-- | A Lens for reading and writing to the basename
--   
--   
--   >>> basename .~ "filename" $ "path/name.png"
--   "path/filename.png"
--   
basename :: Lens' FilePath FilePath

-- | A Lens for reading and writing to the directory
--   
--   
--   >>> "long/path/name.txt" ^. directory
--   "long/path"
--   
directory :: Lens' FilePath FilePath

-- | A Lens for reading and writing to the extension
--   
--   
--   >>> extension .~ ".png" $ "path/name.txt"
--   "path/name.png"
--   
extension :: Lens' FilePath FilePath

-- | A Lens for reading and writing to the full filename
--   
--   
--   >>> filename .~ "name.txt" $ "path/name.png"
--   "path/name.txt"
--   
filename :: Lens' FilePath FilePath

module Numeric.Lens

-- | A prism that shows and reads integers in base-2 through base-36
--   
--   
--   >>> "100" ^? base 16
--   Just 256
--   
--   
--   
--   >>> 1767707668033969 ^. re (base 36)
--   "helloworld"
--   
base :: Integral a => Int -> Prism' String a

-- | This Prism extracts can be used to model the fact that every
--   Integral type is a subset of Integer.
--   
--   Embedding through the Prism only succeeds if the Integer
--   would pass through unmodified when re-extracted.
integral :: (Integral a, Integral b) => Prism Integer Integer a b

-- | 
--   binary = base 2
--   
binary :: Integral a => Prism' String a

-- | 
--   octal = base 8
--   
octal :: Integral a => Prism' String a

-- | 
--   decimal = base 10
--   
decimal :: Integral a => Prism' String a

-- | 
--   hex = base 16
--   
hex :: Integral a => Prism' String a
