lens-4.13: Lenses, Folds and Traversals

Copyright | (C) 2012-15 Edward Kmett
License | BSD-style (see the file LICENSE)
Maintainer | Edward Kmett <ekmett@gmail.com>
Stability | provisional
Portability | Rank2Types
Safe Haskell | Trustworthy
Language | Haskell98

Control.Lens.Indexed

Contents

- Indexing
- Indexed Functors
- Indexed Foldables
  - Indexed Foldable Combinators
- Converting to Folds
- Restricting by Index
- Indexed Traversables
- Indexed Traversable Combinators
- Indexed Folds with Reified Monoid
- Indexed Traversals with Reified Applicative

Description

(The classes in here need to be defined together for `DefaultSignatures` to work.)

Synopsis

- class Conjoined p => Indexable i p where
  - indexed :: p a b -> i -> a -> b
- class (Choice p, Corepresentable p, Comonad (Corep p), Traversable (Corep p), Strong p, Representable p, Monad (Rep p), MonadFix (Rep p), Distributive (Rep p), Costrong p, ArrowLoop p, ArrowApply p, ArrowChoice p) => Conjoined p where
  - distrib :: Functor f => p a b -> p (f a) (f b)
  - conjoined :: ((p ~ (->)) => q (a -> b) r) -> q (p a b) r -> q (p a b) r
- newtype Indexed i a b = Indexed {
  - runIndexed :: i -> a -> b
  }
- (<.) :: Indexable i p => (Indexed i s t -> r) -> ((a -> b) -> s -> t) -> p a b -> r
- (<.>) :: Indexable (i, j) p => (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> p a b -> r
- (.>) :: (st -> r) -> (kab -> st) -> kab -> r
- selfIndex :: Indexable a p => p a fb -> a -> fb
- reindexed :: Indexable j p => (i -> j) -> (Indexed i a b -> r) -> p a b -> r
- icompose :: Indexable p c => (i -> j -> p) -> (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> c a b -> r
- indexing :: Indexable Int p => ((a -> Indexing f b) -> s -> Indexing f t) -> p a (f b) -> s -> f t
- indexing64 :: Indexable Int64 p => ((a -> Indexing64 f b) -> s -> Indexing64 f t) -> p a (f b) -> s -> f t
- class Functor f => FunctorWithIndex i f | f -> i where
  - imap :: (i -> a -> b) -> f a -> f b
  - imapped :: IndexedSetter i (f a) (f b) a b
- class Foldable f => FoldableWithIndex i f | f -> i where
  - ifoldMap :: Monoid m => (i -> a -> m) -> f a -> m
  - ifolded :: IndexedFold i (f a) a
  - ifoldr :: (i -> a -> b -> b) -> b -> f a -> b
  - ifoldl :: (i -> b -> a -> b) -> b -> f a -> b
  - ifoldr' :: (i -> a -> b -> b) -> b -> f a -> b
  - ifoldl' :: (i -> b -> a -> b) -> b -> f a -> b
- iany :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
- iall :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
- inone :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
- none :: Foldable f => (a -> Bool) -> f a -> Bool
- itraverse_ :: (FoldableWithIndex i t, Applicative f) => (i -> a -> f b) -> t a -> f ()
- ifor_ :: (FoldableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f ()
- imapM_ :: (FoldableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m ()
- iforM_ :: (FoldableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m ()
- iconcatMap :: FoldableWithIndex i f => (i -> a -> [b]) -> f a -> [b]
- ifind :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Maybe (i, a)
- ifoldrM :: (FoldableWithIndex i f, Monad m) => (i -> a -> b -> m b) -> b -> f a -> m b
- ifoldlM :: (FoldableWithIndex i f, Monad m) => (i -> b -> a -> m b) -> b -> f a -> m b
- itoList :: FoldableWithIndex i f => f a -> [(i, a)]
- withIndex :: (Indexable i p, Functor f) => p (i, s) (f (j, t)) -> Indexed i s (f t)
- asIndex :: (Indexable i p, Contravariant f, Functor f) => p i (f i) -> Indexed i s (f s)
- indices :: (Indexable i p, Applicative f) => (i -> Bool) -> Optical' p (Indexed i) f a a
- index :: (Indexable i p, Eq i, Applicative f) => i -> Optical' p (Indexed i) f a a
- class (FunctorWithIndex i t, FoldableWithIndex i t, Traversable t) => TraversableWithIndex i t | t -> i where
  - itraverse :: Applicative f => (i -> a -> f b) -> t a -> f (t b)
  - itraversed :: IndexedTraversal i (t a) (t b) a b
- ifor :: (TraversableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f (t b)
- imapM :: (TraversableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m (t b)
- iforM :: (TraversableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m (t b)
- imapAccumR :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b)
- imapAccumL :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b)
- ifoldMapBy :: FoldableWithIndex i t => (r -> r -> r) -> r -> (i -> a -> r) -> t a -> r
- ifoldMapByOf :: IndexedFold i t a -> (r -> r -> r) -> r -> (i -> a -> r) -> t -> r
- itraverseBy :: TraversableWithIndex i t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> t a -> f (t b)
- itraverseByOf :: IndexedTraversal i s t a b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> s -> f t

# Indexing

class Conjoined p => Indexable i p where Source

This class permits overloading of function application for things that also admit a notion of a key or index.

Methods

indexed :: p a b -> i -> a -> b Source

Build a function from an `indexed` function.

Instances

Indexable i (->) Source |
(~) * i j => Indexable i (Indexed j) Source |

class (Choice p, Corepresentable p, Comonad (Corep p), Traversable (Corep p), Strong p, Representable p, Monad (Rep p), MonadFix (Rep p), Distributive (Rep p), Costrong p, ArrowLoop p, ArrowApply p, ArrowChoice p) => Conjoined p where Source

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.

Minimal complete definition

Nothing

Methods

distrib :: Functor f => p a b -> p (f a) (f b) Source

`Conjoined` is strong enough to let us distribute every `Conjoined` `Profunctor` over every Haskell `Functor`. This is effectively a generalization of `fmap`.

conjoined :: ((p ~ (->)) => q (a -> b) r) -> q (p a b) r -> q (p a b) r Source

This permits us to make a decision at an outermost point about whether or not we use an index.

Ideally any use of this function should be done in such a way so that you compute the same answer, but this cannot be enforced at the type level.

Instances

Conjoined (->) Source |
Conjoined ReifiedGetter Source |
Conjoined (Indexed i) Source |

newtype Indexed i a b Source

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

Constructors

Indexed |

Fields

runIndexed :: i -> a -> b

Instances

Category * (Indexed i) Source |
(~) * i j => Indexable i (Indexed j) Source |
Arrow (Indexed i) Source |
ArrowChoice (Indexed i) Source |
ArrowApply (Indexed i) Source |
ArrowLoop (Indexed i) Source |
Representable (Indexed i) Source |
Corepresentable (Indexed i) Source |
Strong (Indexed i) Source |
Choice (Indexed i) Source |
Costrong (Indexed i) Source |
Profunctor (Indexed i) Source |
Conjoined (Indexed i) Source |
Bizarre (Indexed Int) Mafic Source |
Sieve (Indexed i) ((->) i) Source |
Cosieve (Indexed i) ((,) i) Source |
Sellable (Indexed i) (Molten i) Source |
Bizarre (Indexed i) (Molten i) Source |
Monad (Indexed i a) Source |
Functor (Indexed i a) Source |
MonadFix (Indexed i a) Source |
Applicative (Indexed i a) Source |
Apply (Indexed i a) Source |
Bind (Indexed i a) Source |
type Rep (Indexed i) = (->) i Source |
type Corep (Indexed i) = (,) i Source |

(<.) :: Indexable i p => (Indexed i s t -> r) -> ((a -> b) -> s -> t) -> p a b -> r infixr 9 Source

Compose an `Indexed` function with a non-indexed function.

Mnemonically, the `<` points to the indexing we want to preserve.

    >>> let nestedMap = (fmap Map.fromList . Map.fromList) [(1, [(10, "one,ten"), (20, "one,twenty")]), (2, [(30, "two,thirty"), (40,"two,forty")])]
    >>> nestedMap^..(itraversed<.itraversed).withIndex
    [(1,"one,ten"),(1,"one,twenty"),(2,"two,thirty"),(2,"two,forty")]

(<.>) :: Indexable (i, j) p => (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> p a b -> r infixr 9 Source

Composition of `Indexed` functions.

Mnemonically, the `<` and `>` points to the fact that we want to preserve the indices.

    >>> let nestedMap = (fmap Map.fromList . Map.fromList) [(1, [(10, "one,ten"), (20, "one,twenty")]), (2, [(30, "two,thirty"), (40,"two,forty")])]
    >>> nestedMap^..(itraversed<.>itraversed).withIndex
    [((1,10),"one,ten"),((1,20),"one,twenty"),((2,30),"two,thirty"),((2,40),"two,forty")]

(.>) :: (st -> r) -> (kab -> st) -> kab -> r infixr 9 Source

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`.

    >>> let nestedMap = (fmap Map.fromList . Map.fromList) [(1, [(10, "one,ten"), (20, "one,twenty")]), (2, [(30, "two,thirty"), (40,"two,forty")])]
    >>> nestedMap^..(itraversed.>itraversed).withIndex
    [(10,"one,ten"),(20,"one,twenty"),(30,"two,thirty"),(40,"two,forty")]

selfIndex :: Indexable a p => p a fb -> a -> fb Source

Use a value itself as its own index. This is essentially an indexed version of `id`.

Note: When used to modify the value, this can break the index requirements assumed by `indices` and similar, so this is only properly an `IndexedGetter`, but it can be used as more.

    selfIndex :: IndexedGetter a a b

reindexed :: Indexable j p => (i -> j) -> (Indexed i a b -> r) -> p a b -> r Source

Remap the index.

icompose :: Indexable p c => (i -> j -> p) -> (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> c a b -> r Source

Composition of `Indexed` functions with a user supplied function for combining indices.

indexing :: Indexable Int p => ((a -> Indexing f b) -> s -> Indexing f t) -> p a (f b) -> s -> f t Source

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 -> Over 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 Source

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 -> Over p f s t a b

# Indexed Functors

class Functor f => FunctorWithIndex i f | f -> i where Source

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

Minimal complete definition

Nothing

Methods

imap :: (i -> a -> b) -> f a -> f b Source

Map with access to the index.

imapped :: IndexedSetter i (f a) (f b) a b Source

The `IndexedSetter` for a `FunctorWithIndex`.

If you don't need access to the index, then `mapped` is more flexible in what it accepts.

Instances

FunctorWithIndex Int [] Source | The position in the list is available as the index.
FunctorWithIndex Int IntMap Source |
FunctorWithIndex Int Seq Source | The position in the `Seq` is available as the index.
FunctorWithIndex Int NonEmpty Source |
FunctorWithIndex Int Vector Source |
FunctorWithIndex Int Deque Source |
FunctorWithIndex () Identity Source |
FunctorWithIndex () Maybe Source |
FunctorWithIndex i m => FunctorWithIndex i (IdentityT m) Source |
Ix i => FunctorWithIndex i (Array i) Source |
FunctorWithIndex i (Level i) Source |
FunctorWithIndex r ((->) r) Source |
(Eq k, Hashable k) => FunctorWithIndex k (HashMap k) Source |
FunctorWithIndex k (Map k) Source |
FunctorWithIndex k ((,) k) Source |
FunctorWithIndex i f => FunctorWithIndex i (Reverse f) Source |
FunctorWithIndex i f => FunctorWithIndex i (Backwards f) Source |
FunctorWithIndex i (Magma i t b) Source |
FunctorWithIndex [Int] Tree Source |
FunctorWithIndex i f => FunctorWithIndex [i] (Cofree f) Source |
FunctorWithIndex i f => FunctorWithIndex [i] (Free f) Source |
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (Product f g) Source |
FunctorWithIndex i w => FunctorWithIndex (s, i) (TracedT s w) Source |
FunctorWithIndex i m => FunctorWithIndex (e, i) (ReaderT e m) Source |
(FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (i, j) (Compose f g) Source |

# Indexed Foldables

class Foldable f => FoldableWithIndex i f | f -> i where Source

A container that supports folding with an additional index.

Minimal complete definition

Nothing

Methods

ifoldMap :: Monoid m => (i -> a -> m) -> f a -> m Source

Fold a container by mapping value to an arbitrary `Monoid` with access to the index `i`.

When you don't need access to the index then `foldMap` is more flexible in what it accepts.

    foldMap ≡ ifoldMap . const

ifolded :: IndexedFold i (f a) a Source

The `IndexedFold` of a `FoldableWithIndex` container.

``ifolded` `.` `asIndex`` is a fold over the keys of a `FoldableWithIndex`.

    >>> Data.Map.fromList [(2, "hello"), (1, "world")]^..ifolded.asIndex
    [1,2]

ifoldr :: (i -> a -> b -> b) -> b -> f a -> b Source

Right-associative fold of an indexed container with access to the index `i`.

When you don't need access to the index then `foldr` is more flexible in what it accepts.

    foldr ≡ ifoldr . const

ifoldl :: (i -> b -> a -> b) -> b -> f a -> b Source

Left-associative fold of an indexed container with access to the index `i`.

When you don't need access to the index then `foldl` is more flexible in what it accepts.

    foldl ≡ ifoldl . const

ifoldr' :: (i -> a -> b -> b) -> b -> f a -> b Source

Strictly fold right over the elements of a structure with access to the index `i`.

When you don't need access to the index then `foldr'` is more flexible in what it accepts.

    foldr' ≡ ifoldr' . const

ifoldl' :: (i -> b -> a -> b) -> b -> f a -> b Source

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

Instances

FoldableWithIndex Int [] Source |
FoldableWithIndex Int IntMap Source |
FoldableWithIndex Int Seq Source |
FoldableWithIndex Int NonEmpty Source |
FoldableWithIndex Int Vector Source |
FoldableWithIndex Int Deque Source |
FoldableWithIndex () Identity Source |
FoldableWithIndex () Maybe Source |
FoldableWithIndex i m => FoldableWithIndex i (IdentityT m) Source |
Ix i => FoldableWithIndex i (Array i) Source |
FoldableWithIndex i (Level i) Source |
(Eq k, Hashable k) => FoldableWithIndex k (HashMap k) Source |
FoldableWithIndex k (Map k) Source |
FoldableWithIndex k ((,) k) Source |
FoldableWithIndex i f => FoldableWithIndex i (Reverse f) Source |
FoldableWithIndex i f => FoldableWithIndex i (Backwards f) Source |
FoldableWithIndex i (Magma i t b) Source |
FoldableWithIndex [Int] Tree Source |
FoldableWithIndex i f => FoldableWithIndex [i] (Cofree f) Source |
FoldableWithIndex i f => FoldableWithIndex [i] (Free f) Source |
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (Product f g) Source |
(FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (i, j) (Compose f g) Source |

## Indexed Foldable Combinators

iany :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool Source

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

iall :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool Source

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

inone :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool Source

Return whether or not none of the elements in a container satisfy a predicate, with access to the index `i`.

When you don't need access to the index then `none` is more flexible in what it accepts.

    none ≡ inone . const
    inone f ≡ not . iany f

none :: Foldable f => (a -> Bool) -> f a -> Bool Source

Determines whether no elements of the structure satisfy the predicate.

    none f ≡ not . any f

itraverse_ :: (FoldableWithIndex i t, Applicative f) => (i -> a -> f b) -> t a -> f () Source

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

ifor_ :: (FoldableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f () Source

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

imapM_ :: (FoldableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m () Source

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

iforM_ :: (FoldableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m () Source

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

iconcatMap :: FoldableWithIndex i f => (i -> a -> [b]) -> f a -> [b] Source

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

ifind :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Maybe (i, a) Source

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

ifoldrM :: (FoldableWithIndex i f, Monad m) => (i -> a -> b -> m b) -> b -> f a -> m b Source

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

ifoldlM :: (FoldableWithIndex i f, Monad m) => (i -> b -> a -> m b) -> b -> f a -> m b Source

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

itoList :: FoldableWithIndex i f => f a -> [(i, a)] Source

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 snd . itoList

# Converting to Folds

withIndex :: (Indexable i p, Functor f) => p (i, s) (f (j, t)) -> Indexed i s (f t) Source

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.

asIndex :: (Indexable i p, Contravariant f, Functor f) => p i (f i) -> Indexed i s (f s) Source

When composed with an `IndexedFold` or `IndexedTraversal` this yields an (`Indexed`) `Fold` of the indices.

# Restricting by Index

indices :: (Indexable i p, Applicative f) => (i -> Bool) -> Optical' p (Indexed i) f a a Source

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"]

index :: (Indexable i p, Eq i, Applicative f) => i -> Optical' p (Indexed i) f a a Source

This allows you to filter an `IndexedFold`, `IndexedGetter`, `IndexedTraversal` or `IndexedLens` based on an index.

    >>> ["hello","the","world","!!!"]^?traversed.index 2
    Just "world"

# Indexed Traversables

class (FunctorWithIndex i t, FoldableWithIndex i t, Traversable t) => TraversableWithIndex i t | t -> i where Source

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)

Minimal complete definition

Nothing

Methods

itraverse :: Applicative f => (i -> a -> f b) -> t a -> f (t b) Source

Traverse an indexed container.

    itraverse ≡ itraverseOf itraversed

itraversed :: IndexedTraversal i (t a) (t b) a b Source

The `IndexedTraversal` of a `TraversableWithIndex` container.

Instances

TraversableWithIndex Int [] Source |
TraversableWithIndex Int IntMap Source |
TraversableWithIndex Int Seq Source |
TraversableWithIndex Int NonEmpty Source |
TraversableWithIndex Int Vector Source |
TraversableWithIndex Int Deque Source |
TraversableWithIndex () Identity Source |
TraversableWithIndex () Maybe Source |
TraversableWithIndex i m => TraversableWithIndex i (IdentityT m) Source |
Ix i => TraversableWithIndex i (Array i) Source |
TraversableWithIndex i (Level i) Source |
(Eq k, Hashable k) => TraversableWithIndex k (HashMap k) Source |
TraversableWithIndex k (Map k) Source |
TraversableWithIndex k ((,) k) Source |
TraversableWithIndex i f => TraversableWithIndex i (Reverse f) Source |
TraversableWithIndex i f => TraversableWithIndex i (Backwards f) Source |
TraversableWithIndex i (Magma i t b) Source |
TraversableWithIndex [Int] Tree Source |
TraversableWithIndex i f => TraversableWithIndex [i] (Cofree f) Source |
TraversableWithIndex i f => TraversableWithIndex [i] (Free f) Source |
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (Product f g) Source |
(TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (i, j) (Compose f g) Source |

# Indexed Traversable Combinators

ifor :: (TraversableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f (t b) Source

Traverse with an index (and the arguments flipped).

    for a ≡ ifor a . const
    ifor ≡ flip itraverse

imapM :: (TraversableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m (t b) Source

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

iforM :: (TraversableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m (t b) Source

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

imapAccumR :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b) Source

Generalizes `mapAccumR` to add access to the index.

`imapAccumROf` accumulates state from right to left.

    mapAccumR ≡ imapAccumR . const

imapAccumL :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b) Source

Generalizes `mapAccumL` to add access to the index.

`imapAccumLOf` accumulates state from left to right.

    mapAccumLOf ≡ imapAccumL . const

# Indexed Folds with Reified Monoid

ifoldMapBy :: FoldableWithIndex i t => (r -> r -> r) -> r -> (i -> a -> r) -> t a -> r Source

ifoldMapByOf :: IndexedFold i t a -> (r -> r -> r) -> r -> (i -> a -> r) -> t -> r Source

# Indexed Traversals with Reified Applicative

itraverseBy :: TraversableWithIndex i t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> t a -> f (t b) Source

itraverseByOf :: IndexedTraversal i s t a b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> s -> f t Source