base-compat-batteries-0.10.5: base-compat with extra batteries

Safe Haskell | Safe
Language | Haskell98

Data.Monoid.Compat

Synopsis

- class Semigroup a => Monoid a where
  - mempty :: a
  - mappend :: a -> a -> a
  - mconcat :: [a] -> a
- newtype First a = First {
  - getFirst :: Maybe a
  }
- newtype Last a = Last {
  - getLast :: Maybe a
  }
- newtype Ap (f :: k -> Type) (a :: k) :: forall k. (k -> Type) -> k -> Type = Ap {
  - getAp :: f a
  }
- newtype Dual a = Dual {
  - getDual :: a
  }
- newtype Endo a = Endo {
  - appEndo :: a -> a
  }
- newtype All = All {
  - getAll :: Bool
  }
- newtype Any = Any {
  - getAny :: Bool
  }
- newtype Sum a = Sum {
  - getSum :: a
  }
- newtype Product a = Product {
  - getProduct :: a
  }
- newtype Alt (f :: k -> Type) (a :: k) :: forall k. (k -> Type) -> k -> Type = Alt {
  - getAlt :: f a
  }
- (<>) :: Semigroup a => a -> a -> a

# Documentation

class Semigroup a => Monoid a where Source #

The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:

-     x <> mempty = x

-     mempty <> x = x

- `x `<>` (y `<>` z) = (x `<>` y) `<>` z` (`Semigroup` law)

-     mconcat = foldr '(<>)' mempty

The method names refer to the monoid of lists under concatenation, but there are many other instances.

Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define `newtype`s and make those instances of `Monoid`, e.g. `Sum` and `Product`.

NOTE: `Semigroup` is a superclass of `Monoid` since base-4.11.0.0.

Minimal complete definition

mempty

Methods

mempty :: a Source #

Identity of `mappend`

mappend :: a -> a -> a Source #

An associative operation

NOTE: This method is redundant and has the default implementation ``mappend` = '(<>)'` since base-4.11.0.0.

mconcat :: [a] -> a Source #

Fold a list using the monoid.

For most types, the default definition for `mconcat` will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.

Instances

Monoid Ordering | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering Source # mappend :: Ordering -> Ordering -> Ordering Source # mconcat :: [Ordering] -> Ordering Source #
Monoid () | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: () Source # mappend :: () -> () -> () Source # mconcat :: [()] -> () Source #
Monoid All | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All Source # mappend :: All -> All -> All Source # mconcat :: [All] -> All Source #
Monoid Any | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any Source # mappend :: Any -> Any -> Any Source # mconcat :: [Any] -> Any Source #
Monoid [a] | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: [a] Source # mappend :: [a] -> [a] -> [a] Source # mconcat :: [[a]] -> [a] Source #
Semigroup a => Monoid (Maybe a) | Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `e*e = e` and `e*s = s = s*e` for all `s ∈ S`." Since 4.11.0: constraint on inner `a` value generalised from `Monoid` to `Semigroup`. Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Maybe a Source # mappend :: Maybe a -> Maybe a -> Maybe a Source # mconcat :: [Maybe a] -> Maybe a Source #
Monoid a => Monoid (IO a) | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mempty :: IO a Source # mappend :: IO a -> IO a -> IO a Source # mconcat :: [IO a] -> IO a Source #
Monoid (Predicate a) |
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Predicate a Source # mappend :: Predicate a -> Predicate a -> Predicate a Source # mconcat :: [Predicate a] -> Predicate a Source #
Monoid (Comparison a) |
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Comparison a Source # mappend :: Comparison a -> Comparison a -> Comparison a Source # mconcat :: [Comparison a] -> Comparison a Source #
Monoid (Equivalence a) |
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Equivalence a Source # mappend :: Equivalence a -> Equivalence a -> Equivalence a Source # mconcat :: [Equivalence a] -> Equivalence a Source #
(Ord a, Bounded a) => Monoid (Min a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Min a Source # mappend :: Min a -> Min a -> Min a Source # mconcat :: [Min a] -> Min a Source #
(Ord a, Bounded a) => Monoid (Max a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Max a Source # mappend :: Max a -> Max a -> Max a Source # mconcat :: [Max a] -> Max a Source #
Monoid m => Monoid (WrappedMonoid m) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: WrappedMonoid m Source # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source #
Semigroup a => Monoid (Option a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Option a Source # mappend :: Option a -> Option a -> Option a Source # mconcat :: [Option a] -> Option a Source #
Monoid a => Monoid (Identity a) | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods mempty :: Identity a Source # mappend :: Identity a -> Identity a -> Identity a Source # mconcat :: [Identity a] -> Identity a Source #
Monoid (First a) | Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: First a Source # mappend :: First a -> First a -> First a Source # mconcat :: [First a] -> First a Source #
Monoid (Last a) | Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: Last a Source # mappend :: Last a -> Last a -> Last a Source # mconcat :: [Last a] -> Last a Source #
Monoid a => Monoid (Dual a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a Source # mappend :: Dual a -> Dual a -> Dual a Source # mconcat :: [Dual a] -> Dual a Source #
Monoid (Endo a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a Source # mappend :: Endo a -> Endo a -> Endo a Source # mconcat :: [Endo a] -> Endo a Source #
Num a => Monoid (Sum a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a Source # mappend :: Sum a -> Sum a -> Sum a Source # mconcat :: [Sum a] -> Sum a Source #
Num a => Monoid (Product a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a Source # mappend :: Product a -> Product a -> Product a Source # mconcat :: [Product a] -> Product a Source #
Monoid b => Monoid (a -> b) | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: a -> b Source # mappend :: (a -> b) -> (a -> b) -> a -> b Source # mconcat :: [a -> b] -> a -> b Source #
(Monoid a, Monoid b) => Monoid (a, b) | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b) Source # mappend :: (a, b) -> (a, b) -> (a, b) Source # mconcat :: [(a, b)] -> (a, b) Source #
Monoid a => Monoid (Op a b) |
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Op a b Source # mappend :: Op a b -> Op a b -> Op a b Source # mconcat :: [Op a b] -> Op a b Source #
Monoid (Proxy s) | Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods mempty :: Proxy s Source # mappend :: Proxy s -> Proxy s -> Proxy s Source # mconcat :: [Proxy s] -> Proxy s Source #
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c) Source # mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # mconcat :: [(a, b, c)] -> (a, b, c) Source #
Monoid a => Monoid (Const a b) | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods mempty :: Const a b Source # mappend :: Const a b -> Const a b -> Const a b Source # mconcat :: [Const a b] -> Const a b Source #
(Applicative f, Monoid a) => Monoid (Ap f a) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mempty :: Ap f a Source # mappend :: Ap f a -> Ap f a -> Ap f a Source # mconcat :: [Ap f a] -> Ap f a Source #
Alternative f => Monoid (Alt f a) | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Alt f a Source # mappend :: Alt f a -> Alt f a -> Alt f a Source # mconcat :: [Alt f a] -> Alt f a Source #
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d) Source # mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # mconcat :: [(a, b, c, d)] -> (a, b, c, d) Source #
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d, e) Source # mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) Source #

newtype First a Source #

Maybe monoid returning the leftmost non-Nothing value.

``First` a` is isomorphic to ``Alt` `Maybe` a`, but precedes it historically.

    >>> getFirst (First (Just "hello") <> First Nothing <> First (Just "world"))
    Just "hello"

Use of this type is discouraged. Note the following equivalence:

    Data.Monoid.First x === Maybe (Data.Semigroup.First x)

In addition to being equivalent in the structural sense, the two also have `Monoid` instances that behave the same. This type will be marked deprecated in GHC 8.8, and removed in GHC 8.10. Users are advised to use the variant from Data.Semigroup and wrap it in `Maybe`.

Constructors

First |

Fields

- getFirst :: Maybe a

Instances

Monad First | Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: First a -> (a -> First b) -> First b Source # (>>) :: First a -> First b -> First b Source # return :: a -> First a Source # fail :: String -> First a Source #
Functor First | Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> First a -> First b Source # (<$) :: a -> First b -> First a Source #
Applicative First | Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> First a Source # (<*>) :: First (a -> b) -> First a -> First b Source # liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source # (*>) :: First a -> First b -> First b Source # (<*) :: First a -> First b -> First a Source #
Foldable First | Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => First m -> m Source #

foldMap :: Monoid m => (a -> m) -> First a -> m Source #

foldr :: (a -> b -> b) -> b -> First a -> b Source #

foldr' :: (a -> b -> b) -> b -> First a -> b Source #

foldl :: (b -> a -> b) -> b -> First a -> b Source #

foldl' :: (b -> a -> b) -> b -> First a -> b Source #

foldr1 :: (a -> a -> a) -> First a -> a Source #

foldl1 :: (a -> a -> a) -> First a -> a Source #

toList :: First a -> [a] Source #

null :: First a -> Bool Source #

length :: First a -> Int Source #

elem :: Eq a => a -> First a -> Bool Source #

maximum :: Ord a => First a -> a Source #

minimum :: Ord a => First a -> a Source #

sum :: Num a => First a -> a Source #

product :: Num a => First a -> a Source #

Traversable First | Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) Source # sequenceA :: Applicative f => First (f a) -> f (First a) Source # mapM :: Monad m => (a -> m b) -> First a -> m (First b) Source # sequence :: Monad m => First (m a) -> m (First a) Source #
Eq a => Eq (First a) | Since: base-2.1
Instance details Defined in Data.Monoid Methods (==) :: First a -> First a -> Bool Source # (/=) :: First a -> First a -> Bool Source #
Ord a => Ord (First a) | Since: base-2.1
Instance details Defined in Data.Monoid Methods compare :: First a -> First a -> Ordering Source # (<) :: First a -> First a -> Bool Source # (<=) :: First a -> First a -> Bool Source # (>) :: First a -> First a -> Bool Source # (>=) :: First a -> First a -> Bool Source # max :: First a -> First a -> First a Source # min :: First a -> First a -> First a Source #
Read a => Read (First a) | Since: base-2.1
Instance details Defined in Data.Monoid Methods readsPrec :: Int -> ReadS (First a) Source # readList :: ReadS [First a] Source # readPrec :: ReadPrec (First a) Source # readListPrec :: ReadPrec [First a] Source #
Show a => Show (First a) | Since: base-2.1
Instance details Defined in Data.Monoid Methods showsPrec :: Int -> First a -> ShowS Source # show :: First a -> String Source # showList :: [First a] -> ShowS Source #
Generic (First a) |
Instance details Defined in Data.Monoid Associated Types type Rep (First a) :: Type -> Type Source # Methods from :: First a -> Rep (First a) x Source # to :: Rep (First a) x -> First a Source #
Semigroup (First a) | Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: First a -> First a -> First a Source # sconcat :: NonEmpty (First a) -> First a Source # stimes :: Integral b => b -> First a -> First a Source #
Monoid (First a) | Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: First a Source # mappend :: First a -> First a -> First a Source # mconcat :: [First a] -> First a Source #
Generic1 First |
Instance details Defined in Data.Monoid Associated Types type Rep1 First :: k -> Type Source # Methods from1 :: First a -> Rep1 First a Source # to1 :: Rep1 First a -> First a Source #
type Rep (First a) | Since: base-4.7.0.0
Instance details Defined in Data.Monoid type Rep (First a) = D1 (MetaData "First" "Data.Monoid" "base" True) (C1 (MetaCons "First" PrefixI True) (S1 (MetaSel (Just "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe a))))
type Rep1 First | Since: base-4.7.0.0
Instance details Defined in Data.Monoid type Rep1 First = D1 (MetaData "First" "Data.Monoid" "base" True) (C1 (MetaCons "First" PrefixI True) (S1 (MetaSel (Just "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 Maybe)))

newtype Last a Source #

Maybe monoid returning the rightmost non-Nothing value.

``Last` a` is isomorphic to ``Dual` (`First` a)`, and thus to ``Dual` (`Alt` `Maybe` a)`

    >>> getLast (Last (Just "hello") <> Last Nothing <> Last (Just "world"))
    Just "world"

Use of this type is discouraged. Note the following equivalence:

    Data.Monoid.Last x === Maybe (Data.Semigroup.Last x)

In addition to being equivalent in the structural sense, the two also have `Monoid` instances that behave the same. This type will be marked deprecated in GHC 8.8, and removed in GHC 8.10. Users are advised to use the variant from Data.Semigroup and wrap it in `Maybe`.

Constructors

Last |

Fields

- getLast :: Maybe a

Instances

Monad Last | Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Last a -> (a -> Last b) -> Last b Source # (>>) :: Last a -> Last b -> Last b Source # return :: a -> Last a Source # fail :: String -> Last a Source #
Functor Last | Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Last a -> Last b Source # (<$) :: a -> Last b -> Last a Source #
Applicative Last | Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> Last a Source # (<*>) :: Last (a -> b) -> Last a -> Last b Source # liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source # (*>) :: Last a -> Last b -> Last b Source # (<*) :: Last a -> Last b -> Last a Source #
Foldable Last | Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Last m -> m Source #

foldMap :: Monoid m => (a -> m) -> Last a -> m Source #

foldr :: (a -> b -> b) -> b -> Last a -> b Source #

foldr' :: (a -> b -> b) -> b -> Last a -> b Source #

foldl :: (b -> a -> b) -> b -> Last a -> b Source #

foldl' :: (b -> a -> b) -> b -> Last a -> b Source #

foldr1 :: (a -> a -> a) -> Last a -> a Source #

foldl1 :: (a -> a -> a) -> Last a -> a Source #

toList :: Last a -> [a] Source #

null :: Last a -> Bool Source #

length :: Last a -> Int Source #

elem :: Eq a => a -> Last a -> Bool Source #

maximum :: Ord a => Last a -> a Source #

minimum :: Ord a => Last a -> a Source #

sum :: Num a => Last a -> a Source #

product :: Num a => Last a -> a Source #

Traversable Last | Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) Source # sequenceA :: Applicative f => Last (f a) -> f (Last a) Source # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) Source # sequence :: Monad m => Last (m a) -> m (Last a) Source #
Eq a => Eq (Last a) | Since: base-2.1
Instance details Defined in Data.Monoid Methods (==) :: Last a -> Last a -> Bool Source # (/=) :: Last a -> Last a -> Bool Source #
Ord a => Ord (Last a) | Since: base-2.1
Instance details Defined in Data.Monoid Methods compare :: Last a -> Last a -> Ordering Source # (<) :: Last a -> Last a -> Bool Source # (<=) :: Last a -> Last a -> Bool Source # (>) :: Last a -> Last a -> Bool Source # (>=) :: Last a -> Last a -> Bool Source # max :: Last a -> Last a -> Last a Source # min :: Last a -> Last a -> Last a Source #
Read a => Read (Last a) | Since: base-2.1
Instance details Defined in Data.Monoid Methods readsPrec :: Int -> ReadS (Last a) Source # readList :: ReadS [Last a] Source # readPrec :: ReadPrec (Last a) Source # readListPrec :: ReadPrec [Last a] Source #
Show a => Show (Last a) | Since: base-2.1
Instance details Defined in Data.Monoid Methods showsPrec :: Int -> Last a -> ShowS Source # show :: Last a -> String Source # showList :: [Last a] -> ShowS Source #
Generic (Last a) |
Instance details Defined in Data.Monoid Associated Types type Rep (Last a) :: Type -> Type Source # Methods from :: Last a -> Rep (Last a) x Source # to :: Rep (Last a) x -> Last a Source #
Semigroup (Last a) | Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Last a -> Last a -> Last a Source # sconcat :: NonEmpty (Last a) -> Last a Source # stimes :: Integral b => b -> Last a -> Last a Source #
Monoid (Last a) | Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: Last a Source # mappend :: Last a -> Last a -> Last a Source # mconcat :: [Last a] -> Last a Source #
Generic1 Last |
Instance details Defined in Data.Monoid Associated Types type Rep1 Last :: k -> Type Source # Methods from1 :: Last a -> Rep1 Last a Source # to1 :: Rep1 Last a -> Last a Source #
type Rep (Last a) | Since: base-4.7.0.0
Instance details Defined in Data.Monoid type Rep (Last a) = D1 (MetaData "Last" "Data.Monoid" "base" True) (C1 (MetaCons "Last" PrefixI True) (S1 (MetaSel (Just "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe a))))
type Rep1 Last | Since: base-4.7.0.0
Instance details Defined in Data.Monoid type Rep1 Last = D1 (MetaData "Last" "Data.Monoid" "base" True) (C1 (MetaCons "Last" PrefixI True) (S1 (MetaSel (Just "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 Maybe)))

newtype Ap (f :: k -> Type) (a :: k) :: forall k. (k -> Type) -> k -> Type Source #

This data type witnesses the lifting of a `Monoid` into an `Applicative` pointwise.

Since: base-4.12.0.0

Constructors

Ap |

Fields

- getAp :: f a

Instances

Generic1 (Ap f :: k -> Type) |
Instance details Defined in Data.Monoid Associated Types type Rep1 (Ap f) :: k -> Type Source # Methods from1 :: Ap f a -> Rep1 (Ap f) a Source # to1 :: Rep1 (Ap f) a -> Ap f a Source #
Monad f => Monad (Ap f) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b Source # (>>) :: Ap f a -> Ap f b -> Ap f b Source # return :: a -> Ap f a Source # fail :: String -> Ap f a Source #
Functor f => Functor (Ap f) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Ap f a -> Ap f b Source # (<$) :: a -> Ap f b -> Ap f a Source #
MonadFail f => MonadFail (Ap f) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods fail :: String -> Ap f a Source #
Applicative f => Applicative (Ap f) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> Ap f a Source # (<*>) :: Ap f (a -> b) -> Ap f a -> Ap f b Source # liftA2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c Source # (*>) :: Ap f a -> Ap f b -> Ap f b Source # (<*) :: Ap f a -> Ap f b -> Ap f a Source #
Foldable f => Foldable (Ap f) | Since: base-4.12.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Ap f m -> m Source #

foldMap :: Monoid m => (a -> m) -> Ap f a -> m Source #

foldr :: (a -> b -> b) -> b -> Ap f a -> b Source #

foldr' :: (a -> b -> b) -> b -> Ap f a -> b Source #

foldl :: (b -> a -> b) -> b -> Ap f a -> b Source #

foldl' :: (b -> a -> b) -> b -> Ap f a -> b Source #

foldr1 :: (a -> a -> a) -> Ap f a -> a Source #

foldl1 :: (a -> a -> a) -> Ap f a -> a Source #

toList :: Ap f a -> [a] Source #

null :: Ap f a -> Bool Source #

length :: Ap f a -> Int Source #

elem :: Eq a => a -> Ap f a -> Bool Source #

maximum :: Ord a => Ap f a -> a Source #

minimum :: Ord a => Ap f a -> a Source #

sum :: Num a => Ap f a -> a Source #

product :: Num a => Ap f a -> a Source #

Traversable f => Traversable (Ap f) | Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Ap f a -> f0 (Ap f b) Source # sequenceA :: Applicative f0 => Ap f (f0 a) -> f0 (Ap f a) Source # mapM :: Monad m => (a -> m b) -> Ap f a -> m (Ap f b) Source # sequence :: Monad m => Ap f (m a) -> m (Ap f a) Source #
Alternative f => Alternative (Ap f) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods empty :: Ap f a Source # (<|>) :: Ap f a -> Ap f a -> Ap f a Source # some :: Ap f a -> Ap f [a] Source # many :: Ap f a -> Ap f [a] Source #
MonadPlus f => MonadPlus (Ap f) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mzero :: Ap f a Source # mplus :: Ap f a -> Ap f a -> Ap f a Source #
(Applicative f, Bounded a) => Bounded (Ap f a) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods minBound :: Ap f a Source # maxBound :: Ap f a Source #
Enum (f a) => Enum (Ap f a) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods succ :: Ap f a -> Ap f a Source # pred :: Ap f a -> Ap f a Source # toEnum :: Int -> Ap f a Source # fromEnum :: Ap f a -> Int Source # enumFrom :: Ap f a -> [Ap f a] Source # enumFromThen :: Ap f a -> Ap f a -> [Ap f a] Source # enumFromTo :: Ap f a -> Ap f a -> [Ap f a] Source # enumFromThenTo :: Ap f a -> Ap f a -> Ap f a -> [Ap f a] Source #
Eq (f a) => Eq (Ap f a) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (==) :: Ap f a -> Ap f a -> Bool Source # (/=) :: Ap f a -> Ap f a -> Bool Source #
(Applicative f, Num a) => Num (Ap f a) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (+) :: Ap f a -> Ap f a -> Ap f a Source # (-) :: Ap f a -> Ap f a -> Ap f a Source # (*) :: Ap f a -> Ap f a -> Ap f a Source # negate :: Ap f a -> Ap f a Source # abs :: Ap f a -> Ap f a Source # signum :: Ap f a -> Ap f a Source # fromInteger :: Integer -> Ap f a Source #
Ord (f a) => Ord (Ap f a) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods compare :: Ap f a -> Ap f a -> Ordering Source # (<) :: Ap f a -> Ap f a -> Bool Source # (<=) :: Ap f a -> Ap f a -> Bool Source # (>) :: Ap f a -> Ap f a -> Bool Source # (>=) :: Ap f a -> Ap f a -> Bool Source # max :: Ap f a -> Ap f a -> Ap f a Source # min :: Ap f a -> Ap f a -> Ap f a Source #
Read (f a) => Read (Ap f a) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods readsPrec :: Int -> ReadS (Ap f a) Source # readList :: ReadS [Ap f a] Source # readPrec :: ReadPrec (Ap f a) Source # readListPrec :: ReadPrec [Ap f a] Source #
Show (f a) => Show (Ap f a) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods showsPrec :: Int -> Ap f a -> ShowS Source # show :: Ap f a -> String Source # showList :: [Ap f a] -> ShowS Source #
Generic (Ap f a) |
Instance details Defined in Data.Monoid Associated Types type Rep (Ap f a) :: Type -> Type Source # Methods from :: Ap f a -> Rep (Ap f a) x Source # to :: Rep (Ap f a) x -> Ap f a Source #
(Applicative f, Semigroup a) => Semigroup (Ap f a) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Ap f a -> Ap f a -> Ap f a Source # sconcat :: NonEmpty (Ap f a) -> Ap f a Source # stimes :: Integral b => b -> Ap f a -> Ap f a Source #
(Applicative f, Monoid a) => Monoid (Ap f a) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mempty :: Ap f a Source # mappend :: Ap f a -> Ap f a -> Ap f a Source # mconcat :: [Ap f a] -> Ap f a Source #
type Rep1 (Ap f :: k -> Type) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid type Rep1 (Ap f :: k -> Type) = D1 (MetaData "Ap" "Data.Monoid" "base" True) (C1 (MetaCons "Ap" PrefixI True) (S1 (MetaSel (Just "getAp") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 f)))
type Rep (Ap f a) | Since: base-4.12.0.0
Instance details Defined in Data.Monoid type Rep (Ap f a) = D1 (MetaData "Ap" "Data.Monoid" "base" True) (C1 (MetaCons "Ap" PrefixI True) (S1 (MetaSel (Just "getAp") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f a))))

newtype Dual a Source #

The dual of a `Monoid`, obtained by swapping the arguments of `mappend`.

    >>> getDual (mappend (Dual "Hello") (Dual "World"))
    "WorldHello"

Constructors

Dual |

Fields

- getDual :: a

Instances

Monad Dual | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Dual a -> (a -> Dual b) -> Dual b Source # (>>) :: Dual a -> Dual b -> Dual b Source # return :: a -> Dual a Source # fail :: String -> Dual a Source #
Functor Dual | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Dual a -> Dual b Source # (<$) :: a -> Dual b -> Dual a Source #
Applicative Dual | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Dual a Source # (<*>) :: Dual (a -> b) -> Dual a -> Dual b Source # liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source # (*>) :: Dual a -> Dual b -> Dual b Source # (<*) :: Dual a -> Dual b -> Dual a Source #
Foldable Dual | Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Dual m -> m Source #

foldMap :: Monoid m => (a -> m) -> Dual a -> m Source #

foldr :: (a -> b -> b) -> b -> Dual a -> b Source #

foldr' :: (a -> b -> b) -> b -> Dual a -> b Source #

foldl :: (b -> a -> b) -> b -> Dual a -> b Source #

foldl' :: (b -> a -> b) -> b -> Dual a -> b Source #

foldr1 :: (a -> a -> a) -> Dual a -> a Source #

foldl1 :: (a -> a -> a) -> Dual a -> a Source #

toList :: Dual a -> [a] Source #

null :: Dual a -> Bool Source #

length :: Dual a -> Int Source #

elem :: Eq a => a -> Dual a -> Bool Source #

maximum :: Ord a => Dual a -> a Source #

minimum :: Ord a => Dual a -> a Source #

sum :: Num a => Dual a -> a Source #

product :: Num a => Dual a -> a Source #

Traversable Dual | Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) Source # sequenceA :: Applicative f => Dual (f a) -> f (Dual a) Source # mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) Source # sequence :: Monad m => Dual (m a) -> m (Dual a) Source #
Bounded a => Bounded (Dual a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Dual a Source # maxBound :: Dual a Source #
Eq a => Eq (Dual a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Dual a -> Dual a -> Bool Source # (/=) :: Dual a -> Dual a -> Bool Source #
Ord a => Ord (Dual a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Dual a -> Dual a -> Ordering Source # (<) :: Dual a -> Dual a -> Bool Source # (<=) :: Dual a -> Dual a -> Bool Source # (>) :: Dual a -> Dual a -> Bool Source # (>=) :: Dual a -> Dual a -> Bool Source # max :: Dual a -> Dual a -> Dual a Source # min :: Dual a -> Dual a -> Dual a Source #
Read a => Read (Dual a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Dual a) Source # readList :: ReadS [Dual a] Source # readPrec :: ReadPrec (Dual a) Source # readListPrec :: ReadPrec [Dual a] Source #
Show a => Show (Dual a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Dual a -> ShowS Source # show :: Dual a -> String Source # showList :: [Dual a] -> ShowS Source #
Generic (Dual a) |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Dual a) :: Type -> Type Source # Methods from :: Dual a -> Rep (Dual a) x Source # to :: Rep (Dual a) x -> Dual a Source #
Semigroup a => Semigroup (Dual a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Dual a -> Dual a -> Dual a Source # sconcat :: NonEmpty (Dual a) -> Dual a Source # stimes :: Integral b => b -> Dual a -> Dual a Source #
Monoid a => Monoid (Dual a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a Source # mappend :: Dual a -> Dual a -> Dual a Source # mconcat :: [Dual a] -> Dual a Source #
Generic1 Dual |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Dual :: k -> Type Source # Methods from1 :: Dual a -> Rep1 Dual a Source # to1 :: Rep1 Dual a -> Dual a Source #
type Rep (Dual a) | Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep (Dual a) = D1 (MetaData "Dual" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Dual" PrefixI True) (S1 (MetaSel (Just "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep1 Dual | Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep1 Dual = D1 (MetaData "Dual" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Dual" PrefixI True) (S1 (MetaSel (Just "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Endo a Source #

The monoid of endomorphisms under composition.

    >>> let computation = Endo ("Hello, " ++) <> Endo (++ "!")
    >>> appEndo computation "Haskell"
    "Hello, Haskell!"

Constructors

Endo |

Fields

- appEndo :: a -> a

Instances

Generic (Endo a) |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Endo a) :: Type -> Type Source # Methods from :: Endo a -> Rep (Endo a) x Source # to :: Rep (Endo a) x -> Endo a Source #
Semigroup (Endo a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Endo a -> Endo a -> Endo a Source # sconcat :: NonEmpty (Endo a) -> Endo a Source # stimes :: Integral b => b -> Endo a -> Endo a Source #
Monoid (Endo a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a Source # mappend :: Endo a -> Endo a -> Endo a Source # mconcat :: [Endo a] -> Endo a Source #
type Rep (Endo a) | Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep (Endo a) = D1 (MetaData "Endo" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Endo" PrefixI True) (S1 (MetaSel (Just "appEndo") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (a -> a))))

newtype All Source #

Boolean monoid under conjunction (`&&`).

    >>> getAll (All True <> mempty <> All False)
    False

    >>> getAll (mconcat (map (\x -> All (even x)) [2,4,6,7,8]))
    False

Constructors

All |

Fields

- getAll :: Bool

Instances

Bounded All | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: All Source # maxBound :: All Source #
Eq All | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: All -> All -> Bool Source # (/=) :: All -> All -> Bool Source #
Ord All | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: All -> All -> Ordering Source # (<) :: All -> All -> Bool Source # (<=) :: All -> All -> Bool Source # (>) :: All -> All -> Bool Source # (>=) :: All -> All -> Bool Source # max :: All -> All -> All Source # min :: All -> All -> All Source #
Read All | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS All Source # readList :: ReadS [All] Source # readPrec :: ReadPrec All Source # readListPrec :: ReadPrec [All] Source #
Show All | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> All -> ShowS Source # show :: All -> String Source # showList :: [All] -> ShowS Source #
Generic All |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep All :: Type -> Type Source # Methods from :: All -> Rep All x Source # to :: Rep All x -> All Source #
Semigroup All | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: All -> All -> All Source # sconcat :: NonEmpty All -> All Source # stimes :: Integral b => b -> All -> All Source #
Monoid All | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All Source # mappend :: All -> All -> All Source # mconcat :: [All] -> All Source #
type Rep All | Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep All = D1 (MetaData "All" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "All" PrefixI True) (S1 (MetaSel (Just "getAll") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Bool)))

newtype Any Source #

Boolean monoid under disjunction (`||`).

    >>> getAny (Any True <> mempty <> Any False)
    True

    >>> getAny (mconcat (map (\x -> Any (even x)) [2,4,6,7,8]))
    True

Constructors

Any |

Fields

- getAny :: Bool

Instances

Bounded Any | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Any Source # maxBound :: Any Source #
Eq Any | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Any -> Any -> Bool Source # (/=) :: Any -> Any -> Bool Source #
Ord Any | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Any -> Any -> Ordering Source # (<) :: Any -> Any -> Bool Source # (<=) :: Any -> Any -> Bool Source # (>) :: Any -> Any -> Bool Source # (>=) :: Any -> Any -> Bool Source # max :: Any -> Any -> Any Source # min :: Any -> Any -> Any Source #
Read Any | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS Any Source # readList :: ReadS [Any] Source # readPrec :: ReadPrec Any Source # readListPrec :: ReadPrec [Any] Source #
Show Any | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Any -> ShowS Source # show :: Any -> String Source # showList :: [Any] -> ShowS Source #
Generic Any |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep Any :: Type -> Type Source # Methods from :: Any -> Rep Any x Source # to :: Rep Any x -> Any Source #
Semigroup Any | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Any -> Any -> Any Source # sconcat :: NonEmpty Any -> Any Source # stimes :: Integral b => b -> Any -> Any Source #
Monoid Any | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any Source # mappend :: Any -> Any -> Any Source # mconcat :: [Any] -> Any Source #
type Rep Any | Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep Any = D1 (MetaData "Any" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Any" PrefixI True) (S1 (MetaSel (Just "getAny") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Bool)))

newtype Sum a Source #

Monoid under addition.

    >>> getSum (Sum 1 <> Sum 2 <> mempty)
    3

Constructors

Sum |

Fields

- getSum :: a

Instances

Monad Sum | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b Source # (>>) :: Sum a -> Sum b -> Sum b Source # return :: a -> Sum a Source # fail :: String -> Sum a Source #
Functor Sum | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Sum a -> Sum b Source # (<$) :: a -> Sum b -> Sum a Source #
Applicative Sum | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Sum a Source # (<*>) :: Sum (a -> b) -> Sum a -> Sum b Source # liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source # (*>) :: Sum a -> Sum b -> Sum b Source # (<*) :: Sum a -> Sum b -> Sum a Source #
Foldable Sum | Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Sum m -> m Source #

foldMap :: Monoid m => (a -> m) -> Sum a -> m Source #

foldr :: (a -> b -> b) -> b -> Sum a -> b Source #

foldr' :: (a -> b -> b) -> b -> Sum a -> b Source #

foldl :: (b -> a -> b) -> b -> Sum a -> b Source #

foldl' :: (b -> a -> b) -> b -> Sum a -> b Source #

foldr1 :: (a -> a -> a) -> Sum a -> a Source #

foldl1 :: (a -> a -> a) -> Sum a -> a Source #

toList :: Sum a -> [a] Source #

null :: Sum a -> Bool Source #

length :: Sum a -> Int Source #

elem :: Eq a => a -> Sum a -> Bool Source #

maximum :: Ord a => Sum a -> a Source #

minimum :: Ord a => Sum a -> a Source #

sum :: Num a => Sum a -> a Source #

product :: Num a => Sum a -> a Source #

Traversable Sum | Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) Source # sequenceA :: Applicative f => Sum (f a) -> f (Sum a) Source # mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) Source # sequence :: Monad m => Sum (m a) -> m (Sum a) Source #
Bounded a => Bounded (Sum a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Sum a Source # maxBound :: Sum a Source #
Eq a => Eq (Sum a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Sum a -> Sum a -> Bool Source # (/=) :: Sum a -> Sum a -> Bool Source #
Num a => Num (Sum a) | Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Sum a -> Sum a -> Sum a Source # (-) :: Sum a -> Sum a -> Sum a Source # (*) :: Sum a -> Sum a -> Sum a Source # negate :: Sum a -> Sum a Source # abs :: Sum a -> Sum a Source # signum :: Sum a -> Sum a Source # fromInteger :: Integer -> Sum a Source #
Ord a => Ord (Sum a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Sum a -> Sum a -> Ordering Source # (<) :: Sum a -> Sum a -> Bool Source # (<=) :: Sum a -> Sum a -> Bool Source # (>) :: Sum a -> Sum a -> Bool Source # (>=) :: Sum a -> Sum a -> Bool Source # max :: Sum a -> Sum a -> Sum a Source # min :: Sum a -> Sum a -> Sum a Source #
Read a => Read (Sum a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Sum a) Source # readList :: ReadS [Sum a] Source # readPrec :: ReadPrec (Sum a) Source # readListPrec :: ReadPrec [Sum a] Source #
Show a => Show (Sum a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Sum a -> ShowS Source # show :: Sum a -> String Source # showList :: [Sum a] -> ShowS Source #
Generic (Sum a) |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Sum a) :: Type -> Type Source # Methods from :: Sum a -> Rep (Sum a) x Source # to :: Rep (Sum a) x -> Sum a Source #
Num a => Semigroup (Sum a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Sum a -> Sum a -> Sum a Source # sconcat :: NonEmpty (Sum a) -> Sum a Source # stimes :: Integral b => b -> Sum a -> Sum a Source #
Num a => Monoid (Sum a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a Source # mappend :: Sum a -> Sum a -> Sum a Source # mconcat :: [Sum a] -> Sum a Source #
Generic1 Sum |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Sum :: k -> Type Source # Methods from1 :: Sum a -> Rep1 Sum a Source # to1 :: Rep1 Sum a -> Sum a Source #
type Rep (Sum a) | Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep (Sum a) = D1 (MetaData "Sum" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Sum" PrefixI True) (S1 (MetaSel (Just "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep1 Sum | Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep1 Sum = D1 (MetaData "Sum" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Sum" PrefixI True) (S1 (MetaSel (Just "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Product a Source #

Monoid under multiplication.

    >>> getProduct (Product 3 <> Product 4 <> mempty)
    12

Constructors

Product |

Fields

- getProduct :: a

Instances

Monad Product | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Product a -> (a -> Product b) -> Product b Source # (>>) :: Product a -> Product b -> Product b Source # return :: a -> Product a Source # fail :: String -> Product a Source #
Functor Product | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Product a -> Product b Source # (<$) :: a -> Product b -> Product a Source #
Applicative Product | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Product a Source # (<*>) :: Product (a -> b) -> Product a -> Product b Source # liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c Source # (*>) :: Product a -> Product b -> Product b Source # (<*) :: Product a -> Product b -> Product a Source #
Foldable Product | Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Product m -> m Source #

foldMap :: Monoid m => (a -> m) -> Product a -> m Source #

foldr :: (a -> b -> b) -> b -> Product a -> b Source #

foldr' :: (a -> b -> b) -> b -> Product a -> b Source #

foldl :: (b -> a -> b) -> b -> Product a -> b Source #

foldl' :: (b -> a -> b) -> b -> Product a -> b Source #

foldr1 :: (a -> a -> a) -> Product a -> a Source #

foldl1 :: (a -> a -> a) -> Product a -> a Source #

toList :: Product a -> [a] Source #

null :: Product a -> Bool Source #

length :: Product a -> Int Source #

elem :: Eq a => a -> Product a -> Bool Source #

maximum :: Ord a => Product a -> a Source #

minimum :: Ord a => Product a -> a Source #

sum :: Num a => Product a -> a Source #

product :: Num a => Product a -> a Source #

Traversable Product | Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) Source # sequenceA :: Applicative f => Product (f a) -> f (Product a) Source # mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) Source # sequence :: Monad m => Product (m a) -> m (Product a) Source #
Bounded a => Bounded (Product a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Product a Source # maxBound :: Product a Source #
Eq a => Eq (Product a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Product a -> Product a -> Bool Source # (/=) :: Product a -> Product a -> Bool Source #
Num a => Num (Product a) | Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Product a -> Product a -> Product a Source # (-) :: Product a -> Product a -> Product a Source # (*) :: Product a -> Product a -> Product a Source # negate :: Product a -> Product a Source # abs :: Product a -> Product a Source # signum :: Product a -> Product a Source # fromInteger :: Integer -> Product a Source #
Ord a => Ord (Product a) | Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: Product a -> Product a -> Ordering Source #

(<) :: Product a -> Product a -> Bool Source #

(<=) :: Product a -> Product a -> Bool Source #

(>) :: Product a -> Product a -> Bool Source #

(>=) :: Product a -> Product a -> Bool Source #

max :: Product a -> Product a -> Product a Source #

min :: Product a -> Product a -> Product a Source #

Read a => Read (Product a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Product a) Source # readList :: ReadS [Product a] Source # readPrec :: ReadPrec (Product a) Source # readListPrec :: ReadPrec [Product a] Source #
Show a => Show (Product a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Product a -> ShowS Source # show :: Product a -> String Source # showList :: [Product a] -> ShowS Source #
Generic (Product a) |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Product a) :: Type -> Type Source # Methods from :: Product a -> Rep (Product a) x Source # to :: Rep (Product a) x -> Product a Source #
Num a => Semigroup (Product a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Product a -> Product a -> Product a Source # sconcat :: NonEmpty (Product a) -> Product a Source # stimes :: Integral b => b -> Product a -> Product a Source #
Num a => Monoid (Product a) | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a Source # mappend :: Product a -> Product a -> Product a Source # mconcat :: [Product a] -> Product a Source #
Generic1 Product |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Product :: k -> Type Source # Methods from1 :: Product a -> Rep1 Product a Source # to1 :: Rep1 Product a -> Product a Source #
type Rep (Product a) | Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep (Product a) = D1 (MetaData "Product" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Product" PrefixI True) (S1 (MetaSel (Just "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep1 Product | Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal type Rep1 Product = D1 (MetaData "Product" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Product" PrefixI True) (S1 (MetaSel (Just "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Alt (f :: k -> Type) (a :: k) :: forall k. (k -> Type) -> k -> Type Source #

Monoid under `<|>`.

Since: base-4.8.0.0

Constructors

Alt |

Fields

- getAlt :: f a

Instances

Generic1 (Alt f :: k -> Type) |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 (Alt f) :: k -> Type Source # Methods from1 :: Alt f a -> Rep1 (Alt f) a Source # to1 :: Rep1 (Alt f) a -> Alt f a Source #
Monad f => Monad (Alt f) | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Alt f a -> (a -> Alt f b) -> Alt f b Source # (>>) :: Alt f a -> Alt f b -> Alt f b Source # return :: a -> Alt f a Source # fail :: String -> Alt f a Source #
Functor f => Functor (Alt f) | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Alt f a -> Alt f b Source # (<$) :: a -> Alt f b -> Alt f a Source #
Applicative f => Applicative (Alt f) | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Alt f a Source # (<*>) :: Alt f (a -> b) -> Alt f a -> Alt f b Source # liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c Source # (*>) :: Alt f a -> Alt f b -> Alt f b Source # (<*) :: Alt f a -> Alt f b -> Alt f a Source #
Foldable f => Foldable (Alt f) | Since: base-4.12.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Alt f m -> m Source #

foldMap :: Monoid m => (a -> m) -> Alt f a -> m Source #

foldr :: (a -> b -> b) -> b -> Alt f a -> b Source #

foldr' :: (a -> b -> b) -> b -> Alt f a -> b Source #

foldl :: (b -> a -> b) -> b -> Alt f a -> b Source #

foldl' :: (b -> a -> b) -> b -> Alt f a -> b Source #

foldr1 :: (a -> a -> a) -> Alt f a -> a Source #

foldl1 :: (a -> a -> a) -> Alt f a -> a Source #

toList :: Alt f a -> [a] Source #

null :: Alt f a -> Bool Source #

length :: Alt f a -> Int Source #

elem :: Eq a => a -> Alt f a -> Bool Source #

maximum :: Ord a => Alt f a -> a Source #

minimum :: Ord a => Alt f a -> a Source #

sum :: Num a => Alt f a -> a Source #

product :: Num a => Alt f a -> a Source #

Traversable f => Traversable (Alt f) | Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b) Source # sequenceA :: Applicative f0 => Alt f (f0 a) -> f0 (Alt f a) Source # mapM :: Monad m => (a -> m b) -> Alt f a -> m (Alt f b) Source # sequence :: Monad m => Alt f (m a) -> m (Alt f a) Source #
Contravariant f => Contravariant (Alt f) |
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Alt f b -> Alt f a Source # (>$) :: b -> Alt f b -> Alt f a Source #
Alternative f => Alternative (Alt f) | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods empty :: Alt f a Source # (<|>) :: Alt f a -> Alt f a -> Alt f a Source # some :: Alt f a -> Alt f [a] Source # many :: Alt f a -> Alt f [a] Source #
MonadPlus f => MonadPlus (Alt f) | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mzero :: Alt f a Source # mplus :: Alt f a -> Alt f a -> Alt f a Source #
Enum (f a) => Enum (Alt f a) | Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

succ :: Alt f a -> Alt f a Source #

pred :: Alt f a -> Alt f a Source #

toEnum :: Int -> Alt f a Source #

fromEnum :: Alt f a -> Int Source #

enumFrom :: Alt f a -> [Alt f a] Source #

enumFromThen :: Alt f a -> Alt f a -> [Alt f a] Source #

enumFromTo :: Alt f a -> Alt f a -> [Alt f a] Source #

enumFromThenTo :: Alt f a -> Alt f a -> Alt f a -> [Alt f a] Source #

Eq (f a) => Eq (Alt f a) | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Alt f a -> Alt f a -> Bool Source # (/=) :: Alt f a -> Alt f a -> Bool Source #
Num (f a) => Num (Alt f a) | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Alt f a -> Alt f a -> Alt f a Source # (-) :: Alt f a -> Alt f a -> Alt f a Source # (*) :: Alt f a -> Alt f a -> Alt f a Source # negate :: Alt f a -> Alt f a Source # abs :: Alt f a -> Alt f a Source # signum :: Alt f a -> Alt f a Source # fromInteger :: Integer -> Alt f a Source #
Ord (f a) => Ord (Alt f a) | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods compare :: Alt f a -> Alt f a -> Ordering Source # (<) :: Alt f a -> Alt f a -> Bool Source # (<=) :: Alt f a -> Alt f a -> Bool Source # (>) :: Alt f a -> Alt f a -> Bool Source # (>=) :: Alt f a -> Alt f a -> Bool Source # max :: Alt f a -> Alt f a -> Alt f a Source # min :: Alt f a -> Alt f a -> Alt f a Source #
Read (f a) => Read (Alt f a) | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Alt f a) Source # readList :: ReadS [Alt f a] Source # readPrec :: ReadPrec (Alt f a) Source # readListPrec :: ReadPrec [Alt f a] Source #
Show (f a) => Show (Alt f a) | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Alt f a -> ShowS Source # show :: Alt f a -> String Source # showList :: [Alt f a] -> ShowS Source #
Generic (Alt f a) |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Alt f a) :: Type -> Type Source # Methods from :: Alt f a -> Rep (Alt f a) x Source # to :: Rep (Alt f a) x -> Alt f a Source #
Alternative f => Semigroup (Alt f a) | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Alt f a -> Alt f a -> Alt f a Source # sconcat :: NonEmpty (Alt f a) -> Alt f a Source # stimes :: Integral b => b -> Alt f a -> Alt f a Source #
Alternative f => Monoid (Alt f a) | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Alt f a Source # mappend :: Alt f a -> Alt f a -> Alt f a Source # mconcat :: [Alt f a] -> Alt f a Source #
type Rep1 (Alt f :: k -> Type) | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal type Rep1 (Alt f :: k -> Type) = D1 (MetaData "Alt" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Alt" PrefixI True) (S1 (MetaSel (Just "getAlt") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 f)))
type Rep (Alt f a) | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal type Rep (Alt f a) = D1 (MetaData "Alt" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Alt" PrefixI True) (S1 (MetaSel (Just "getAlt") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f a))))

(<>) :: Semigroup a => a -> a -> a infixr 6 Source #

An associative operation.