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/Haskell 8

Data.Semigroup

Copyright	(C) 2011-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	[email protected]
Stability	provisional
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell2010

Semigroups
Re-exported monoids from Data.Monoid
A better monoid for Maybe
Difference lists of a semigroup
ArgMin, ArgMax

Description

In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup generalizes a monoid in that there might not exist an identity element. It also (originally) generalized a group (a monoid with all inverses) to a type where every element did not have to have an inverse, thus the name semigroup.

The use of (<>) in this module conflicts with an operator with the same name that is being exported by Data.Monoid. However, this package re-exports (most of) the contents of Data.Monoid, so to use semigroups and monoids in the same package just

import Data.Semigroup

Since: 4.9.0.0

class Semigroup a where Source

The class of semigroups (types with an associative binary operation).

Since: 4.9.0.0

Methods

(<>) :: a -> a -> a infixr 6 Source

An associative operation.

(a <> b) <> c = a <> (b <> c)

If a is also a Monoid we further require

(<>) = mappend

(<>) :: Monoid a => a -> a -> a infixr 6 Source

An associative operation.

(a <> b) <> c = a <> (b <> c)

If a is also a Monoid we further require

(<>) = mappend

sconcat :: NonEmpty a -> a Source

Reduce a non-empty list with <>

The default definition should be sufficient, but this can be overridden for efficiency.

stimes :: Integral b => b -> a -> a Source

Repeat a value n times.

Given that this works on a Semigroup it is allowed to fail if you request 0 or fewer repetitions, and the default definition will do so.

By making this a member of the class, idempotent semigroups and monoids can upgrade this to execute in O(1) by picking stimes = stimesIdempotent or stimes = stimesIdempotentMonoid respectively.

Instances

Semigroup Ordering	Since: 4.9.0.0
Methods (<>) :: Ordering -> Ordering -> Ordering Source sconcat :: NonEmpty Ordering -> Ordering Source stimes :: Integral b => b -> Ordering -> Ordering Source
Semigroup ()	Since: 4.9.0.0
Methods (<>) :: () -> () -> () Source sconcat :: NonEmpty () -> () Source stimes :: Integral b => b -> () -> () Source
Semigroup Any	Since: 4.9.0.0
Methods (<>) :: Any -> Any -> Any Source sconcat :: NonEmpty Any -> Any Source stimes :: Integral b => b -> Any -> Any Source
Semigroup All	Since: 4.9.0.0
Methods (<>) :: All -> All -> All Source sconcat :: NonEmpty All -> All Source stimes :: Integral b => b -> All -> All Source
Semigroup Lifetime	Since: 4.10.0.0
Methods (<>) :: Lifetime -> Lifetime -> Lifetime Source sconcat :: NonEmpty Lifetime -> Lifetime Source stimes :: Integral b => b -> Lifetime -> Lifetime Source
Semigroup Event	Since: 4.10.0.0
Methods (<>) :: Event -> Event -> Event Source sconcat :: NonEmpty Event -> Event Source stimes :: Integral b => b -> Event -> Event Source
Semigroup Void	Since: 4.9.0.0
Methods (<>) :: Void -> Void -> Void Source sconcat :: NonEmpty Void -> Void Source stimes :: Integral b => b -> Void -> Void Source
Semigroup [a]	Since: 4.9.0.0
Methods (<>) :: [a] -> [a] -> [a] Source sconcat :: NonEmpty [a] -> [a] Source stimes :: Integral b => b -> [a] -> [a] Source
Semigroup a => Semigroup (Maybe a)	Since: 4.9.0.0
Methods (<>) :: Maybe a -> Maybe a -> Maybe a Source sconcat :: NonEmpty (Maybe a) -> Maybe a Source stimes :: Integral b => b -> Maybe a -> Maybe a Source
Semigroup a => Semigroup (IO a)	Since: 4.10.0.0
Methods (<>) :: IO a -> IO a -> IO a Source sconcat :: NonEmpty (IO a) -> IO a Source stimes :: Integral b => b -> IO a -> IO a Source
Semigroup (Last a)	Since: 4.9.0.0
Methods (<>) :: Last a -> Last a -> Last a Source sconcat :: NonEmpty (Last a) -> Last a Source stimes :: Integral b => b -> Last a -> Last a Source
Semigroup (First a)	Since: 4.9.0.0
Methods (<>) :: First a -> First a -> First a Source sconcat :: NonEmpty (First a) -> First a Source stimes :: Integral b => b -> First a -> First a Source
Num a => Semigroup (Product a)	Since: 4.9.0.0
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 => Semigroup (Sum a)	Since: 4.9.0.0
Methods (<>) :: Sum a -> Sum a -> Sum a Source sconcat :: NonEmpty (Sum a) -> Sum a Source stimes :: Integral b => b -> Sum a -> Sum a Source
Semigroup (Endo a)	Since: 4.9.0.0
Methods (<>) :: Endo a -> Endo a -> Endo a Source sconcat :: NonEmpty (Endo a) -> Endo a Source stimes :: Integral b => b -> Endo a -> Endo a Source
Semigroup a => Semigroup (Dual a)	Since: 4.9.0.0
Methods (<>) :: Dual a -> Dual a -> Dual a Source sconcat :: NonEmpty (Dual a) -> Dual a Source stimes :: Integral b => b -> Dual a -> Dual a Source
Semigroup a => Semigroup (Identity a)	Since: 4.9.0.0
Methods (<>) :: Identity a -> Identity a -> Identity a Source sconcat :: NonEmpty (Identity a) -> Identity a Source stimes :: Integral b => b -> Identity a -> Identity a Source
Semigroup (NonEmpty a)	Since: 4.9.0.0
Methods (<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a Source sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a Source stimes :: Integral b => b -> NonEmpty a -> NonEmpty a Source
Semigroup a => Semigroup (Option a)	Since: 4.9.0.0
Methods (<>) :: Option a -> Option a -> Option a Source sconcat :: NonEmpty (Option a) -> Option a Source stimes :: Integral b => b -> Option a -> Option a Source
Monoid m => Semigroup (WrappedMonoid m)	Since: 4.9.0.0
Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m Source stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m Source
Semigroup (Last a)	Since: 4.9.0.0
Methods (<>) :: Last a -> Last a -> Last a Source sconcat :: NonEmpty (Last a) -> Last a Source stimes :: Integral b => b -> Last a -> Last a Source
Semigroup (First a)	Since: 4.9.0.0
Methods (<>) :: First a -> First a -> First a Source sconcat :: NonEmpty (First a) -> First a Source stimes :: Integral b => b -> First a -> First a Source
Ord a => Semigroup (Max a)	Since: 4.9.0.0
Methods (<>) :: Max a -> Max a -> Max a Source sconcat :: NonEmpty (Max a) -> Max a Source stimes :: Integral b => b -> Max a -> Max a Source
Ord a => Semigroup (Min a)	Since: 4.9.0.0
Methods (<>) :: Min a -> Min a -> Min a Source sconcat :: NonEmpty (Min a) -> Min a Source stimes :: Integral b => b -> Min a -> Min a Source
Semigroup b => Semigroup (a -> b)	Since: 4.9.0.0
Methods (<>) :: (a -> b) -> (a -> b) -> a -> b Source sconcat :: NonEmpty (a -> b) -> a -> b Source stimes :: Integral b => b -> (a -> b) -> a -> b Source
Semigroup (Either a b)	Since: 4.9.0.0
Methods (<>) :: Either a b -> Either a b -> Either a b Source sconcat :: NonEmpty (Either a b) -> Either a b Source stimes :: Integral b => b -> Either a b -> Either a b Source
(Semigroup a, Semigroup b) => Semigroup (a, b)	Since: 4.9.0.0
Methods (<>) :: (a, b) -> (a, b) -> (a, b) Source sconcat :: NonEmpty (a, b) -> (a, b) Source stimes :: Integral b => b -> (a, b) -> (a, b) Source
Semigroup (Proxy k s)	Since: 4.9.0.0
Methods (<>) :: Proxy k s -> Proxy k s -> Proxy k s Source sconcat :: NonEmpty (Proxy k s) -> Proxy k s Source stimes :: Integral b => b -> Proxy k s -> Proxy k s Source
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c)	Since: 4.9.0.0
Methods (<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) Source sconcat :: NonEmpty (a, b, c) -> (a, b, c) Source stimes :: Integral b => b -> (a, b, c) -> (a, b, c) Source
Alternative f => Semigroup (Alt * f a)	Since: 4.9.0.0
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
Semigroup a => Semigroup (Const k a b)	Since: 4.9.0.0
Methods (<>) :: Const k a b -> Const k a b -> Const k a b Source sconcat :: NonEmpty (Const k a b) -> Const k a b Source stimes :: Integral b => b -> Const k a b -> Const k a b Source
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d)	Since: 4.9.0.0
Methods (<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) Source stimes :: Integral b => b -> (a, b, c, d) -> (a, b, c, d) Source
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e)	Since: 4.9.0.0
Methods (<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e) Source stimes :: Integral b => b -> (a, b, c, d, e) -> (a, b, c, d, e) Source

stimesMonoid :: (Integral b, Monoid a) => b -> a -> a Source

This is a valid definition of stimes for a Monoid.

Unlike the default definition of stimes, it is defined for 0 and so it should be preferred where possible.

stimesIdempotent :: Integral b => b -> a -> a Source

This is a valid definition of stimes for an idempotent Semigroup.

When x <> x = x, this definition should be preferred, because it works in O(1) rather than O(log n).

stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a Source

This is a valid definition of stimes for an idempotent Monoid.

When mappend x x = x, this definition should be preferred, because it works in O(1) rather than O(log n)

mtimesDefault :: (Integral b, Monoid a) => b -> a -> a Source

Repeat a value n times.

mtimesDefault n a = a <> a <> ... <> a  -- using <> (n-1) times

Implemented using stimes and mempty.

This is a suitable definition for an mtimes member of Monoid.

Semigroups

newtype Min a Source

Constructors

Min
Fields getMin :: a

Instances

Monad Min	Since: 4.9.0.0
Methods (>>=) :: Min a -> (a -> Min b) -> Min b Source (>>) :: Min a -> Min b -> Min b Source return :: a -> Min a Source fail :: String -> Min a Source
Functor Min	Since: 4.9.0.0
Methods fmap :: (a -> b) -> Min a -> Min b Source (<$) :: a -> Min b -> Min a Source
MonadFix Min	Since: 4.9.0.0
Methods mfix :: (a -> Min a) -> Min a Source
Applicative Min	Since: 4.9.0.0
Methods pure :: a -> Min a Source (<>) :: Min (a -> b) -> Min a -> Min b Source liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c Source (>) :: Min a -> Min b -> Min b Source (<*) :: Min a -> Min b -> Min a Source
Foldable Min	Since: 4.9.0.0
Methods fold :: Monoid m => Min m -> m Source foldMap :: Monoid m => (a -> m) -> Min a -> m Source foldr :: (a -> b -> b) -> b -> Min a -> b Source foldr' :: (a -> b -> b) -> b -> Min a -> b Source foldl :: (b -> a -> b) -> b -> Min a -> b Source foldl' :: (b -> a -> b) -> b -> Min a -> b Source foldr1 :: (a -> a -> a) -> Min a -> a Source foldl1 :: (a -> a -> a) -> Min a -> a Source toList :: Min a -> [a] Source null :: Min a -> Bool Source length :: Min a -> Int Source elem :: Eq a => a -> Min a -> Bool Source maximum :: Ord a => Min a -> a Source minimum :: Ord a => Min a -> a Source sum :: Num a => Min a -> a Source product :: Num a => Min a -> a Source
Traversable Min	Since: 4.9.0.0
Methods traverse :: Applicative f => (a -> f b) -> Min a -> f (Min b) Source sequenceA :: Applicative f => Min (f a) -> f (Min a) Source mapM :: Monad m => (a -> m b) -> Min a -> m (Min b) Source sequence :: Monad m => Min (m a) -> m (Min a) Source
Bounded a => Bounded (Min a)
Methods minBound :: Min a Source maxBound :: Min a Source
Enum a => Enum (Min a)	Since: 4.9.0.0
Methods succ :: Min a -> Min a Source pred :: Min a -> Min a Source toEnum :: Int -> Min a Source fromEnum :: Min a -> Int Source enumFrom :: Min a -> [Min a] Source enumFromThen :: Min a -> Min a -> [Min a] Source enumFromTo :: Min a -> Min a -> [Min a] Source enumFromThenTo :: Min a -> Min a -> Min a -> [Min a] Source
Eq a => Eq (Min a)
Methods (==) :: Min a -> Min a -> Bool Source (/=) :: Min a -> Min a -> Bool Source
Data a => Data (Min a)
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Min a -> c (Min a) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Min a) Source toConstr :: Min a -> Constr Source dataTypeOf :: Min a -> DataType Source dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Min a)) Source dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Min a)) Source gmapT :: (forall b. Data b => b -> b) -> Min a -> Min a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r Source gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r Source gmapQ :: (forall d. Data d => d -> u) -> Min a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Min a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) Source
Num a => Num (Min a)	Since: 4.9.0.0
Methods (+) :: Min a -> Min a -> Min a Source (-) :: Min a -> Min a -> Min a Source (*) :: Min a -> Min a -> Min a Source negate :: Min a -> Min a Source abs :: Min a -> Min a Source signum :: Min a -> Min a Source fromInteger :: Integer -> Min a Source
Ord a => Ord (Min a)
Methods compare :: Min a -> Min a -> Ordering Source (<) :: Min a -> Min a -> Bool Source (<=) :: Min a -> Min a -> Bool Source (>) :: Min a -> Min a -> Bool Source (>=) :: Min a -> Min a -> Bool Source max :: Min a -> Min a -> Min a Source min :: Min a -> Min a -> Min a Source
Read a => Read (Min a)
Methods readsPrec :: Int -> ReadS (Min a) Source readList :: ReadS [Min a] Source readPrec :: ReadPrec (Min a) Source readListPrec :: ReadPrec [Min a] Source
Show a => Show (Min a)
Methods showsPrec :: Int -> Min a -> ShowS Source show :: Min a -> String Source showList :: [Min a] -> ShowS Source
Generic (Min a)
Associated Types type Rep (Min a) :: * -> * Source Methods from :: Min a -> Rep (Min a) x Source to :: Rep (Min a) x -> Min a Source
Ord a => Semigroup (Min a)	Since: 4.9.0.0
Methods (<>) :: Min a -> Min a -> Min a Source sconcat :: NonEmpty (Min a) -> Min a Source stimes :: Integral b => b -> Min a -> Min a Source
(Ord a, Bounded a) => Monoid (Min a)	Since: 4.9.0.0
Methods mempty :: Min a Source mappend :: Min a -> Min a -> Min a Source mconcat :: [Min a] -> Min a Source
Generic1 * Min
Associated Types type Rep1 Min (f :: Min -> ) :: k -> Source Methods from1 :: f a -> Rep1 Min f a Source to1 :: Rep1 Min f a -> f a Source
type Rep (Min a)
type Rep (Min a) = D1 * (MetaData "Min" "Data.Semigroup" "base" True) (C1 * (MetaCons "Min" PrefixI True) (S1 * (MetaSel (Just Symbol "getMin") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Min
type Rep1 * Min = D1 * (MetaData "Min" "Data.Semigroup" "base" True) (C1 * (MetaCons "Min" PrefixI True) (S1 * (MetaSel (Just Symbol "getMin") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Max a Source

Constructors

Max
Fields getMax :: a

Instances

Monad Max	Since: 4.9.0.0
Methods (>>=) :: Max a -> (a -> Max b) -> Max b Source (>>) :: Max a -> Max b -> Max b Source return :: a -> Max a Source fail :: String -> Max a Source
Functor Max	Since: 4.9.0.0
Methods fmap :: (a -> b) -> Max a -> Max b Source (<$) :: a -> Max b -> Max a Source
MonadFix Max	Since: 4.9.0.0
Methods mfix :: (a -> Max a) -> Max a Source
Applicative Max	Since: 4.9.0.0
Methods pure :: a -> Max a Source (<>) :: Max (a -> b) -> Max a -> Max b Source liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c Source (>) :: Max a -> Max b -> Max b Source (<*) :: Max a -> Max b -> Max a Source
Foldable Max	Since: 4.9.0.0
Methods fold :: Monoid m => Max m -> m Source foldMap :: Monoid m => (a -> m) -> Max a -> m Source foldr :: (a -> b -> b) -> b -> Max a -> b Source foldr' :: (a -> b -> b) -> b -> Max a -> b Source foldl :: (b -> a -> b) -> b -> Max a -> b Source foldl' :: (b -> a -> b) -> b -> Max a -> b Source foldr1 :: (a -> a -> a) -> Max a -> a Source foldl1 :: (a -> a -> a) -> Max a -> a Source toList :: Max a -> [a] Source null :: Max a -> Bool Source length :: Max a -> Int Source elem :: Eq a => a -> Max a -> Bool Source maximum :: Ord a => Max a -> a Source minimum :: Ord a => Max a -> a Source sum :: Num a => Max a -> a Source product :: Num a => Max a -> a Source
Traversable Max	Since: 4.9.0.0
Methods traverse :: Applicative f => (a -> f b) -> Max a -> f (Max b) Source sequenceA :: Applicative f => Max (f a) -> f (Max a) Source mapM :: Monad m => (a -> m b) -> Max a -> m (Max b) Source sequence :: Monad m => Max (m a) -> m (Max a) Source
Bounded a => Bounded (Max a)
Methods minBound :: Max a Source maxBound :: Max a Source
Enum a => Enum (Max a)	Since: 4.9.0.0
Methods succ :: Max a -> Max a Source pred :: Max a -> Max a Source toEnum :: Int -> Max a Source fromEnum :: Max a -> Int Source enumFrom :: Max a -> [Max a] Source enumFromThen :: Max a -> Max a -> [Max a] Source enumFromTo :: Max a -> Max a -> [Max a] Source enumFromThenTo :: Max a -> Max a -> Max a -> [Max a] Source
Eq a => Eq (Max a)
Methods (==) :: Max a -> Max a -> Bool Source (/=) :: Max a -> Max a -> Bool Source
Data a => Data (Max a)
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Max a -> c (Max a) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Max a) Source toConstr :: Max a -> Constr Source dataTypeOf :: Max a -> DataType Source dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Max a)) Source dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Max a)) Source gmapT :: (forall b. Data b => b -> b) -> Max a -> Max a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r Source gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r Source gmapQ :: (forall d. Data d => d -> u) -> Max a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Max a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) Source
Num a => Num (Max a)	Since: 4.9.0.0
Methods (+) :: Max a -> Max a -> Max a Source (-) :: Max a -> Max a -> Max a Source (*) :: Max a -> Max a -> Max a Source negate :: Max a -> Max a Source abs :: Max a -> Max a Source signum :: Max a -> Max a Source fromInteger :: Integer -> Max a Source
Ord a => Ord (Max a)
Methods compare :: Max a -> Max a -> Ordering Source (<) :: Max a -> Max a -> Bool Source (<=) :: Max a -> Max a -> Bool Source (>) :: Max a -> Max a -> Bool Source (>=) :: Max a -> Max a -> Bool Source max :: Max a -> Max a -> Max a Source min :: Max a -> Max a -> Max a Source
Read a => Read (Max a)
Methods readsPrec :: Int -> ReadS (Max a) Source readList :: ReadS [Max a] Source readPrec :: ReadPrec (Max a) Source readListPrec :: ReadPrec [Max a] Source
Show a => Show (Max a)
Methods showsPrec :: Int -> Max a -> ShowS Source show :: Max a -> String Source showList :: [Max a] -> ShowS Source
Generic (Max a)
Associated Types type Rep (Max a) :: * -> * Source Methods from :: Max a -> Rep (Max a) x Source to :: Rep (Max a) x -> Max a Source
Ord a => Semigroup (Max a)	Since: 4.9.0.0
Methods (<>) :: Max a -> Max a -> Max a Source sconcat :: NonEmpty (Max a) -> Max a Source stimes :: Integral b => b -> Max a -> Max a Source
(Ord a, Bounded a) => Monoid (Max a)	Since: 4.9.0.0
Methods mempty :: Max a Source mappend :: Max a -> Max a -> Max a Source mconcat :: [Max a] -> Max a Source
Generic1 * Max
Associated Types type Rep1 Max (f :: Max -> ) :: k -> Source Methods from1 :: f a -> Rep1 Max f a Source to1 :: Rep1 Max f a -> f a Source
type Rep (Max a)
type Rep (Max a) = D1 * (MetaData "Max" "Data.Semigroup" "base" True) (C1 * (MetaCons "Max" PrefixI True) (S1 * (MetaSel (Just Symbol "getMax") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Max
type Rep1 * Max = D1 * (MetaData "Max" "Data.Semigroup" "base" True) (C1 * (MetaCons "Max" PrefixI True) (S1 * (MetaSel (Just Symbol "getMax") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype First a Source

Use Option (First a) to get the behavior of First from Data.Monoid.

Constructors

First
Fields getFirst :: a

Instances

Monad First	Since: 4.9.0.0
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: 4.9.0.0
Methods fmap :: (a -> b) -> First a -> First b Source (<$) :: a -> First b -> First a Source
MonadFix First	Since: 4.9.0.0
Methods mfix :: (a -> First a) -> First a Source
Applicative First	Since: 4.9.0.0
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: 4.9.0.0
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: 4.9.0.0
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
Bounded a => Bounded (First a)
Methods minBound :: First a Source maxBound :: First a Source
Enum a => Enum (First a)	Since: 4.9.0.0
Methods succ :: First a -> First a Source pred :: First a -> First a Source toEnum :: Int -> First a Source fromEnum :: First a -> Int Source enumFrom :: First a -> [First a] Source enumFromThen :: First a -> First a -> [First a] Source enumFromTo :: First a -> First a -> [First a] Source enumFromThenTo :: First a -> First a -> First a -> [First a] Source
Eq a => Eq (First a)
Methods (==) :: First a -> First a -> Bool Source (/=) :: First a -> First a -> Bool Source
Data a => Data (First a)
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> First a -> c (First a) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a) Source toConstr :: First a -> Constr Source dataTypeOf :: First a -> DataType Source dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (First a)) Source dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a)) Source gmapT :: (forall b. Data b => b -> b) -> First a -> First a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r Source gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r Source gmapQ :: (forall d. Data d => d -> u) -> First a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source
Ord a => Ord (First a)
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)
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)
Methods showsPrec :: Int -> First a -> ShowS Source show :: First a -> String Source showList :: [First a] -> ShowS Source
Generic (First a)
Associated Types type Rep (First a) :: * -> * Source Methods from :: First a -> Rep (First a) x Source to :: Rep (First a) x -> First a Source
Semigroup (First a)	Since: 4.9.0.0
Methods (<>) :: First a -> First a -> First a Source sconcat :: NonEmpty (First a) -> First a Source stimes :: Integral b => b -> First a -> First a Source
Generic1 * First
Associated Types type Rep1 First (f :: First -> ) :: k -> Source Methods from1 :: f a -> Rep1 First f a Source to1 :: Rep1 First f a -> f a Source
type Rep (First a)
type Rep (First a) = D1 * (MetaData "First" "Data.Semigroup" "base" True) (C1 * (MetaCons "First" PrefixI True) (S1 * (MetaSel (Just Symbol "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * First
type Rep1 * First = D1 * (MetaData "First" "Data.Semigroup" "base" True) (C1 * (MetaCons "First" PrefixI True) (S1 * (MetaSel (Just Symbol "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Last a Source

Use Option (Last a) to get the behavior of Last from Data.Monoid

Constructors

Last
Fields getLast :: a

Instances

Monad Last	Since: 4.9.0.0
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: 4.9.0.0
Methods fmap :: (a -> b) -> Last a -> Last b Source (<$) :: a -> Last b -> Last a Source
MonadFix Last	Since: 4.9.0.0
Methods mfix :: (a -> Last a) -> Last a Source
Applicative Last	Since: 4.9.0.0
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: 4.9.0.0
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: 4.9.0.0
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
Bounded a => Bounded (Last a)
Methods minBound :: Last a Source maxBound :: Last a Source
Enum a => Enum (Last a)	Since: 4.9.0.0
Methods succ :: Last a -> Last a Source pred :: Last a -> Last a Source toEnum :: Int -> Last a Source fromEnum :: Last a -> Int Source enumFrom :: Last a -> [Last a] Source enumFromThen :: Last a -> Last a -> [Last a] Source enumFromTo :: Last a -> Last a -> [Last a] Source enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] Source
Eq a => Eq (Last a)
Methods (==) :: Last a -> Last a -> Bool Source (/=) :: Last a -> Last a -> Bool Source
Data a => Data (Last a)
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Last a -> c (Last a) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a) Source toConstr :: Last a -> Constr Source dataTypeOf :: Last a -> DataType Source dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Last a)) Source dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a)) Source gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r Source gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r Source gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source
Ord a => Ord (Last a)
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)
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)
Methods showsPrec :: Int -> Last a -> ShowS Source show :: Last a -> String Source showList :: [Last a] -> ShowS Source
Generic (Last a)
Associated Types type Rep (Last a) :: * -> * Source Methods from :: Last a -> Rep (Last a) x Source to :: Rep (Last a) x -> Last a Source
Semigroup (Last a)	Since: 4.9.0.0
Methods (<>) :: Last a -> Last a -> Last a Source sconcat :: NonEmpty (Last a) -> Last a Source stimes :: Integral b => b -> Last a -> Last a Source
Generic1 * Last
Associated Types type Rep1 Last (f :: Last -> ) :: k -> Source Methods from1 :: f a -> Rep1 Last f a Source to1 :: Rep1 Last f a -> f a Source
type Rep (Last a)
type Rep (Last a) = D1 * (MetaData "Last" "Data.Semigroup" "base" True) (C1 * (MetaCons "Last" PrefixI True) (S1 * (MetaSel (Just Symbol "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Last
type Rep1 * Last = D1 * (MetaData "Last" "Data.Semigroup" "base" True) (C1 * (MetaCons "Last" PrefixI True) (S1 * (MetaSel (Just Symbol "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype WrappedMonoid m Source

Provide a Semigroup for an arbitrary Monoid.

Constructors

WrapMonoid
Fields unwrapMonoid :: m

Instances

Bounded m => Bounded (WrappedMonoid m)
Methods minBound :: WrappedMonoid m Source maxBound :: WrappedMonoid m Source
Enum a => Enum (WrappedMonoid a)	Since: 4.9.0.0
Methods succ :: WrappedMonoid a -> WrappedMonoid a Source pred :: WrappedMonoid a -> WrappedMonoid a Source toEnum :: Int -> WrappedMonoid a Source fromEnum :: WrappedMonoid a -> Int Source enumFrom :: WrappedMonoid a -> [WrappedMonoid a] Source enumFromThen :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source enumFromTo :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source enumFromThenTo :: WrappedMonoid a -> WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source
Eq m => Eq (WrappedMonoid m)
Methods (==) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source (/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source
Data m => Data (WrappedMonoid m)
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> WrappedMonoid m -> c (WrappedMonoid m) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (WrappedMonoid m) Source toConstr :: WrappedMonoid m -> Constr Source dataTypeOf :: WrappedMonoid m -> DataType Source dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (WrappedMonoid m)) Source dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (WrappedMonoid m)) Source gmapT :: (forall b. Data b => b -> b) -> WrappedMonoid m -> WrappedMonoid m Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r Source gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r Source gmapQ :: (forall d. Data d => d -> u) -> WrappedMonoid m -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> WrappedMonoid m -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> WrappedMonoid m -> m (WrappedMonoid m) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> WrappedMonoid m -> m (WrappedMonoid m) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> WrappedMonoid m -> m (WrappedMonoid m) Source
Ord m => Ord (WrappedMonoid m)
Methods compare :: WrappedMonoid m -> WrappedMonoid m -> Ordering Source (<) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source (<=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source (>) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source (>=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source max :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source min :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source
Read m => Read (WrappedMonoid m)
Methods readsPrec :: Int -> ReadS (WrappedMonoid m) Source readList :: ReadS [WrappedMonoid m] Source readPrec :: ReadPrec (WrappedMonoid m) Source readListPrec :: ReadPrec [WrappedMonoid m] Source
Show m => Show (WrappedMonoid m)
Methods showsPrec :: Int -> WrappedMonoid m -> ShowS Source show :: WrappedMonoid m -> String Source showList :: [WrappedMonoid m] -> ShowS Source
Generic (WrappedMonoid m)
Associated Types type Rep (WrappedMonoid m) :: * -> * Source Methods from :: WrappedMonoid m -> Rep (WrappedMonoid m) x Source to :: Rep (WrappedMonoid m) x -> WrappedMonoid m Source
Monoid m => Semigroup (WrappedMonoid m)	Since: 4.9.0.0
Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m Source stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m Source
Monoid m => Monoid (WrappedMonoid m)	Since: 4.9.0.0
Methods mempty :: WrappedMonoid m Source mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source
Generic1 * WrappedMonoid
Associated Types type Rep1 WrappedMonoid (f :: WrappedMonoid -> ) :: k -> Source Methods from1 :: f a -> Rep1 WrappedMonoid f a Source to1 :: Rep1 WrappedMonoid f a -> f a Source
type Rep (WrappedMonoid m)
type Rep (WrappedMonoid m) = D1 * (MetaData "WrappedMonoid" "Data.Semigroup" "base" True) (C1 * (MetaCons "WrapMonoid" PrefixI True) (S1 * (MetaSel (Just Symbol "unwrapMonoid") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * m)))
type Rep1 * WrappedMonoid
type Rep1 * WrappedMonoid = D1 * (MetaData "WrappedMonoid" "Data.Semigroup" "base" True) (C1 * (MetaCons "WrapMonoid" PrefixI True) (S1 * (MetaSel (Just Symbol "unwrapMonoid") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

Re-exported monoids from Data.Monoid

class Monoid a where Source

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

```
mappend mempty x = x
```
```
mappend x mempty = x
```

mappend x (mappend y z) = mappend (mappend x y) z

```
mconcat = foldr mappend 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 newtypes and make those instances of Monoid, e.g. Sum and Product.

Minimal complete definition

mempty, mappend

Methods

mempty :: a Source

Identity of mappend

mappend :: a -> a -> a Source

An associative operation

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: 2.1
Methods mempty :: Ordering Source mappend :: Ordering -> Ordering -> Ordering Source mconcat :: [Ordering] -> Ordering Source
Monoid ()	Since: 2.1
Methods mempty :: () Source mappend :: () -> () -> () Source mconcat :: [()] -> () Source
Monoid Any	Since: 2.1
Methods mempty :: Any Source mappend :: Any -> Any -> Any Source mconcat :: [Any] -> Any Source
Monoid All	Since: 2.1
Methods mempty :: All Source mappend :: All -> All -> All Source mconcat :: [All] -> All Source
Monoid Lifetime	`mappend` takes the longer of two lifetimes. Since: 4.8.0.0
Methods mempty :: Lifetime Source mappend :: Lifetime -> Lifetime -> Lifetime Source mconcat :: [Lifetime] -> Lifetime Source
Monoid Event	Since: 4.3.1.0
Methods mempty :: Event Source mappend :: Event -> Event -> Event Source mconcat :: [Event] -> Event Source
Monoid [a]	Since: 2.1
Methods mempty :: [a] Source mappend :: [a] -> [a] -> [a] Source mconcat :: [[a]] -> [a] Source
Monoid 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 `ee = e` and `es = s = s*e` for all `s ∈ S`." Since there used to be no "Semigroup" typeclass providing just `mappend`, we use `Monoid` instead. Since: 2.1
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: 4.9.0.0
Methods mempty :: IO a Source mappend :: IO a -> IO a -> IO a Source mconcat :: [IO a] -> IO a Source
Monoid (Last a)	Since: 2.1
Methods mempty :: Last a Source mappend :: Last a -> Last a -> Last a Source mconcat :: [Last a] -> Last a Source
Monoid (First a)	Since: 2.1
Methods mempty :: First a Source mappend :: First a -> First a -> First a Source mconcat :: [First a] -> First a Source
Num a => Monoid (Product a)	Since: 2.1
Methods mempty :: Product a Source mappend :: Product a -> Product a -> Product a Source mconcat :: [Product a] -> Product a Source
Num a => Monoid (Sum a)	Since: 2.1
Methods mempty :: Sum a Source mappend :: Sum a -> Sum a -> Sum a Source mconcat :: [Sum a] -> Sum a Source
Monoid (Endo a)	Since: 2.1
Methods mempty :: Endo a Source mappend :: Endo a -> Endo a -> Endo a Source mconcat :: [Endo a] -> Endo a Source
Monoid a => Monoid (Dual a)	Since: 2.1
Methods mempty :: Dual a Source mappend :: Dual a -> Dual a -> Dual a Source mconcat :: [Dual a] -> Dual a Source
Monoid a => Monoid (Identity a)
Methods mempty :: Identity a Source mappend :: Identity a -> Identity a -> Identity a Source mconcat :: [Identity a] -> Identity a Source
Semigroup a => Monoid (Option a)	Since: 4.9.0.0
Methods mempty :: Option a Source mappend :: Option a -> Option a -> Option a Source mconcat :: [Option a] -> Option a Source
Monoid m => Monoid (WrappedMonoid m)	Since: 4.9.0.0
Methods mempty :: WrappedMonoid m Source mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source
(Ord a, Bounded a) => Monoid (Max a)	Since: 4.9.0.0
Methods mempty :: Max a Source mappend :: Max a -> Max a -> Max a Source mconcat :: [Max a] -> Max a Source
(Ord a, Bounded a) => Monoid (Min a)	Since: 4.9.0.0
Methods mempty :: Min a Source mappend :: Min a -> Min a -> Min a Source mconcat :: [Min a] -> Min a Source
Monoid b => Monoid (a -> b)	Since: 2.1
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: 2.1
Methods mempty :: (a, b) Source mappend :: (a, b) -> (a, b) -> (a, b) Source mconcat :: [(a, b)] -> (a, b) Source
Monoid (Proxy k s)	Since: 4.7.0.0
Methods mempty :: Proxy k s Source mappend :: Proxy k s -> Proxy k s -> Proxy k s Source mconcat :: [Proxy k s] -> Proxy k s Source
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)	Since: 2.1
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
Alternative f => Monoid (Alt * f a)	Since: 4.8.0.0
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 (Const k a b)
Methods mempty :: Const k a b Source mappend :: Const k a b -> Const k a b -> Const k a b Source mconcat :: [Const k a b] -> Const k a b Source
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d)	Since: 2.1
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: 2.1
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 Dual a Source

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

Constructors

Dual
Fields getDual :: a

Instances

Monad Dual	Since: 4.8.0.0
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: 4.8.0.0
Methods fmap :: (a -> b) -> Dual a -> Dual b Source (<$) :: a -> Dual b -> Dual a Source
MonadFix Dual	Since: 4.8.0.0
Methods mfix :: (a -> Dual a) -> Dual a Source
Applicative Dual	Since: 4.8.0.0
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: 4.8.0.0
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: 4.8.0.0
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
MonadZip Dual	Since: 4.8.0.0
Methods mzip :: Dual a -> Dual b -> Dual (a, b) Source mzipWith :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source munzip :: Dual (a, b) -> (Dual a, Dual b) Source
Bounded a => Bounded (Dual a)
Methods minBound :: Dual a Source maxBound :: Dual a Source
Eq a => Eq (Dual a)
Methods (==) :: Dual a -> Dual a -> Bool Source (/=) :: Dual a -> Dual a -> Bool Source
Data a => Data (Dual a)	Since: 4.8.0.0
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dual a -> c (Dual a) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dual a) Source toConstr :: Dual a -> Constr Source dataTypeOf :: Dual a -> DataType Source dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Dual a)) Source dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Dual a)) Source gmapT :: (forall b. Data b => b -> b) -> Dual a -> Dual a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r Source gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r Source gmapQ :: (forall d. Data d => d -> u) -> Dual a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Dual a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source
Ord a => Ord (Dual a)
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)
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)
Methods showsPrec :: Int -> Dual a -> ShowS Source show :: Dual a -> String Source showList :: [Dual a] -> ShowS Source
Generic (Dual a)
Associated Types type Rep (Dual a) :: * -> * Source Methods from :: Dual a -> Rep (Dual a) x Source to :: Rep (Dual a) x -> Dual a Source
Semigroup a => Semigroup (Dual a)	Since: 4.9.0.0
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: 2.1
Methods mempty :: Dual a Source mappend :: Dual a -> Dual a -> Dual a Source mconcat :: [Dual a] -> Dual a Source
Generic1 * Dual
Associated Types type Rep1 Dual (f :: Dual -> ) :: k -> Source Methods from1 :: f a -> Rep1 Dual f a Source to1 :: Rep1 Dual f a -> f a Source
type Rep (Dual a)
type Rep (Dual a) = D1 * (MetaData "Dual" "Data.Monoid" "base" True) (C1 * (MetaCons "Dual" PrefixI True) (S1 * (MetaSel (Just Symbol "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Dual
type Rep1 * Dual = D1 * (MetaData "Dual" "Data.Monoid" "base" True) (C1 * (MetaCons "Dual" PrefixI True) (S1 * (MetaSel (Just Symbol "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Endo a Source

The monoid of endomorphisms under composition.

Constructors

Endo
Fields appEndo :: a -> a

Instances

Generic (Endo a)
Associated Types type Rep (Endo a) :: * -> * Source Methods from :: Endo a -> Rep (Endo a) x Source to :: Rep (Endo a) x -> Endo a Source
Semigroup (Endo a)	Since: 4.9.0.0
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: 2.1
Methods mempty :: Endo a Source mappend :: Endo a -> Endo a -> Endo a Source mconcat :: [Endo a] -> Endo a Source
type Rep (Endo a)
type Rep (Endo a) = D1 * (MetaData "Endo" "Data.Monoid" "base" True) (C1 * (MetaCons "Endo" PrefixI True) (S1 * (MetaSel (Just Symbol "appEndo") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (a -> a))))

newtype All Source

Boolean monoid under conjunction (&&).

Constructors

All
Fields getAll :: Bool

Instances

Bounded All
Methods minBound :: All Source maxBound :: All Source
Eq All
Methods (==) :: All -> All -> Bool Source (/=) :: All -> All -> Bool Source
Data All	Since: 4.8.0.0
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> All -> c All Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c All Source toConstr :: All -> Constr Source dataTypeOf :: All -> DataType Source dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c All) Source dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c All) Source gmapT :: (forall b. Data b => b -> b) -> All -> All Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> All -> r Source gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> All -> r Source gmapQ :: (forall d. Data d => d -> u) -> All -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> All -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> All -> m All Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All Source
Ord All
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
Methods readsPrec :: Int -> ReadS All Source readList :: ReadS [All] Source readPrec :: ReadPrec All Source readListPrec :: ReadPrec [All] Source
Show All
Methods showsPrec :: Int -> All -> ShowS Source show :: All -> String Source showList :: [All] -> ShowS Source
Generic All
Associated Types type Rep All :: * -> * Source Methods from :: All -> Rep All x Source to :: Rep All x -> All Source
Semigroup All	Since: 4.9.0.0
Methods (<>) :: All -> All -> All Source sconcat :: NonEmpty All -> All Source stimes :: Integral b => b -> All -> All Source
Monoid All	Since: 2.1
Methods mempty :: All Source mappend :: All -> All -> All Source mconcat :: [All] -> All Source
type Rep All
type Rep All = D1 * (MetaData "All" "Data.Monoid" "base" True) (C1 * (MetaCons "All" PrefixI True) (S1 * (MetaSel (Just Symbol "getAll") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Bool)))

newtype Any Source

Boolean monoid under disjunction (||).

Constructors

Any
Fields getAny :: Bool

Instances

Bounded Any
Methods minBound :: Any Source maxBound :: Any Source
Eq Any
Methods (==) :: Any -> Any -> Bool Source (/=) :: Any -> Any -> Bool Source
Data Any	Since: 4.8.0.0
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Any -> c Any Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Any Source toConstr :: Any -> Constr Source dataTypeOf :: Any -> DataType Source dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c Any) Source dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Any) Source gmapT :: (forall b. Data b => b -> b) -> Any -> Any Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r Source gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r Source gmapQ :: (forall d. Data d => d -> u) -> Any -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Any -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Any -> m Any Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any Source
Ord Any
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
Methods readsPrec :: Int -> ReadS Any Source readList :: ReadS [Any] Source readPrec :: ReadPrec Any Source readListPrec :: ReadPrec [Any] Source
Show Any
Methods showsPrec :: Int -> Any -> ShowS Source show :: Any -> String Source showList :: [Any] -> ShowS Source
Generic Any
Associated Types type Rep Any :: * -> * Source Methods from :: Any -> Rep Any x Source to :: Rep Any x -> Any Source
Semigroup Any	Since: 4.9.0.0
Methods (<>) :: Any -> Any -> Any Source sconcat :: NonEmpty Any -> Any Source stimes :: Integral b => b -> Any -> Any Source
Monoid Any	Since: 2.1
Methods mempty :: Any Source mappend :: Any -> Any -> Any Source mconcat :: [Any] -> Any Source
type Rep Any
type Rep Any = D1 * (MetaData "Any" "Data.Monoid" "base" True) (C1 * (MetaCons "Any" PrefixI True) (S1 * (MetaSel (Just Symbol "getAny") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Bool)))

newtype Sum a Source

Monoid under addition.

Constructors

Sum
Fields getSum :: a

Instances

Monad Sum	Since: 4.8.0.0
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: 4.8.0.0
Methods fmap :: (a -> b) -> Sum a -> Sum b Source (<$) :: a -> Sum b -> Sum a Source
MonadFix Sum	Since: 4.8.0.0
Methods mfix :: (a -> Sum a) -> Sum a Source
Applicative Sum	Since: 4.8.0.0
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: 4.8.0.0
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: 4.8.0.0
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
MonadZip Sum	Since: 4.8.0.0
Methods mzip :: Sum a -> Sum b -> Sum (a, b) Source mzipWith :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source munzip :: Sum (a, b) -> (Sum a, Sum b) Source
Bounded a => Bounded (Sum a)
Methods minBound :: Sum a Source maxBound :: Sum a Source
Eq a => Eq (Sum a)
Methods (==) :: Sum a -> Sum a -> Bool Source (/=) :: Sum a -> Sum a -> Bool Source
Data a => Data (Sum a)	Since: 4.8.0.0
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Sum a -> c (Sum a) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum a) Source toConstr :: Sum a -> Constr Source dataTypeOf :: Sum a -> DataType Source dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Sum a)) Source dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum a)) Source gmapT :: (forall b. Data b => b -> b) -> Sum a -> Sum a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r Source gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r Source gmapQ :: (forall d. Data d => d -> u) -> Sum a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source
Num a => Num (Sum a)
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)
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)
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)
Methods showsPrec :: Int -> Sum a -> ShowS Source show :: Sum a -> String Source showList :: [Sum a] -> ShowS Source
Generic (Sum a)
Associated Types type Rep (Sum a) :: * -> * Source Methods from :: Sum a -> Rep (Sum a) x Source to :: Rep (Sum a) x -> Sum a Source
Num a => Semigroup (Sum a)	Since: 4.9.0.0
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: 2.1
Methods mempty :: Sum a Source mappend :: Sum a -> Sum a -> Sum a Source mconcat :: [Sum a] -> Sum a Source
Generic1 * Sum
Associated Types type Rep1 Sum (f :: Sum -> ) :: k -> Source Methods from1 :: f a -> Rep1 Sum f a Source to1 :: Rep1 Sum f a -> f a Source
type Rep (Sum a)
type Rep (Sum a) = D1 * (MetaData "Sum" "Data.Monoid" "base" True) (C1 * (MetaCons "Sum" PrefixI True) (S1 * (MetaSel (Just Symbol "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Sum
type Rep1 * Sum = D1 * (MetaData "Sum" "Data.Monoid" "base" True) (C1 * (MetaCons "Sum" PrefixI True) (S1 * (MetaSel (Just Symbol "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Product a Source

Monoid under multiplication.

Constructors

Product
Fields getProduct :: a

Instances

Monad Product	Since: 4.8.0.0
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: 4.8.0.0
Methods fmap :: (a -> b) -> Product a -> Product b Source (<$) :: a -> Product b -> Product a Source
MonadFix Product	Since: 4.8.0.0
Methods mfix :: (a -> Product a) -> Product a Source
Applicative Product	Since: 4.8.0.0
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: 4.8.0.0
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: 4.8.0.0
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
MonadZip Product	Since: 4.8.0.0
Methods mzip :: Product a -> Product b -> Product (a, b) Source mzipWith :: (a -> b -> c) -> Product a -> Product b -> Product c Source munzip :: Product (a, b) -> (Product a, Product b) Source
Bounded a => Bounded (Product a)
Methods minBound :: Product a Source maxBound :: Product a Source
Eq a => Eq (Product a)
Methods (==) :: Product a -> Product a -> Bool Source (/=) :: Product a -> Product a -> Bool Source
Data a => Data (Product a)	Since: 4.8.0.0
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Product a -> c (Product a) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product a) Source toConstr :: Product a -> Constr Source dataTypeOf :: Product a -> DataType Source dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Product a)) Source dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product a)) Source gmapT :: (forall b. Data b => b -> b) -> Product a -> Product a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r Source gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r Source gmapQ :: (forall d. Data d => d -> u) -> Product a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Product a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source
Num a => Num (Product a)
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)
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)
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)
Methods showsPrec :: Int -> Product a -> ShowS Source show :: Product a -> String Source showList :: [Product a] -> ShowS Source
Generic (Product a)
Associated Types type Rep (Product a) :: * -> * Source Methods from :: Product a -> Rep (Product a) x Source to :: Rep (Product a) x -> Product a Source
Num a => Semigroup (Product a)	Since: 4.9.0.0
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: 2.1
Methods mempty :: Product a Source mappend :: Product a -> Product a -> Product a Source mconcat :: [Product a] -> Product a Source
Generic1 * Product
Associated Types type Rep1 Product (f :: Product -> ) :: k -> Source Methods from1 :: f a -> Rep1 Product f a Source to1 :: Rep1 Product f a -> f a Source
type Rep (Product a)
type Rep (Product a) = D1 * (MetaData "Product" "Data.Monoid" "base" True) (C1 * (MetaCons "Product" PrefixI True) (S1 * (MetaSel (Just Symbol "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Product
type Rep1 * Product = D1 * (MetaData "Product" "Data.Monoid" "base" True) (C1 * (MetaCons "Product" PrefixI True) (S1 * (MetaSel (Just Symbol "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

A better monoid for Maybe

newtype Option a Source

Option is effectively Maybe with a better instance of Monoid, built off of an underlying Semigroup instead of an underlying Monoid.

Ideally, this type would not exist at all and we would just fix the Monoid instance of Maybe

Constructors

Option
Fields getOption :: Maybe a

Instances

Monad Option	Since: 4.9.0.0
Methods (>>=) :: Option a -> (a -> Option b) -> Option b Source (>>) :: Option a -> Option b -> Option b Source return :: a -> Option a Source fail :: String -> Option a Source
Functor Option	Since: 4.9.0.0
Methods fmap :: (a -> b) -> Option a -> Option b Source (<$) :: a -> Option b -> Option a Source
MonadFix Option	Since: 4.9.0.0
Methods mfix :: (a -> Option a) -> Option a Source
Applicative Option	Since: 4.9.0.0
Methods pure :: a -> Option a Source (<>) :: Option (a -> b) -> Option a -> Option b Source liftA2 :: (a -> b -> c) -> Option a -> Option b -> Option c Source (>) :: Option a -> Option b -> Option b Source (<*) :: Option a -> Option b -> Option a Source
Foldable Option	Since: 4.9.0.0
Methods fold :: Monoid m => Option m -> m Source foldMap :: Monoid m => (a -> m) -> Option a -> m Source foldr :: (a -> b -> b) -> b -> Option a -> b Source foldr' :: (a -> b -> b) -> b -> Option a -> b Source foldl :: (b -> a -> b) -> b -> Option a -> b Source foldl' :: (b -> a -> b) -> b -> Option a -> b Source foldr1 :: (a -> a -> a) -> Option a -> a Source foldl1 :: (a -> a -> a) -> Option a -> a Source toList :: Option a -> [a] Source null :: Option a -> Bool Source length :: Option a -> Int Source elem :: Eq a => a -> Option a -> Bool Source maximum :: Ord a => Option a -> a Source minimum :: Ord a => Option a -> a Source sum :: Num a => Option a -> a Source product :: Num a => Option a -> a Source
Traversable Option	Since: 4.9.0.0
Methods traverse :: Applicative f => (a -> f b) -> Option a -> f (Option b) Source sequenceA :: Applicative f => Option (f a) -> f (Option a) Source mapM :: Monad m => (a -> m b) -> Option a -> m (Option b) Source sequence :: Monad m => Option (m a) -> m (Option a) Source
MonadPlus Option	Since: 4.9.0.0
Methods mzero :: Option a Source mplus :: Option a -> Option a -> Option a Source
Alternative Option	Since: 4.9.0.0
Methods empty :: Option a Source (<\|>) :: Option a -> Option a -> Option a Source some :: Option a -> Option [a] Source many :: Option a -> Option [a] Source
Eq a => Eq (Option a)
Methods (==) :: Option a -> Option a -> Bool Source (/=) :: Option a -> Option a -> Bool Source
Data a => Data (Option a)
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Option a -> c (Option a) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Option a) Source toConstr :: Option a -> Constr Source dataTypeOf :: Option a -> DataType Source dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Option a)) Source dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Option a)) Source gmapT :: (forall b. Data b => b -> b) -> Option a -> Option a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Option a -> r Source gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Option a -> r Source gmapQ :: (forall d. Data d => d -> u) -> Option a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Option a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) Source
Ord a => Ord (Option a)
Methods compare :: Option a -> Option a -> Ordering Source (<) :: Option a -> Option a -> Bool Source (<=) :: Option a -> Option a -> Bool Source (>) :: Option a -> Option a -> Bool Source (>=) :: Option a -> Option a -> Bool Source max :: Option a -> Option a -> Option a Source min :: Option a -> Option a -> Option a Source
Read a => Read (Option a)
Methods readsPrec :: Int -> ReadS (Option a) Source readList :: ReadS [Option a] Source readPrec :: ReadPrec (Option a) Source readListPrec :: ReadPrec [Option a] Source
Show a => Show (Option a)
Methods showsPrec :: Int -> Option a -> ShowS Source show :: Option a -> String Source showList :: [Option a] -> ShowS Source
Generic (Option a)
Associated Types type Rep (Option a) :: * -> * Source Methods from :: Option a -> Rep (Option a) x Source to :: Rep (Option a) x -> Option a Source
Semigroup a => Semigroup (Option a)	Since: 4.9.0.0
Methods (<>) :: Option a -> Option a -> Option a Source sconcat :: NonEmpty (Option a) -> Option a Source stimes :: Integral b => b -> Option a -> Option a Source
Semigroup a => Monoid (Option a)	Since: 4.9.0.0
Methods mempty :: Option a Source mappend :: Option a -> Option a -> Option a Source mconcat :: [Option a] -> Option a Source
Generic1 * Option
Associated Types type Rep1 Option (f :: Option -> ) :: k -> Source Methods from1 :: f a -> Rep1 Option f a Source to1 :: Rep1 Option f a -> f a Source
type Rep (Option a)
type Rep (Option a) = D1 * (MetaData "Option" "Data.Semigroup" "base" True) (C1 * (MetaCons "Option" PrefixI True) (S1 * (MetaSel (Just Symbol "getOption") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (Maybe a))))
type Rep1 * Option
type Rep1 * Option = D1 * (MetaData "Option" "Data.Semigroup" "base" True) (C1 * (MetaCons "Option" PrefixI True) (S1 * (MetaSel (Just Symbol "getOption") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 * Maybe)))

option :: b -> (a -> b) -> Option a -> b Source

Fold an Option case-wise, just like maybe.

Difference lists of a semigroup

diff :: Semigroup m => m -> Endo m Source

This lets you use a difference list of a Semigroup as a Monoid.

cycle1 :: Semigroup m => m -> m Source

A generalization of cycle to an arbitrary Semigroup. May fail to terminate for some values in some semigroups.

ArgMin, ArgMax

data Arg a b Source

Arg isn't itself a Semigroup in its own right, but it can be placed inside Min and Max to compute an arg min or arg max.

Constructors

Arg a b

Instances

Bifunctor Arg	Since: 4.9.0.0
Methods bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d Source first :: (a -> b) -> Arg a c -> Arg b c Source second :: (b -> c) -> Arg a b -> Arg a c Source
Bifoldable Arg	Since: 4.10.0.0
Methods bifold :: Monoid m => Arg m m -> m Source bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Arg a b -> m Source bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Arg a b -> c Source bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Arg a b -> c Source
Bitraversable Arg	Since: 4.10.0.0
Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d) Source
Functor (Arg a)	Since: 4.9.0.0
Methods fmap :: (a -> b) -> Arg a a -> Arg a b Source (<$) :: a -> Arg a b -> Arg a a Source
Foldable (Arg a)	Since: 4.9.0.0
Methods fold :: Monoid m => Arg a m -> m Source foldMap :: Monoid m => (a -> m) -> Arg a a -> m Source foldr :: (a -> b -> b) -> b -> Arg a a -> b Source foldr' :: (a -> b -> b) -> b -> Arg a a -> b Source foldl :: (b -> a -> b) -> b -> Arg a a -> b Source foldl' :: (b -> a -> b) -> b -> Arg a a -> b Source foldr1 :: (a -> a -> a) -> Arg a a -> a Source foldl1 :: (a -> a -> a) -> Arg a a -> a Source toList :: Arg a a -> [a] Source null :: Arg a a -> Bool Source length :: Arg a a -> Int Source elem :: Eq a => a -> Arg a a -> Bool Source maximum :: Ord a => Arg a a -> a Source minimum :: Ord a => Arg a a -> a Source sum :: Num a => Arg a a -> a Source product :: Num a => Arg a a -> a Source
Traversable (Arg a)	Since: 4.9.0.0
Methods traverse :: Applicative f => (a -> f b) -> Arg a a -> f (Arg a b) Source sequenceA :: Applicative f => Arg a (f a) -> f (Arg a a) Source mapM :: Monad m => (a -> m b) -> Arg a a -> m (Arg a b) Source sequence :: Monad m => Arg a (m a) -> m (Arg a a) Source
Generic1 * (Arg a)
Associated Types type Rep1 (Arg a) (f :: Arg a -> ) :: k -> Source Methods from1 :: f a -> Rep1 (Arg a) f a Source to1 :: Rep1 (Arg a) f a -> f a Source
Eq a => Eq (Arg a b)	Since: 4.9.0.0
Methods (==) :: Arg a b -> Arg a b -> Bool Source (/=) :: Arg a b -> Arg a b -> Bool Source
(Data b, Data a) => Data (Arg a b)
Methods gfoldl :: (forall d c. Data d => c (d -> c) -> d -> c c) -> (forall g. g -> c g) -> Arg a b -> c (Arg a b) Source gunfold :: (forall c r. Data c => c (c -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Arg a b) Source toConstr :: Arg a b -> Constr Source dataTypeOf :: Arg a b -> DataType Source dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Arg a b)) Source dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Arg a b)) Source gmapT :: (forall c. Data c => c -> c) -> Arg a b -> Arg a b Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r Source gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r Source gmapQ :: (forall d. Data d => d -> u) -> Arg a b -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Arg a b -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) Source
Ord a => Ord (Arg a b)	Since: 4.9.0.0
Methods compare :: Arg a b -> Arg a b -> Ordering Source (<) :: Arg a b -> Arg a b -> Bool Source (<=) :: Arg a b -> Arg a b -> Bool Source (>) :: Arg a b -> Arg a b -> Bool Source (>=) :: Arg a b -> Arg a b -> Bool Source max :: Arg a b -> Arg a b -> Arg a b Source min :: Arg a b -> Arg a b -> Arg a b Source
(Read b, Read a) => Read (Arg a b)
Methods readsPrec :: Int -> ReadS (Arg a b) Source readList :: ReadS [Arg a b] Source readPrec :: ReadPrec (Arg a b) Source readListPrec :: ReadPrec [Arg a b] Source
(Show b, Show a) => Show (Arg a b)
Methods showsPrec :: Int -> Arg a b -> ShowS Source show :: Arg a b -> String Source showList :: [Arg a b] -> ShowS Source
Generic (Arg a b)
Associated Types type Rep (Arg a b) :: * -> * Source Methods from :: Arg a b -> Rep (Arg a b) x Source to :: Rep (Arg a b) x -> Arg a b Source
type Rep1 * (Arg a)
type Rep1 * (Arg a) = D1 * (MetaData "Arg" "Data.Semigroup" "base" False) (C1 * (MetaCons "Arg" PrefixI False) ((::) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1)))
type Rep (Arg a b)
type Rep (Arg a b) = D1 * (MetaData "Arg" "Data.Semigroup" "base" False) (C1 * (MetaCons "Arg" PrefixI False) ((::) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * b))))

type ArgMin a b = Min (Arg a b) Source

type ArgMax a b = Max (Arg a b) Source

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.2.1/docs/html/libraries/base-4.10.0.0/Data-Semigroup.html

Data.Semigroup

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