Copyright	(C) 2011-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	libraries@haskell.org
Stability	provisional
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell2010

Data.Semigroup

Contents

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

Synopsis

Documentation

class Semigroup a where #

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

Since: 4.9.0.0

Methods

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

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 #

An associative operation.

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

If a is also a Monoid we further require

(<>) = mappend

sconcat :: NonEmpty a -> a #

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 #

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

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

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 #

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 #

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 #

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 #

Constructors

Min
Fields getMin :: a

Instances

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

Constructors

Max
Fields getMax :: a

Instances

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

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 # (>>) :: First a -> First b -> First b # return :: a -> First a # fail :: String -> First a #
Functor First #	Since: 4.9.0.0
Methods fmap :: (a -> b) -> First a -> First b # (<$) :: a -> First b -> First a #
MonadFix First #	Since: 4.9.0.0
Methods mfix :: (a -> First a) -> First a #
Applicative First #	Since: 4.9.0.0
Methods pure :: a -> First a # (<>) :: First (a -> b) -> First a -> First b # liftA2 :: (a -> b -> c) -> First a -> First b -> First c # (>) :: First a -> First b -> First b # (<*) :: First a -> First b -> First a #
Foldable First #	Since: 4.9.0.0
Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # toList :: First a -> [a] # null :: First a -> Bool # length :: First a -> Int # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # sum :: Num a => First a -> a # product :: Num a => First a -> a #
Traversable First #	Since: 4.9.0.0
Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) # sequenceA :: Applicative f => First (f a) -> f (First a) # mapM :: Monad m => (a -> m b) -> First a -> m (First b) # sequence :: Monad m => First (m a) -> m (First a) #
Bounded a => Bounded (First a) #
Methods minBound :: First a # maxBound :: First a #
Enum a => Enum (First a) #	Since: 4.9.0.0
Methods succ :: First a -> First a # pred :: First a -> First a # toEnum :: Int -> First a # fromEnum :: First a -> Int # enumFrom :: First a -> [First a] # enumFromThen :: First a -> First a -> [First a] # enumFromTo :: First a -> First a -> [First a] # enumFromThenTo :: First a -> First a -> First a -> [First a] #
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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a) # toConstr :: First a -> Constr # dataTypeOf :: First a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (First a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a)) # gmapT :: (forall b. Data b => b -> b) -> First a -> First a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r # gmapQ :: (forall d. Data d => d -> u) -> First a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) #
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) # readList :: ReadS [First a] # readPrec :: ReadPrec (First a) # readListPrec :: ReadPrec [First a] #
Show a => Show (First a) #
Methods showsPrec :: Int -> First a -> ShowS # show :: First a -> String # showList :: [First a] -> ShowS #
Generic (First a) #
Associated Types type Rep (First a) :: * -> * # Methods from :: First a -> Rep (First a) x # to :: Rep (First a) x -> First a #
Semigroup (First a) #	Since: 4.9.0.0
Methods (<>) :: First a -> First a -> First a # sconcat :: NonEmpty (First a) -> First a # stimes :: Integral b => b -> First a -> First a #
Generic1 * First #
Associated Types type Rep1 First (f :: First -> ) :: k -> # Methods from1 :: f a -> Rep1 First f a # to1 :: Rep1 First f a -> f a #
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 #

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 # (>>) :: Last a -> Last b -> Last b # return :: a -> Last a # fail :: String -> Last a #
Functor Last #	Since: 4.9.0.0
Methods fmap :: (a -> b) -> Last a -> Last b # (<$) :: a -> Last b -> Last a #
MonadFix Last #	Since: 4.9.0.0
Methods mfix :: (a -> Last a) -> Last a #
Applicative Last #	Since: 4.9.0.0
Methods pure :: a -> Last a # (<>) :: Last (a -> b) -> Last a -> Last b # liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c # (>) :: Last a -> Last b -> Last b # (<*) :: Last a -> Last b -> Last a #
Foldable Last #	Since: 4.9.0.0
Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # toList :: Last a -> [a] # null :: Last a -> Bool # length :: Last a -> Int # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # minimum :: Ord a => Last a -> a # sum :: Num a => Last a -> a # product :: Num a => Last a -> a #
Traversable Last #	Since: 4.9.0.0
Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) # sequenceA :: Applicative f => Last (f a) -> f (Last a) # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) # sequence :: Monad m => Last (m a) -> m (Last a) #
Bounded a => Bounded (Last a) #
Methods minBound :: Last a # maxBound :: Last a #
Enum a => Enum (Last a) #	Since: 4.9.0.0
Methods succ :: Last a -> Last a # pred :: Last a -> Last a # toEnum :: Int -> Last a # fromEnum :: Last a -> Int # enumFrom :: Last a -> [Last a] # enumFromThen :: Last a -> Last a -> [Last a] # enumFromTo :: Last a -> Last a -> [Last a] # enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] #
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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a) # toConstr :: Last a -> Constr # dataTypeOf :: Last a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Last a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a)) # gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r # gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) #
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) # readList :: ReadS [Last a] # readPrec :: ReadPrec (Last a) # readListPrec :: ReadPrec [Last a] #
Show a => Show (Last a) #
Methods showsPrec :: Int -> Last a -> ShowS # show :: Last a -> String # showList :: [Last a] -> ShowS #
Generic (Last a) #
Associated Types type Rep (Last a) :: * -> * # Methods from :: Last a -> Rep (Last a) x # to :: Rep (Last a) x -> Last a #
Semigroup (Last a) #	Since: 4.9.0.0
Methods (<>) :: Last a -> Last a -> Last a # sconcat :: NonEmpty (Last a) -> Last a # stimes :: Integral b => b -> Last a -> Last a #
Generic1 * Last #
Associated Types type Rep1 Last (f :: Last -> ) :: k -> # Methods from1 :: f a -> Rep1 Last f a # to1 :: Rep1 Last f a -> f a #
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 #

Provide a Semigroup for an arbitrary Monoid.

Constructors

WrapMonoid
Fields unwrapMonoid :: m

Instances

Bounded m => Bounded (WrappedMonoid m) #
Methods minBound :: WrappedMonoid m # maxBound :: WrappedMonoid m #
Enum a => Enum (WrappedMonoid a) #	Since: 4.9.0.0
Methods succ :: WrappedMonoid a -> WrappedMonoid a # pred :: WrappedMonoid a -> WrappedMonoid a # toEnum :: Int -> WrappedMonoid a # fromEnum :: WrappedMonoid a -> Int # enumFrom :: WrappedMonoid a -> [WrappedMonoid a] # enumFromThen :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] # enumFromTo :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] # enumFromThenTo :: WrappedMonoid a -> WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] #
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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (WrappedMonoid m) # toConstr :: WrappedMonoid m -> Constr # dataTypeOf :: WrappedMonoid m -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (WrappedMonoid m)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (WrappedMonoid m)) # gmapT :: (forall b. Data b => b -> b) -> WrappedMonoid m -> WrappedMonoid m # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r # gmapQ :: (forall d. Data d => d -> u) -> WrappedMonoid m -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> WrappedMonoid m -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> WrappedMonoid m -> m (WrappedMonoid m) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> WrappedMonoid m -> m (WrappedMonoid m) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> WrappedMonoid m -> m (WrappedMonoid m) #
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) # readList :: ReadS [WrappedMonoid m] # readPrec :: ReadPrec (WrappedMonoid m) # readListPrec :: ReadPrec [WrappedMonoid m] #
Show m => Show (WrappedMonoid m) #
Methods showsPrec :: Int -> WrappedMonoid m -> ShowS # show :: WrappedMonoid m -> String # showList :: [WrappedMonoid m] -> ShowS #
Generic (WrappedMonoid m) #
Associated Types type Rep (WrappedMonoid m) :: * -> * # Methods from :: WrappedMonoid m -> Rep (WrappedMonoid m) x # to :: Rep (WrappedMonoid m) x -> WrappedMonoid m #
Monoid m => Semigroup (WrappedMonoid m) #	Since: 4.9.0.0
Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m #
Monoid m => Monoid (WrappedMonoid m) #	Since: 4.9.0.0
Methods mempty :: WrappedMonoid m # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # mconcat :: [WrappedMonoid m] -> WrappedMonoid m #
Generic1 * WrappedMonoid #
Associated Types type Rep1 WrappedMonoid (f :: WrappedMonoid -> ) :: k -> # Methods from1 :: f a -> Rep1 WrappedMonoid f a # to1 :: Rep1 WrappedMonoid f a -> f a #
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 #

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 #

Identity of mappend

mappend :: a -> a -> a #

An associative operation

mconcat :: [a] -> a #

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 # mappend :: Ordering -> Ordering -> Ordering # mconcat :: [Ordering] -> Ordering #
Monoid () #	Since: 2.1
Methods mempty :: () # mappend :: () -> () -> () # mconcat :: [()] -> () #
Monoid Any #	Since: 2.1
Methods mempty :: Any # mappend :: Any -> Any -> Any # mconcat :: [Any] -> Any #
Monoid All #	Since: 2.1
Methods mempty :: All # mappend :: All -> All -> All # mconcat :: [All] -> All #
Monoid Lifetime #	`mappend` takes the longer of two lifetimes. Since: 4.8.0.0
Methods mempty :: Lifetime # mappend :: Lifetime -> Lifetime -> Lifetime # mconcat :: [Lifetime] -> Lifetime #
Monoid Event #	Since: 4.3.1.0
Methods mempty :: Event # mappend :: Event -> Event -> Event # mconcat :: [Event] -> Event #
Monoid [a] #	Since: 2.1
Methods mempty :: [a] # mappend :: [a] -> [a] -> [a] # mconcat :: [[a]] -> [a] #
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 = se` 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 # mappend :: Maybe a -> Maybe a -> Maybe a # mconcat :: [Maybe a] -> Maybe a #
Monoid a => Monoid (IO a) #	Since: 4.9.0.0
Methods mempty :: IO a # mappend :: IO a -> IO a -> IO a # mconcat :: [IO a] -> IO a #
Monoid (Last a) #	Since: 2.1
Methods mempty :: Last a # mappend :: Last a -> Last a -> Last a # mconcat :: [Last a] -> Last a #
Monoid (First a) #	Since: 2.1
Methods mempty :: First a # mappend :: First a -> First a -> First a # mconcat :: [First a] -> First a #
Num a => Monoid (Product a) #	Since: 2.1
Methods mempty :: Product a # mappend :: Product a -> Product a -> Product a # mconcat :: [Product a] -> Product a #
Num a => Monoid (Sum a) #	Since: 2.1
Methods mempty :: Sum a # mappend :: Sum a -> Sum a -> Sum a # mconcat :: [Sum a] -> Sum a #
Monoid (Endo a) #	Since: 2.1
Methods mempty :: Endo a # mappend :: Endo a -> Endo a -> Endo a # mconcat :: [Endo a] -> Endo a #
Monoid a => Monoid (Dual a) #	Since: 2.1
Methods mempty :: Dual a # mappend :: Dual a -> Dual a -> Dual a # mconcat :: [Dual a] -> Dual a #
Monoid a => Monoid (Identity a) #
Methods mempty :: Identity a # mappend :: Identity a -> Identity a -> Identity a # mconcat :: [Identity a] -> Identity a #
Semigroup a => Monoid (Option a) #	Since: 4.9.0.0
Methods mempty :: Option a # mappend :: Option a -> Option a -> Option a # mconcat :: [Option a] -> Option a #
Monoid m => Monoid (WrappedMonoid m) #	Since: 4.9.0.0
Methods mempty :: WrappedMonoid m # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # mconcat :: [WrappedMonoid m] -> WrappedMonoid m #
(Ord a, Bounded a) => Monoid (Max a) #	Since: 4.9.0.0
Methods mempty :: Max a # mappend :: Max a -> Max a -> Max a # mconcat :: [Max a] -> Max a #
(Ord a, Bounded a) => Monoid (Min a) #	Since: 4.9.0.0
Methods mempty :: Min a # mappend :: Min a -> Min a -> Min a # mconcat :: [Min a] -> Min a #
Monoid b => Monoid (a -> b) #	Since: 2.1
Methods mempty :: a -> b # mappend :: (a -> b) -> (a -> b) -> a -> b # mconcat :: [a -> b] -> a -> b #
(Monoid a, Monoid b) => Monoid (a, b) #	Since: 2.1
Methods mempty :: (a, b) # mappend :: (a, b) -> (a, b) -> (a, b) # mconcat :: [(a, b)] -> (a, b) #
Monoid (Proxy k s) #	Since: 4.7.0.0
Methods mempty :: Proxy k s # mappend :: Proxy k s -> Proxy k s -> Proxy k s # mconcat :: [Proxy k s] -> Proxy k s #
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) #	Since: 2.1
Methods mempty :: (a, b, c) # mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) # mconcat :: [(a, b, c)] -> (a, b, c) #
Alternative f => Monoid (Alt * f a) #	Since: 4.8.0.0
Methods mempty :: Alt * f a # mappend :: Alt * f a -> Alt * f a -> Alt * f a # mconcat :: [Alt * f a] -> Alt * f a #
Monoid a => Monoid (Const k a b) #
Methods mempty :: Const k a b # mappend :: Const k a b -> Const k a b -> Const k a b # mconcat :: [Const k a b] -> Const k a b #
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) #	Since: 2.1
Methods mempty :: (a, b, c, d) # mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # mconcat :: [(a, b, c, d)] -> (a, b, c, d) #
(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) # mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) #

newtype Dual a #

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 # (>>) :: Dual a -> Dual b -> Dual b # return :: a -> Dual a # fail :: String -> Dual a #
Functor Dual #	Since: 4.8.0.0
Methods fmap :: (a -> b) -> Dual a -> Dual b # (<$) :: a -> Dual b -> Dual a #
MonadFix Dual #	Since: 4.8.0.0
Methods mfix :: (a -> Dual a) -> Dual a #
Applicative Dual #	Since: 4.8.0.0
Methods pure :: a -> Dual a # (<>) :: Dual (a -> b) -> Dual a -> Dual b # liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c # (>) :: Dual a -> Dual b -> Dual b # (<*) :: Dual a -> Dual b -> Dual a #
Foldable Dual #	Since: 4.8.0.0
Methods fold :: Monoid m => Dual m -> m # foldMap :: Monoid m => (a -> m) -> Dual a -> m # foldr :: (a -> b -> b) -> b -> Dual a -> b # foldr' :: (a -> b -> b) -> b -> Dual a -> b # foldl :: (b -> a -> b) -> b -> Dual a -> b # foldl' :: (b -> a -> b) -> b -> Dual a -> b # foldr1 :: (a -> a -> a) -> Dual a -> a # foldl1 :: (a -> a -> a) -> Dual a -> a # toList :: Dual a -> [a] # null :: Dual a -> Bool # length :: Dual a -> Int # elem :: Eq a => a -> Dual a -> Bool # maximum :: Ord a => Dual a -> a # minimum :: Ord a => Dual a -> a # sum :: Num a => Dual a -> a # product :: Num a => Dual a -> a #
Traversable Dual #	Since: 4.8.0.0
Methods traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) # sequenceA :: Applicative f => Dual (f a) -> f (Dual a) # mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) # sequence :: Monad m => Dual (m a) -> m (Dual a) #
MonadZip Dual #	Since: 4.8.0.0
Methods mzip :: Dual a -> Dual b -> Dual (a, b) # mzipWith :: (a -> b -> c) -> Dual a -> Dual b -> Dual c # munzip :: Dual (a, b) -> (Dual a, Dual b) #
Bounded a => Bounded (Dual a) #
Methods minBound :: Dual a # maxBound :: Dual a #
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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dual a) # toConstr :: Dual a -> Constr # dataTypeOf :: Dual a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Dual a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Dual a)) # gmapT :: (forall b. Data b => b -> b) -> Dual a -> Dual a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r # gmapQ :: (forall d. Data d => d -> u) -> Dual a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Dual a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) #
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) # readList :: ReadS [Dual a] # readPrec :: ReadPrec (Dual a) # readListPrec :: ReadPrec [Dual a] #
Show a => Show (Dual a) #
Methods showsPrec :: Int -> Dual a -> ShowS # show :: Dual a -> String # showList :: [Dual a] -> ShowS #
Generic (Dual a) #
Associated Types type Rep (Dual a) :: * -> * # Methods from :: Dual a -> Rep (Dual a) x # to :: Rep (Dual a) x -> Dual a #
Semigroup a => Semigroup (Dual a) #	Since: 4.9.0.0
Methods (<>) :: Dual a -> Dual a -> Dual a # sconcat :: NonEmpty (Dual a) -> Dual a # stimes :: Integral b => b -> Dual a -> Dual a #
Monoid a => Monoid (Dual a) #	Since: 2.1
Methods mempty :: Dual a # mappend :: Dual a -> Dual a -> Dual a # mconcat :: [Dual a] -> Dual a #
Generic1 * Dual #
Associated Types type Rep1 Dual (f :: Dual -> ) :: k -> # Methods from1 :: f a -> Rep1 Dual f a # to1 :: Rep1 Dual f a -> f a #
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 #

The monoid of endomorphisms under composition.

Constructors

Endo
Fields appEndo :: a -> a

Instances

Generic (Endo a) #
Associated Types type Rep (Endo a) :: * -> * # Methods from :: Endo a -> Rep (Endo a) x # to :: Rep (Endo a) x -> Endo a #
Semigroup (Endo a) #	Since: 4.9.0.0
Methods (<>) :: Endo a -> Endo a -> Endo a # sconcat :: NonEmpty (Endo a) -> Endo a # stimes :: Integral b => b -> Endo a -> Endo a #
Monoid (Endo a) #	Since: 2.1
Methods mempty :: Endo a # mappend :: Endo a -> Endo a -> Endo a # mconcat :: [Endo a] -> Endo a #
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 #

Boolean monoid under conjunction (&&).

Constructors

All
Fields getAll :: Bool

Instances

Bounded All #
Methods minBound :: All # maxBound :: All #
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 # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c All # toConstr :: All -> Constr # dataTypeOf :: All -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c All) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c All) # gmapT :: (forall b. Data b => b -> b) -> All -> All # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> All -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> All -> r # gmapQ :: (forall d. Data d => d -> u) -> All -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> All -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> All -> m All # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All #
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 # readList :: ReadS [All] # readPrec :: ReadPrec All # readListPrec :: ReadPrec [All] #
Show All #
Methods showsPrec :: Int -> All -> ShowS # show :: All -> String # showList :: [All] -> ShowS #
Generic All #
Associated Types type Rep All :: * -> * # Methods from :: All -> Rep All x # to :: Rep All x -> All #
Semigroup All #	Since: 4.9.0.0
Methods (<>) :: All -> All -> All # sconcat :: NonEmpty All -> All # stimes :: Integral b => b -> All -> All #
Monoid All #	Since: 2.1
Methods mempty :: All # mappend :: All -> All -> All # mconcat :: [All] -> All #
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 #

Boolean monoid under disjunction (||).

Constructors

Any
Fields getAny :: Bool

Instances

Bounded Any #
Methods minBound :: Any # maxBound :: Any #
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 # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Any # toConstr :: Any -> Constr # dataTypeOf :: Any -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c Any) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Any) # gmapT :: (forall b. Data b => b -> b) -> Any -> Any # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r # gmapQ :: (forall d. Data d => d -> u) -> Any -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Any -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Any -> m Any # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any #
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 # readList :: ReadS [Any] # readPrec :: ReadPrec Any # readListPrec :: ReadPrec [Any] #
Show Any #
Methods showsPrec :: Int -> Any -> ShowS # show :: Any -> String # showList :: [Any] -> ShowS #
Generic Any #
Associated Types type Rep Any :: * -> * # Methods from :: Any -> Rep Any x # to :: Rep Any x -> Any #
Semigroup Any #	Since: 4.9.0.0
Methods (<>) :: Any -> Any -> Any # sconcat :: NonEmpty Any -> Any # stimes :: Integral b => b -> Any -> Any #
Monoid Any #	Since: 2.1
Methods mempty :: Any # mappend :: Any -> Any -> Any # mconcat :: [Any] -> Any #
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 #

Monoid under addition.

Constructors

Sum
Fields getSum :: a

Instances

Monad Sum #	Since: 4.8.0.0
Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b # (>>) :: Sum a -> Sum b -> Sum b # return :: a -> Sum a # fail :: String -> Sum a #
Functor Sum #	Since: 4.8.0.0
Methods fmap :: (a -> b) -> Sum a -> Sum b # (<$) :: a -> Sum b -> Sum a #
MonadFix Sum #	Since: 4.8.0.0
Methods mfix :: (a -> Sum a) -> Sum a #
Applicative Sum #	Since: 4.8.0.0
Methods pure :: a -> Sum a # (<>) :: Sum (a -> b) -> Sum a -> Sum b # liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c # (>) :: Sum a -> Sum b -> Sum b # (<*) :: Sum a -> Sum b -> Sum a #
Foldable Sum #	Since: 4.8.0.0
Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # toList :: Sum a -> [a] # null :: Sum a -> Bool # length :: Sum a -> Int # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # minimum :: Ord a => Sum a -> a # sum :: Num a => Sum a -> a # product :: Num a => Sum a -> a #
Traversable Sum #	Since: 4.8.0.0
Methods traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) # sequenceA :: Applicative f => Sum (f a) -> f (Sum a) # mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) # sequence :: Monad m => Sum (m a) -> m (Sum a) #
MonadZip Sum #	Since: 4.8.0.0
Methods mzip :: Sum a -> Sum b -> Sum (a, b) # mzipWith :: (a -> b -> c) -> Sum a -> Sum b -> Sum c # munzip :: Sum (a, b) -> (Sum a, Sum b) #
Bounded a => Bounded (Sum a) #
Methods minBound :: Sum a # maxBound :: Sum a #
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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum a) # toConstr :: Sum a -> Constr # dataTypeOf :: Sum a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Sum a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum a)) # gmapT :: (forall b. Data b => b -> b) -> Sum a -> Sum a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r # gmapQ :: (forall d. Data d => d -> u) -> Sum a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) #
Num a => Num (Sum a) #
Methods (+) :: Sum a -> Sum a -> Sum a # (-) :: Sum a -> Sum a -> Sum a # (*) :: Sum a -> Sum a -> Sum a # negate :: Sum a -> Sum a # abs :: Sum a -> Sum a # signum :: Sum a -> Sum a # fromInteger :: Integer -> Sum a #
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) # readList :: ReadS [Sum a] # readPrec :: ReadPrec (Sum a) # readListPrec :: ReadPrec [Sum a] #
Show a => Show (Sum a) #
Methods showsPrec :: Int -> Sum a -> ShowS # show :: Sum a -> String # showList :: [Sum a] -> ShowS #
Generic (Sum a) #
Associated Types type Rep (Sum a) :: * -> * # Methods from :: Sum a -> Rep (Sum a) x # to :: Rep (Sum a) x -> Sum a #
Num a => Semigroup (Sum a) #	Since: 4.9.0.0
Methods (<>) :: Sum a -> Sum a -> Sum a # sconcat :: NonEmpty (Sum a) -> Sum a # stimes :: Integral b => b -> Sum a -> Sum a #
Num a => Monoid (Sum a) #	Since: 2.1
Methods mempty :: Sum a # mappend :: Sum a -> Sum a -> Sum a # mconcat :: [Sum a] -> Sum a #
Generic1 * Sum #
Associated Types type Rep1 Sum (f :: Sum -> ) :: k -> # Methods from1 :: f a -> Rep1 Sum f a # to1 :: Rep1 Sum f a -> f a #
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 #

Monoid under multiplication.

Constructors

Product
Fields getProduct :: a

Instances

Monad Product #	Since: 4.8.0.0
Methods (>>=) :: Product a -> (a -> Product b) -> Product b # (>>) :: Product a -> Product b -> Product b # return :: a -> Product a # fail :: String -> Product a #
Functor Product #	Since: 4.8.0.0
Methods fmap :: (a -> b) -> Product a -> Product b # (<$) :: a -> Product b -> Product a #
MonadFix Product #	Since: 4.8.0.0
Methods mfix :: (a -> Product a) -> Product a #
Applicative Product #	Since: 4.8.0.0
Methods pure :: a -> Product a # (<>) :: Product (a -> b) -> Product a -> Product b # liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c # (>) :: Product a -> Product b -> Product b # (<*) :: Product a -> Product b -> Product a #
Foldable Product #	Since: 4.8.0.0
Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # toList :: Product a -> [a] # null :: Product a -> Bool # length :: Product a -> Int # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # sum :: Num a => Product a -> a # product :: Num a => Product a -> a #
Traversable Product #	Since: 4.8.0.0
Methods traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) # sequenceA :: Applicative f => Product (f a) -> f (Product a) # mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) # sequence :: Monad m => Product (m a) -> m (Product a) #
MonadZip Product #	Since: 4.8.0.0
Methods mzip :: Product a -> Product b -> Product (a, b) # mzipWith :: (a -> b -> c) -> Product a -> Product b -> Product c # munzip :: Product (a, b) -> (Product a, Product b) #
Bounded a => Bounded (Product a) #
Methods minBound :: Product a # maxBound :: Product a #
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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product a) # toConstr :: Product a -> Constr # dataTypeOf :: Product a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Product a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product a)) # gmapT :: (forall b. Data b => b -> b) -> Product a -> Product a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r # gmapQ :: (forall d. Data d => d -> u) -> Product a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Product a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) #
Num a => Num (Product a) #
Methods (+) :: Product a -> Product a -> Product a # (-) :: Product a -> Product a -> Product a # (*) :: Product a -> Product a -> Product a # negate :: Product a -> Product a # abs :: Product a -> Product a # signum :: Product a -> Product a # fromInteger :: Integer -> Product a #
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) # readList :: ReadS [Product a] # readPrec :: ReadPrec (Product a) # readListPrec :: ReadPrec [Product a] #
Show a => Show (Product a) #
Methods showsPrec :: Int -> Product a -> ShowS # show :: Product a -> String # showList :: [Product a] -> ShowS #
Generic (Product a) #
Associated Types type Rep (Product a) :: * -> * # Methods from :: Product a -> Rep (Product a) x # to :: Rep (Product a) x -> Product a #
Num a => Semigroup (Product a) #	Since: 4.9.0.0
Methods (<>) :: Product a -> Product a -> Product a # sconcat :: NonEmpty (Product a) -> Product a # stimes :: Integral b => b -> Product a -> Product a #
Num a => Monoid (Product a) #	Since: 2.1
Methods mempty :: Product a # mappend :: Product a -> Product a -> Product a # mconcat :: [Product a] -> Product a #
Generic1 * Product #
Associated Types type Rep1 Product (f :: Product -> ) :: k -> # Methods from1 :: f a -> Rep1 Product f a # to1 :: Rep1 Product f a -> f a #
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 #

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

Fold an Option case-wise, just like maybe.

Difference lists of a semigroup

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

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

cycle1 :: Semigroup m => m -> m #

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

ArgMin, ArgMax

data Arg a b #

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 # first :: (a -> b) -> Arg a c -> Arg b c # second :: (b -> c) -> Arg a b -> Arg a c #
Bifoldable Arg #	Since: 4.10.0.0
Methods bifold :: Monoid m => Arg m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Arg a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Arg a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Arg a b -> c #
Bitraversable Arg #	Since: 4.10.0.0
Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d) #
Functor (Arg a) #	Since: 4.9.0.0
Methods fmap :: (a -> b) -> Arg a a -> Arg a b # (<$) :: a -> Arg a b -> Arg a a #
Foldable (Arg a) #	Since: 4.9.0.0
Methods fold :: Monoid m => Arg a m -> m # foldMap :: Monoid m => (a -> m) -> Arg a a -> m # foldr :: (a -> b -> b) -> b -> Arg a a -> b # foldr' :: (a -> b -> b) -> b -> Arg a a -> b # foldl :: (b -> a -> b) -> b -> Arg a a -> b # foldl' :: (b -> a -> b) -> b -> Arg a a -> b # foldr1 :: (a -> a -> a) -> Arg a a -> a # foldl1 :: (a -> a -> a) -> Arg a a -> a # toList :: Arg a a -> [a] # null :: Arg a a -> Bool # length :: Arg a a -> Int # elem :: Eq a => a -> Arg a a -> Bool # maximum :: Ord a => Arg a a -> a # minimum :: Ord a => Arg a a -> a # sum :: Num a => Arg a a -> a # product :: Num a => Arg a a -> a #
Traversable (Arg a) #	Since: 4.9.0.0
Methods traverse :: Applicative f => (a -> f b) -> Arg a a -> f (Arg a b) # sequenceA :: Applicative f => Arg a (f a) -> f (Arg a a) # mapM :: Monad m => (a -> m b) -> Arg a a -> m (Arg a b) # sequence :: Monad m => Arg a (m a) -> m (Arg a a) #
Generic1 * (Arg a) #
Associated Types type Rep1 (Arg a) (f :: Arg a -> ) :: k -> # Methods from1 :: f a -> Rep1 (Arg a) f a # to1 :: Rep1 (Arg a) f a -> f a #
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) # gunfold :: (forall c r. Data c => c (c -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Arg a b) # toConstr :: Arg a b -> Constr # dataTypeOf :: Arg a b -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Arg a b)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Arg a b)) # gmapT :: (forall c. Data c => c -> c) -> Arg a b -> Arg a b # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r # gmapQ :: (forall d. Data d => d -> u) -> Arg a b -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Arg a b -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) #
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) # readList :: ReadS [Arg a b] # readPrec :: ReadPrec (Arg a b) # readListPrec :: ReadPrec [Arg a b] #
(Show b, Show a) => Show (Arg a b) #
Methods showsPrec :: Int -> Arg a b -> ShowS # show :: Arg a b -> String # showList :: [Arg a b] -> ShowS #
Generic (Arg a b) #
Associated Types type Rep (Arg a b) :: * -> * # Methods from :: Arg a b -> Rep (Arg a b) x # to :: Rep (Arg a b) x -> Arg a b #
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) #

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