base-4.9.1.0: Basic libraries

Copyright(C) 2011-2015 Edward Kmett
LicenseBSD-style (see the file LICENSE)
Maintainerlibraries@haskell.org
Stabilityprovisional
Portabilityportable
Safe HaskellTrustworthy
LanguageHaskell2010

Data.Semigroup

Contents

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 # 
Semigroup () # 

Methods

(<>) :: () -> () -> () #

sconcat :: NonEmpty () -> () #

stimes :: Integral b => b -> () -> () #

Semigroup Any # 

Methods

(<>) :: Any -> Any -> Any #

sconcat :: NonEmpty Any -> Any #

stimes :: Integral b => b -> Any -> Any #

Semigroup All # 

Methods

(<>) :: All -> All -> All #

sconcat :: NonEmpty All -> All #

stimes :: Integral b => b -> All -> All #

Semigroup Void # 

Methods

(<>) :: Void -> Void -> Void #

sconcat :: NonEmpty Void -> Void #

stimes :: Integral b => b -> Void -> Void #

Semigroup [a] # 

Methods

(<>) :: [a] -> [a] -> [a] #

sconcat :: NonEmpty [a] -> [a] #

stimes :: Integral b => b -> [a] -> [a] #

Semigroup a => Semigroup (Maybe a) # 

Methods

(<>) :: Maybe a -> Maybe a -> Maybe a #

sconcat :: NonEmpty (Maybe a) -> Maybe a #

stimes :: Integral b => b -> Maybe a -> Maybe a #

Semigroup (Last a) # 

Methods

(<>) :: Last a -> Last a -> Last a #

sconcat :: NonEmpty (Last a) -> Last a #

stimes :: Integral b => b -> Last a -> Last a #

Semigroup (First a) # 

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) # 

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) # 

Methods

(<>) :: Sum a -> Sum a -> Sum a #

sconcat :: NonEmpty (Sum a) -> Sum a #

stimes :: Integral b => b -> Sum a -> Sum a #

Semigroup (Endo a) # 

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) # 

Methods

(<>) :: Dual a -> Dual a -> Dual a #

sconcat :: NonEmpty (Dual a) -> Dual a #

stimes :: Integral b => b -> Dual a -> Dual a #

Semigroup (NonEmpty a) # 

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) # 

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) # 
Semigroup (Last a) # 

Methods

(<>) :: Last a -> Last a -> Last a #

sconcat :: NonEmpty (Last a) -> Last a #

stimes :: Integral b => b -> Last a -> Last a #

Semigroup (First a) # 

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) # 

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) # 

Methods

(<>) :: Min a -> Min a -> Min a #

sconcat :: NonEmpty (Min a) -> Min a #

stimes :: Integral b => b -> Min a -> Min a #

Semigroup a => Semigroup (Identity a) # 

Methods

(<>) :: Identity a -> Identity a -> Identity a #

sconcat :: NonEmpty (Identity a) -> Identity a #

stimes :: Integral b => b -> Identity a -> Identity a #

Semigroup b => Semigroup (a -> b) # 

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) # 

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) # 

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) # 

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) # 

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) # 

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) # 

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) # 

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) # 

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

Instances

Monad Min # 

Methods

(>>=) :: Min a -> (a -> Min b) -> Min b #

(>>) :: Min a -> Min b -> Min b #

return :: a -> Min a #

fail :: String -> Min a #

Functor Min # 

Methods

fmap :: (a -> b) -> Min a -> Min b #

(<$) :: a -> Min b -> Min a #

MonadFix Min # 

Methods

mfix :: (a -> Min a) -> Min a #

Applicative Min # 

Methods

pure :: a -> Min a #

(<*>) :: Min (a -> b) -> Min a -> Min b #

(*>) :: Min a -> Min b -> Min b #

(<*) :: Min a -> Min b -> Min a #

Foldable Min # 

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 # 

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) #

Generic1 Min # 

Associated Types

type Rep1 (Min :: * -> *) :: * -> * #

Methods

from1 :: Min a -> Rep1 Min a #

to1 :: Rep1 Min a -> Min a #

Bounded a => Bounded (Min a) # 

Methods

minBound :: Min a #

maxBound :: Min a #

Enum a => Enum (Min a) # 

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) # 

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) # 
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) # 

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) # 

Methods

mempty :: Min a #

mappend :: Min a -> Min a -> Min a #

mconcat :: [Min a] -> Min 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))
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)))

newtype Max a #

Constructors

Max 

Fields

Instances

Monad Max # 

Methods

(>>=) :: Max a -> (a -> Max b) -> Max b #

(>>) :: Max a -> Max b -> Max b #

return :: a -> Max a #

fail :: String -> Max a #

Functor Max # 

Methods

fmap :: (a -> b) -> Max a -> Max b #

(<$) :: a -> Max b -> Max a #

MonadFix Max # 

Methods

mfix :: (a -> Max a) -> Max a #

Applicative Max # 

Methods

pure :: a -> Max a #

(<*>) :: Max (a -> b) -> Max a -> Max b #

(*>) :: Max a -> Max b -> Max b #

(<*) :: Max a -> Max b -> Max a #

Foldable Max # 

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 # 

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) #

Generic1 Max # 

Associated Types

type Rep1 (Max :: * -> *) :: * -> * #

Methods

from1 :: Max a -> Rep1 Max a #

to1 :: Rep1 Max a -> Max a #

Bounded a => Bounded (Max a) # 

Methods

minBound :: Max a #

maxBound :: Max a #

Enum a => Enum (Max a) # 

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) # 

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) # 
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) # 

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) # 

Methods

mempty :: Max a #

mappend :: Max a -> Max a -> Max a #

mconcat :: [Max a] -> Max 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))
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)))

newtype First a #

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

Constructors

First 

Fields

Instances

Monad First # 

Methods

(>>=) :: First a -> (a -> First b) -> First b #

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

return :: a -> First a #

fail :: String -> First a #

Functor First # 

Methods

fmap :: (a -> b) -> First a -> First b #

(<$) :: a -> First b -> First a #

MonadFix First # 

Methods

mfix :: (a -> First a) -> First a #

Applicative First # 

Methods

pure :: a -> First a #

(<*>) :: First (a -> b) -> First a -> First b #

(*>) :: First a -> First b -> First b #

(<*) :: First a -> First b -> First a #

Foldable First # 

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 # 

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) #

Generic1 First # 

Associated Types

type Rep1 (First :: * -> *) :: * -> * #

Methods

from1 :: First a -> Rep1 First a #

to1 :: Rep1 First a -> First a #

Bounded a => Bounded (First a) # 

Methods

minBound :: First a #

maxBound :: First a #

Enum a => Enum (First a) # 

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) # 
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) # 

Methods

(<>) :: First a -> First a -> First a #

sconcat :: NonEmpty (First a) -> First a #

stimes :: Integral b => b -> First a -> First 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))
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)))

newtype Last a #

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

Constructors

Last 

Fields

Instances

Monad Last # 

Methods

(>>=) :: Last a -> (a -> Last b) -> Last b #

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

return :: a -> Last a #

fail :: String -> Last a #

Functor Last # 

Methods

fmap :: (a -> b) -> Last a -> Last b #

(<$) :: a -> Last b -> Last a #

MonadFix Last # 

Methods

mfix :: (a -> Last a) -> Last a #

Applicative Last # 

Methods

pure :: a -> Last a #

(<*>) :: Last (a -> b) -> Last a -> Last b #

(*>) :: Last a -> Last b -> Last b #

(<*) :: Last a -> Last b -> Last a #

Foldable Last # 

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 # 

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) #

Generic1 Last # 

Associated Types

type Rep1 (Last :: * -> *) :: * -> * #

Methods

from1 :: Last a -> Rep1 Last a #

to1 :: Rep1 Last a -> Last a #

Bounded a => Bounded (Last a) # 

Methods

minBound :: Last a #

maxBound :: Last a #

Enum a => Enum (Last a) # 

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) # 
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) # 

Methods

(<>) :: Last a -> Last a -> Last a #

sconcat :: NonEmpty (Last a) -> Last a #

stimes :: Integral b => b -> Last a -> Last 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))
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)))

newtype WrappedMonoid m #

Provide a Semigroup for an arbitrary Monoid.

Constructors

WrapMonoid 

Fields

Instances

Generic1 WrappedMonoid # 

Associated Types

type Rep1 (WrappedMonoid :: * -> *) :: * -> * #

Bounded a => Bounded (WrappedMonoid a) # 
Enum a => Enum (WrappedMonoid a) # 
Eq m => Eq (WrappedMonoid m) # 
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) # 
Read m => Read (WrappedMonoid m) # 
Show m => Show (WrappedMonoid m) # 
Generic (WrappedMonoid m) # 

Associated Types

type Rep (WrappedMonoid m) :: * -> * #

Monoid m => Semigroup (WrappedMonoid m) # 
Monoid m => Monoid (WrappedMonoid 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))
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)))

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 # 
Monoid () # 

Methods

mempty :: () #

mappend :: () -> () -> () #

mconcat :: [()] -> () #

Monoid Any # 

Methods

mempty :: Any #

mappend :: Any -> Any -> Any #

mconcat :: [Any] -> Any #

Monoid All # 

Methods

mempty :: All #

mappend :: All -> All -> All #

mconcat :: [All] -> All #

Monoid [a] # 

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 e*e = e and e*s = s = s*e for all s ∈ S." Since there is no "Semigroup" typeclass providing just mappend, we use Monoid instead.

Methods

mempty :: Maybe a #

mappend :: Maybe a -> Maybe a -> Maybe a #

mconcat :: [Maybe a] -> Maybe a #

Monoid a => Monoid (IO a) # 

Methods

mempty :: IO a #

mappend :: IO a -> IO a -> IO a #

mconcat :: [IO a] -> IO a #

Monoid (Last a) # 

Methods

mempty :: Last a #

mappend :: Last a -> Last a -> Last a #

mconcat :: [Last a] -> Last a #

Monoid (First a) # 

Methods

mempty :: First a #

mappend :: First a -> First a -> First a #

mconcat :: [First a] -> First a #

Num a => Monoid (Product a) # 

Methods

mempty :: Product a #

mappend :: Product a -> Product a -> Product a #

mconcat :: [Product a] -> Product a #

Num a => Monoid (Sum a) # 

Methods

mempty :: Sum a #

mappend :: Sum a -> Sum a -> Sum a #

mconcat :: [Sum a] -> Sum a #

Monoid (Endo a) # 

Methods

mempty :: Endo a #

mappend :: Endo a -> Endo a -> Endo a #

mconcat :: [Endo a] -> Endo a #

Monoid a => Monoid (Dual a) # 

Methods

mempty :: Dual a #

mappend :: Dual a -> Dual a -> Dual a #

mconcat :: [Dual a] -> Dual a #

Semigroup a => Monoid (Option a) # 

Methods

mempty :: Option a #

mappend :: Option a -> Option a -> Option a #

mconcat :: [Option a] -> Option a #

Monoid m => Monoid (WrappedMonoid m) # 
(Ord a, Bounded a) => Monoid (Max a) # 

Methods

mempty :: Max a #

mappend :: Max a -> Max a -> Max a #

mconcat :: [Max a] -> Max a #

(Ord a, Bounded a) => Monoid (Min a) # 

Methods

mempty :: Min a #

mappend :: Min a -> Min a -> Min a #

mconcat :: [Min a] -> Min a #

Monoid a => Monoid (Identity a) # 

Methods

mempty :: Identity a #

mappend :: Identity a -> Identity a -> Identity a #

mconcat :: [Identity a] -> Identity a #

Monoid b => Monoid (a -> b) # 

Methods

mempty :: a -> b #

mappend :: (a -> b) -> (a -> b) -> a -> b #

mconcat :: [a -> b] -> a -> b #

(Monoid a, Monoid b) => Monoid (a, b) # 

Methods

mempty :: (a, b) #

mappend :: (a, b) -> (a, b) -> (a, b) #

mconcat :: [(a, b)] -> (a, b) #

Monoid (Proxy k s) # 

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) # 

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) # 

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) # 

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) # 

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

Instances

Monad Dual # 

Methods

(>>=) :: Dual a -> (a -> Dual b) -> Dual b #

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

return :: a -> Dual a #

fail :: String -> Dual a #

Functor Dual # 

Methods

fmap :: (a -> b) -> Dual a -> Dual b #

(<$) :: a -> Dual b -> Dual a #

MonadFix Dual # 

Methods

mfix :: (a -> Dual a) -> Dual a #

Applicative Dual # 

Methods

pure :: a -> Dual a #

(<*>) :: Dual (a -> b) -> Dual a -> Dual b #

(*>) :: Dual a -> Dual b -> Dual b #

(<*) :: Dual a -> Dual b -> Dual a #

Foldable Dual # 

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 # 

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) #

Generic1 Dual # 

Associated Types

type Rep1 (Dual :: * -> *) :: * -> * #

Methods

from1 :: Dual a -> Rep1 Dual a #

to1 :: Rep1 Dual a -> Dual a #

MonadZip Dual # 

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) # 

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) # 
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) # 

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) # 

Methods

mempty :: Dual a #

mappend :: Dual a -> Dual a -> Dual a #

mconcat :: [Dual a] -> Dual 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))
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)))

newtype Endo a #

The monoid of endomorphisms under composition.

Constructors

Endo 

Fields

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) # 

Methods

(<>) :: Endo a -> Endo a -> Endo a #

sconcat :: NonEmpty (Endo a) -> Endo a #

stimes :: Integral b => b -> Endo a -> Endo a #

Monoid (Endo a) # 

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

Instances

Bounded All # 

Methods

minBound :: All #

maxBound :: All #

Eq All # 

Methods

(==) :: All -> All -> Bool Source #

(/=) :: All -> All -> Bool Source #

Data All # 

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 # 
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 # 

Methods

(<>) :: All -> All -> All #

sconcat :: NonEmpty All -> All #

stimes :: Integral b => b -> All -> All #

Monoid All # 

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

Instances

Bounded Any # 

Methods

minBound :: Any #

maxBound :: Any #

Eq Any # 

Methods

(==) :: Any -> Any -> Bool Source #

(/=) :: Any -> Any -> Bool Source #

Data Any # 

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 # 
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 # 

Methods

(<>) :: Any -> Any -> Any #

sconcat :: NonEmpty Any -> Any #

stimes :: Integral b => b -> Any -> Any #

Monoid Any # 

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

Instances

Monad Sum # 

Methods

(>>=) :: Sum a -> (a -> Sum b) -> Sum b #

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

return :: a -> Sum a #

fail :: String -> Sum a #

Functor Sum # 

Methods

fmap :: (a -> b) -> Sum a -> Sum b #

(<$) :: a -> Sum b -> Sum a #

MonadFix Sum # 

Methods

mfix :: (a -> Sum a) -> Sum a #

Applicative Sum # 

Methods

pure :: a -> Sum a #

(<*>) :: Sum (a -> b) -> Sum a -> Sum b #

(*>) :: Sum a -> Sum b -> Sum b #

(<*) :: Sum a -> Sum b -> Sum a #

Foldable Sum # 

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 # 

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) #

Generic1 Sum # 

Associated Types

type Rep1 (Sum :: * -> *) :: * -> * #

Methods

from1 :: Sum a -> Rep1 Sum a #

to1 :: Rep1 Sum a -> Sum a #

MonadZip Sum # 

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) # 

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) # 
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) # 

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) # 

Methods

mempty :: Sum a #

mappend :: Sum a -> Sum a -> Sum a #

mconcat :: [Sum a] -> Sum 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))
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)))

newtype Product a #

Monoid under multiplication.

Constructors

Product 

Fields

Instances

Monad Product # 

Methods

(>>=) :: Product a -> (a -> Product b) -> Product b #

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

return :: a -> Product a #

fail :: String -> Product a #

Functor Product # 

Methods

fmap :: (a -> b) -> Product a -> Product b #

(<$) :: a -> Product b -> Product a #

MonadFix Product # 

Methods

mfix :: (a -> Product a) -> Product a #

Applicative Product # 

Methods

pure :: a -> Product a #

(<*>) :: Product (a -> b) -> Product a -> Product b #

(*>) :: Product a -> Product b -> Product b #

(<*) :: Product a -> Product b -> Product a #

Foldable Product # 

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 # 

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) #

Generic1 Product # 

Associated Types

type Rep1 (Product :: * -> *) :: * -> * #

Methods

from1 :: Product a -> Rep1 Product a #

to1 :: Rep1 Product a -> Product a #

MonadZip Product # 

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) # 
Eq a => Eq (Product a) # 

Methods

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

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

Data a => Data (Product a) # 

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) # 
Read a => Read (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) # 

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) # 

Methods

mempty :: Product a #

mappend :: Product a -> Product a -> Product a #

mconcat :: [Product a] -> Product 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))
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)))

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

Instances

Monad Option # 

Methods

(>>=) :: Option a -> (a -> Option b) -> Option b #

(>>) :: Option a -> Option b -> Option b #

return :: a -> Option a #

fail :: String -> Option a #

Functor Option # 

Methods

fmap :: (a -> b) -> Option a -> Option b #

(<$) :: a -> Option b -> Option a #

MonadFix Option # 

Methods

mfix :: (a -> Option a) -> Option a #

Applicative Option # 

Methods

pure :: a -> Option a #

(<*>) :: Option (a -> b) -> Option a -> Option b #

(*>) :: Option a -> Option b -> Option b #

(<*) :: Option a -> Option b -> Option a #

Foldable Option # 

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 # 

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) #

Generic1 Option # 

Associated Types

type Rep1 (Option :: * -> *) :: * -> * #

Methods

from1 :: Option a -> Rep1 Option a #

to1 :: Rep1 Option a -> Option a #

MonadPlus Option # 

Methods

mzero :: Option a #

mplus :: Option a -> Option a -> Option a #

Alternative Option # 

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) # 
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) # 

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) # 

Methods

mempty :: Option a #

mappend :: Option a -> Option a -> Option a #

mconcat :: [Option a] -> Option 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)))
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))))

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 # 

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 #

Functor (Arg a) # 

Methods

fmap :: (a -> b) -> Arg a a -> Arg a b #

(<$) :: a -> Arg a b -> Arg a a #

Foldable (Arg a) # 

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) # 

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 :: * -> *) :: * -> * #

Methods

from1 :: Arg a a -> Rep1 (Arg a) a #

to1 :: Rep1 (Arg a) a -> Arg a a #

Eq a => Eq (Arg a b) # 

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) # 

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 Rep (Arg a b) # 

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

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