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

class Semigroup a where
stimesMonoid :: (Integral b, Monoid a) => b -> a -> a
stimesIdempotent :: Integral b => b -> a -> a
stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a
mtimesDefault :: (Integral b, Monoid a) => b -> a -> a
newtype Min a = Min {
- getMin :: a
}
newtype Max a = Max {
- getMax :: a
}
newtype First a = First {
- getFirst :: a
}
newtype Last a = Last {
- getLast :: a
}
newtype WrappedMonoid m = WrapMonoid {
- unwrapMonoid :: m
}
class Monoid a where
newtype Dual a = Dual {
- getDual :: a
}
newtype Endo a = Endo {
- appEndo :: a -> a
}
newtype All = All {
- getAll :: Bool
}
newtype Any = Any {
- getAny :: Bool
}
newtype Sum a = Sum {
- getSum :: a
}
newtype Product a = Product {
- getProduct :: a
}
newtype Option a = Option {
- getOption :: Maybe a
}
option :: b -> (a -> b) -> Option a -> b
diff :: Semigroup m => m -> Endo m
cycle1 :: Semigroup m => m -> m
data Arg a b = Arg a b
type ArgMin a b = Min (Arg a b)
type ArgMax a b = Max (Arg a b)

Documentation

class Semigroup a where Source #

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

Since: 4.9.0.0

Methods

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

An associative operation.

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

If a is also a Monoid we further require

(<> ) = mappend

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

An associative operation.

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

If a is also a Monoid we further require

(<> ) = mappend

sconcat :: NonEmpty a -> a Source #

Reduce a non-empty list with <>

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

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

Repeat a value n times.

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

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

Instances

Semigroup Ordering Source #

Since: 4.9.0.0

Methods

(<>) :: Ordering -> Ordering -> Ordering Source #

sconcat :: NonEmpty Ordering -> Ordering Source #

stimes :: Integral b => b -> Ordering -> Ordering Source #

Semigroup () Source #

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty () -> () Source #

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

Semigroup Any Source #

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty Any -> Any Source #

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

Semigroup All Source #

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty All -> All Source #

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

Semigroup Lifetime Source #

Since: 4.10.0.0

Methods

(<>) :: Lifetime -> Lifetime -> Lifetime Source #

sconcat :: NonEmpty Lifetime -> Lifetime Source #

stimes :: Integral b => b -> Lifetime -> Lifetime Source #

Semigroup Event Source #

Since: 4.10.0.0

Methods

(<>) :: Event -> Event -> Event Source #

sconcat :: NonEmpty Event -> Event Source #

stimes :: Integral b => b -> Event -> Event Source #

Semigroup Void Source #

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty Void -> Void Source #

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

Semigroup [a] Source #

Since: 4.9.0.0

Methods

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

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

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

Semigroup a => Semigroup (Maybe a) Source #

Since: 4.9.0.0

Methods

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

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

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

Semigroup a => Semigroup (IO a) Source #

Since: 4.10.0.0

Methods

(<>) :: IO a -> IO a -> IO a Source #

sconcat :: NonEmpty (IO a) -> IO a Source #

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

Semigroup (Last a) Source #

Since: 4.9.0.0

Methods

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

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

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

Semigroup (First a) Source #

Since: 4.9.0.0

Methods

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

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

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

Num a => Semigroup (Product a) Source #

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty (Product a) -> Product a Source #

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

Num a => Semigroup (Sum a) Source #

Since: 4.9.0.0

Methods

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

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

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

Semigroup (Endo a) Source #

Since: 4.9.0.0

Methods

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

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

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

Semigroup a => Semigroup (Dual a) Source #

Since: 4.9.0.0

Methods

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

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

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

Semigroup a => Semigroup (Identity a) Source #

Since: 4.9.0.0

Methods

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

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

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

Semigroup (NonEmpty a) Source #

Since: 4.9.0.0

Methods

(<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a Source #

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

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

Semigroup a => Semigroup (Option a) Source #

Since: 4.9.0.0

Methods

(<>) :: Option a -> Option a -> Option a Source #

sconcat :: NonEmpty (Option a) -> Option a Source #

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

Monoid m => Semigroup (WrappedMonoid m) Source #

Since: 4.9.0.0

Methods

(<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source #

sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m Source #

stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m Source #

Semigroup (Last a) Source #

Since: 4.9.0.0

Methods

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

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

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

Semigroup (First a) Source #

Since: 4.9.0.0

Methods

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

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

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

Ord a => Semigroup (Max a) Source #

Since: 4.9.0.0

Methods

(<>) :: Max a -> Max a -> Max a Source #

sconcat :: NonEmpty (Max a) -> Max a Source #

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

Ord a => Semigroup (Min a) Source #

Since: 4.9.0.0

Methods

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

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

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

Semigroup b => Semigroup (a -> b) Source #

Since: 4.9.0.0

Methods

(<>) :: (a -> b) -> (a -> b) -> a -> b Source #

sconcat :: NonEmpty (a -> b) -> a -> b Source #

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

Semigroup (Either a b) Source #

Since: 4.9.0.0

Methods

(<>) :: Either a b -> Either a b -> Either a b Source #

sconcat :: NonEmpty (Either a b) -> Either a b Source #

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

(Semigroup a, Semigroup b) => Semigroup (a, b) Source #

Since: 4.9.0.0

Methods

(<>) :: (a, b) -> (a, b) -> (a, b) Source #

sconcat :: NonEmpty (a, b) -> (a, b) Source #

stimes :: Integral b => b -> (a, b) -> (a, b) Source #

Semigroup (Proxy k s) Source #

Since: 4.9.0.0

Methods

(<>) :: Proxy k s -> Proxy k s -> Proxy k s Source #

sconcat :: NonEmpty (Proxy k s) -> Proxy k s Source #

stimes :: Integral b => b -> Proxy k s -> Proxy k s Source #

(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) Source #

Since: 4.9.0.0

Methods

(<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) Source #

sconcat :: NonEmpty (a, b, c) -> (a, b, c) Source #

stimes :: Integral b => b -> (a, b, c) -> (a, b, c) Source #

Alternative f => Semigroup (Alt * f a) Source #

Since: 4.9.0.0

Methods

(<>) :: Alt * f a -> Alt * f a -> Alt * f a Source #

sconcat :: NonEmpty (Alt * f a) -> Alt * f a Source #

stimes :: Integral b => b -> Alt * f a -> Alt * f a Source #

Semigroup a => Semigroup (Const k a b) Source #

Since: 4.9.0.0

Methods

(<>) :: Const k a b -> Const k a b -> Const k a b Source #

sconcat :: NonEmpty (Const k a b) -> Const k a b Source #

stimes :: Integral b => b -> Const k a b -> Const k a b Source #

(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) Source #

Since: 4.9.0.0

Methods

(<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source #

sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) Source #

stimes :: Integral b => b -> (a, b, c, d) -> (a, b, c, d) Source #

(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) Source #

Since: 4.9.0.0

Methods

(<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source #

sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e) Source #

stimes :: Integral b => b -> (a, b, c, d, e) -> (a, b, c, d, e) Source #

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

This is a valid definition of stimes for a Monoid .

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

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

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

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

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

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

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

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

Repeat a value n times.

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

Implemented using stimes and mempty .

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

Semigroups

newtype Min a Source #

Constructors

Min

Fields

getMin :: a

Instances

Monad Min Source #

Since: 4.9.0.0

Methods

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

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

return :: a -> Min a Source #

fail :: String -> Min a Source #

Functor Min Source #

Since: 4.9.0.0

Methods

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

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

MonadFix Min Source #

Since: 4.9.0.0

Methods

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

Applicative Min Source #

Since: 4.9.0.0

Methods

pure :: a -> Min a Source #

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

liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c Source #

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

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

Foldable Min Source #

Since: 4.9.0.0

Methods

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

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

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

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

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

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

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

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

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

null :: Min a -> Bool Source #

length :: Min a -> Int Source #

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

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

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

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

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

Traversable Min Source #

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Min a -> f (Min b) Source #

sequenceA :: Applicative f => Min (f a) -> f (Min a) Source #

mapM :: Monad m => (a -> m b) -> Min a -> m (Min b) Source #

sequence :: Monad m => Min (m a) -> m (Min a) Source #

Bounded a => Bounded (Min a) Source #

Methods

minBound :: Min a Source #

maxBound :: Min a Source #

Enum a => Enum (Min a) Source #

Since: 4.9.0.0

Methods

succ :: Min a -> Min a Source #

pred :: Min a -> Min a Source #

toEnum :: Int -> Min a Source #

fromEnum :: Min a -> Int Source #

enumFrom :: Min a -> [Min a] Source #

enumFromThen :: Min a -> Min a -> [Min a] Source #

enumFromTo :: Min a -> Min a -> [Min a] Source #

enumFromThenTo :: Min a -> Min a -> Min a -> [Min a] Source #

Eq a => Eq (Min a) Source #

Methods

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

(/=) :: Min a -> Min a -> Bool #

Data a => Data (Min a) Source #

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Min a -> c (Min a) Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Min a) Source #

toConstr :: Min a -> Constr Source #

dataTypeOf :: Min a -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Min a)) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Min a)) Source #

gmapT :: (forall b. Data b => b -> b) -> Min a -> Min a Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Min a -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Min a -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) Source #

Num a => Num (Min a) Source #

Since: 4.9.0.0

Methods

(+) :: Min a -> Min a -> Min a Source #

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

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

negate :: Min a -> Min a Source #

abs :: Min a -> Min a Source #

signum :: Min a -> Min a Source #

fromInteger :: Integer -> Min a Source #

Ord a => Ord (Min a) Source #

Methods

compare :: Min a -> Min a -> Ordering #

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

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

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

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

max :: Min a -> Min a -> Min a #

min :: Min a -> Min a -> Min a #

Read a => Read (Min a) Source #

Methods

readsPrec :: Int -> ReadS (Min a) Source #

readList :: ReadS [Min a] Source #

readPrec :: ReadPrec (Min a) Source #

readListPrec :: ReadPrec [Min a] Source #

Show a => Show (Min a) Source #

Methods

showsPrec :: Int -> Min a -> ShowS Source #

show :: Min a -> String Source #

showList :: [Min a] -> ShowS Source #

Generic (Min a) Source #

Associated Types

type Rep (Min a) :: * -> * Source #

Methods

from :: Min a -> Rep (Min a) x Source #

to :: Rep (Min a) x -> Min a Source #

Ord a => Semigroup (Min a) Source #

Since: 4.9.0.0

Methods

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

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

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

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

Since: 4.9.0.0

Methods

mempty :: Min a Source #

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

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

Generic1 * Min Source #

Associated Types

type Rep1 Min (f :: Min -> *) :: k -> * Source #

Methods

from1 :: f a -> Rep1 Min f a Source #

to1 :: Rep1 Min f a -> f a Source #

type Rep (Min a) Source #

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 Source #

type Rep1 * Min = D1 * (MetaData "Min" "Data.Semigroup" "base" True) (C1 * (MetaCons "Min" PrefixI True) (S1 * (MetaSel (Just Symbol "getMin") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Max a Source #

Constructors

Max

Fields

getMax :: a

Instances

Monad Max Source #

Since: 4.9.0.0

Methods

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

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

return :: a -> Max a Source #

fail :: String -> Max a Source #

Functor Max Source #

Since: 4.9.0.0

Methods

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

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

MonadFix Max Source #

Since: 4.9.0.0

Methods

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

Applicative Max Source #

Since: 4.9.0.0

Methods

pure :: a -> Max a Source #

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

liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c Source #

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

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

Foldable Max Source #

Since: 4.9.0.0

Methods

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

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

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

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

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

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

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

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

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

null :: Max a -> Bool Source #

length :: Max a -> Int Source #

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

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

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

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

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

Traversable Max Source #

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Max a -> f (Max b) Source #

sequenceA :: Applicative f => Max (f a) -> f (Max a) Source #

mapM :: Monad m => (a -> m b) -> Max a -> m (Max b) Source #

sequence :: Monad m => Max (m a) -> m (Max a) Source #

Bounded a => Bounded (Max a) Source #

Methods

minBound :: Max a Source #

maxBound :: Max a Source #

Enum a => Enum (Max a) Source #

Since: 4.9.0.0

Methods

succ :: Max a -> Max a Source #

pred :: Max a -> Max a Source #

toEnum :: Int -> Max a Source #

fromEnum :: Max a -> Int Source #

enumFrom :: Max a -> [Max a] Source #

enumFromThen :: Max a -> Max a -> [Max a] Source #

enumFromTo :: Max a -> Max a -> [Max a] Source #

enumFromThenTo :: Max a -> Max a -> Max a -> [Max a] Source #

Eq a => Eq (Max a) Source #

Methods

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

(/=) :: Max a -> Max a -> Bool #

Data a => Data (Max a) Source #

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Max a -> c (Max a) Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Max a) Source #

toConstr :: Max a -> Constr Source #

dataTypeOf :: Max a -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Max a)) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Max a)) Source #

gmapT :: (forall b. Data b => b -> b) -> Max a -> Max a Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Max a -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Max a -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) Source #

Num a => Num (Max a) Source #

Since: 4.9.0.0

Methods

(+) :: Max a -> Max a -> Max a Source #

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

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

negate :: Max a -> Max a Source #

abs :: Max a -> Max a Source #

signum :: Max a -> Max a Source #

fromInteger :: Integer -> Max a Source #

Ord a => Ord (Max a) Source #

Methods

compare :: Max a -> Max a -> Ordering #

(<) :: Max a -> Max a -> Bool #

(<=) :: Max a -> Max a -> Bool #

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

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

max :: Max a -> Max a -> Max a #

min :: Max a -> Max a -> Max a #

Read a => Read (Max a) Source #

Methods

readsPrec :: Int -> ReadS (Max a) Source #

readList :: ReadS [Max a] Source #

readPrec :: ReadPrec (Max a) Source #

readListPrec :: ReadPrec [Max a] Source #

Show a => Show (Max a) Source #

Methods

showsPrec :: Int -> Max a -> ShowS Source #

show :: Max a -> String Source #

showList :: [Max a] -> ShowS Source #

Generic (Max a) Source #

Associated Types

type Rep (Max a) :: * -> * Source #

Methods

from :: Max a -> Rep (Max a) x Source #

to :: Rep (Max a) x -> Max a Source #

Ord a => Semigroup (Max a) Source #

Since: 4.9.0.0

Methods

(<>) :: Max a -> Max a -> Max a Source #

sconcat :: NonEmpty (Max a) -> Max a Source #

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

(Ord a, Bounded a) => Monoid (Max a) Source #

Since: 4.9.0.0

Methods

mempty :: Max a Source #

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

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

Generic1 * Max Source #

Associated Types

type Rep1 Max (f :: Max -> *) :: k -> * Source #

Methods

from1 :: f a -> Rep1 Max f a Source #

to1 :: Rep1 Max f a -> f a Source #

type Rep (Max a) Source #

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 Source #

type Rep1 * Max = D1 * (MetaData "Max" "Data.Semigroup" "base" True) (C1 * (MetaCons "Max" PrefixI True) (S1 * (MetaSel (Just Symbol "getMax") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype First a Source #

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

Constructors

First

Fields

getFirst :: a

Instances

Monad First Source #

Since: 4.9.0.0

Methods

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

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

return :: a -> First a Source #

fail :: String -> First a Source #

Functor First Source #

Since: 4.9.0.0

Methods

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

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

MonadFix First Source #

Since: 4.9.0.0

Methods

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

Applicative First Source #

Since: 4.9.0.0

Methods

pure :: a -> First a Source #

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

liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source #

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

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

Foldable First Source #

Since: 4.9.0.0

Methods

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

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

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

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

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

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

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

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

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

null :: First a -> Bool Source #

length :: First a -> Int Source #

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

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

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

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

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

Traversable First Source #

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> First a -> f (First b) Source #

sequenceA :: Applicative f => First (f a) -> f (First a) Source #

mapM :: Monad m => (a -> m b) -> First a -> m (First b) Source #

sequence :: Monad m => First (m a) -> m (First a) Source #

Bounded a => Bounded (First a) Source #

Methods

minBound :: First a Source #

maxBound :: First a Source #

Enum a => Enum (First a) Source #

Since: 4.9.0.0

Methods

succ :: First a -> First a Source #

pred :: First a -> First a Source #

toEnum :: Int -> First a Source #

fromEnum :: First a -> Int Source #

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

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

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

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

Eq a => Eq (First a) Source #

Methods

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

(/=) :: First a -> First a -> Bool #

Data a => Data (First a) Source #

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> First a -> c (First a) Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a) Source #

toConstr :: First a -> Constr Source #

dataTypeOf :: First a -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (First a)) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a)) Source #

gmapT :: (forall b. Data b => b -> b) -> First a -> First a Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> First a -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source #

Ord a => Ord (First a) Source #

Methods

compare :: First a -> First a -> Ordering #

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

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

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

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

max :: First a -> First a -> First a #

min :: First a -> First a -> First a #

Read a => Read (First a) Source #

Methods

readsPrec :: Int -> ReadS (First a) Source #

readList :: ReadS [First a] Source #

readPrec :: ReadPrec (First a) Source #

readListPrec :: ReadPrec [First a] Source #

Show a => Show (First a) Source #

Methods

showsPrec :: Int -> First a -> ShowS Source #

show :: First a -> String Source #

showList :: [First a] -> ShowS Source #

Generic (First a) Source #

Associated Types

type Rep (First a) :: * -> * Source #

Methods

from :: First a -> Rep (First a) x Source #

to :: Rep (First a) x -> First a Source #

Semigroup (First a) Source #

Since: 4.9.0.0

Methods

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

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

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

Generic1 * First Source #

Associated Types

type Rep1 First (f :: First -> *) :: k -> * Source #

Methods

from1 :: f a -> Rep1 First f a Source #

to1 :: Rep1 First f a -> f a Source #

type Rep (First a) Source #

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 Source #

type Rep1 * First = D1 * (MetaData "First" "Data.Semigroup" "base" True) (C1 * (MetaCons "First" PrefixI True) (S1 * (MetaSel (Just Symbol "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Last a Source #

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

Constructors

Last

Fields

getLast :: a

Instances

Monad Last Source #

Since: 4.9.0.0

Methods

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

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

return :: a -> Last a Source #

fail :: String -> Last a Source #

Functor Last Source #

Since: 4.9.0.0

Methods

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

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

MonadFix Last Source #

Since: 4.9.0.0

Methods

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

Applicative Last Source #

Since: 4.9.0.0

Methods

pure :: a -> Last a Source #

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

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source #

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

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

Foldable Last Source #

Since: 4.9.0.0

Methods

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

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

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

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

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

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

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

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

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

null :: Last a -> Bool Source #

length :: Last a -> Int Source #

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

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

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

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

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

Traversable Last Source #

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) Source #

sequenceA :: Applicative f => Last (f a) -> f (Last a) Source #

mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) Source #

sequence :: Monad m => Last (m a) -> m (Last a) Source #

Bounded a => Bounded (Last a) Source #

Methods

minBound :: Last a Source #

maxBound :: Last a Source #

Enum a => Enum (Last a) Source #

Since: 4.9.0.0

Methods

succ :: Last a -> Last a Source #

pred :: Last a -> Last a Source #

toEnum :: Int -> Last a Source #

fromEnum :: Last a -> Int Source #

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

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

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

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

Eq a => Eq (Last a) Source #

Methods

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

(/=) :: Last a -> Last a -> Bool #

Data a => Data (Last a) Source #

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Last a -> c (Last a) Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a) Source #

toConstr :: Last a -> Constr Source #

dataTypeOf :: Last a -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Last a)) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a)) Source #

gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source #

Ord a => Ord (Last a) Source #

Methods

compare :: Last a -> Last a -> Ordering #

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

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

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

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

max :: Last a -> Last a -> Last a #

min :: Last a -> Last a -> Last a #

Read a => Read (Last a) Source #

Methods

readsPrec :: Int -> ReadS (Last a) Source #

readList :: ReadS [Last a] Source #

readPrec :: ReadPrec (Last a) Source #

readListPrec :: ReadPrec [Last a] Source #

Show a => Show (Last a) Source #

Methods

showsPrec :: Int -> Last a -> ShowS Source #

show :: Last a -> String Source #

showList :: [Last a] -> ShowS Source #

Generic (Last a) Source #

Associated Types

type Rep (Last a) :: * -> * Source #

Methods

from :: Last a -> Rep (Last a) x Source #

to :: Rep (Last a) x -> Last a Source #

Semigroup (Last a) Source #

Since: 4.9.0.0

Methods

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

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

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

Generic1 * Last Source #

Associated Types

type Rep1 Last (f :: Last -> *) :: k -> * Source #

Methods

from1 :: f a -> Rep1 Last f a Source #

to1 :: Rep1 Last f a -> f a Source #

type Rep (Last a) Source #

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 Source #

type Rep1 * Last = D1 * (MetaData "Last" "Data.Semigroup" "base" True) (C1 * (MetaCons "Last" PrefixI True) (S1 * (MetaSel (Just Symbol "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype WrappedMonoid m Source #

Provide a Semigroup for an arbitrary Monoid.

Constructors

WrapMonoid

Fields

unwrapMonoid :: m

Instances

Bounded m => Bounded (WrappedMonoid m) Source #

Methods

minBound :: WrappedMonoid m Source #

maxBound :: WrappedMonoid m Source #

Enum a => Enum (WrappedMonoid a) Source #

Since: 4.9.0.0

Methods

succ :: WrappedMonoid a -> WrappedMonoid a Source #

pred :: WrappedMonoid a -> WrappedMonoid a Source #

toEnum :: Int -> WrappedMonoid a Source #

fromEnum :: WrappedMonoid a -> Int Source #

enumFrom :: WrappedMonoid a -> [WrappedMonoid a] Source #

enumFromThen :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source #

enumFromTo :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source #

enumFromThenTo :: WrappedMonoid a -> WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source #

Eq m => Eq (WrappedMonoid m) Source #

Methods

(==) :: WrappedMonoid m -> WrappedMonoid m -> Bool #

(/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool #

Data m => Data (WrappedMonoid m) Source #

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> WrappedMonoid m -> c (WrappedMonoid m) Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (WrappedMonoid m) Source #

toConstr :: WrappedMonoid m -> Constr Source #

dataTypeOf :: WrappedMonoid m -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (WrappedMonoid m)) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (WrappedMonoid m)) Source #

gmapT :: (forall b. Data b => b -> b) -> WrappedMonoid m -> WrappedMonoid m Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> WrappedMonoid m -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> WrappedMonoid m -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> WrappedMonoid m -> m (WrappedMonoid m) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> WrappedMonoid m -> m (WrappedMonoid m) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> WrappedMonoid m -> m (WrappedMonoid m) Source #

Ord m => Ord (WrappedMonoid m) Source #

Methods

compare :: WrappedMonoid m -> WrappedMonoid m -> Ordering #

(<) :: WrappedMonoid m -> WrappedMonoid m -> Bool #

(<=) :: WrappedMonoid m -> WrappedMonoid m -> Bool #

(>) :: WrappedMonoid m -> WrappedMonoid m -> Bool #

(>=) :: WrappedMonoid m -> WrappedMonoid m -> Bool #

max :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m #

min :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m #

Read m => Read (WrappedMonoid m) Source #

Methods

readsPrec :: Int -> ReadS (WrappedMonoid m) Source #

readList :: ReadS [WrappedMonoid m] Source #

readPrec :: ReadPrec (WrappedMonoid m) Source #

readListPrec :: ReadPrec [WrappedMonoid m] Source #

Show m => Show (WrappedMonoid m) Source #

Methods

showsPrec :: Int -> WrappedMonoid m -> ShowS Source #

show :: WrappedMonoid m -> String Source #

showList :: [WrappedMonoid m] -> ShowS Source #

Generic (WrappedMonoid m) Source #

Associated Types

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

Methods

from :: WrappedMonoid m -> Rep (WrappedMonoid m) x Source #

to :: Rep (WrappedMonoid m) x -> WrappedMonoid m Source #

Monoid m => Semigroup (WrappedMonoid m) Source #

Since: 4.9.0.0

Methods

(<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source #

sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m Source #

stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m Source #

Monoid m => Monoid (WrappedMonoid m) Source #

Since: 4.9.0.0

Methods

mempty :: WrappedMonoid m Source #

mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source #

mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source #

Generic1 * WrappedMonoid Source #

Associated Types

type Rep1 WrappedMonoid (f :: WrappedMonoid -> *) :: k -> * Source #

Methods

from1 :: f a -> Rep1 WrappedMonoid f a Source #

to1 :: Rep1 WrappedMonoid f a -> f a Source #

type Rep (WrappedMonoid m) Source #

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 Source #

type Rep1 * WrappedMonoid = D1 * (MetaData "WrappedMonoid" "Data.Semigroup" "base" True) (C1 * (MetaCons "WrapMonoid" PrefixI True) (S1 * (MetaSel (Just Symbol "unwrapMonoid") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

Re-exported monoids from Data.Monoid

class Monoid a where Source #

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

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

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

```
mconcat = foldr  mappend mempty
```

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

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

Minimal complete definition

mempty, mappend

Methods

mempty :: a Source #

Identity of mappend

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

An associative operation

mconcat :: [a] -> a Source #

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

Instances

Monoid Ordering Source #

Since: 2.1

Methods

mempty :: Ordering Source #

mappend :: Ordering -> Ordering -> Ordering Source #

mconcat :: [Ordering] -> Ordering Source #

Monoid () Source #

Since: 2.1

Methods

mempty :: () Source #

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

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

Monoid Any Source #

Since: 2.1

Methods

mempty :: Any Source #

mappend :: Any -> Any -> Any Source #

mconcat :: [Any] -> Any Source #

Monoid All Source #

Since: 2.1

Methods

mempty :: All Source #

mappend :: All -> All -> All Source #

mconcat :: [All] -> All Source #

Monoid Lifetime Source #

mappend takes the longer of two lifetimes.

Since: 4.8.0.0

Methods

mempty :: Lifetime Source #

mappend :: Lifetime -> Lifetime -> Lifetime Source #

mconcat :: [Lifetime] -> Lifetime Source #

Monoid Event Source #

Since: 4.3.1.0

Methods

mempty :: Event Source #

mappend :: Event -> Event -> Event Source #

mconcat :: [Event] -> Event Source #

Monoid [a] Source #

Since: 2.1

Methods

mempty :: [a] Source #

mappend :: [a] -> [a] -> [a] Source #

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

Monoid a => Monoid (Maybe a) Source #

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 used to be no "Semigroup" typeclass providing just mappend , we use Monoid instead.

Since: 2.1

Methods

mempty :: Maybe a Source #

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

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

Monoid a => Monoid (IO a) Source #

Since: 4.9.0.0

Methods

mempty :: IO a Source #

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

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

Monoid (Last a) Source #

Since: 2.1

Methods

mempty :: Last a Source #

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

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

Monoid (First a) Source #

Since: 2.1

Methods

mempty :: First a Source #

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

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

Num a => Monoid (Product a) Source #

Since: 2.1

Methods

mempty :: Product a Source #

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

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

Num a => Monoid (Sum a) Source #

Since: 2.1

Methods

mempty :: Sum a Source #

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

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

Monoid (Endo a) Source #

Since: 2.1

Methods

mempty :: Endo a Source #

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

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

Monoid a => Monoid (Dual a) Source #

Since: 2.1

Methods

mempty :: Dual a Source #

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

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

Monoid a => Monoid (Identity a) Source #

Methods

mempty :: Identity a Source #

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

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

Semigroup a => Monoid (Option a) Source #

Since: 4.9.0.0

Methods

mempty :: Option a Source #

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

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

Monoid m => Monoid (WrappedMonoid m) Source #

Since: 4.9.0.0

Methods

mempty :: WrappedMonoid m Source #

mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source #

mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source #

(Ord a, Bounded a) => Monoid (Max a) Source #

Since: 4.9.0.0

Methods

mempty :: Max a Source #

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

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

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

Since: 4.9.0.0

Methods

mempty :: Min a Source #

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

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

Monoid b => Monoid (a -> b) Source #

Since: 2.1

Methods

mempty :: a -> b Source #

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

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

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

Since: 2.1

Methods

mempty :: (a, b) Source #

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

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

Monoid (Proxy k s) Source #

Since: 4.7.0.0

Methods

mempty :: Proxy k s Source #

mappend :: Proxy k s -> Proxy k s -> Proxy k s Source #

mconcat :: [Proxy k s] -> Proxy k s Source #

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

Since: 2.1

Methods

mempty :: (a, b, c) Source #

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

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

Alternative f => Monoid (Alt * f a) Source #

Since: 4.8.0.0

Methods

mempty :: Alt * f a Source #

mappend :: Alt * f a -> Alt * f a -> Alt * f a Source #

mconcat :: [Alt * f a] -> Alt * f a Source #

Monoid a => Monoid (Const k a b) Source #

Methods

mempty :: Const k a b Source #

mappend :: Const k a b -> Const k a b -> Const k a b Source #

mconcat :: [Const k a b] -> Const k a b Source #

(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) Source #

Since: 2.1

Methods

mempty :: (a, b, c, d) Source #

mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source #

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

(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) Source #

Since: 2.1

Methods

mempty :: (a, b, c, d, e) Source #

mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source #

mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) Source #

newtype Dual a Source #

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

Constructors

Dual

Fields

getDual :: a

Instances

Monad Dual Source #

Since: 4.8.0.0

Methods

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

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

return :: a -> Dual a Source #

fail :: String -> Dual a Source #

Functor Dual Source #

Since: 4.8.0.0

Methods

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

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

MonadFix Dual Source #

Since: 4.8.0.0

Methods

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

Applicative Dual Source #

Since: 4.8.0.0

Methods

pure :: a -> Dual a Source #

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

liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source #

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

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

Foldable Dual Source #

Since: 4.8.0.0

Methods

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

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

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

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

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

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

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

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

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

null :: Dual a -> Bool Source #

length :: Dual a -> Int Source #

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

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

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

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

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

Traversable Dual Source #

Since: 4.8.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) Source #

sequenceA :: Applicative f => Dual (f a) -> f (Dual a) Source #

mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) Source #

sequence :: Monad m => Dual (m a) -> m (Dual a) Source #

MonadZip Dual Source #

Since: 4.8.0.0

Methods

mzip :: Dual a -> Dual b -> Dual (a, b) Source #

mzipWith :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source #

munzip :: Dual (a, b) -> (Dual a, Dual b) Source #

Bounded a => Bounded (Dual a) Source #

Methods

minBound :: Dual a Source #

maxBound :: Dual a Source #

Eq a => Eq (Dual a) Source #

Methods

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

(/=) :: Dual a -> Dual a -> Bool #

Data a => Data (Dual a) Source #

Since: 4.8.0.0

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dual a -> c (Dual a) Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dual a) Source #

toConstr :: Dual a -> Constr Source #

dataTypeOf :: Dual a -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Dual a)) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Dual a)) Source #

gmapT :: (forall b. Data b => b -> b) -> Dual a -> Dual a Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Dual a -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Dual a -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source #

Ord a => Ord (Dual a) Source #

Methods

compare :: Dual a -> Dual a -> Ordering #

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

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

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

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

max :: Dual a -> Dual a -> Dual a #

min :: Dual a -> Dual a -> Dual a #

Read a => Read (Dual a) Source #

Methods

readsPrec :: Int -> ReadS (Dual a) Source #

readList :: ReadS [Dual a] Source #

readPrec :: ReadPrec (Dual a) Source #

readListPrec :: ReadPrec [Dual a] Source #

Show a => Show (Dual a) Source #

Methods

showsPrec :: Int -> Dual a -> ShowS Source #

show :: Dual a -> String Source #

showList :: [Dual a] -> ShowS Source #

Generic (Dual a) Source #

Associated Types

type Rep (Dual a) :: * -> * Source #

Methods

from :: Dual a -> Rep (Dual a) x Source #

to :: Rep (Dual a) x -> Dual a Source #

Semigroup a => Semigroup (Dual a) Source #

Since: 4.9.0.0

Methods

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

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

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

Monoid a => Monoid (Dual a) Source #

Since: 2.1

Methods

mempty :: Dual a Source #

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

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

Generic1 * Dual Source #

Associated Types

type Rep1 Dual (f :: Dual -> *) :: k -> * Source #

Methods

from1 :: f a -> Rep1 Dual f a Source #

to1 :: Rep1 Dual f a -> f a Source #

type Rep (Dual a) Source #

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 Source #

type Rep1 * Dual = D1 * (MetaData "Dual" "Data.Monoid" "base" True) (C1 * (MetaCons "Dual" PrefixI True) (S1 * (MetaSel (Just Symbol "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Endo a Source #

The monoid of endomorphisms under composition.

Constructors

Endo

Fields

appEndo :: a -> a

Instances

Generic (Endo a) Source #

Associated Types

type Rep (Endo a) :: * -> * Source #

Methods

from :: Endo a -> Rep (Endo a) x Source #

to :: Rep (Endo a) x -> Endo a Source #

Semigroup (Endo a) Source #

Since: 4.9.0.0

Methods

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

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

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

Monoid (Endo a) Source #

Since: 2.1

Methods

mempty :: Endo a Source #

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

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

type Rep (Endo a) Source #

type Rep (Endo a) = D1 * (MetaData "Endo" "Data.Monoid" "base" True) (C1 * (MetaCons "Endo" PrefixI True) (S1 * (MetaSel (Just Symbol "appEndo") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (a -> a))))

newtype All Source #

Boolean monoid under conjunction (&& ).

Constructors

All

Fields

getAll :: Bool

Instances

Bounded All Source #

Methods

minBound :: All Source #

maxBound :: All Source #

Eq All Source #

Methods

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

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

Data All Source #

Since: 4.8.0.0

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> All -> c All Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c All Source #

toConstr :: All -> Constr Source #

dataTypeOf :: All -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c All) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c All) Source #

gmapT :: (forall b. Data b => b -> b) -> All -> All Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> All -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> All -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> All -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> All -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> All -> m All Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All Source #

Ord All Source #

Methods

compare :: All -> All -> Ordering #

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

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

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

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

max :: All -> All -> All #

min :: All -> All -> All #

Read All Source #

Methods

readsPrec :: Int -> ReadS All Source #

readList :: ReadS [All] Source #

readPrec :: ReadPrec All Source #

readListPrec :: ReadPrec [All] Source #

Show All Source #

Methods

showsPrec :: Int -> All -> ShowS Source #

show :: All -> String Source #

showList :: [All] -> ShowS Source #

Generic All Source #

Associated Types

type Rep All :: * -> * Source #

Methods

from :: All -> Rep All x Source #

to :: Rep All x -> All Source #

Semigroup All Source #

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty All -> All Source #

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

Monoid All Source #

Since: 2.1

Methods

mempty :: All Source #

mappend :: All -> All -> All Source #

mconcat :: [All] -> All Source #

type Rep All Source #

type Rep All = D1 * (MetaData "All" "Data.Monoid" "base" True) (C1 * (MetaCons "All" PrefixI True) (S1 * (MetaSel (Just Symbol "getAll") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Bool)))

newtype Any Source #

Boolean monoid under disjunction (|| ).

Constructors

Any

Fields

getAny :: Bool

Instances

Bounded Any Source #

Methods

minBound :: Any Source #

maxBound :: Any Source #

Eq Any Source #

Methods

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

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

Data Any Source #

Since: 4.8.0.0

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Any -> c Any Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Any Source #

toConstr :: Any -> Constr Source #

dataTypeOf :: Any -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c Any) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Any) Source #

gmapT :: (forall b. Data b => b -> b) -> Any -> Any Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Any -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Any -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Any -> m Any Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any Source #

Ord Any Source #

Methods

compare :: Any -> Any -> Ordering #

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

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

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

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

max :: Any -> Any -> Any #

min :: Any -> Any -> Any #

Read Any Source #

Methods

readsPrec :: Int -> ReadS Any Source #

readList :: ReadS [Any] Source #

readPrec :: ReadPrec Any Source #

readListPrec :: ReadPrec [Any] Source #

Show Any Source #

Methods

showsPrec :: Int -> Any -> ShowS Source #

show :: Any -> String Source #

showList :: [Any] -> ShowS Source #

Generic Any Source #

Associated Types

type Rep Any :: * -> * Source #

Methods

from :: Any -> Rep Any x Source #

to :: Rep Any x -> Any Source #

Semigroup Any Source #

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty Any -> Any Source #

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

Monoid Any Source #

Since: 2.1

Methods

mempty :: Any Source #

mappend :: Any -> Any -> Any Source #

mconcat :: [Any] -> Any Source #

type Rep Any Source #

type Rep Any = D1 * (MetaData "Any" "Data.Monoid" "base" True) (C1 * (MetaCons "Any" PrefixI True) (S1 * (MetaSel (Just Symbol "getAny") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Bool)))

newtype Sum a Source #

Monoid under addition.

Constructors

Sum

Fields

getSum :: a

Instances

Monad Sum Source #

Since: 4.8.0.0

Methods

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

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

return :: a -> Sum a Source #

fail :: String -> Sum a Source #

Functor Sum Source #

Since: 4.8.0.0

Methods

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

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

MonadFix Sum Source #

Since: 4.8.0.0

Methods

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

Applicative Sum Source #

Since: 4.8.0.0

Methods

pure :: a -> Sum a Source #

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

liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source #

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

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

Foldable Sum Source #

Since: 4.8.0.0

Methods

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

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

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

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

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

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

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

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

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

null :: Sum a -> Bool Source #

length :: Sum a -> Int Source #

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

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

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

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

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

Traversable Sum Source #

Since: 4.8.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) Source #

sequenceA :: Applicative f => Sum (f a) -> f (Sum a) Source #

mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) Source #

sequence :: Monad m => Sum (m a) -> m (Sum a) Source #

MonadZip Sum Source #

Since: 4.8.0.0

Methods

mzip :: Sum a -> Sum b -> Sum (a, b) Source #

mzipWith :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source #

munzip :: Sum (a, b) -> (Sum a, Sum b) Source #

Bounded a => Bounded (Sum a) Source #

Methods

minBound :: Sum a Source #

maxBound :: Sum a Source #

Eq a => Eq (Sum a) Source #

Methods

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

(/=) :: Sum a -> Sum a -> Bool #

Data a => Data (Sum a) Source #

Since: 4.8.0.0

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Sum a -> c (Sum a) Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum a) Source #

toConstr :: Sum a -> Constr Source #

dataTypeOf :: Sum a -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Sum a)) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum a)) Source #

gmapT :: (forall b. Data b => b -> b) -> Sum a -> Sum a Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Sum a -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum a -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source #

Num a => Num (Sum a) Source #

Methods

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

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

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

negate :: Sum a -> Sum a Source #

abs :: Sum a -> Sum a Source #

signum :: Sum a -> Sum a Source #

fromInteger :: Integer -> Sum a Source #

Ord a => Ord (Sum a) Source #

Methods

compare :: Sum a -> Sum a -> Ordering #

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

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

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

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

max :: Sum a -> Sum a -> Sum a #

min :: Sum a -> Sum a -> Sum a #

Read a => Read (Sum a) Source #

Methods

readsPrec :: Int -> ReadS (Sum a) Source #

readList :: ReadS [Sum a] Source #

readPrec :: ReadPrec (Sum a) Source #

readListPrec :: ReadPrec [Sum a] Source #

Show a => Show (Sum a) Source #

Methods

showsPrec :: Int -> Sum a -> ShowS Source #

show :: Sum a -> String Source #

showList :: [Sum a] -> ShowS Source #

Generic (Sum a) Source #

Associated Types

type Rep (Sum a) :: * -> * Source #

Methods

from :: Sum a -> Rep (Sum a) x Source #

to :: Rep (Sum a) x -> Sum a Source #

Num a => Semigroup (Sum a) Source #

Since: 4.9.0.0

Methods

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

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

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

Num a => Monoid (Sum a) Source #

Since: 2.1

Methods

mempty :: Sum a Source #

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

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

Generic1 * Sum Source #

Associated Types

type Rep1 Sum (f :: Sum -> *) :: k -> * Source #

Methods

from1 :: f a -> Rep1 Sum f a Source #

to1 :: Rep1 Sum f a -> f a Source #

type Rep (Sum a) Source #

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 Source #

type Rep1 * Sum = D1 * (MetaData "Sum" "Data.Monoid" "base" True) (C1 * (MetaCons "Sum" PrefixI True) (S1 * (MetaSel (Just Symbol "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Product a Source #

Monoid under multiplication.

Constructors

Product

Fields

getProduct :: a

Instances

Monad Product Source #

Since: 4.8.0.0

Methods

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

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

return :: a -> Product a Source #

fail :: String -> Product a Source #

Functor Product Source #

Since: 4.8.0.0

Methods

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

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

MonadFix Product Source #

Since: 4.8.0.0

Methods

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

Applicative Product Source #

Since: 4.8.0.0

Methods

pure :: a -> Product a Source #

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

liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c Source #

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

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

Foldable Product Source #

Since: 4.8.0.0

Methods

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

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

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

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

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

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

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

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

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

null :: Product a -> Bool Source #

length :: Product a -> Int Source #

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

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

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

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

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

Traversable Product Source #

Since: 4.8.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) Source #

sequenceA :: Applicative f => Product (f a) -> f (Product a) Source #

mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) Source #

sequence :: Monad m => Product (m a) -> m (Product a) Source #

MonadZip Product Source #

Since: 4.8.0.0

Methods

mzip :: Product a -> Product b -> Product (a, b) Source #

mzipWith :: (a -> b -> c) -> Product a -> Product b -> Product c Source #

munzip :: Product (a, b) -> (Product a, Product b) Source #

Bounded a => Bounded (Product a) Source #

Methods

minBound :: Product a Source #

maxBound :: Product a Source #

Eq a => Eq (Product a) Source #

Methods

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

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

Data a => Data (Product a) Source #

Since: 4.8.0.0

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Product a -> c (Product a) Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product a) Source #

toConstr :: Product a -> Constr Source #

dataTypeOf :: Product a -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Product a)) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product a)) Source #

gmapT :: (forall b. Data b => b -> b) -> Product a -> Product a Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Product a -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Product a -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source #

Num a => Num (Product a) Source #

Methods

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

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

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

negate :: Product a -> Product a Source #

abs :: Product a -> Product a Source #

signum :: Product a -> Product a Source #

fromInteger :: Integer -> Product a Source #

Ord a => Ord (Product a) Source #

Methods

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

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

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

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

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

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

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

Read a => Read (Product a) Source #

Methods

readsPrec :: Int -> ReadS (Product a) Source #

readList :: ReadS [Product a] Source #

readPrec :: ReadPrec (Product a) Source #

readListPrec :: ReadPrec [Product a] Source #

Show a => Show (Product a) Source #

Methods

showsPrec :: Int -> Product a -> ShowS Source #

show :: Product a -> String Source #

showList :: [Product a] -> ShowS Source #

Generic (Product a) Source #

Associated Types

type Rep (Product a) :: * -> * Source #

Methods

from :: Product a -> Rep (Product a) x Source #

to :: Rep (Product a) x -> Product a Source #

Num a => Semigroup (Product a) Source #

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty (Product a) -> Product a Source #

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

Num a => Monoid (Product a) Source #

Since: 2.1

Methods

mempty :: Product a Source #

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

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

Generic1 * Product Source #

Associated Types

type Rep1 Product (f :: Product -> *) :: k -> * Source #

Methods

from1 :: f a -> Rep1 Product f a Source #

to1 :: Rep1 Product f a -> f a Source #

type Rep (Product a) Source #

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 Source #

type Rep1 * Product = D1 * (MetaData "Product" "Data.Monoid" "base" True) (C1 * (MetaCons "Product" PrefixI True) (S1 * (MetaSel (Just Symbol "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

A better monoid for Maybe

newtype Option a Source #

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

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

Constructors

Option

Fields

getOption :: Maybe a

Instances

Monad Option Source #

Since: 4.9.0.0

Methods

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

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

return :: a -> Option a Source #

fail :: String -> Option a Source #

Functor Option Source #

Since: 4.9.0.0

Methods

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

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

MonadFix Option Source #

Since: 4.9.0.0

Methods

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

Applicative Option Source #

Since: 4.9.0.0

Methods

pure :: a -> Option a Source #

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

liftA2 :: (a -> b -> c) -> Option a -> Option b -> Option c Source #

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

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

Foldable Option Source #

Since: 4.9.0.0

Methods

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

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

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

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

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

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

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

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

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

null :: Option a -> Bool Source #

length :: Option a -> Int Source #

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

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

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

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

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

Traversable Option Source #

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Option a -> f (Option b) Source #

sequenceA :: Applicative f => Option (f a) -> f (Option a) Source #

mapM :: Monad m => (a -> m b) -> Option a -> m (Option b) Source #

sequence :: Monad m => Option (m a) -> m (Option a) Source #

MonadPlus Option Source #

Since: 4.9.0.0

Methods

mzero :: Option a Source #

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

Alternative Option Source #

Since: 4.9.0.0

Methods

empty :: Option a Source #

(<|>) :: Option a -> Option a -> Option a Source #

some :: Option a -> Option [a] Source #

many :: Option a -> Option [a] Source #

Eq a => Eq (Option a) Source #

Methods

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

(/=) :: Option a -> Option a -> Bool #

Data a => Data (Option a) Source #

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Option a -> c (Option a) Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Option a) Source #

toConstr :: Option a -> Constr Source #

dataTypeOf :: Option a -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Option a)) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Option a)) Source #

gmapT :: (forall b. Data b => b -> b) -> Option a -> Option a Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Option a -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Option a -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Option a -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Option a -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) Source #

Ord a => Ord (Option a) Source #

Methods

compare :: Option a -> Option a -> Ordering #

(<) :: Option a -> Option a -> Bool #

(<=) :: Option a -> Option a -> Bool #

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

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

max :: Option a -> Option a -> Option a #

min :: Option a -> Option a -> Option a #

Read a => Read (Option a) Source #

Methods

readsPrec :: Int -> ReadS (Option a) Source #

readList :: ReadS [Option a] Source #

readPrec :: ReadPrec (Option a) Source #

readListPrec :: ReadPrec [Option a] Source #

Show a => Show (Option a) Source #

Methods

showsPrec :: Int -> Option a -> ShowS Source #

show :: Option a -> String Source #

showList :: [Option a] -> ShowS Source #

Generic (Option a) Source #

Associated Types

type Rep (Option a) :: * -> * Source #

Methods

from :: Option a -> Rep (Option a) x Source #

to :: Rep (Option a) x -> Option a Source #

Semigroup a => Semigroup (Option a) Source #

Since: 4.9.0.0

Methods

(<>) :: Option a -> Option a -> Option a Source #

sconcat :: NonEmpty (Option a) -> Option a Source #

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

Semigroup a => Monoid (Option a) Source #

Since: 4.9.0.0

Methods

mempty :: Option a Source #

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

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

Generic1 * Option Source #

Associated Types

type Rep1 Option (f :: Option -> *) :: k -> * Source #

Methods

from1 :: f a -> Rep1 Option f a Source #

to1 :: Rep1 Option f a -> f a Source #

type Rep (Option a) Source #

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 Source #

type Rep1 * Option = D1 * (MetaData "Option" "Data.Semigroup" "base" True) (C1 * (MetaCons "Option" PrefixI True) (S1 * (MetaSel (Just Symbol "getOption") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 * Maybe)))

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

Fold an Option case-wise, just like maybe .

Difference lists of a semigroup

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

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

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

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

ArgMin, ArgMax

data Arg a b Source #

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

Constructors

Arg a b

Instances

Bifunctor Arg Source #

Since: 4.9.0.0

Methods

bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d Source #

first :: (a -> b) -> Arg a c -> Arg b c Source #

second :: (b -> c) -> Arg a b -> Arg a c Source #

Bifoldable Arg Source #

Since: 4.10.0.0

Methods

bifold :: Monoid m => Arg m m -> m Source #

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Arg a b -> m Source #

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Arg a b -> c Source #

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Arg a b -> c Source #

Bitraversable Arg Source #

Since: 4.10.0.0

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d) Source #

Functor (Arg a) Source #

Since: 4.9.0.0

Methods

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

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

Foldable (Arg a) Source #

Since: 4.9.0.0

Methods

fold :: Monoid m => Arg a m -> m Source #

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

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

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

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

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

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

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

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

null :: Arg a a -> Bool Source #

length :: Arg a a -> Int Source #

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

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

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

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

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

Traversable (Arg a) Source #

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Arg a a -> f (Arg a b) Source #

sequenceA :: Applicative f => Arg a (f a) -> f (Arg a a) Source #

mapM :: Monad m => (a -> m b) -> Arg a a -> m (Arg a b) Source #

sequence :: Monad m => Arg a (m a) -> m (Arg a a) Source #

Generic1 * (Arg a) Source #

Associated Types

type Rep1 (Arg a) (f :: Arg a -> *) :: k -> * Source #

Methods

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

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

Eq a => Eq (Arg a b) Source #

Since: 4.9.0.0

Methods

(==) :: Arg a b -> Arg a b -> Bool #

(/=) :: Arg a b -> Arg a b -> Bool #

(Data b, Data a) => Data (Arg a b) Source #

Methods

gfoldl :: (forall d c. Data d => c (d -> c) -> d -> c c) -> (forall g. g -> c g) -> Arg a b -> c (Arg a b) Source #

gunfold :: (forall c r. Data c => c (c -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Arg a b) Source #

toConstr :: Arg a b -> Constr Source #

dataTypeOf :: Arg a b -> DataType Source #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Arg a b)) Source #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Arg a b)) Source #

gmapT :: (forall c. Data c => c -> c) -> Arg a b -> Arg a b Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r Source #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Arg a b -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Arg a b -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) Source #

Ord a => Ord (Arg a b) Source #

Since: 4.9.0.0

Methods

compare :: Arg a b -> Arg a b -> Ordering #

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

(<=) :: Arg a b -> Arg a b -> Bool #

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

(>=) :: Arg a b -> Arg a b -> Bool #

max :: Arg a b -> Arg a b -> Arg a b #

min :: Arg a b -> Arg a b -> Arg a b #

(Read b, Read a) => Read (Arg a b) Source #

Methods

readsPrec :: Int -> ReadS (Arg a b) Source #

readList :: ReadS [Arg a b] Source #

readPrec :: ReadPrec (Arg a b) Source #

readListPrec :: ReadPrec [Arg a b] Source #

(Show b, Show a) => Show (Arg a b) Source #

Methods

showsPrec :: Int -> Arg a b -> ShowS Source #

show :: Arg a b -> String Source #

showList :: [Arg a b] -> ShowS Source #

Generic (Arg a b) Source #

Associated Types

type Rep (Arg a b) :: * -> * Source #

Methods

from :: Arg a b -> Rep (Arg a b) x Source #

to :: Rep (Arg a b) x -> Arg a b Source #

type Rep1 * (Arg a) Source #

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) Source #

type Rep (Arg a b) = D1 * (MetaData "Arg" "Data.Semigroup" "base" False) (C1 * (MetaCons "Arg" PrefixI False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * b))))

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

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