base-4.14.0.0: Basic libraries
Copyright(C) 2011-2015 Edward Kmett
LicenseBSD-style (see the file LICENSE)
Maintainerlibraries@haskell.org
Stabilityprovisional
Portabilityportable
Safe HaskellTrustworthy
LanguageHaskell2010

Data.Semigroup

Description

A type a is a Semigroup if it provides an associative function (<>) that lets you combine any two values of type a into one. Where being associative means that the following must always hold:

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

Examples

Expand

The Min Semigroup instance for Int is defined to always pick the smaller number: >>> Min 1 <> Min 2 <> Min 3 <> Min 4 :: Min Int Min {getMin = 1}

If we need to combine multiple values we can use the sconcat function to do so. We need to ensure however that we have at least one value to operate on, since otherwise our result would be undefined. It is for this reason that sconcat uses Data.List.NonEmpty.NonEmpty - a list that can never be empty:

>>> (1 :| [])
1 :| []               -- equivalent to [1] but guaranteed to be non-empty
>>> (1 :| [2, 3, 4])
1 :| [2,3,4]          -- equivalent to [1,2,3,4] but guaranteed to be non-empty

Equipped with this guaranteed to be non-empty data structure, we can combine values using sconcat and a Semigroup of our choosing. We can try the Min and Max instances of Int which pick the smallest, or largest number respectively:

>>> sconcat (1 :| [2, 3, 4]) :: Min Int
Min {getMin = 1}
>>> sconcat (1 :| [2, 3, 4]) :: Max Int
Max {getMax = 4}

String concatenation is another example of a Semigroup instance:

>>> "foo" <> "bar"
"foobar"

A Semigroup is a generalization of a Monoid. Yet unlike the Semigroup, the Monoid requires the presence of a neutral element (mempty) in addition to the associative operator. The requirement for a neutral element prevents many types from being a full Monoid, like Data.List.NonEmpty.NonEmpty.

Note that 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: base-4.9.0.0

Synopsis

Documentation

class Semigroup a where Source #

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

Instances should satisfy the following:

Associativity
x <> (y <> z) = (x <> y) <> z

Since: base-4.9.0.0

Minimal complete definition

(<>)

Methods

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

An associative operation.

>>> [1,2,3] <> [4,5,6]
[1,2,3,4,5,6]

sconcat :: NonEmpty a -> a Source #

Reduce a non-empty list with <>

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

>>> import Data.List.NonEmpty
>>> sconcat $ "Hello" :| [" ", "Haskell", "!"]
"Hello Haskell!"

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 \(\mathcal{O}(1)\) by picking stimes = stimesIdempotent or stimes = stimesIdempotentMonoid respectively.

>>> stimes 4 [1]
[1,1,1,1]

Instances

Instances details
Semigroup Ordering #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Semigroup () #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

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

Semigroup Any #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

sconcat :: NonEmpty Any -> Any Source #

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

Semigroup All #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

sconcat :: NonEmpty All -> All Source #

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

Semigroup Lifetime #

Since: base-4.10.0.0

Instance details

Defined in GHC.Event.Internal

Semigroup Event #

Since: base-4.10.0.0

Instance details

Defined in GHC.Event.Internal

Semigroup Void #

Since: base-4.9.0.0

Instance details

Defined in Data.Void

Semigroup [a] #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

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

Semigroup a => Semigroup (Maybe a) #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

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

Semigroup a => Semigroup (IO a) #

Since: base-4.10.0.0

Instance details

Defined in GHC.Base

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 p => Semigroup (Par1 p) #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: Par1 p -> Par1 p -> Par1 p Source #

sconcat :: NonEmpty (Par1 p) -> Par1 p Source #

stimes :: Integral b => b -> Par1 p -> Par1 p Source #

Semigroup (NonEmpty a) #

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Semigroup a => Semigroup (Down a) #

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Methods

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

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

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

Num a => Semigroup (Product a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Num a => Semigroup (Sum a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Semigroup (Endo a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Semigroup a => Semigroup (Dual a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Semigroup (Last a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

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

Semigroup (First a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

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

Semigroup a => Semigroup (Identity a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Semigroup a => Semigroup (Option a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

Monoid m => Semigroup (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Semigroup (Last a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

Semigroup (First a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

Ord a => Semigroup (Max a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

Ord a => Semigroup (Min a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 (Equivalence a) #

(<>) on equivalences uses logical conjunction (&&) on the results. Without newtypes this equals liftA2 (liftA2 (&&)).

(<>) :: Equivalence a -> Equivalence a -> Equivalence a
Equivalence equiv <> Equivalence equiv' = Equivalence a b ->
  equiv a b && equiv a b
Instance details

Defined in Data.Functor.Contravariant

Semigroup (Comparison a) #

(<>) on comparisons combines results with (<>) @Ordering. Without newtypes this equals liftA2 (liftA2 (<>)).

(<>) :: Comparison a -> Comparison a -> Comparison a
Comparison cmp <> Comparison cmp' = Comparison a a' ->
  cmp a a' <> cmp a a'
Instance details

Defined in Data.Functor.Contravariant

Semigroup (Predicate a) #

(<>) on predicates uses logical conjunction (&&) on the results. Without newtypes this equals liftA2 (&&).

(<>) :: Predicate a -> Predicate a -> Predicate a
Predicate pred <> Predicate pred' = Predicate a ->
  pred a && pred' a
Instance details

Defined in Data.Functor.Contravariant

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

stimes :: Integral b0 => b0 -> (a -> b) -> a -> b Source #

Semigroup (Either a b) #

Since: base-4.9.0.0

Instance details

Defined in Data.Either

Methods

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

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

stimes :: Integral b0 => b0 -> Either a b -> Either a b Source #

Semigroup (V1 p) #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: V1 p -> V1 p -> V1 p Source #

sconcat :: NonEmpty (V1 p) -> V1 p Source #

stimes :: Integral b => b -> V1 p -> V1 p Source #

Semigroup (U1 p) #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: U1 p -> U1 p -> U1 p Source #

sconcat :: NonEmpty (U1 p) -> U1 p Source #

stimes :: Integral b => b -> U1 p -> U1 p Source #

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

stimes :: Integral b0 => b0 -> (a, b) -> (a, b) Source #

Semigroup a => Semigroup (ST s a) #

Since: base-4.11.0.0

Instance details

Defined in GHC.ST

Methods

(<>) :: ST s a -> ST s a -> ST s a Source #

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

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

Semigroup (Proxy s) #

Since: base-4.9.0.0

Instance details

Defined in Data.Proxy

Methods

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

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

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

Semigroup a => Semigroup (Op a b) #

(<>) @(Op a b) without newtypes is (<>) @(b->a) = liftA2 (<>). This lifts the Semigroup operation (<>) over the output of a.

(<>) :: Op a b -> Op a b -> Op a b
Op f <> Op g = Op a -> f a <> g a
Instance details

Defined in Data.Functor.Contravariant

Methods

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

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

stimes :: Integral b0 => b0 -> Op a b -> Op a b Source #

Semigroup (f p) => Semigroup (Rec1 f p) #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: Rec1 f p -> Rec1 f p -> Rec1 f p Source #

sconcat :: NonEmpty (Rec1 f p) -> Rec1 f p Source #

stimes :: Integral b => b -> Rec1 f p -> Rec1 f p Source #

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c) Source #

Alternative f => Semigroup (Alt f a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

(Applicative f, Semigroup a) => Semigroup (Ap f a) #

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

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

Semigroup a => Semigroup (Const a b) #

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

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

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

stimes :: Integral b0 => b0 -> Const a b -> Const a b Source #

Semigroup c => Semigroup (K1 i c p) #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: K1 i c p -> K1 i c p -> K1 i c p Source #

sconcat :: NonEmpty (K1 i c p) -> K1 i c p Source #

stimes :: Integral b => b -> K1 i c p -> K1 i c p Source #

(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p Source #

sconcat :: NonEmpty ((f :*: g) p) -> (f :*: g) p Source #

stimes :: Integral b => b -> (f :*: g) p -> (f :*: g) p Source #

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

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 b0 => b0 -> (a, b, c, d) -> (a, b, c, d) Source #

Semigroup (f p) => Semigroup (M1 i c f p) #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: M1 i c f p -> M1 i c f p -> M1 i c f p Source #

sconcat :: NonEmpty (M1 i c f p) -> M1 i c f p Source #

stimes :: Integral b => b -> M1 i c f p -> M1 i c f p Source #

Semigroup (f (g p)) => Semigroup ((f :.: g) p) #

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p Source #

sconcat :: NonEmpty ((f :.: g) p) -> (f :.: g) p Source #

stimes :: Integral b => b -> (f :.: g) p -> (f :.: g) p Source #

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

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

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 b0 => b0 -> (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 \(\mathcal{O}(1)\) rather than \(\mathcal{O}(\log n)\).

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 \(\mathcal{O}(1)\) rather than \(\mathcal{O}(\log n)\)

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

Instances

Instances details
Monad Min #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

return :: a -> Min a Source #

Functor Min #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

MonadFix Min #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

Applicative Min #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Min a Source #

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

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

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

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

Foldable Min #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

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

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

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

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

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

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

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

null :: Min a -> Bool Source #

length :: Min a -> Int Source #

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

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

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

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

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

Traversable Min #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Enum a => Enum (Min a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Data a => Data (Min a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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

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

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

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

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

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

Num a => Num (Min a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Show a => Show (Min a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

show :: Min a -> String Source #

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

Generic (Min a) # 
Instance details

Defined in Data.Semigroup

Associated Types

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

Methods

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

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

Ord a => Semigroup (Min a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mempty :: Min a Source #

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

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

Generic1 Min # 
Instance details

Defined in Data.Semigroup

Associated Types

type Rep1 Min :: k -> Type Source #

Methods

from1 :: forall (a :: k). Min a -> Rep1 Min a Source #

to1 :: forall (a :: k). Rep1 Min a -> Min a Source #

type Rep (Min a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep (Min a) = D1 ('MetaData "Min" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Min" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMin") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 Min #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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

newtype Max a Source #

Constructors

Max 

Fields

Instances

Instances details
Monad Max #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

return :: a -> Max a Source #

Functor Max #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

MonadFix Max #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

Applicative Max #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Max a Source #

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

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

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

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

Foldable Max #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

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

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

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

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

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

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

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

null :: Max a -> Bool Source #

length :: Max a -> Int Source #

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

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

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

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

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

Traversable Max #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Enum a => Enum (Max a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Data a => Data (Max a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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

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

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

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

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

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

Num a => Num (Max a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Show a => Show (Max a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

show :: Max a -> String Source #

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

Generic (Max a) # 
Instance details

Defined in Data.Semigroup

Associated Types

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

Methods

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

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

Ord a => Semigroup (Max a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

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

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mempty :: Max a Source #

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

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

Generic1 Max # 
Instance details

Defined in Data.Semigroup

Associated Types

type Rep1 Max :: k -> Type Source #

Methods

from1 :: forall (a :: k). Max a -> Rep1 Max a Source #

to1 :: forall (a :: k). Rep1 Max a -> Max a Source #

type Rep (Max a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep (Max a) = D1 ('MetaData "Max" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Max" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMax") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 Max #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep1 Max = D1 ('MetaData "Max" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Max" 'PrefixI 'True) (S1 ('MetaSel ('Just "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

Instances

Instances details
Monad First #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

return :: a -> First a Source #

Functor First #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

MonadFix First #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

Applicative First #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> First a Source #

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

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

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

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

Foldable First #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

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

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

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

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

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

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

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

null :: First a -> Bool Source #

length :: First a -> Int Source #

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

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

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

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

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

Traversable First #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Enum a => Enum (First a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Data a => Data (First a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 :: forall r r'. (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) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

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

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

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

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

Read a => Read (First a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Show a => Show (First a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Generic (First a) # 
Instance details

Defined in Data.Semigroup

Associated Types

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

Methods

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

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

Semigroup (First a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 # 
Instance details

Defined in Data.Semigroup

Associated Types

type Rep1 First :: k -> Type Source #

Methods

from1 :: forall (a :: k). First a -> Rep1 First a Source #

to1 :: forall (a :: k). Rep1 First a -> First a Source #

type Rep (First a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep (First a) = D1 ('MetaData "First" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 First #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep1 First = D1 ('MetaData "First" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "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

Instances

Instances details
Monad Last #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

return :: a -> Last a Source #

Functor Last #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

MonadFix Last #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

Applicative Last #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Last a Source #

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

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

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

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

Foldable Last #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

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

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

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

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

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

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

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

null :: Last a -> Bool Source #

length :: Last a -> Int Source #

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

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

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

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

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

Traversable Last #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Enum a => Enum (Last a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Data a => Data (Last a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 :: forall r r'. (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) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

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

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

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

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

Read a => Read (Last a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Show a => Show (Last a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

show :: Last a -> String Source #

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

Generic (Last a) # 
Instance details

Defined in Data.Semigroup

Associated Types

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

Methods

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

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

Semigroup (Last a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 # 
Instance details

Defined in Data.Semigroup

Associated Types

type Rep1 Last :: k -> Type Source #

Methods

from1 :: forall (a :: k). Last a -> Rep1 Last a Source #

to1 :: forall (a :: k). Rep1 Last a -> Last a Source #

type Rep (Last a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep (Last a) = D1 ('MetaData "Last" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 Last #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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

newtype WrappedMonoid m Source #

Provide a Semigroup for an arbitrary Monoid.

NOTE: This is not needed anymore since Semigroup became a superclass of Monoid in base-4.11 and this newtype be deprecated at some point in the future.

Constructors

WrapMonoid 

Fields

Instances

Instances details
Bounded m => Bounded (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Enum a => Enum (WrappedMonoid a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Eq m => Eq (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Data m => Data (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 :: forall r r'. (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 m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) Source #

gmapMp :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) Source #

gmapMo :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) Source #

Ord m => Ord (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Read m => Read (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Show m => Show (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Generic (WrappedMonoid m) # 
Instance details

Defined in Data.Semigroup

Associated Types

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

Monoid m => Semigroup (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Monoid m => Monoid (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Generic1 WrappedMonoid # 
Instance details

Defined in Data.Semigroup

Associated Types

type Rep1 WrappedMonoid :: k -> Type Source #

Methods

from1 :: forall (a :: k). WrappedMonoid a -> Rep1 WrappedMonoid a Source #

to1 :: forall (a :: k). Rep1 WrappedMonoid a -> WrappedMonoid a Source #

type Rep (WrappedMonoid m) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep (WrappedMonoid m) = D1 ('MetaData "WrappedMonoid" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "WrapMonoid" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonoid") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 m)))
type Rep1 WrappedMonoid #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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

Re-exported monoids from Data.Monoid

newtype Dual a Source #

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

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

Constructors

Dual 

Fields

Instances

Instances details
Monad Dual #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Dual a Source #

Functor Dual #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

MonadFix Dual #

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

Applicative Dual #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Dual a Source #

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

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

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

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

Foldable Dual #

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

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

null :: Dual a -> Bool Source #

length :: Dual a -> Int Source #

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

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

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

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

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

Traversable Dual #

Since: base-4.8.0.0

Instance details

Defined in Data.Traversable

Methods

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

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

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

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

MonadZip Dual #

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Zip

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) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Eq a => Eq (Dual a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Data a => Data (Dual a) #

Since: base-4.8.0.0

Instance details

Defined in Data.Data

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 :: forall r r'. (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) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

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

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

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

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

Read a => Read (Dual a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show a => Show (Dual a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

show :: Dual a -> String Source #

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

Generic (Dual a) # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

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

Methods

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

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

Semigroup a => Semigroup (Dual a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Monoid a => Monoid (Dual a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Dual a Source #

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

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

Generic1 Dual # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Dual :: k -> Type Source #

Methods

from1 :: forall (a :: k). Dual a -> Rep1 Dual a Source #

to1 :: forall (a :: k). Rep1 Dual a -> Dual a Source #

type Rep (Dual a) #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep (Dual a) = D1 ('MetaData "Dual" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 Dual #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

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

newtype Endo a Source #

The monoid of endomorphisms under composition.

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

Constructors

Endo 

Fields

Instances

Instances details
Generic (Endo a) # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

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

Methods

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

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

Semigroup (Endo a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Monoid (Endo a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Endo a Source #

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

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

type Rep (Endo a) #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

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

newtype All Source #

Boolean monoid under conjunction (&&).

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

Constructors

All 

Fields

Instances

Instances details
Bounded All #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Eq All #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Data All #

Since: base-4.8.0.0

Instance details

Defined in Data.Data

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 :: forall r r'. (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 #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: All -> All -> Ordering Source #

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

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

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

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

max :: All -> All -> All Source #

min :: All -> All -> All Source #

Read All #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show All #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Generic All # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep All :: Type -> Type Source #

Methods

from :: All -> Rep All x Source #

to :: Rep All x -> All Source #

Semigroup All #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

sconcat :: NonEmpty All -> All Source #

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

Monoid All #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

type Rep All #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

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

newtype Any Source #

Boolean monoid under disjunction (||).

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

Constructors

Any 

Fields

Instances

Instances details
Bounded Any #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Eq Any #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Data Any #

Since: base-4.8.0.0

Instance details

Defined in Data.Data

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 :: forall r r'. (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 #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: Any -> Any -> Ordering Source #

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

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

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

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

max :: Any -> Any -> Any Source #

min :: Any -> Any -> Any Source #

Read Any #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show Any #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Generic Any # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep Any :: Type -> Type Source #

Methods

from :: Any -> Rep Any x Source #

to :: Rep Any x -> Any Source #

Semigroup Any #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

sconcat :: NonEmpty Any -> Any Source #

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

Monoid Any #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

type Rep Any #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

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

newtype Sum a Source #

Monoid under addition.

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

Constructors

Sum 

Fields

Instances

Instances details
Monad Sum #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Sum a Source #

Functor Sum #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

MonadFix Sum #

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

Applicative Sum #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Sum a Source #

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

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

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

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

Foldable Sum #

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

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

null :: Sum a -> Bool Source #

length :: Sum a -> Int Source #

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

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

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

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

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

Traversable Sum #

Since: base-4.8.0.0

Instance details

Defined in Data.Traversable

Methods

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

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

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

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

MonadZip Sum #

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Zip

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) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Eq a => Eq (Sum a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Data a => Data (Sum a) #

Since: base-4.8.0.0

Instance details

Defined in Data.Data

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 :: forall r r'. (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) #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

negate :: Sum a -> Sum a Source #

abs :: Sum a -> Sum a Source #

signum :: Sum a -> Sum a Source #

fromInteger :: Integer -> Sum a Source #

Ord a => Ord (Sum a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

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

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

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

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

Read a => Read (Sum a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show a => Show (Sum a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

show :: Sum a -> String Source #

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

Generic (Sum a) # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

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

Methods

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

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

Num a => Semigroup (Sum a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Num a => Monoid (Sum a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Sum a Source #

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

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

Generic1 Sum # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Sum :: k -> Type Source #

Methods

from1 :: forall (a :: k). Sum a -> Rep1 Sum a Source #

to1 :: forall (a :: k). Rep1 Sum a -> Sum a Source #

type Rep (Sum a) #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep (Sum a) = D1 ('MetaData "Sum" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 Sum #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

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

newtype Product a Source #

Monoid under multiplication.

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

Constructors

Product 

Fields

Instances

Instances details
Monad Product #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Product a Source #

Functor Product #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

MonadFix Product #

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

Applicative Product #

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Product a Source #

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

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

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

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

Foldable Product #

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

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

null :: Product a -> Bool Source #

length :: Product a -> Int Source #

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

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

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

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

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

Traversable Product #

Since: base-4.8.0.0

Instance details

Defined in Data.Traversable

Methods

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

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

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

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

MonadZip Product #

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Zip

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) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Eq a => Eq (Product a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Data a => Data (Product a) #

Since: base-4.8.0.0

Instance details

Defined in Data.Data

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 :: forall r r'. (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) #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

Ord a => Ord (Product a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Read a => Read (Product a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show a => Show (Product a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Generic (Product a) # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

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

Methods

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

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

Num a => Semigroup (Product a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Num a => Monoid (Product a) #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Generic1 Product # 
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Product :: k -> Type Source #

Methods

from1 :: forall (a :: k). Product a -> Rep1 Product a Source #

to1 :: forall (a :: k). Rep1 Product a -> Product a Source #

type Rep (Product a) #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

type Rep (Product a) = D1 ('MetaData "Product" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep1 Product #

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

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

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.

In GHC 8.4 and higher, the Monoid instance for Maybe has been corrected to lift a Semigroup instance instead of a Monoid instance. Consequently, this type is no longer useful. It will be marked deprecated in GHC 8.8 and removed in GHC 8.10.

Constructors

Option 

Fields

Instances

Instances details
Monad Option #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

return :: a -> Option a Source #

Functor Option #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

MonadFix Option #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

Applicative Option #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

pure :: a -> Option a Source #

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

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

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

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

Foldable Option #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

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

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

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

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

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

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

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

null :: Option a -> Bool Source #

length :: Option a -> Int Source #

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

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

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

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

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

Traversable Option #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

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

MonadPlus Option #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mzero :: Option a Source #

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

Alternative Option #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Data a => Data (Option a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 :: forall r r'. (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) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Show a => Show (Option a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Generic (Option a) # 
Instance details

Defined in Data.Semigroup

Associated Types

type Rep (Option a) :: Type -> Type Source #

Methods

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

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

Semigroup a => Semigroup (Option a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

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

Semigroup a => Monoid (Option a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Generic1 Option # 
Instance details

Defined in Data.Semigroup

Associated Types

type Rep1 Option :: k -> Type Source #

Methods

from1 :: forall (a :: k). Option a -> Rep1 Option a Source #

to1 :: forall (a :: k). Rep1 Option a -> Option a Source #

type Rep (Option a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep (Option a) = D1 ('MetaData "Option" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Option" 'PrefixI 'True) (S1 ('MetaSel ('Just "getOption") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Maybe a))))
type Rep1 Option #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep1 Option = D1 ('MetaData "Option" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Option" 'PrefixI 'True) (S1 ('MetaSel ('Just "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.

Example:

Expand
>>> let hello = diff "Hello, "
>>> appEndo hello "World!"
"Hello, World!"
>>> appEndo (hello <> mempty) "World!"
"Hello, World!"
>>> appEndo (mempty <> hello) "World!"
"Hello, World!"
>>> let world = diff "World"
>>> let excl = diff "!"
>>> appEndo (hello <> (world <> excl)) mempty
"Hello, World!"
>>> appEndo ((hello <> world) <> excl) mempty
"Hello, World!"

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.

>>> minimum [ Arg (x * x) x | x <- [-10 .. 10] ]
Arg 0 0

Constructors

Arg 

Fields

  • a

    The argument used for comparisons in Eq and Ord.

  • b

    The "value" exposed via the Functor, Foldable etc. instances.

Instances

Instances details
Bifunctor Arg #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d Source #

first :: (a -> b) -> Arg a c -> Arg b c Source #

second :: (b -> c) -> Arg a b -> Arg a c Source #

Bifoldable Arg #

Since: base-4.10.0.0

Instance details

Defined in Data.Semigroup

Methods

bifold :: Monoid m => Arg m m -> m Source #

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Arg a b -> m Source #

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Arg a b -> c Source #

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Arg a b -> c Source #

Bitraversable Arg #

Since: base-4.10.0.0

Instance details

Defined in Data.Semigroup

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d) Source #

Functor (Arg a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a0 -> b) -> Arg a a0 -> Arg a b Source #

(<$) :: a0 -> Arg a b -> Arg a a0 Source #

Foldable (Arg a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fold :: Monoid m => Arg a m -> m Source #

foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source #

foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source #

foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source #

foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source #

foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source #

foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source #

foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source #

foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source #

toList :: Arg a a0 -> [a0] Source #

null :: Arg a a0 -> Bool Source #

length :: Arg a a0 -> Int Source #

elem :: Eq a0 => a0 -> Arg a a0 -> Bool Source #

maximum :: Ord a0 => Arg a a0 -> a0 Source #

minimum :: Ord a0 => Arg a a0 -> a0 Source #

sum :: Num a0 => Arg a a0 -> a0 Source #

product :: Num a0 => Arg a a0 -> a0 Source #

Traversable (Arg a) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

traverse :: Applicative f => (a0 -> f b) -> Arg a a0 -> f (Arg a b) Source #

sequenceA :: Applicative f => Arg a (f a0) -> f (Arg a a0) Source #

mapM :: Monad m => (a0 -> m b) -> Arg a a0 -> m (Arg a b) Source #

sequence :: Monad m => Arg a (m a0) -> m (Arg a a0) Source #

Generic1 (Arg a :: Type -> Type) # 
Instance details

Defined in Data.Semigroup

Associated Types

type Rep1 (Arg a) :: k -> Type Source #

Methods

from1 :: forall (a0 :: k). Arg a a0 -> Rep1 (Arg a) a0 Source #

to1 :: forall (a0 :: k). Rep1 (Arg a) a0 -> Arg a a0 Source #

Eq a => Eq (Arg a b) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(==) :: Arg a b -> Arg a b -> Bool Source #

(/=) :: Arg a b -> Arg a b -> Bool Source #

(Data a, Data b) => Data (Arg a b) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Arg a b -> c (Arg a b) Source #

gunfold :: (forall b0 r. Data b0 => c (b0 -> 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 b0. Data b0 => b0 -> b0) -> Arg a b -> Arg a b Source #

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

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

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

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

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

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

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

Ord a => Ord (Arg a b) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 a, Read b) => Read (Arg a b) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

(Show a, Show b) => Show (Arg a b) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Arg a b -> ShowS Source #

show :: Arg a b -> String Source #

showList :: [Arg a b] -> ShowS Source #

Generic (Arg a b) # 
Instance details

Defined in Data.Semigroup

Associated Types

type Rep (Arg a b) :: Type -> Type Source #

Methods

from :: Arg a b -> Rep (Arg a b) x Source #

to :: Rep (Arg a b) x -> Arg a b Source #

type Rep1 (Arg a :: Type -> Type) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

type Rep (Arg a b) #

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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

>>> Min (Arg 0 ()) <> Min (Arg 1 ())
Min {getMin = Arg 0 ()}

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

>>> Max (Arg 0 ()) <> Max (Arg 1 ())
Max {getMax = Arg 1 ()}