Data.Semigroup

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

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

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 (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 ByteArray Source	Since: base-4.17.0.0
Instance details Defined in Data.Array.Byte Methods (<>) :: ByteArray -> ByteArray -> ByteArray Source sconcat :: NonEmpty ByteArray -> ByteArray Source stimes :: Integral b => b -> ByteArray -> ByteArray Source
Semigroup All Source	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 Any Source	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 Void Source	Since: base-4.9.0.0
Instance details Defined in Data.Void Methods (<>) :: Void -> Void -> Void Source sconcat :: NonEmpty Void -> Void Source stimes :: Integral b => b -> Void -> Void Source
Semigroup Event Source	Since: base-4.10.0.0
Instance details Defined in GHC.Event.Internal.Types Methods (<>) :: Event -> Event -> Event Source sconcat :: NonEmpty Event -> Event Source stimes :: Integral b => b -> Event -> Event Source
Semigroup Lifetime Source	Since: base-4.10.0.0
Instance details Defined in GHC.Event.Internal.Types Methods (<>) :: Lifetime -> Lifetime -> Lifetime Source sconcat :: NonEmpty Lifetime -> Lifetime Source stimes :: Integral b => b -> Lifetime -> Lifetime Source
Semigroup Ordering Source	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Ordering -> Ordering -> Ordering Source sconcat :: NonEmpty Ordering -> Ordering Source stimes :: Integral b => b -> Ordering -> Ordering Source
Semigroup () Source	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: () -> () -> () Source sconcat :: NonEmpty () -> () Source stimes :: Integral b => b -> () -> () Source
Bits a => Semigroup (And a) Source	Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: And a -> And a -> And a Source sconcat :: NonEmpty (And a) -> And a Source stimes :: Integral b => b -> And a -> And a Source
FiniteBits a => Semigroup (Iff a) Source	This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: Iff a -> Iff a -> Iff a Source sconcat :: NonEmpty (Iff a) -> Iff a Source stimes :: Integral b => b -> Iff a -> Iff a Source
Bits a => Semigroup (Ior a) Source	Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: Ior a -> Ior a -> Ior a Source sconcat :: NonEmpty (Ior a) -> Ior a Source stimes :: Integral b => b -> Ior a -> Ior a Source
Bits a => Semigroup (Xor a) Source	Since: base-4.16
Instance details Defined in Data.Bits Methods (<>) :: Xor a -> Xor a -> Xor a Source sconcat :: NonEmpty (Xor a) -> Xor a Source stimes :: Integral b => b -> Xor a -> Xor a Source
Semigroup (Comparison a) Source	`(<>)` 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 Methods (<>) :: Comparison a -> Comparison a -> Comparison a Source sconcat :: NonEmpty (Comparison a) -> Comparison a Source stimes :: Integral b => b -> Comparison a -> Comparison a Source
Semigroup (Equivalence a) Source	`(<>)` 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 Methods (<>) :: Equivalence a -> Equivalence a -> Equivalence a Source sconcat :: NonEmpty (Equivalence a) -> Equivalence a Source stimes :: Integral b => b -> Equivalence a -> Equivalence a Source
Semigroup (Predicate a) Source	`(<>)` 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 Methods (<>) :: Predicate a -> Predicate a -> Predicate a Source sconcat :: NonEmpty (Predicate a) -> Predicate a Source stimes :: Integral b => b -> Predicate a -> Predicate a Source
Semigroup a => Semigroup (Identity a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity 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 (First a) Source	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 (Last a) Source	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 a => Semigroup (Down a) Source	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
Semigroup (First a) Source	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
Semigroup (Last a) Source	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
Ord a => Semigroup (Max a) Source	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) Source	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
Monoid m => Semigroup (WrappedMonoid m) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup 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 a => Semigroup (Dual a) Source	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 (Endo a) Source	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
Num a => Semigroup (Product a) Source	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) Source	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 a => Semigroup (STM a) Source	Since: base-4.17.0.0
Instance details Defined in GHC.Conc.Sync Methods (<>) :: STM a -> STM a -> STM a Source sconcat :: NonEmpty (STM a) -> STM a Source stimes :: Integral b => b -> STM a -> STM a Source
(Generic a, Semigroup (Rep a ())) => Semigroup (Generically a) Source	Since: base-4.17.0.0
Instance details Defined in GHC.Generics Methods (<>) :: Generically a -> Generically a -> Generically a Source sconcat :: NonEmpty (Generically a) -> Generically a Source stimes :: Integral b => b -> Generically a -> Generically a Source
Semigroup p => Semigroup (Par1 p) Source	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 a => Semigroup (IO a) Source	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 (NonEmpty a) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Base 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 (Maybe a) Source	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 (a) Source	Since: base-4.15
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] Source	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 (Either a b) Source	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 a => Semigroup (Op a b) Source	`(<>) @(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 (Proxy s) Source	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 (U1 p) Source	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 (V1 p) Source	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 a => Semigroup (ST s a) Source	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 b => Semigroup (a -> b) Source	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 b) => Semigroup (a, b) Source	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 (Const a b) Source	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
(Applicative f, Semigroup a) => Semigroup (Ap f a) Source	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
Alternative f => Semigroup (Alt f a) Source	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
Semigroup (f p) => Semigroup (Rec1 f p) Source	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) Source	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
(Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a) Source	Since: base-4.16.0.0
Instance details Defined in Data.Functor.Product Methods (<>) :: Product f g a -> Product f g a -> Product f g a Source sconcat :: NonEmpty (Product f g a) -> Product f g a Source stimes :: Integral b => b -> Product f g a -> Product f g a Source
(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) Source	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 c => Semigroup (K1 i c p) Source	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 a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) Source	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 (g a)) => Semigroup (Compose f g a) Source	Since: base-4.16.0.0
Instance details Defined in Data.Functor.Compose Methods (<>) :: Compose f g a -> Compose f g a -> Compose f g a Source sconcat :: NonEmpty (Compose f g a) -> Compose f g a Source stimes :: Integral b => b -> Compose f g a -> Compose f g a Source
Semigroup (f (g p)) => Semigroup ((f :.: g) p) Source	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 (f p) => Semigroup (M1 i c f p) Source	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 a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) Source	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

In many cases, `stimes 0 a` for a Monoid will produce mempty. However, there are situations when it cannot do so. In particular, the following situation is fairly common:

data T a = ...

class Constraint1 a
class Constraint1 a => Constraint2 a

instance Constraint1 a => Semigroup (T a) instance Constraint2 a => Monoid (T a) @

Since Constraint1 is insufficient to implement mempty, stimes for T a cannot do so.

When working with such a type, or when working polymorphically with Semigroup instances, mtimesDefault should be used when the multiplier might be zero. It is implemented using stimes when the multiplier is nonzero and mempty when it is zero.

Semigroups

newtype Min a Source

Constructors

Min
Fields getMin :: a

Instances

Instances details

MonadFix Min Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mfix :: (a -> Min a) -> Min a Source
Foldable Min Source	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 Source	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
Applicative Min Source	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
Functor Min Source	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
Monad Min Source	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
Generic1 Min Source
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
Data a => Data (Min a) Source	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
(Ord a, Bounded a) => Monoid (Min a) Source	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
Ord a => Semigroup (Min a) Source	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
Bounded a => Bounded (Min a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: Min a Source maxBound :: Min a Source
Enum a => Enum (Min a) Source	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
Generic (Min a) Source
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
Num a => Num (Min a) Source	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
Read a => Read (Min a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup 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	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
Eq a => Eq (Min a) Source	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
Ord a => Ord (Min a) Source	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
type Rep1 Min Source	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))
type Rep (Min a) Source	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)))

newtype Max a Source

Constructors

Max
Fields getMax :: a

Instances

Instances details

MonadFix Max Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mfix :: (a -> Max a) -> Max a Source
Foldable Max Source	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 Source	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
Applicative Max Source	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
Functor Max Source	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
Monad Max Source	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
Generic1 Max Source
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
Data a => Data (Max a) Source	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
(Ord a, Bounded a) => Monoid (Max a) Source	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
Ord a => Semigroup (Max a) Source	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
Bounded a => Bounded (Max a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: Max a Source maxBound :: Max a Source
Enum a => Enum (Max a) Source	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
Generic (Max a) Source
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
Num a => Num (Max a) Source	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
Read a => Read (Max a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup 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	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
Eq a => Eq (Max a) Source	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
Ord a => Ord (Max a) Source	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
type Rep1 Max Source	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))
type Rep (Max a) Source	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)))

newtype First a Source

Constructors

First
Fields getFirst :: a

Instances

Instances details

MonadFix First Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mfix :: (a -> First a) -> First a Source
Foldable First Source	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 Source	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
Applicative First Source	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
Functor First Source	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
Monad First Source	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
Generic1 First Source
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
Data a => Data (First a) Source	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
Semigroup (First a) Source	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
Bounded a => Bounded (First a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: First a Source maxBound :: First a Source
Enum a => Enum (First a) Source	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
Generic (First a) Source
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
Read a => Read (First a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup 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	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> First a -> ShowS Source show :: First a -> String Source showList :: [First a] -> ShowS Source
Eq a => Eq (First a) Source	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
Ord a => Ord (First a) Source	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
type Rep1 First Source	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))
type Rep (First a) Source	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)))

newtype Last a Source

Constructors

Last
Fields getLast :: a

Instances

Instances details

MonadFix Last Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mfix :: (a -> Last a) -> Last a Source
Foldable Last Source	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 Source	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
Applicative Last Source	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
Functor Last Source	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
Monad Last Source	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
Generic1 Last Source
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
Data a => Data (Last a) Source	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
Semigroup (Last a) Source	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
Bounded a => Bounded (Last a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: Last a Source maxBound :: Last a Source
Enum a => Enum (Last a) Source	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
Generic (Last a) Source
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
Read a => Read (Last a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup 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	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
Eq a => Eq (Last a) Source	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
Ord a => Ord (Last a) Source	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
type Rep1 Last Source	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))
type Rep (Last a) Source	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)))

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 unwrapMonoid :: m

Instances

Instances details

Generic1 WrappedMonoid Source
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
Data m => Data (WrappedMonoid m) Source	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
Monoid m => Monoid (WrappedMonoid m) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: WrappedMonoid m Source mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source
Monoid m => Semigroup (WrappedMonoid m) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m Source stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m Source
Bounded m => Bounded (WrappedMonoid m) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods minBound :: WrappedMonoid m Source maxBound :: WrappedMonoid m Source
Enum a => Enum (WrappedMonoid a) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup 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
Generic (WrappedMonoid m) Source
Instance details Defined in Data.Semigroup Associated Types type Rep (WrappedMonoid m) :: Type -> Type Source Methods from :: WrappedMonoid m -> Rep (WrappedMonoid m) x Source to :: Rep (WrappedMonoid m) x -> WrappedMonoid m Source
Read m => Read (WrappedMonoid m) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup 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	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods showsPrec :: Int -> WrappedMonoid m -> ShowS Source show :: WrappedMonoid m -> String Source showList :: [WrappedMonoid m] -> ShowS Source
Eq m => Eq (WrappedMonoid m) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods (==) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source (/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source
Ord m => Ord (WrappedMonoid m) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods compare :: WrappedMonoid m -> WrappedMonoid m -> Ordering Source (<) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source (<=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source (>) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source (>=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source max :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source min :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source
type Rep1 WrappedMonoid Source	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))
type Rep (WrappedMonoid m) Source	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)))

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 getDual :: a

Instances

Instances details

MonadFix Dual Source	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Dual a) -> Dual a Source
MonadZip Dual Source	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
Foldable Dual Source	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 Source	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
Applicative Dual Source	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
Functor Dual Source	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
Monad Dual Source	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
Generic1 Dual Source
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
Data a => Data (Dual a) Source	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
Monoid a => Monoid (Dual a) Source	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
Semigroup a => Semigroup (Dual a) Source	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
Bounded a => Bounded (Dual a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Dual a Source maxBound :: Dual a Source
Generic (Dual a) Source
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
Read a => Read (Dual a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal 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	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
Eq a => Eq (Dual a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Dual a -> Dual a -> Bool Source (/=) :: Dual a -> Dual a -> Bool Source
Ord a => Ord (Dual a) Source	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
type Rep1 Dual Source	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))
type Rep (Dual a) Source	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)))

newtype Endo a Source

The monoid of endomorphisms under composition.

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

Constructors

Endo
Fields appEndo :: a -> a

Instances

Instances details

Monoid (Endo a) Source	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
Semigroup (Endo a) Source	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
Generic (Endo a) Source
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
type Rep (Endo a) Source	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 getAll :: Bool

Instances

Instances details

Data All Source	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
Monoid All Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All Source mappend :: All -> All -> All Source mconcat :: [All] -> All Source
Semigroup All Source	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
Bounded All Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: All Source maxBound :: All Source
Generic All Source
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
Read All Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS All Source readList :: ReadS [All] Source readPrec :: ReadPrec All Source readListPrec :: ReadPrec [All] Source
Show All Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> All -> ShowS Source show :: All -> String Source showList :: [All] -> ShowS Source
Eq All Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: All -> All -> Bool Source (/=) :: All -> All -> Bool Source
Ord All Source	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
type Rep All Source	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 getAny :: Bool

Instances

Instances details

Data Any Source	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
Monoid Any Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any Source mappend :: Any -> Any -> Any Source mconcat :: [Any] -> Any Source
Semigroup Any Source	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
Bounded Any Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Any Source maxBound :: Any Source
Generic Any Source
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
Read Any Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS Any Source readList :: ReadS [Any] Source readPrec :: ReadPrec Any Source readListPrec :: ReadPrec [Any] Source
Show Any Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Any -> ShowS Source show :: Any -> String Source showList :: [Any] -> ShowS Source
Eq Any Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Any -> Any -> Bool Source (/=) :: Any -> Any -> Bool Source
Ord Any Source	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
type Rep Any Source	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 getSum :: a

Instances

Instances details

MonadFix Sum Source	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Sum a) -> Sum a Source
MonadZip Sum Source	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
Foldable Sum Source	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 Source	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
Applicative Sum Source	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
Functor Sum Source	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
Monad Sum Source	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
Generic1 Sum Source
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
Data a => Data (Sum a) Source	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 => Monoid (Sum a) Source	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
Num a => Semigroup (Sum a) Source	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
Bounded a => Bounded (Sum a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Sum a Source maxBound :: Sum a Source
Generic (Sum a) Source
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 => Num (Sum a) Source	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
Read a => Read (Sum a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal 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	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
Eq a => Eq (Sum a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Sum a -> Sum a -> Bool Source (/=) :: Sum a -> Sum a -> Bool Source
Ord a => Ord (Sum a) Source	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
type Rep1 Sum Source	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))
type Rep (Sum a) Source	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)))

newtype Product a Source

Monoid under multiplication.

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

Constructors

Product
Fields getProduct :: a

Instances

Instances details

MonadFix Product Source	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Product a) -> Product a Source
MonadZip Product Source	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
Foldable Product Source	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 Source	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
Applicative Product Source	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
Functor Product Source	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
Monad Product Source	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
Generic1 Product Source
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
Data a => Data (Product a) Source	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 => Monoid (Product a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a Source mappend :: Product a -> Product a -> Product a Source mconcat :: [Product a] -> Product a Source
Num a => Semigroup (Product a) Source	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
Bounded a => Bounded (Product a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Product a Source maxBound :: Product a Source
Generic (Product a) Source
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 => Num (Product a) Source	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal 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
Read a => Read (Product a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal 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	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Product a -> ShowS Source show :: Product a -> String Source showList :: [Product a] -> ShowS Source
Eq a => Eq (Product a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Product a -> Product a -> Bool Source (/=) :: Product a -> Product a -> Bool Source
Ord a => Ord (Product a) Source	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Product a -> Product a -> Ordering Source (<) :: Product a -> Product a -> Bool Source (<=) :: Product a -> Product a -> Bool Source (>) :: Product a -> Product a -> Bool Source (>=) :: Product a -> Product a -> Bool Source max :: Product a -> Product a -> Product a Source min :: Product a -> Product a -> Product a Source
type Rep1 Product Source	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))
type Rep (Product a) Source	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)))

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

Bifoldable Arg Source	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
Bifunctor Arg Source	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
Bitraversable Arg Source	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
Generic1 (Arg a :: Type -> Type) Source
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
Foldable (Arg a) Source	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) Source	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
Functor (Arg a) Source	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
(Data a, Data b) => Data (Arg a b) Source	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
Generic (Arg a b) Source
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
(Read a, Read b) => Read (Arg a b) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup 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 a, Show b) => Show (Arg a b) Source	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
Eq a => Eq (Arg a b) Source	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
Ord a => Ord (Arg a b) Source	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
type Rep1 (Arg a :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep1 (Arg a :: Type -> Type) = D1 ('MetaData "Arg" "Data.Semigroup" "base" 'False) (C1 ('MetaCons "Arg" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
type Rep (Arg a b) Source	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup type Rep (Arg a b) = D1 ('MetaData "Arg" "Data.Semigroup" "base" 'False) (C1 ('MetaCons "Arg" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 b)))

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 ()}

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/9.4.2/docs/libraries/base-4.17.0.0/Data-Semigroup.html

Data.Semigroup

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