Safe Haskell	None
Language	Haskell2010

Data.Commutative

Synopsis

Documentation

class Commutative a where Source

Methods

commute Source

Arguments

:: a
-> a
-> a	Abelian magma - `x commute y == y commute x`. Note that the commutative behaviour should be embedded in the instance. For distinguished commutes, more information is needed - like a predicate as is the case for `commuteVia` and `commuteViaM`.

Instances

Commutative () Source
Commutative All Source
Commutative Any Source
Num a => Commutative (Sum a) Source
Num a => Commutative (Product a) Source
Commutative (OneOf a) Source
Commutative (CommEndo a) Source

(<~>) :: Commutative a => a -> a -> a Source

class Commutative a => CommutativeId a where Source

Methods

cempty Source

Arguments

:: a	Identity element - `x commute cempty == cempty commute x == x`

Instances

CommutativeId () Source
CommutativeId All Source
CommutativeId Any Source
Num a => CommutativeId (Sum a) Source
Num a => CommutativeId (Product a) Source
CommutativeId (CommEndo a) Source

commuteVia :: Bool -> (a -> a -> a) -> a -> a -> a Source

flip when False - simple & pure "predicative" commute.

commuteViaF :: Functor f => f Bool -> (a -> a -> a) -> a -> a -> f a Source

Lifted predicative behaviour.

newtype CommEndo a Source

Endomorphisms commutative over composition. Warning: The Commutative instance uses unsafePerformIO to randomly pick the order.

Constructors

CommEndo
Fields appCommEndo :: a -> a

Instances

CommutativeId (CommEndo a) Source
Commutative (CommEndo a) Source

newtype OneOf a Source

In the case of two Just values, the commutative instance randomly chooses one of them. Warning: The Commutative instance uses unsafePerformIO to randomly pick the order.

Constructors

OneOf
Fields getOneOf :: Maybe a

Instances

Eq a => Eq (OneOf a) Source
Show a => Show (OneOf a) Source
Commutative (OneOf a) Source

pick1 :: a -> a -> a Source