Data.Semigroup.Commutative

Documentation

class Semigroup g => Commutative g

An Commutative semigroup is a Semigroup that follows the rule:

a <> b == b <> a

Instances

Commutative ()

Trivial commutative semigroup.

Defined in Data.Semigroup.Commutative

Commutative IntSet

Since: 0.0.2.0

Defined in Data.Semigroup.Commutative

Commutative a => Commutative (Maybe a)

Since: 0.0.1.0

Defined in Data.Semigroup.Commutative

Commutative a => Commutative (Identity a)

Identity lifts commutative semigroups pointwise (at only one point).

Defined in Data.Semigroup.Commutative

Commutative a => Commutative (Dual a)

Defined in Data.Semigroup.Commutative

Num a => Commutative (Sum a)

Defined in Data.Semigroup.Commutative

CommutativeProduct a => Commutative (Product a)

Defined in Data.Semigroup.Commutative

Commutative a => Commutative (Down a)

Defined in Data.Semigroup.Commutative

Ord a => Commutative (Set a)

Since: 0.0.2.0

Defined in Data.Semigroup.Commutative

Commutative b => Commutative (a -> b)

Functions lift commutative semigroups pointwise.

Defined in Data.Semigroup.Commutative

(Commutative a, Commutative b) => Commutative (a, b)

Product commutative semigroup. A Pair of commutative semigroups gives rise to a commutative semigroup

Defined in Data.Semigroup.Commutative

Commutative a => Commutative (Op a b)

Defined in Data.Semigroup.Commutative

Commutative (Proxy x)

Trivial commutative semigroup, Functor style.

Defined in Data.Semigroup.Commutative

(Commutative a, Commutative b, Commutative c) => Commutative (a, b, c)

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Commutative a => Commutative (Const a x)

Const lifts commutative semigroups into a functor.

Defined in Data.Semigroup.Commutative

(Commutative (f a), Commutative (g a)) => Commutative ((f :*: g) a)

Product of commutative semigroups, Functor style.

Defined in Data.Semigroup.Commutative

(Commutative a, Commutative b, Commutative c, Commutative d) => Commutative (a, b, c, d)

Defined in Data.Semigroup.Commutative

Commutative (f (g a)) => Commutative ((f :.: g) a)

Defined in Data.Semigroup.Commutative

(Commutative a, Commutative b, Commutative c, Commutative d, Commutative e) => Commutative (a, b, c, d, e)

Defined in Data.Semigroup.Commutative