Module

Data.Group

Package: purescript-group
Repository: morganthomas/purescript-group

#Group Source

class (Monoid g) <= Group g  where

A Group is a Monoid with inverses. Instances must satisfy the following law in addition to the monoid laws:

Inverse: forall x. ginverse x <> x = mempty = x <> ginverse x

Members

ginverse :: g -> g

Instances

Group Unit
(Group g) => Group (Dual g)
(Ring r) => Group (Additive r)

#CommutativeSemigroup Source

class (Semigroup g) <= CommutativeSemigroup g

A CommutativeSemigroup is a Semigroup with a commutative operation. Instances must satisfy the following law in addition to the group laws:

Commutativity: forall x, y. x <> y = y <> x

Instances

CommutativeSemigroup Void
CommutativeSemigroup Unit
(CommutativeSemigroup g) => CommutativeSemigroup (Dual g)
(Ring r) => CommutativeSemigroup (Additive r)

#Abelian Source

type Abelian a b = Group a => CommutativeSemigroup a => b

Modules: Data.Group