Data.Monoid.Cancellative

This module defines the Monoid => CommutativeMonoid => ReductiveMonoid => CancellativeMonoid constraint synonym hierarchy.

Since most practical monoids in Haskell are not commutative, the last two of these synonyms have two symmetric superclasses each:

• LeftReductiveMonoid
• LeftCancellativeMonoid
• RightReductiveMonoid
• RightCancellativeMonoid

This module and its constraint synonyms are provided for compatibility with the older versions of the monoid-sublasses library. Starting with version 1.0, the classes from the Data.Semigroup.Cancellative module are recommended instead.

Documentation

module Data.Semigroup.Cancellative

module Data.Monoid.GCD

Symmetric, commutative monoid classes

type CommutativeMonoid m = (Monoid m, Commutative m)

type ReductiveMonoid m = (Monoid m, Reductive m)

type CancellativeMonoid m = (Monoid m, Cancellative m)

Asymmetric monoid classes

type LeftReductiveMonoid m = (Monoid m, LeftReductive m)

type RightReductiveMonoid m = (Monoid m, RightReductive m)

type LeftCancellativeMonoid m = (Monoid m, LeftCancellative m)

type RightCancellativeMonoid m = (Monoid m, RightCancellative m)