Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Monoid.Cancellative

Contents

Symmetric, commutative monoid classes
Asymmetric monoid classes

Description

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:

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.

Synopsis

module Data.Semigroup.Cancellative
module Data.Monoid.GCD
type CommutativeMonoid m = (Monoid m, Commutative m)
type ReductiveMonoid m = (Monoid m, Reductive m)
type CancellativeMonoid m = (Monoid m, Cancellative m)
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)

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) #