Modulemonoid-subclasses-1.2.6.1Haskell2010

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.

Contents

Symmetric, commutative monoid classes
Asymmetric monoid classes

Synopsis

type CommutativeMonoid
type ReductiveMonoid
type CancellativeMonoid
type LeftReductiveMonoid
type RightReductiveMonoid
type LeftCancellativeMonoid
type RightCancellativeMonoid

Packagemonoid-subclasses-1.2.6.1
Exports7
LanguageHaskell2010
LicenceBSD-3-Clause
SourceCancellative.hs

module Data.Semigroup.Cancellative

module Data.Monoid.GCD

Symmetric, commutative monoid classes

typetype CommutativeMonoid m = (Monoid m, Commutative m)

typetype ReductiveMonoid m = (Monoid m, Reductive m)

typetype CancellativeMonoid m = (Monoid m, Cancellative m)

Asymmetric monoid classes

typetype LeftReductiveMonoid m = (Monoid m, LeftReductive m)

typetype RightReductiveMonoid m = (Monoid m, RightReductive m)

typetype LeftCancellativeMonoid m = (Monoid m, LeftCancellative m)

typetype RightCancellativeMonoid m = (Monoid m, RightCancellative m)