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.

7 types

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

3 declarations

typetype CommutativeMonoid m = (Monoid m, Commutative m)

typetype ReductiveMonoid m = (Monoid m, Reductive m)

typetype CancellativeMonoid m = (Monoid m, Cancellative m)

Asymmetric monoid classes

4 declarations

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)