| Safe Haskell | Safe-Inferred |
|---|
HLearn.Algebra.Structures
Contents
Description
These algebraic structures have sacrificed generality in favor of being easily used with the standard Haskell Prelude. The fact that monoids are not guaranteed to be semigroups makes this difficult.
- class Semigroup g => RegularSemigroup g where
- inverse :: g -> g
- class (RegularSemigroup g, Monoid g) => Group g
- data RegularSemigroup sg => RegSG2Group sg
- module Data.Semigroup
Type classes
class Semigroup g => RegularSemigroup g whereSource
Semigroups that also have an inverse. See https://en.wikipedia.org/wiki/Regular_semigroup
Instances
| (Semigroup (RegSG2Group sg), RegularSemigroup sg) => RegularSemigroup (RegSG2Group sg) |
class (RegularSemigroup g, Monoid g) => Group g Source
Regular semigroups that also have an identity; alternatively, monoids where every element has a unique inverse. See https://en.wikipedia.org/wiki/Group_(mathematics)
Instances
| (RegularSemigroup (RegSG2Group sg), Monoid (RegSG2Group sg), RegularSemigroup sg) => Group (RegSG2Group sg) |
Free Structures
data RegularSemigroup sg => RegSG2Group sg Source
Convert any regular semigroup into a group (and thus also a monoid) by adding a unique identity element
Instances
| (Eq sg, RegularSemigroup sg) => Eq (RegSG2Group sg) | |
| (Eq (RegSG2Group sg), Ord sg, RegularSemigroup sg) => Ord (RegSG2Group sg) | |
| (Read sg, RegularSemigroup sg) => Read (RegSG2Group sg) | |
| (Show sg, RegularSemigroup sg) => Show (RegSG2Group sg) | |
| RegularSemigroup sg => Monoid (RegSG2Group sg) | |
| RegularSemigroup sg => Semigroup (RegSG2Group sg) | |
| (RegularSemigroup (RegSG2Group sg), Monoid (RegSG2Group sg), RegularSemigroup sg) => Group (RegSG2Group sg) | |
| (Semigroup (RegSG2Group sg), RegularSemigroup sg) => RegularSemigroup (RegSG2Group sg) |
module Data.Semigroup