Semigroups in Kotlin

A Kotlin implementation of finite Semigroups in the Kotlin programming language.

The main abstraction is Semigroup<T>, which consists of a set of elements of type T and an associative map of the elements of the set.

Abstractions

The main abstract functions are:

• generation of a semigroup from a set of elements and a composition function,
• calculations of Green's relations on a semigroup,
• direct, semi-direct and bilateral semi-direct (or double, or Zappa) products of two semigroups.

Concrete Semigroups

There are utility functions for generating:

• left- and right-zero semigroups,
• the full transformation monoid on a set {1, ..., n},
• the monoid of order-preserving transformations on {1, ..., n},
• cyclig groups,
• symmetric groups.