abstract-algebra

Examples of monoids/semigroups in programming

It is well-known that monoids are stunningly ubiquitous in programing. They are so ubiquitous and so useful that I, as a 'hobby project', am working on a system that is completely based on their properties (distributed data aggregation). To make the system useful I need useful monoids :) I already know of these: Numeric or matrix sum ...

Is there any algebraic structures used in functional programming other then monoid?

I recently getting to know about functional programming (in Haskell and Scala). It's capabilities and elegance is quite charming. But when I met Monads, which makes use of an algebraic structure named Monoid, I was surprised and glad to see the theoretic knowledge I have been learning from Mathematics is made use of in programming. T...