Monoids
In mathematics, Monoids can be considered as categories with a single object. They capture the idea of function composition within a set. In fact, all functions from a set into itself naturally form a Monoid with respect to function composition.
In computer science, there are different types of Monoid, such as free, transition, syntactic, trace, and history. A set of strings built from a given set of characters is a free Monoid. The transition Monoid and syntactic Monoid are used to describe finite state machines, whereas trace Monoids and history Monoids provide a foundation for process calculi and concurrent computing.
Simply put, in computer science, a Monoid is a set, a binary operation, and an element of the set with the following rules:
- Associativity of binary operations
- The element is the identity
Simply put, a structure is a Monoid if the structure is a Semigroup with an element that is the identity. So let's define a new protocol that extends our Semigroupprotocol:
protocol Monoid...
