An interface for a type with a binary, associative operator over it.
"A semigroup is an algebraic structure consisting of a set together with an associative binary operation" (wikipedia).
"The term 'semigroup' is standard, but semi-monoid would be more systematic." ncatlab
Modules that implement the semigroup interface are a structural subtype of the better known Monoids interface. Semigroups are differentiated from Monoids by the absence of a unit (or identity) element. in their specification.
module type Seed = sig ... endmodule type S = sig ... endA semigroup is a set of objects with an associative binary operation over it
module type S1 = sig ... endLaw notes the laws that should be obeyed by any instantiation of Semigroup in the form of predicates that should be true for any arguments of the appropriate type.
Functions and module functors for creating implementations of Semigroups
make op is an implementation of Semigroup generated from the operation op.
module Bool : sig ... endSemigroups over bool
module Int : sig ... endSemigroups over int
module Option : sig ... endSemigroups over option types
module Endo : sig ... endEndo is a semigroup where the operator is the composition of functions with input and output of the same type.
module Dual : sig ... endDual allows constructing the dual semigroup for a given semigroup. I.e., a semigroup with the arguments of it's operator reversed.