Monoid Functor

(*A monoid is an algebraic structure consisting of a set together with a single associative binary 
operation and an identity element. E.g., the set of booleans with the or operator is a monoid whose identity is false. *)


module type OPERATIONTYPE =
	sig
		type a and b 
		val op: a -> a -> a
		val identity : a
	end;;


(*functor that take a concrete module and verify if it is a Monoid*)
module Monoid (OP: OPERATIONTYPE)=
	struct
		let rec verifyidentity = function
			| [h]->OP.op h OP.identity =h
			| h::tl -> OP.op h (OP.identity)=h && verifyidentity tl
		
		let rec verifyassoc = function
			| [h]-> true
			| f::s::t::tl -> OP.op (OP.op f s) t = OP.op f (OP.op s t) && verifyassoc tl	
	end;;


(*examples of monoid*)
module SumInt = 
	struct
		type a=int and b=int list
		let op = fun x y -> x+y
		let identity = 0 
	end;;

module Orbool=
	struct
		type a=bool and b=bool list
		let op= fun x y -> x || y
		let identity = false
	end;;