checks a relation for transitive property

transitive.ml

//checks for existence of (b,c)
let rec exists_bc(b,r) =
	match r with
	[] -> false
	| (x,c)::tail -> (x == b) || exists_bc(b,tail);;

//constructs the list of relations that must exist for element a
let rec create_ac(a,b,r) =
	match r with
	[] -> []
	| (x,c)::tail -> if (x == b) 
			then (a,c)::create_ac(a,b,tail) 
			else create_ac(a,b,tail);;

//creates a list of lists 
let rec createList og_set r = 
	match r with 
	[] -> [] 
	| (a,b)::tail -> if exists_bc(b,og_set) 
			then create_ac(a,b,og_set)::createList og_set tail 
			else createList og_set tail;;

//check if relation exists in set
let rec exists(a,b,set) = 
	match set with 
	[] -> false
	|(x,y)::tail -> (a == x && b == y) || exists(a,b,tail);;

//check if relations are subset of set
let rec list_exists(list,set) = 
	match list with 
	[] -> true
	|(x,y)::tail -> exists(x,y,set) && list_exists(tail,set);;

//check if relations of all lists are subsets of set
let rec isTran og_set l = 
	match l with 
	[] -> true
	| list::tail -> list_exists(list,og_set) && isTran og_set tail;;