(** Map of an id to a type *)
module IdentifierMap = Map.Make (Identifier)
(** Map type *)
type t = Type.t IdentifierMap.t
(* Empty substitution *)
let empty = IdentifierMap.empty
(** Create a substitution with one element *)
let singleton id ty = IdentifierMap.singleton id ty
(** Apply substitution to a type *)
let rec apply subst = function
| Type.Int -> Type.Int
| Type.Var id as t ->
(* Look for a substitution in the map *)
(match IdentifierMap.find_opt id subst with
| Some ty' -> apply subst ty'
| None -> t)
| Type.Product (ty1, ty2) -> Type.Product (apply subst ty1, apply subst ty2)
| Type.Arrow (ty1, ty2) -> Type.Arrow (apply subst ty1, apply subst ty2)
;;
(** Compose two substitutions *)
let compose s2 s1 =
IdentifierMap.merge
(fun _ ty1 ty2 ->
match ty1, ty2 with
(* If we have 2, we pick one of them *)
| Some ty1', Some _ -> Some (apply s2 ty1')
(* If we have 1, we pick the one we have *)
| Some ty1', None -> Some (apply s2 ty1')
| None, Some ty2' -> Some (apply s2 ty2')
(* If we have 0, we return nothing *)
| None, None -> None)
s1
s2
