Commit 6ad4282d authored by POTTIER Francois's avatar POTTIER Francois

Detailed pre- and postconditions for the typechecker. Untested.

parent baf7df27
......@@ -88,8 +88,28 @@ let (--) ty1 ty2 =
(* The type-checker. *)
(* Precondition: the term [t] that we started with satisfies global uniqueness.
So, the term [t] that we are looking satisfies global uniqueness and avoids
the set of in-scope type variables, [env.tyvars]. *)
(* Precondition: if [env] maps [x] to some type [ty], then the bound variables
of [ty] are disjoint with [env.tyvars] and with the bound variables of [t],
and [ty] has no shadowing. *)
(* Postcondition: if [typeof env t] returns a type [ty], then the bound variables
of [ty] are disjoint with [env.tyvars], and [ty] has no shadowing. *)
let rec typeof env (t : nominal_term) : nominal_typ =
match t with
(* Test the preconditions stated above. *)
assert (guq_term t);
assert (avoids_term env.tyvars t);
assert (
let bad = Atom.Set.union env.tyvars (ba_term t) in
TermVarMap.for_all (fun _x ty ->
avoids_typ bad ty
) env.tevars
let ty = match t with
| TeVar x ->
lookup env x
| TeAbs (x, ty1, t) ->
......@@ -107,17 +127,26 @@ let rec typeof env (t : nominal_term) : nominal_typ =
| TeTyApp (t, ty2) ->
let a, ty1 = as_forall (typeof env t) in
(* We need ba(ty1) # [ty2/a] for this substitution to be safe. *)
(* We have ba(ty1) # a because the type a.ty1 is satisfies no-shadowing. *)
(* We have ba(ty1) # a because the type a.ty1 satisfies no-shadowing. *)
assert (not (Atom.Set.mem a (ba_typ ty1)));
(* We have ba(ty1) # fa(ty2) because fa(ty2) is a subset of dom(env), that is,
env.tyvars, and typeof has the postcondition ba(\result) # env.tyvars. *)
subst_TyVar_typ1 (fun ty -> ty) ty2 a ty1
env.tyvars, and the result of typeof avoids env.tyvars. *)
(* We must copy when grafting so as to ensure that the result of the
substitution enjoys no-shadowing. *)
subst_TyVar_typ1 copy_typ ty2 a ty1
(* Conversely, I believe that we could choose to copy [ty1] and not copy
[ty2] when grafting: *)
(* subst_TyVar_typ1 (fun ty2 -> ty2) ty2 a (copy_typ ty1) *)
| TePair (t1, t2) ->
TyProduct (typeof env t1, typeof env t2)
| TeProj (i, t) ->
assert (i = 1 || i = 2);
let ty1, ty2 = as_product (typeof env t) in
if i = 1 then ty1 else ty2
(* Test the postcondition stated above. *)
assert (avoids_typ env.tyvars ty);
let typeof =
typeof empty
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