--- a/src/Pure/type_infer.ML Tue Apr 19 16:13:04 2011 +0200
+++ b/src/Pure/type_infer.ML Tue Apr 19 20:47:02 2011 +0200
@@ -1,7 +1,7 @@
(* Title: Pure/type_infer.ML
Author: Stefan Berghofer and Markus Wenzel, TU Muenchen
-Representation of type-inference problems. Simple type inference.
+Basic representation of type-inference problems.
*)
signature TYPE_INFER =
@@ -18,10 +18,6 @@
val deref: typ Vartab.table -> typ -> typ
val finish: Proof.context -> typ Vartab.table -> typ list * term list -> typ list * term list
val fixate: Proof.context -> term list -> term list
- val prepare: Proof.context -> (string -> typ option) -> (string * int -> typ option) ->
- term list -> int * term list
- val infer_types: Proof.context -> (string -> typ option) -> (indexname -> typ option) ->
- term list -> term list
end;
structure Type_Infer: TYPE_INFER =
@@ -70,96 +66,6 @@
-(** prepare types/terms: create inference parameters **)
-
-(* prepare_typ *)
-
-fun prepare_typ typ params_idx =
- let
- val (params', idx) = fold_atyps
- (fn TVar (xi, S) =>
- (fn ps_idx as (ps, idx) =>
- if is_param xi andalso not (Vartab.defined ps xi)
- then (Vartab.update (xi, mk_param idx S) ps, idx + 1) else ps_idx)
- | _ => I) typ params_idx;
-
- fun prepare (T as Type (a, Ts)) idx =
- if T = dummyT then (mk_param idx [], idx + 1)
- else
- let val (Ts', idx') = fold_map prepare Ts idx
- in (Type (a, Ts'), idx') end
- | prepare (T as TVar (xi, _)) idx =
- (case Vartab.lookup params' xi of
- NONE => T
- | SOME p => p, idx)
- | prepare (TFree ("'_dummy_", S)) idx = (mk_param idx S, idx + 1)
- | prepare (T as TFree _) idx = (T, idx);
-
- val (typ', idx') = prepare typ idx;
- in (typ', (params', idx')) end;
-
-
-(* prepare_term *)
-
-fun prepare_term ctxt const_type tm (vparams, params, idx) =
- let
- fun add_vparm xi (ps_idx as (ps, idx)) =
- if not (Vartab.defined ps xi) then
- (Vartab.update (xi, mk_param idx []) ps, idx + 1)
- else ps_idx;
-
- val (vparams', idx') = fold_aterms
- (fn Var (_, Type ("_polymorphic_", _)) => I
- | Var (xi, _) => add_vparm xi
- | Free (x, _) => add_vparm (x, ~1)
- | _ => I)
- tm (vparams, idx);
- fun var_param xi = the (Vartab.lookup vparams' xi);
-
- fun polyT_of T idx = apsnd snd (prepare_typ (paramify_vars T) (Vartab.empty, idx));
-
- fun constraint T t ps =
- if T = dummyT then (t, ps)
- else
- let val (T', ps') = prepare_typ T ps
- in (Type.constraint T' t, ps') end;
-
- fun prepare (Const ("_type_constraint_", T) $ t) ps_idx =
- let
- fun err () =
- error ("Malformed internal type constraint: " ^ Syntax.string_of_typ ctxt T);
- val A = (case T of Type ("fun", [A, B]) => if A = B then A else err () | _ => err ());
- val (A', ps_idx') = prepare_typ A ps_idx;
- val (t', ps_idx'') = prepare t ps_idx';
- in (Const ("_type_constraint_", A' --> A') $ t', ps_idx'') end
- | prepare (Const (c, T)) (ps, idx) =
- (case const_type c of
- SOME U =>
- let val (U', idx') = polyT_of U idx
- in constraint T (Const (c, U')) (ps, idx') end
- | NONE => error ("Undeclared constant: " ^ quote c))
- | prepare (Var (xi, Type ("_polymorphic_", [T]))) (ps, idx) =
- let val (T', idx') = polyT_of T idx
- in (Var (xi, T'), (ps, idx')) end
- | prepare (Var (xi, T)) ps_idx = constraint T (Var (xi, var_param xi)) ps_idx
- | prepare (Free (x, T)) ps_idx = constraint T (Free (x, var_param (x, ~1))) ps_idx
- | prepare (Bound i) ps_idx = (Bound i, ps_idx)
- | prepare (Abs (x, T, t)) ps_idx =
- let
- val (T', ps_idx') = prepare_typ T ps_idx;
- val (t', ps_idx'') = prepare t ps_idx';
- in (Abs (x, T', t'), ps_idx'') end
- | prepare (t $ u) ps_idx =
- let
- val (t', ps_idx') = prepare t ps_idx;
- val (u', ps_idx'') = prepare u ps_idx';
- in (t' $ u', ps_idx'') end;
-
- val (tm', (params', idx'')) = prepare tm (params, idx');
- in (tm', (vparams', params', idx'')) end;
-
-
-
(** results **)
(* dereferenced views *)
@@ -219,149 +125,4 @@
val (inst, _) = fold_rev subst_param (fold Term.add_tvars ts []) ([], used);
in (map o map_types) (Term_Subst.instantiateT inst) ts end;
-
-
-(** order-sorted unification of types **)
-
-exception NO_UNIFIER of string * typ Vartab.table;
-
-fun unify ctxt =
- let
- val thy = Proof_Context.theory_of ctxt;
- val arity_sorts = Type.arity_sorts (Context.pretty ctxt) (Sign.tsig_of thy);
-
-
- (* adjust sorts of parameters *)
-
- fun not_of_sort x S' S =
- "Variable " ^ x ^ "::" ^ Syntax.string_of_sort ctxt S' ^ " not of sort " ^
- Syntax.string_of_sort ctxt S;
-
- fun meet (_, []) tye_idx = tye_idx
- | meet (Type (a, Ts), S) (tye_idx as (tye, _)) =
- meets (Ts, arity_sorts a S handle ERROR msg => raise NO_UNIFIER (msg, tye)) tye_idx
- | meet (TFree (x, S'), S) (tye_idx as (tye, _)) =
- if Sign.subsort thy (S', S) then tye_idx
- else raise NO_UNIFIER (not_of_sort x S' S, tye)
- | meet (TVar (xi, S'), S) (tye_idx as (tye, idx)) =
- if Sign.subsort thy (S', S) then tye_idx
- else if is_param xi then
- (Vartab.update_new (xi, mk_param idx (Sign.inter_sort thy (S', S))) tye, idx + 1)
- else raise NO_UNIFIER (not_of_sort (Term.string_of_vname xi) S' S, tye)
- and meets (T :: Ts, S :: Ss) (tye_idx as (tye, _)) =
- meets (Ts, Ss) (meet (deref tye T, S) tye_idx)
- | meets _ tye_idx = tye_idx;
-
-
- (* occurs check and assignment *)
-
- fun occurs_check tye xi (TVar (xi', _)) =
- if xi = xi' then raise NO_UNIFIER ("Occurs check!", tye)
- else
- (case Vartab.lookup tye xi' of
- NONE => ()
- | SOME T => occurs_check tye xi T)
- | occurs_check tye xi (Type (_, Ts)) = List.app (occurs_check tye xi) Ts
- | occurs_check _ _ _ = ();
-
- fun assign xi (T as TVar (xi', _)) S env =
- if xi = xi' then env
- else env |> meet (T, S) |>> Vartab.update_new (xi, T)
- | assign xi T S (env as (tye, _)) =
- (occurs_check tye xi T; env |> meet (T, S) |>> Vartab.update_new (xi, T));
-
-
- (* unification *)
-
- fun show_tycon (a, Ts) =
- quote (Syntax.string_of_typ ctxt (Type (a, replicate (length Ts) dummyT)));
-
- fun unif (T1, T2) (env as (tye, _)) =
- (case pairself (`is_paramT o deref tye) (T1, T2) of
- ((true, TVar (xi, S)), (_, T)) => assign xi T S env
- | ((_, T), (true, TVar (xi, S))) => assign xi T S env
- | ((_, Type (a, Ts)), (_, Type (b, Us))) =>
- if a <> b then
- raise NO_UNIFIER
- ("Clash of types " ^ show_tycon (a, Ts) ^ " and " ^ show_tycon (b, Us), tye)
- else fold unif (Ts ~~ Us) env
- | ((_, T), (_, U)) => if T = U then env else raise NO_UNIFIER ("", tye));
-
- in unif end;
-
-
-
-(** simple type inference **)
-
-(* infer *)
-
-fun infer ctxt =
- let
- (* errors *)
-
- fun prep_output tye bs ts Ts =
- let
- val (Ts_bTs', ts') = finish ctxt tye (Ts @ map snd bs, ts);
- val (Ts', Ts'') = chop (length Ts) Ts_bTs';
- fun prep t =
- let val xs = rev (Term.variant_frees t (rev (map fst bs ~~ Ts'')))
- in Term.subst_bounds (map Syntax_Trans.mark_boundT xs, t) end;
- in (map prep ts', Ts') end;
-
- fun err_loose i = error ("Loose bound variable: B." ^ string_of_int i);
-
- fun unif_failed msg =
- "Type unification failed" ^ (if msg = "" then "" else ": " ^ msg) ^ "\n\n";
-
- fun err_appl msg tye bs t T u U =
- let val ([t', u'], [T', U']) = prep_output tye bs [t, u] [T, U]
- in error (unif_failed msg ^ Type.appl_error ctxt t' T' u' U' ^ "\n") end;
-
-
- (* main *)
-
- fun inf _ (Const (_, T)) tye_idx = (T, tye_idx)
- | inf _ (Free (_, T)) tye_idx = (T, tye_idx)
- | inf _ (Var (_, T)) tye_idx = (T, tye_idx)
- | inf bs (Bound i) tye_idx =
- (snd (nth bs i handle Subscript => err_loose i), tye_idx)
- | inf bs (Abs (x, T, t)) tye_idx =
- let val (U, tye_idx') = inf ((x, T) :: bs) t tye_idx
- in (T --> U, tye_idx') end
- | inf bs (t $ u) tye_idx =
- let
- val (T, tye_idx') = inf bs t tye_idx;
- val (U, (tye, idx)) = inf bs u tye_idx';
- val V = mk_param idx [];
- val tye_idx'' = unify ctxt (U --> V, T) (tye, idx + 1)
- handle NO_UNIFIER (msg, tye') => err_appl msg tye' bs t T u U;
- in (V, tye_idx'') end;
-
- in inf [] end;
-
-
-(* main interfaces *)
-
-fun prepare ctxt const_type var_type raw_ts =
- let
- val get_type = the_default dummyT o var_type;
- val constrain_vars = Term.map_aterms
- (fn Free (x, T) => Type.constraint T (Free (x, get_type (x, ~1)))
- | Var (xi, T) => Type.constraint T (Var (xi, get_type xi))
- | t => t);
-
- val ts = burrow_types (Syntax.check_typs ctxt) raw_ts;
- val idx = param_maxidx_of ts + 1;
- val (ts', (_, _, idx')) =
- fold_map (prepare_term ctxt const_type o constrain_vars) ts
- (Vartab.empty, Vartab.empty, idx);
- in (idx', ts') end;
-
-fun infer_types ctxt const_type var_type raw_ts =
- let
- val (idx, ts) = prepare ctxt const_type var_type raw_ts;
- val (tye, _) = fold (snd oo infer ctxt) ts (Vartab.empty, idx);
- val (_, ts') = finish ctxt tye ([], ts);
- in ts' end;
-
end;