src/Pure/type_infer.ML

 
 
 
 (** pretyps and preterms **)
 
-(*links to parameters may get instantiated, anything else is rigid*)
+(*parameters may get instantiated, anything else is rigid*)
 datatype pretyp =
   PType of string * pretyp list |
   PTFree of string * sort |
   PTVar of indexname * sort |
-  Param of sort |
-  Link of pretyp ref;
+  Param of int * sort;
 
 datatype preterm =
   PConst of string * pretyp |
   PFree of string * pretyp |
   PVar of indexname * pretyp |

   Constraint of preterm * pretyp;
 
 
 (* utils *)
 
-val mk_param = Link o ref o Param;
-
-fun deref (T as Link (ref (Param _))) = T
-  | deref (Link (ref T)) = deref T
-  | deref T = T;
+fun deref tye (T as Param (i, S)) = (case Inttab.lookup tye i of
+      NONE => T
+    | SOME U => deref tye U)
+  | deref tye T = T;
 
 fun fold_pretyps f (PConst (_, T)) x = f T x
   | fold_pretyps f (PFree (_, T)) x = f T x
   | fold_pretyps f (PVar (_, T)) x = f T x
   | fold_pretyps _ (PBound _) x = x

 
 (** raw typs/terms to pretyps/preterms **)
 
 (* pretyp_of *)
 
-fun pretyp_of is_para typ params =
-  let
-    val params' = fold_atyps
+fun pretyp_of is_para typ params_idx =
+  let
+    val (params', idx) = fold_atyps
       (fn TVar (xi as (x, _), S) =>
-          (fn ps =>
+          (fn ps_idx as (ps, idx) =>
             if is_para xi andalso not (Vartab.defined ps xi)
-            then Vartab.update (xi, mk_param S) ps else ps)
-        | _ => I) typ params;
-
-    fun pre_of (TVar (v as (xi, _))) =
+            then (Vartab.update (xi, Param (idx, S)) ps, idx + 1) else ps_idx)
+        | _ => I) typ params_idx;
+
+    fun pre_of (TVar (v as (xi, _))) idx =
           (case Vartab.lookup params' xi of
             NONE => PTVar v
-          | SOME p => p)
-      | pre_of (TFree ("'_dummy_", S)) = mk_param S
-      | pre_of (TFree v) = PTFree v
-      | pre_of (T as Type (a, Ts)) =
-          if T = dummyT then mk_param []
-          else PType (a, map pre_of Ts);
-  in (pre_of typ, params') end;
+          | SOME p => p, idx)
+      | pre_of (TFree ("'_dummy_", S)) idx = (Param (idx, S), idx + 1)
+      | pre_of (TFree v) idx = (PTFree v, idx)
+      | pre_of (T as Type (a, Ts)) idx =
+          if T = dummyT then (Param (idx, []), idx + 1)
+          else
+            let val (Ts', idx') = fold_map pre_of Ts idx
+            in (PType (a, Ts'), idx') end;
+
+    val (ptyp, idx') = pre_of typ idx;
+  in (ptyp, (params', idx')) end;
 
 
 (* preterm_of *)
 
-fun preterm_of const_type is_para tm (vparams, params) =
-  let
-    fun add_vparm xi ps =
+fun preterm_of const_type is_para 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 []) ps
-      else ps;
-
-    val vparams' = fold_aterms
+        (Vartab.update (xi, 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;
+      tm (vparams, idx);
     fun var_param xi = the (Vartab.lookup vparams' xi);
 
     val preT_of = pretyp_of is_para;
-    fun polyT_of T = fst (pretyp_of (K true) T Vartab.empty);
+    fun polyT_of T idx = apsnd snd (pretyp_of (K true) T (Vartab.empty, idx));
 
     fun constraint T t ps =
       if T = dummyT then (t, ps)
       else
         let val (T', ps') = preT_of T ps
         in (Constraint (t, T'), ps') end;
 
-    fun pre_of (Const (c, T)) ps =
+    fun pre_of (Const (c, T)) (ps, idx) =
           (case const_type c of
-            SOME U => constraint T (PConst (c, polyT_of U)) ps
+            SOME U =>
+              let val (pU, idx') = polyT_of U idx
+              in constraint T (PConst (c, pU)) (ps, idx') end
           | NONE => raise TYPE ("No such constant: " ^ quote c, [], []))
-      | pre_of (Var (xi, Type ("_polymorphic_", [T]))) ps = (PVar (xi, polyT_of T), ps)
-      | pre_of (Var (xi, T)) ps = constraint T (PVar (xi, var_param xi)) ps
-      | pre_of (Free (x, T)) ps = constraint T (PFree (x, var_param (x, ~1))) ps
-      | pre_of (Const ("_type_constraint_", Type ("fun", [T, _])) $ t) ps =
-          pre_of t ps |-> constraint T
-      | pre_of (Bound i) ps = (PBound i, ps)
-      | pre_of (Abs (x, T, t)) ps =
+      | pre_of (Var (xi, Type ("_polymorphic_", [T]))) (ps, idx) =
+          let val (pT, idx') = polyT_of T idx
+          in (PVar (xi, pT), (ps, idx')) end
+      | pre_of (Var (xi, T)) ps_idx = constraint T (PVar (xi, var_param xi)) ps_idx
+      | pre_of (Free (x, T)) ps_idx = constraint T (PFree (x, var_param (x, ~1))) ps_idx
+      | pre_of (Const ("_type_constraint_", Type ("fun", [T, _])) $ t) ps_idx =
+          pre_of t ps_idx |-> constraint T
+      | pre_of (Bound i) ps_idx = (PBound i, ps_idx)
+      | pre_of (Abs (x, T, t)) ps_idx =
           let
-            val (T', ps') = preT_of T ps;
-            val (t', ps'') = pre_of t ps';
-          in (PAbs (x, T', t'), ps'') end
-      | pre_of (t $ u) ps =
+            val (T', ps_idx') = preT_of T ps_idx;
+            val (t', ps_idx'') = pre_of t ps_idx';
+          in (PAbs (x, T', t'), ps_idx'') end
+      | pre_of (t $ u) ps_idx =
           let
-            val (t', ps') = pre_of t ps;
-            val (u', ps'') = pre_of u ps';
-          in (PAppl (t', u'), ps'') end;
-
-    val (tm', params') = pre_of tm params;
-  in (tm', (vparams', params')) end;
+            val (t', ps_idx') = pre_of t ps_idx;
+            val (u', ps_idx'') = pre_of u ps_idx';
+          in (PAppl (t', u'), ps_idx'') end;
+
+    val (tm', (params', idx'')) = pre_of tm (params, idx');
+  in (tm', (vparams', params', idx'')) end;
 
 
 
 (** pretyps/terms to typs/terms **)
 
 (* add_parms *)
 
-fun add_parmsT (PType (_, Ts)) rs = fold add_parmsT Ts rs
-  | add_parmsT (Link (r as ref (Param _))) rs = insert (op =) r rs
-  | add_parmsT (Link (ref T)) rs = add_parmsT T rs
-  | add_parmsT _ rs = rs;
-
-val add_parms = fold_pretyps add_parmsT;
+fun add_parmsT tye T = case deref tye T of
+    PType (_, Ts) => fold (add_parmsT tye) Ts
+  | Param (i, _) => insert (op =) i
+  | _ => I;
+
+fun add_parms tye = fold_pretyps (add_parmsT tye);
 
 
 (* add_names *)
 
-fun add_namesT (PType (_, Ts)) = fold add_namesT Ts
-  | add_namesT (PTFree (x, _)) = Name.declare x
-  | add_namesT (PTVar ((x, _), _)) = Name.declare x
-  | add_namesT (Link (ref T)) = add_namesT T
-  | add_namesT (Param _) = I;
-
-val add_names = fold_pretyps add_namesT;
+fun add_namesT tye T = case deref tye T of
+    PType (_, Ts) => fold (add_namesT tye) Ts
+  | PTFree (x, _) => Name.declare x
+  | PTVar ((x, _), _) => Name.declare x
+  | Param _ => I;
+
+fun add_names tye = fold_pretyps (add_namesT tye);
 
 
 (* simple_typ/term_of *)
 
-(*deref links, fail on params*)
-fun simple_typ_of (PType (a, Ts)) = Type (a, map simple_typ_of Ts)
-  | simple_typ_of (PTFree v) = TFree v
-  | simple_typ_of (PTVar v) = TVar v
-  | simple_typ_of (Link (ref T)) = simple_typ_of T
-  | simple_typ_of (Param _) = sys_error "simple_typ_of: illegal Param";
+fun simple_typ_of tye f T = case deref tye T of
+    PType (a, Ts) => Type (a, map (simple_typ_of tye f) Ts)
+  | PTFree v => TFree v
+  | PTVar v => TVar v
+  | Param (i, S) => TVar (f i, S);
 
 (*convert types, drop constraints*)
-fun simple_term_of (PConst (c, T)) = Const (c, simple_typ_of T)
-  | simple_term_of (PFree (x, T)) = Free (x, simple_typ_of T)
-  | simple_term_of (PVar (xi, T)) = Var (xi, simple_typ_of T)
-  | simple_term_of (PBound i) = Bound i
-  | simple_term_of (PAbs (x, T, t)) = Abs (x, simple_typ_of T, simple_term_of t)
-  | simple_term_of (PAppl (t, u)) = simple_term_of t $ simple_term_of u
-  | simple_term_of (Constraint (t, _)) = simple_term_of t;
-
-
-(* typs_terms_of *)                             (*DESTRUCTIVE*)
-
-fun typs_terms_of used maxidx (Ts, ts) =
-  let
-    fun elim (r as ref (Param S), x) = r := PTVar ((x, maxidx + 1), S)
-      | elim _ = ();
-
-    val used' = fold add_names ts (fold add_namesT Ts used);
-    val parms = rev (fold add_parms ts (fold add_parmsT Ts []));
+fun simple_term_of tye f (PConst (c, T)) = Const (c, simple_typ_of tye f T)
+  | simple_term_of tye f (PFree (x, T)) = Free (x, simple_typ_of tye f T)
+  | simple_term_of tye f (PVar (xi, T)) = Var (xi, simple_typ_of tye f T)
+  | simple_term_of tye f (PBound i) = Bound i
+  | simple_term_of tye f (PAbs (x, T, t)) =
+      Abs (x, simple_typ_of tye f T, simple_term_of tye f t)
+  | simple_term_of tye f (PAppl (t, u)) =
+      simple_term_of tye f t $ simple_term_of tye f u
+  | simple_term_of tye f (Constraint (t, _)) = simple_term_of tye f t;
+
+
+(* typs_terms_of *)
+
+fun typs_terms_of tye used maxidx (Ts, ts) =
+  let
+    val used' = fold (add_names tye) ts (fold (add_namesT tye) Ts used);
+    val parms = rev (fold (add_parms tye) ts (fold (add_parmsT tye) Ts []));
     val names = Name.invents used' ("?" ^ Name.aT) (length parms);
-    val _ = ListPair.app elim (parms, names);
-  in (map simple_typ_of Ts, map simple_term_of ts) end;
-
-
-
-(** order-sorted unification of types **)       (*DESTRUCTIVE*)
-
-exception NO_UNIFIER of string;
+    val tab = Inttab.make (parms ~~ names);
+    fun f i = (the (Inttab.lookup tab i), maxidx + 1);
+  in (map (simple_typ_of tye f) Ts, map (simple_term_of tye f) ts) end;
+
+
+
+(** order-sorted unification of types **)
+
+exception NO_UNIFIER of string * pretyp Inttab.table;
 
 fun unify pp tsig =
   let
 
     (* adjust sorts of parameters *)
 
     fun not_of_sort x S' S =
       "Variable " ^ x ^ "::" ^ Pretty.string_of_sort pp S' ^ " not of sort " ^
         Pretty.string_of_sort pp S;
 
-    fun meet (_, []) = ()
-      | meet (Link (r as (ref (Param S'))), S) =
-          if Type.subsort tsig (S', S) then ()
-          else r := mk_param (Type.inter_sort tsig (S', S))
-      | meet (Link (ref T), S) = meet (T, S)
-      | meet (PType (a, Ts), S) =
-          ListPair.app meet (Ts, Type.arity_sorts pp tsig a S
-            handle ERROR msg => raise NO_UNIFIER msg)
-      | meet (PTFree (x, S'), S) =
-          if Type.subsort tsig (S', S) then ()
-          else raise NO_UNIFIER (not_of_sort x S' S)
-      | meet (PTVar (xi, S'), S) =
-          if Type.subsort tsig (S', S) then ()
-          else raise NO_UNIFIER (not_of_sort (Term.string_of_vname xi) S' S)
-      | meet (Param _, _) = sys_error "meet";
+    fun meet (_, []) tye_idx = tye_idx
+      | meet (Param (i, S'), S) (tye_idx as (tye, idx)) =
+          if Type.subsort tsig (S', S) then tye_idx
+          else (Inttab.update_new (i,
+            Param (idx, Type.inter_sort tsig (S', S))) tye, idx + 1)
+      | meet (PType (a, Ts), S) (tye_idx as (tye, _)) =
+          meets (Ts, Type.arity_sorts pp tsig a S
+            handle ERROR msg => raise NO_UNIFIER (msg, tye)) tye_idx
+      | meet (PTFree (x, S'), S) (tye_idx as (tye, _)) =
+          if Type.subsort tsig (S', S) then tye_idx
+          else raise NO_UNIFIER (not_of_sort x S' S, tye)
+      | meet (PTVar (xi, S'), S) (tye_idx as (tye, _)) =
+          if Type.subsort tsig (S', S) then tye_idx
+          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 assigment *)
 
-    fun occurs_check r (Link (r' as ref T)) =
-          if r = r' then raise NO_UNIFIER "Occurs check!"
-          else occurs_check r T
-      | occurs_check r (PType (_, Ts)) = List.app (occurs_check r) Ts
-      | occurs_check _ _ = ();
-
-    fun assign r T S =
-      (case deref T of
-        T' as Link (r' as ref (Param _)) =>
-          if r = r' then () else (meet (T', S); r := T')
-      | T' => (occurs_check r T'; meet (T', S); r := T'));
+    fun occurs_check tye i (Param (i', S)) =
+          if i = i' then raise NO_UNIFIER ("Occurs check!", tye)
+          else (case Inttab.lookup tye i' of
+              NONE => ()
+            | SOME T => occurs_check tye i T)
+      | occurs_check tye i (PType (_, Ts)) = List.app (occurs_check tye i) Ts
+      | occurs_check _ _ _ = ();
+
+    fun assign i (T as Param (i', _)) S (tye_idx as (tye, idx)) =
+          if i = i' then tye_idx
+          else meet (T, S) (Inttab.update_new (i, T) tye, idx)
+      | assign i T S (tye, idx) =
+          (occurs_check tye i T; meet (T, S) (Inttab.update_new (i, T) tye, idx));
 
 
     (* unification *)
 
-    fun unif (Link (r as ref (Param S)), T) = assign r T S
-      | unif (T, Link (r as ref (Param S))) = assign r T S
-      | unif (Link (ref T), U) = unif (T, U)
-      | unif (T, Link (ref U)) = unif (T, U)
-      | unif (PType (a, Ts), PType (b, Us)) =
+    fun unif (T1, T2) (tye_idx as (tye, idx)) = case (deref tye T1, deref tye T2) of
+        (Param (i, S), T) => assign i T S tye_idx
+      | (T, Param (i, S)) => assign i T S tye_idx
+      | (PType (a, Ts), PType (b, Us)) =>
           if a <> b then
-            raise NO_UNIFIER ("Clash of types " ^ quote a ^ " and " ^ quote b)
-          else ListPair.app unif (Ts, Us)
-      | unif (T, U) = if T = U then () else raise NO_UNIFIER "";
+            raise NO_UNIFIER ("Clash of types " ^ quote a ^ " and " ^ quote b, tye)
+          else fold unif (Ts ~~ Us) tye_idx
+      | (T, U) => if T = U then tye_idx else raise NO_UNIFIER ("", tye);
 
   in unif end;
 
 
 

     [Pretty.str "Operand:", Pretty.brk 3, Pretty.term pp u,
       Pretty.str " ::", Pretty.brk 1, Pretty.typ pp U]),
   ""];
 
 
-(* infer *)                                     (*DESTRUCTIVE*)
+(* infer *)
 
 fun infer pp tsig =
   let
     (* errors *)
 
     fun unif_failed msg =
       "Type unification failed" ^ (if msg = "" then "" else ": " ^ msg) ^ "\n";
 
-    fun prep_output bs ts Ts =
+    fun prep_output tye bs ts Ts =
       let
-        val (Ts_bTs', ts') = typs_terms_of Name.context ~1 (Ts @ map snd bs, ts);
+        val (Ts_bTs', ts') = typs_terms_of tye Name.context ~1 (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.mark_boundT xs, t) end;
       in (map prep ts', Ts') end;
 
     fun err_loose i =
       raise TYPE ("Loose bound variable: B." ^ string_of_int i, [], []);
 
-    fun err_appl msg bs t T u U =
+    fun err_appl msg tye bs t T u U =
       let
-        val ([t', u'], [T', U']) = prep_output bs [t, u] [T, U];
+        val ([t', u'], [T', U']) = prep_output tye bs [t, u] [T, U];
         val why =
           (case T' of
             Type ("fun", _) => "Incompatible operand type"
           | _ => "Operator not of function type");
         val text = unif_failed msg ^ cat_lines (appl_error pp why t' T' u' U');
       in raise TYPE (text, [T', U'], [t', u']) end;
 
-    fun err_constraint msg bs t T U =
+    fun err_constraint msg tye bs t T U =
       let
-        val ([t'], [T', U']) = prep_output bs [t] [T, U];
+        val ([t'], [T', U']) = prep_output tye bs [t] [T, U];
         val text = cat_lines
          [unif_failed msg,
           "Cannot meet type constraint:", "",
           Pretty.string_of (Pretty.block
            [Pretty.str "Term:", Pretty.brk 2, Pretty.term pp t',

 
     (* main *)
 
     val unif = unify pp tsig;
 
-    fun inf _ (PConst (_, T)) = T
-      | inf _ (PFree (_, T)) = T
-      | inf _ (PVar (_, T)) = T
-      | inf bs (PBound i) = snd (nth bs i handle Subscript => err_loose i)
-      | inf bs (PAbs (x, T, t)) = PType ("fun", [T, inf ((x, T) :: bs) t])
-      | inf bs (PAppl (t, u)) =
+    fun inf _ (PConst (_, T)) tye_idx = (T, tye_idx)
+      | inf _ (PFree (_, T)) tye_idx = (T, tye_idx)
+      | inf _ (PVar (_, T)) tye_idx = (T, tye_idx)
+      | inf bs (PBound i) tye_idx =
+          (snd (nth bs i handle Subscript => err_loose i), tye_idx)
+      | inf bs (PAbs (x, T, t)) tye_idx =
+          let val (U, tye_idx') = inf ((x, T) :: bs) t tye_idx
+          in (PType ("fun", [T, U]), tye_idx') end
+      | inf bs (PAppl (t, u)) tye_idx =
           let
-            val T = inf bs t;
-            val U = inf bs u;
-            val V = mk_param [];
+            val (T, tye_idx') = inf bs t tye_idx;
+            val (U, (tye, idx)) = inf bs u tye_idx';
+            val V = Param (idx, []);
             val U_to_V = PType ("fun", [U, V]);
-            val _ = unif (U_to_V, T) handle NO_UNIFIER msg => err_appl msg bs t T u U;
-          in V end
-      | inf bs (Constraint (t, U)) =
-          let val T = inf bs t in
-            unif (T, U) handle NO_UNIFIER msg => err_constraint msg bs t T U;
-            T
+            val tye_idx'' = unif (U_to_V, T) (tye, idx + 1)
+              handle NO_UNIFIER (msg, tye') => err_appl msg tye' bs t T u U;
+          in (V, tye_idx'') end
+      | inf bs (Constraint (t, U)) tye_idx =
+          let val (T, tye_idx') = inf bs t tye_idx in
+            (T,
+             unif (T, U) tye_idx'
+             handle NO_UNIFIER (msg, tye) => err_constraint msg tye bs t T U)
           end;
 
   in inf [] end;
 
 

         | Var (xi, T) => constrain T (Var (xi, get_type xi))
         | t => t);
 
     (*convert to preterms*)
     val ts = burrow_types check_typs raw_ts;
-    val (ts', _) =
-      fold_map (preterm_of const_type is_param o constrain_vars) ts (Vartab.empty, Vartab.empty);
+    val (ts', (_, _, idx)) =
+      fold_map (preterm_of const_type is_param o constrain_vars) ts
+      (Vartab.empty, Vartab.empty, 0);
 
     (*do type inference*)
-    val _ = List.app (ignore o infer pp tsig) ts';
-  in #2 (typs_terms_of used maxidx ([], ts')) end;
+    val (tye, _) = fold (snd oo infer pp tsig) ts' (Inttab.empty, idx);
+  in #2 (typs_terms_of tye used maxidx ([], ts')) end;
 
 end;