# HG changeset patch
# User wenzelm
# Date 861207332 -7200
# Node ID d35fca99b3be0dccbdf7fdec46c0c0cf53a443f4
# Parent  d128ae3e742135763ba02bd9f3e1e6128eb30d88
Type inference (isolated from type.ML, completely reimplemented).

diff -r d128ae3e7421 -r d35fca99b3be src/Pure/type_infer.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Pure/type_infer.ML	Wed Apr 16 18:15:32 1997 +0200
@@ -0,0 +1,380 @@
+(*  Title:      Pure/type_infer.ML
+    ID:         $Id$
+    Author:     Stefan Berghofer and Markus Wenzel, TU Muenchen
+
+Type inference.
+*)
+
+signature TYPE_INFER =
+sig
+  val infer_types: (string -> typ option) -> Sorts.classrel -> Sorts.arities
+    -> string list -> bool -> (indexname -> bool) -> term list -> typ list
+    -> term list * typ list * (indexname * typ) list
+end;
+
+structure TypeInfer: TYPE_INFER =
+struct
+
+
+(** generic utils **)
+
+fun seq2 _ [] [] = ()
+  | seq2 f (x :: xs) (y :: ys) = (f x y; seq2 f xs ys)
+  | seq2 _ _ _ = raise LIST "seq2";
+
+fun scan _ (xs, []) = (xs, [])
+  | scan f (xs, y :: ys) =
+      let
+        val (xs', y') = f (xs, y);
+        val (xs'', ys') = scan f (xs', ys);
+      in (xs'', y' :: ys') end;
+
+
+
+(** term encodings **)
+
+(*
+  Flavours of term encodings:
+
+    parse trees (type term):
+      A very complicated structure produced by the syntax module's
+      read functions.  Encodes types and sorts as terms; may contain
+      explicit constraints and partial typing information (where
+      dummyT serves as wildcard).
+
+      Parse trees are INTERNAL! Users should never encounter them,
+      except in parse / print translation functions.
+
+    raw terms (type term):
+      Provide the user interface to type inferences.  They may contain
+      partial type information (dummyT is wildcard) or explicit type
+      constraints (introduced via constrain: term -> typ -> term).
+
+      The type inference function also lets users specify a certain
+      subset of TVars to be treated as non-rigid inference parameters.
+
+    preterms (type preterm):
+      The internal representation for type inference.
+
+    well-typed term (type term):
+      Fully typed lambda terms to be accepted by appropriate
+      certification functions.
+*)
+
+
+
+(** pretyps and preterms **)
+
+(*links to 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;
+
+datatype preterm =
+  PConst of string * pretyp |
+  PFree of string * pretyp |
+  PVar of indexname * pretyp |
+  PBound of int |
+  PAbs of string * pretyp * preterm |
+  PAppl of preterm * preterm |
+  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 foldl_pretyps f (x, PConst (_, T)) = f (x, T)
+  | foldl_pretyps f (x, PFree (_, T)) = f (x, T)
+  | foldl_pretyps f (x, PVar (_, T)) = f (x, T)
+  | foldl_pretyps _ (x, PBound _) = x
+  | foldl_pretyps f (x, PAbs (_, T, t)) = foldl_pretyps f (f (x, T), t)
+  | foldl_pretyps f (x, PAppl (t, u)) = foldl_pretyps f (foldl_pretyps f (x, t), u)
+  | foldl_pretyps f (x, Constraint (t, T)) = f (foldl_pretyps f (x, t), T);
+
+
+
+(** raw typs/terms to pretyps/preterms **)
+
+(* pretyp(s)_of *)
+
+fun pretyp_of is_param (params, typ) =
+  let
+    fun add_parms (ps, TVar (xi as (x, _), S)) =
+          if is_param xi andalso is_none (assoc (ps, xi))
+          then (xi, mk_param S) :: ps else ps
+      | add_parms (ps, TFree _) = ps
+      | add_parms (ps, Type (_, Ts)) = foldl add_parms (ps, Ts);
+
+    val params' = add_parms (params, typ);
+
+    fun pre_of (TVar (v as (xi, _))) =
+          (case assoc (params', xi) of
+            None => PTVar v
+          | Some p => p)
+      | 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 (params', pre_of typ) end;
+
+fun pretyps_of is_param = scan (pretyp_of is_param);
+
+
+(* preterm(s)_of *)
+
+fun preterm_of const_type is_param ((vparams, params), tm) =
+  let
+    fun add_vparm (ps, xi) =
+      if is_none (assoc (ps, xi)) then
+        (xi, mk_param []) :: ps
+      else ps;
+
+    fun add_vparms (ps, Var (xi, _)) = add_vparm (ps, xi)
+      | add_vparms (ps, Free (x, _)) = add_vparm (ps, (x, ~1))
+      | add_vparms (ps, Abs (_, _, t)) = add_vparms (ps, t)
+      | add_vparms (ps, t $ u) = add_vparms (add_vparms (ps, t), u)
+      | add_vparms (ps, _) = ps;
+
+    val vparams' = add_vparms (vparams, tm);
+    fun var_param xi = the (assoc (vparams', xi));
+
+
+    val preT_of = pretyp_of is_param;
+
+    fun constrain (ps, t) T =
+      if T = dummyT then (ps, t)
+      else
+        let val (ps', T') = preT_of (ps, T) in
+          (ps', Constraint (t, T'))
+        end;
+
+    fun pre_of (ps, Const (c, T)) =
+          (case const_type c of
+            Some U => constrain (ps, PConst (c, snd (pretyp_of (K true) ([], U)))) T
+          | None => raise_type ("No such constant: " ^ quote c) [] [])
+      | pre_of (ps, Free (x, T)) = constrain (ps, PFree (x, var_param (x, ~1))) T
+      | pre_of (ps, Var (xi, T)) = constrain (ps, PVar (xi, var_param xi)) T
+      | pre_of (ps, Const ("_type_constraint_", T) $ t) = constrain (pre_of (ps, t)) T
+      | pre_of (ps, Bound i) = (ps, PBound i)
+      | pre_of (ps, Abs (x, T, t)) =
+          let
+            val (ps', T') = preT_of (ps, T);
+            val (ps'', t') = pre_of (ps', t);
+          in (ps'', PAbs (x, T', t')) end
+      | pre_of (ps, t $ u) =
+          let
+            val (ps', t') = pre_of (ps, t);
+            val (ps'', u') = pre_of (ps', u);
+          in (ps'', PAppl (t', u')) end;
+
+
+    val (params', tm') = pre_of (params, tm);
+  in
+    ((vparams', params'), tm')
+  end;
+
+fun preterms_of const_type is_param = scan (preterm_of const_type is_param);
+
+
+
+(** pretyps/terms to typs/terms **)
+
+(* add_parms *)
+
+fun add_parmsT (rs, PType (_, Ts)) = foldl add_parmsT (rs, Ts)
+  | add_parmsT (rs, Link (r as ref (Param _))) = r ins rs
+  | add_parmsT (rs, Link (ref T)) = add_parmsT (rs, T)
+  | add_parmsT (rs, _) = rs;
+
+val add_parms = foldl_pretyps add_parmsT;
+
+
+(* add_names *)
+
+fun add_namesT (xs, PType (_, Ts)) = foldl add_namesT (xs, Ts)
+  | add_namesT (xs, PTFree (x, _)) = x ins xs
+  | add_namesT (xs, PTVar ((x, _), _)) = x ins xs
+  | add_namesT (xs, Link (ref T)) = add_namesT (xs, T)
+  | add_namesT (xs, Param _) = xs;
+
+val add_names = foldl_pretyps add_namesT;
+
+
+(* 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";
+
+(*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 mk_var prfx (Ts, ts) =
+  let
+    fun elim (r as ref (Param S)) x = r := mk_var (x, S)
+      | elim _ _ = ();
+
+    val used' = foldl add_names (foldl add_namesT (used, Ts), ts);
+    val parms = rev (foldl add_parms (foldl add_parmsT ([], Ts), ts));
+    val pre_names = replicate (length parms) (prfx ^ "'");
+    val names = variantlist (pre_names, prfx ^ "'" :: used');
+  in
+    seq2 elim parms names;
+    (map simple_typ_of Ts, map simple_term_of ts)
+  end;
+
+
+
+(** order-sorted unification of types **)       (*DESTRUCTIVE*)
+
+exception NO_UNIFIER of string;
+
+
+fun unify classrel arities =
+  let
+
+    (* adjust sorts of parameters *)
+
+    fun not_in_sort x S' S =
+      "Type variable " ^ x ^ "::" ^ Sorts.str_of_sort S' ^ " not in sort " ^
+        Sorts.str_of_sort S;
+
+    fun meet _ [] = ()
+      | meet (Link (r as (ref (Param S')))) S =
+          if Sorts.sort_le classrel (S', S) then ()
+          else r := mk_param (Sorts.inter_sort classrel (S', S))
+      | meet (Link (ref T)) S = meet T S
+      | meet (PType (a, Ts)) S =
+          seq2 meet Ts (Sorts.mg_domain classrel arities a S
+            handle TYPE (msg, _, _) => raise NO_UNIFIER msg)
+      | meet (PTFree (x, S')) S =
+          if Sorts.sort_le classrel (S', S) then ()
+          else raise NO_UNIFIER (not_in_sort x S' S)
+      | meet (PTVar (xi, S')) S =
+          if Sorts.sort_le classrel (S', S) then ()
+          else raise NO_UNIFIER (not_in_sort (Syntax.string_of_vname xi) S' S)
+      | meet (Param _) _ = sys_error "meet";
+
+
+    (* 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)) = seq (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 (r := T'; meet T' S)
+      | T' => (occurs_check r T'; r := T'; meet T' S));
+
+
+    (* 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)) =
+          if a <> b then raise NO_UNIFIER ("Clash of " ^ a ^ ", " ^ b ^ "!")
+          else seq2 unif Ts Us
+      | unif T U = if T = U then () else raise NO_UNIFIER "Unification failed!";
+
+  in unif end;
+
+
+
+(** type inference **)
+
+(* infer *)                                     (*DESTRUCTIVE*)
+
+fun infer classrel arities =
+  let
+    val unif = unify classrel arities;
+
+    fun err msg1 msg2 bs ts Ts =
+      let
+        val (Ts_bTs', ts') = typs_terms_of [] PTFree "??" (Ts @ map snd bs, ts);
+        val len = length Ts;
+        val Ts' = take (len, Ts_bTs');
+        val xs = map Free (map fst bs ~~ drop (len, Ts_bTs'));
+        val ts'' = map (fn t => subst_bounds (xs, t)) ts';
+      in
+        raise_type (msg1 ^ " " ^ msg2) Ts' ts''
+      end;
+
+    fun inf _ (PConst (_, T)) = T
+      | inf _ (PFree (_, T)) = T
+      | inf _ (PVar (_, T)) = T
+      | inf bs (PBound i) = snd (nth_elem (i, bs)
+          handle LIST _ => raise_type "Loose bound variable" [] [Bound i])
+      | inf bs (PAbs (x, T, t)) = PType ("fun", [T, inf ((x, T) :: bs) t])
+      | inf bs (PAppl (t, u)) =
+          let
+            val T = inf bs t;
+            val U = inf bs u;
+            val V = mk_param [];
+            val U_to_V = PType ("fun", [U, V]);
+            val _ = unif U_to_V T handle NO_UNIFIER msg =>
+              err msg "Bad function application." bs [PAppl (t, u)] [U_to_V, U];
+          in V end
+      | inf bs (Constraint (t, U)) =
+          let val T = inf bs t in
+            unif T U handle NO_UNIFIER msg =>
+              err msg "Cannot meet type constraint." bs [t] [T, U];
+            T
+          end;
+
+  in inf [] end;
+
+
+(* infer_types *)
+
+fun infer_types const_type classrel arities used freeze is_param ts Ts =
+  let
+    (*convert to preterms/typs*)
+    val (Tps, Ts') = pretyps_of (K true) ([], Ts);
+    val ((vps, ps), ts') = preterms_of const_type is_param (([], Tps), ts);
+
+    (*run type inference*)
+    val tTs' = ListPair.map Constraint (ts', Ts');
+    val _ = seq (fn t => (infer classrel arities t; ())) tTs';
+
+    (*collect result unifier*)
+    fun ch_var (xi, Link (r as ref (Param S))) = (r := PTVar (xi, S); None)
+      | ch_var xi_T = Some xi_T;
+    val env = mapfilter ch_var Tps;
+
+    (*convert back to terms/typs*)
+    val mk_var =
+      if freeze then PTFree
+      else (fn (x, S) => PTVar ((x, 0), S));
+    val (final_Ts, final_ts) = typs_terms_of used mk_var "" (Ts', ts');
+    val final_env = map (apsnd simple_typ_of) env;
+  in
+    (final_ts, final_Ts, final_env)
+  end;
+
+end;