src/Pure/type_infer.ML
author berghofe
Thu Jul 23 09:38:22 2009 +0200 (2009-07-23)
changeset 32141 31cd1ea502aa
parent 32033 f92df23c3305
child 32146 4937d9836824
permissions -rw-r--r--
Purely functional type inference.
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(*  Title:      Pure/type_infer.ML
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    Author:     Stefan Berghofer and Markus Wenzel, TU Muenchen
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Simple type inference.
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*)
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signature TYPE_INFER =
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sig
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  val anyT: sort -> typ
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  val polymorphicT: typ -> typ
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  val constrain: typ -> term -> term
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  val is_param: indexname -> bool
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  val param: int -> string * sort -> typ
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  val paramify_vars: typ -> typ
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  val paramify_dummies: typ -> int -> typ * int
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  val fixate_params: Name.context -> term list -> term list
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  val appl_error: Pretty.pp -> string -> term -> typ -> term -> typ -> string list
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  val infer_types: Pretty.pp -> Type.tsig -> (typ list -> typ list) ->
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    (string -> typ option) -> (indexname -> typ option) -> Name.context -> int ->
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    term list -> term list
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end;
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structure TypeInfer: TYPE_INFER =
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struct
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(** type parameters and constraints **)
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fun anyT S = TFree ("'_dummy_", S);
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(*indicate polymorphic Vars*)
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fun polymorphicT T = Type ("_polymorphic_", [T]);
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val constrain = Syntax.type_constraint;
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(* user parameters *)
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fun is_param (x, _: int) = String.isPrefix "?" x;
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fun param i (x, S) = TVar (("?" ^ x, i), S);
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val paramify_vars =
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  perhaps (Term_Subst.map_atypsT_option (fn TVar ((x, i), S) => SOME (param i (x, S)) | _ => NONE));
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val paramify_dummies =
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  let
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    fun dummy S maxidx = (param (maxidx + 1) ("'dummy", S), maxidx + 1);
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    fun paramify (TFree ("'_dummy_", S)) maxidx = dummy S maxidx
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      | paramify (Type ("dummy", _)) maxidx = dummy [] maxidx
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      | paramify (Type (a, Ts)) maxidx =
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          let val (Ts', maxidx') = fold_map paramify Ts maxidx
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          in (Type (a, Ts'), maxidx') end
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      | paramify T maxidx = (T, maxidx);
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  in paramify end;
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fun fixate_params name_context ts =
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  let
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    fun subst_param (xi, S) (inst, used) =
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      if is_param xi then
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        let
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          val [a] = Name.invents used Name.aT 1;
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          val used' = Name.declare a used;
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        in (((xi, S), TFree (a, S)) :: inst, used') end
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      else (inst, used);
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    val name_context' = (fold o fold_types) Term.declare_typ_names ts name_context;
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    val (inst, _) = fold_rev subst_param (fold Term.add_tvars ts []) ([], name_context');
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  in (map o map_types) (Term_Subst.instantiateT inst) ts end;
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(** pretyps and preterms **)
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(*parameters may get instantiated, anything else is rigid*)
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datatype pretyp =
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  PType of string * pretyp list |
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  PTFree of string * sort |
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  PTVar of indexname * sort |
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  Param of int * sort;
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datatype preterm =
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  PConst of string * pretyp |
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  PFree of string * pretyp |
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  PVar of indexname * pretyp |
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  PBound of int |
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  PAbs of string * pretyp * preterm |
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  PAppl of preterm * preterm |
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  Constraint of preterm * pretyp;
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(* utils *)
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fun deref tye (T as Param (i, S)) = (case Inttab.lookup tye i of
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      NONE => T
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    | SOME U => deref tye U)
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  | deref tye T = T;
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fun fold_pretyps f (PConst (_, T)) x = f T x
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  | fold_pretyps f (PFree (_, T)) x = f T x
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  | fold_pretyps f (PVar (_, T)) x = f T x
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  | fold_pretyps _ (PBound _) x = x
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  | fold_pretyps f (PAbs (_, T, t)) x = fold_pretyps f t (f T x)
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  | fold_pretyps f (PAppl (t, u)) x = fold_pretyps f u (fold_pretyps f t x)
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  | fold_pretyps f (Constraint (t, T)) x = f T (fold_pretyps f t x);
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(** raw typs/terms to pretyps/preterms **)
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(* pretyp_of *)
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fun pretyp_of is_para typ params_idx =
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  let
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    val (params', idx) = fold_atyps
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      (fn TVar (xi as (x, _), S) =>
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          (fn ps_idx as (ps, idx) =>
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            if is_para xi andalso not (Vartab.defined ps xi)
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            then (Vartab.update (xi, Param (idx, S)) ps, idx + 1) else ps_idx)
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        | _ => I) typ params_idx;
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    fun pre_of (TVar (v as (xi, _))) idx =
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          (case Vartab.lookup params' xi of
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            NONE => PTVar v
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          | SOME p => p, idx)
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      | pre_of (TFree ("'_dummy_", S)) idx = (Param (idx, S), idx + 1)
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      | pre_of (TFree v) idx = (PTFree v, idx)
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      | pre_of (T as Type (a, Ts)) idx =
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          if T = dummyT then (Param (idx, []), idx + 1)
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          else
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            let val (Ts', idx') = fold_map pre_of Ts idx
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            in (PType (a, Ts'), idx') end;
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    val (ptyp, idx') = pre_of typ idx;
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  in (ptyp, (params', idx')) end;
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(* preterm_of *)
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fun preterm_of const_type is_para tm (vparams, params, idx) =
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  let
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    fun add_vparm xi (ps_idx as (ps, idx)) =
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      if not (Vartab.defined ps xi) then
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        (Vartab.update (xi, Param (idx, [])) ps, idx + 1)
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      else ps_idx;
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    val (vparams', idx') = fold_aterms
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      (fn Var (_, Type ("_polymorphic_", _)) => I
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        | Var (xi, _) => add_vparm xi
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        | Free (x, _) => add_vparm (x, ~1)
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        | _ => I)
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      tm (vparams, idx);
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    fun var_param xi = the (Vartab.lookup vparams' xi);
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    val preT_of = pretyp_of is_para;
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    fun polyT_of T idx = apsnd snd (pretyp_of (K true) T (Vartab.empty, idx));
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    fun constraint T t ps =
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      if T = dummyT then (t, ps)
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      else
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        let val (T', ps') = preT_of T ps
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        in (Constraint (t, T'), ps') end;
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    fun pre_of (Const (c, T)) (ps, idx) =
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          (case const_type c of
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            SOME U =>
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              let val (pU, idx') = polyT_of U idx
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              in constraint T (PConst (c, pU)) (ps, idx') end
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          | NONE => raise TYPE ("No such constant: " ^ quote c, [], []))
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      | pre_of (Var (xi, Type ("_polymorphic_", [T]))) (ps, idx) =
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          let val (pT, idx') = polyT_of T idx
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          in (PVar (xi, pT), (ps, idx')) end
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      | pre_of (Var (xi, T)) ps_idx = constraint T (PVar (xi, var_param xi)) ps_idx
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      | pre_of (Free (x, T)) ps_idx = constraint T (PFree (x, var_param (x, ~1))) ps_idx
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      | pre_of (Const ("_type_constraint_", Type ("fun", [T, _])) $ t) ps_idx =
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          pre_of t ps_idx |-> constraint T
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      | pre_of (Bound i) ps_idx = (PBound i, ps_idx)
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      | pre_of (Abs (x, T, t)) ps_idx =
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          let
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            val (T', ps_idx') = preT_of T ps_idx;
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            val (t', ps_idx'') = pre_of t ps_idx';
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          in (PAbs (x, T', t'), ps_idx'') end
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      | pre_of (t $ u) ps_idx =
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          let
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            val (t', ps_idx') = pre_of t ps_idx;
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            val (u', ps_idx'') = pre_of u ps_idx';
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          in (PAppl (t', u'), ps_idx'') end;
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    val (tm', (params', idx'')) = pre_of tm (params, idx');
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  in (tm', (vparams', params', idx'')) end;
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(** pretyps/terms to typs/terms **)
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(* add_parms *)
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fun add_parmsT tye T = case deref tye T of
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    PType (_, Ts) => fold (add_parmsT tye) Ts
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  | Param (i, _) => insert (op =) i
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  | _ => I;
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fun add_parms tye = fold_pretyps (add_parmsT tye);
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(* add_names *)
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fun add_namesT tye T = case deref tye T of
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    PType (_, Ts) => fold (add_namesT tye) Ts
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  | PTFree (x, _) => Name.declare x
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  | PTVar ((x, _), _) => Name.declare x
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  | Param _ => I;
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fun add_names tye = fold_pretyps (add_namesT tye);
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(* simple_typ/term_of *)
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fun simple_typ_of tye f T = case deref tye T of
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    PType (a, Ts) => Type (a, map (simple_typ_of tye f) Ts)
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  | PTFree v => TFree v
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  | PTVar v => TVar v
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  | Param (i, S) => TVar (f i, S);
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(*convert types, drop constraints*)
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fun simple_term_of tye f (PConst (c, T)) = Const (c, simple_typ_of tye f T)
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  | simple_term_of tye f (PFree (x, T)) = Free (x, simple_typ_of tye f T)
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  | simple_term_of tye f (PVar (xi, T)) = Var (xi, simple_typ_of tye f T)
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  | simple_term_of tye f (PBound i) = Bound i
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  | simple_term_of tye f (PAbs (x, T, t)) =
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      Abs (x, simple_typ_of tye f T, simple_term_of tye f t)
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  | simple_term_of tye f (PAppl (t, u)) =
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      simple_term_of tye f t $ simple_term_of tye f u
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  | simple_term_of tye f (Constraint (t, _)) = simple_term_of tye f t;
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(* typs_terms_of *)
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fun typs_terms_of tye used maxidx (Ts, ts) =
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  let
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    val used' = fold (add_names tye) ts (fold (add_namesT tye) Ts used);
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    val parms = rev (fold (add_parms tye) ts (fold (add_parmsT tye) Ts []));
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    val names = Name.invents used' ("?" ^ Name.aT) (length parms);
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    val tab = Inttab.make (parms ~~ names);
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    fun f i = (the (Inttab.lookup tab i), maxidx + 1);
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  in (map (simple_typ_of tye f) Ts, map (simple_term_of tye f) ts) end;
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(** order-sorted unification of types **)
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exception NO_UNIFIER of string * pretyp Inttab.table;
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fun unify pp tsig =
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  let
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    (* adjust sorts of parameters *)
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    fun not_of_sort x S' S =
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      "Variable " ^ x ^ "::" ^ Pretty.string_of_sort pp S' ^ " not of sort " ^
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        Pretty.string_of_sort pp S;
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    fun meet (_, []) tye_idx = tye_idx
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      | meet (Param (i, S'), S) (tye_idx as (tye, idx)) =
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          if Type.subsort tsig (S', S) then tye_idx
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          else (Inttab.update_new (i,
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            Param (idx, Type.inter_sort tsig (S', S))) tye, idx + 1)
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      | meet (PType (a, Ts), S) (tye_idx as (tye, _)) =
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          meets (Ts, Type.arity_sorts pp tsig a S
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            handle ERROR msg => raise NO_UNIFIER (msg, tye)) tye_idx
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      | meet (PTFree (x, S'), S) (tye_idx as (tye, _)) =
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          if Type.subsort tsig (S', S) then tye_idx
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          else raise NO_UNIFIER (not_of_sort x S' S, tye)
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      | meet (PTVar (xi, S'), S) (tye_idx as (tye, _)) =
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          if Type.subsort tsig (S', S) then tye_idx
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          else raise NO_UNIFIER (not_of_sort (Term.string_of_vname xi) S' S, tye)
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    and meets (T :: Ts, S :: Ss) (tye_idx as (tye, _)) =
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          meets (Ts, Ss) (meet (deref tye T, S) tye_idx)
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      | meets _ tye_idx = tye_idx;
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    (* occurs check and assigment *)
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    fun occurs_check tye i (Param (i', S)) =
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          if i = i' then raise NO_UNIFIER ("Occurs check!", tye)
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          else (case Inttab.lookup tye i' of
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              NONE => ()
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            | SOME T => occurs_check tye i T)
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      | occurs_check tye i (PType (_, Ts)) = List.app (occurs_check tye i) Ts
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      | occurs_check _ _ _ = ();
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    fun assign i (T as Param (i', _)) S (tye_idx as (tye, idx)) =
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          if i = i' then tye_idx
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          else meet (T, S) (Inttab.update_new (i, T) tye, idx)
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      | assign i T S (tye, idx) =
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          (occurs_check tye i T; meet (T, S) (Inttab.update_new (i, T) tye, idx));
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    (* unification *)
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    fun unif (T1, T2) (tye_idx as (tye, idx)) = case (deref tye T1, deref tye T2) of
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        (Param (i, S), T) => assign i T S tye_idx
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      | (T, Param (i, S)) => assign i T S tye_idx
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      | (PType (a, Ts), PType (b, Us)) =>
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          if a <> b then
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            raise NO_UNIFIER ("Clash of types " ^ quote a ^ " and " ^ quote b, tye)
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          else fold unif (Ts ~~ Us) tye_idx
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      | (T, U) => if T = U then tye_idx else raise NO_UNIFIER ("", tye);
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  in unif end;
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(** type inference **)
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(* appl_error *)
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fun appl_error pp why t T u U =
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 ["Type error in application: " ^ why,
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  "",
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  Pretty.string_of (Pretty.block
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    [Pretty.str "Operator:", Pretty.brk 2, Pretty.term pp t,
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      Pretty.str " ::", Pretty.brk 1, Pretty.typ pp T]),
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  Pretty.string_of (Pretty.block
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    [Pretty.str "Operand:", Pretty.brk 3, Pretty.term pp u,
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      Pretty.str " ::", Pretty.brk 1, Pretty.typ pp U]),
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  ""];
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   327
nipkow@5635
   328
berghofe@32141
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(* infer *)
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wenzelm@19465
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fun infer pp tsig =
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  let
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    (* errors *)
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    fun unif_failed msg =
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      "Type unification failed" ^ (if msg = "" then "" else ": " ^ msg) ^ "\n";
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berghofe@32141
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    fun prep_output tye bs ts Ts =
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      let
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        val (Ts_bTs', ts') = typs_terms_of tye Name.context ~1 (Ts @ map snd bs, ts);
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        val (Ts', Ts'') = chop (length Ts) Ts_bTs';
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        fun prep t =
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          let val xs = rev (Term.variant_frees t (rev (map fst bs ~~ Ts'')))
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          in Term.subst_bounds (map Syntax.mark_boundT xs, t) end;
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      in (map prep ts', Ts') end;
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    fun err_loose i =
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      raise TYPE ("Loose bound variable: B." ^ string_of_int i, [], []);
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    fun err_appl msg tye bs t T u U =
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      let
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        val ([t', u'], [T', U']) = prep_output tye bs [t, u] [T, U];
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        val why =
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          (case T' of
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            Type ("fun", _) => "Incompatible operand type"
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          | _ => "Operator not of function type");
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        val text = unif_failed msg ^ cat_lines (appl_error pp why t' T' u' U');
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      in raise TYPE (text, [T', U'], [t', u']) end;
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berghofe@32141
   360
    fun err_constraint msg tye bs t T U =
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      let
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        val ([t'], [T', U']) = prep_output tye bs [t] [T, U];
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        val text = cat_lines
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         [unif_failed msg,
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          "Cannot meet type constraint:", "",
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          Pretty.string_of (Pretty.block
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           [Pretty.str "Term:", Pretty.brk 2, Pretty.term pp t',
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            Pretty.str " ::", Pretty.brk 1, Pretty.typ pp T']),
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          Pretty.string_of (Pretty.block
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           [Pretty.str "Type:", Pretty.brk 2, Pretty.typ pp U']), ""];
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      in raise TYPE (text, [T', U'], [t']) end;
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wenzelm@2979
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wenzelm@2979
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    (* main *)
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wenzelm@19465
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    val unif = unify pp tsig;
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berghofe@32141
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    fun inf _ (PConst (_, T)) tye_idx = (T, tye_idx)
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      | inf _ (PFree (_, T)) tye_idx = (T, tye_idx)
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      | inf _ (PVar (_, T)) tye_idx = (T, tye_idx)
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      | inf bs (PBound i) tye_idx =
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          (snd (nth bs i handle Subscript => err_loose i), tye_idx)
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      | inf bs (PAbs (x, T, t)) tye_idx =
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          let val (U, tye_idx') = inf ((x, T) :: bs) t tye_idx
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          in (PType ("fun", [T, U]), tye_idx') end
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      | inf bs (PAppl (t, u)) tye_idx =
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          let
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            val (T, tye_idx') = inf bs t tye_idx;
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            val (U, (tye, idx)) = inf bs u tye_idx';
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            val V = Param (idx, []);
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            val U_to_V = PType ("fun", [U, V]);
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            val tye_idx'' = unif (U_to_V, T) (tye, idx + 1)
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   393
              handle NO_UNIFIER (msg, tye') => err_appl msg tye' bs t T u U;
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   394
          in (V, tye_idx'') end
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   395
      | inf bs (Constraint (t, U)) tye_idx =
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   396
          let val (T, tye_idx') = inf bs t tye_idx in
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            (T,
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   398
             unif (T, U) tye_idx'
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   399
             handle NO_UNIFIER (msg, tye) => err_constraint msg tye bs t T U)
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   400
          end;
wenzelm@2957
   401
wenzelm@2957
   402
  in inf [] end;
wenzelm@2957
   403
wenzelm@2957
   404
wenzelm@22698
   405
(* infer_types *)
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   406
wenzelm@27263
   407
fun infer_types pp tsig check_typs const_type var_type used maxidx raw_ts =
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   408
  let
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   409
    (*constrain vars*)
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    val get_type = the_default dummyT o var_type;
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   411
    val constrain_vars = Term.map_aterms
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   412
      (fn Free (x, T) => constrain T (Free (x, get_type (x, ~1)))
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   413
        | Var (xi, T) => constrain T (Var (xi, get_type xi))
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   414
        | t => t);
wenzelm@22698
   415
wenzelm@27263
   416
    (*convert to preterms*)
wenzelm@27263
   417
    val ts = burrow_types check_typs raw_ts;
berghofe@32141
   418
    val (ts', (_, _, idx)) =
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   419
      fold_map (preterm_of const_type is_param o constrain_vars) ts
berghofe@32141
   420
      (Vartab.empty, Vartab.empty, 0);
wenzelm@2957
   421
wenzelm@27263
   422
    (*do type inference*)
berghofe@32141
   423
    val (tye, _) = fold (snd oo infer pp tsig) ts' (Inttab.empty, idx);
berghofe@32141
   424
  in #2 (typs_terms_of tye used maxidx ([], ts')) end;
wenzelm@14788
   425
wenzelm@2957
   426
end;