wenzelm@256: (*  Title:      Pure/type.ML
clasohm@0:     ID:         $Id$
wenzelm@14790:     Author:     Tobias Nipkow, Lawrence C Paulson, and Markus Wenzel
clasohm@0: 
wenzelm@14790: Type signatures and certified types, special treatment of type vars,
wenzelm@14790: matching and unification of types, extend and merge type signatures.
clasohm@0: *)
clasohm@0: 
clasohm@0: signature TYPE =
wenzelm@2964: sig
wenzelm@14790:   (*type signatures and certified types*)
wenzelm@14790:   datatype decl =
wenzelm@14790:     LogicalType of int |
wenzelm@14989:     Abbreviation of string list * typ * bool |
wenzelm@14790:     Nonterminal
wenzelm@14790:   type tsig
wenzelm@14790:   val rep_tsig: tsig ->
wenzelm@19642:    {classes: NameSpace.T * Sorts.algebra,
wenzelm@14790:     default: sort,
wenzelm@16370:     types: (decl * stamp) NameSpace.table,
wenzelm@14790:     log_types: string list,
wenzelm@14790:     witness: (typ * sort) option}
wenzelm@14790:   val empty_tsig: tsig
wenzelm@14790:   val defaultS: tsig -> sort
wenzelm@14790:   val logical_types: tsig -> string list
wenzelm@14790:   val universal_witness: tsig -> (typ * sort) option
wenzelm@14790:   val eq_sort: tsig -> sort * sort -> bool
wenzelm@14790:   val subsort: tsig -> sort * sort -> bool
wenzelm@14790:   val of_sort: tsig -> typ * sort -> bool
wenzelm@19464:   val inter_sort: tsig -> sort * sort -> sort
wenzelm@14790:   val cert_class: tsig -> class -> class
wenzelm@14790:   val cert_sort: tsig -> sort -> sort
wenzelm@14790:   val witness_sorts: tsig -> sort list -> sort list -> (typ * sort) list
wenzelm@14993:   val cert_typ: tsig -> typ -> typ
wenzelm@14993:   val cert_typ_syntax: tsig -> typ -> typ
wenzelm@16340:   val cert_typ_abbrev: tsig -> typ -> typ
wenzelm@19464:   val arity_number: tsig -> string -> int
wenzelm@19464:   val arity_sorts: Pretty.pp -> tsig -> string -> sort -> sort list
wenzelm@14790: 
wenzelm@14790:   (*special treatment of type vars*)
wenzelm@14790:   val strip_sorts: typ -> typ
wenzelm@621:   val no_tvars: typ -> typ
berghofe@15797:   val varify: term * (string * sort) list -> term * ((string * sort) * indexname) list
wenzelm@16289:   val freeze_thaw_type: typ -> typ * (typ -> typ)
wenzelm@16289:   val freeze_type: typ -> typ
wenzelm@16289:   val freeze_thaw: term -> term * (term -> term)
wenzelm@16289:   val freeze: term -> term
wenzelm@2964: 
wenzelm@14790:   (*matching and unification*)
wenzelm@2964:   exception TYPE_MATCH
berghofe@15797:   type tyenv
berghofe@15797:   val lookup: tyenv * (indexname * sort) -> typ option
wenzelm@16946:   val typ_match: tsig -> typ * typ -> tyenv -> tyenv
wenzelm@14790:   val typ_instance: tsig -> typ * typ -> bool
wenzelm@16946:   val raw_match: typ * typ -> tyenv -> tyenv
wenzelm@19694:   val raw_matches: typ list * typ list -> tyenv -> tyenv
wenzelm@16946:   val raw_instance: typ * typ -> bool
wenzelm@2964:   exception TUNIFY
wenzelm@16946:   val unify: tsig -> typ * typ -> tyenv * int -> tyenv * int
wenzelm@16946:   val raw_unify: typ * typ -> tyenv -> tyenv
wenzelm@19696:   val raw_unifys: typ list * typ list -> tyenv -> tyenv
wenzelm@17804:   val could_unify: typ * typ -> bool
wenzelm@19696:   val could_unifys: typ list * typ list -> bool
berghofe@16650:   val eq_type: tyenv -> typ * typ -> bool
clasohm@0: 
wenzelm@14790:   (*extend and merge type signatures*)
wenzelm@19515:   val add_class: Pretty.pp -> NameSpace.naming -> bstring * class list -> tsig -> tsig
wenzelm@16370:   val hide_classes: bool -> string list -> tsig -> tsig
wenzelm@14790:   val set_defsort: sort -> tsig -> tsig
wenzelm@16370:   val add_types: NameSpace.naming -> (bstring * int) list -> tsig -> tsig
wenzelm@16370:   val add_abbrevs: NameSpace.naming -> (string * string list * typ) list -> tsig -> tsig
wenzelm@16370:   val add_nonterminals: NameSpace.naming -> string list -> tsig -> tsig
wenzelm@16370:   val hide_types: bool -> string list -> tsig -> tsig
wenzelm@19515:   val add_arity: Pretty.pp -> arity -> tsig -> tsig
wenzelm@19515:   val add_classrel: Pretty.pp -> class * class -> tsig -> tsig
wenzelm@14830:   val merge_tsigs: Pretty.pp -> tsig * tsig -> tsig
wenzelm@2964: end;
wenzelm@2964: 
wenzelm@2964: structure Type: TYPE =
clasohm@0: struct
clasohm@0: 
wenzelm@14790: (** type signatures and certified types **)
wenzelm@2964: 
wenzelm@14790: (* type declarations *)
wenzelm@14790: 
wenzelm@14790: datatype decl =
wenzelm@14790:   LogicalType of int |
wenzelm@14989:   Abbreviation of string list * typ * bool |
wenzelm@14790:   Nonterminal;
wenzelm@14790: 
wenzelm@14790: fun str_of_decl (LogicalType _) = "logical type constructor"
wenzelm@14790:   | str_of_decl (Abbreviation _) = "type abbreviation"
wenzelm@14790:   | str_of_decl Nonterminal = "syntactic type";
wenzelm@14790: 
wenzelm@14790: 
wenzelm@14790: (* type tsig *)
wenzelm@14790: 
wenzelm@14790: datatype tsig =
wenzelm@14790:   TSig of {
wenzelm@19642:     classes: NameSpace.T * Sorts.algebra,   (*order-sorted algebra of type classes*)
wenzelm@16370:     default: sort,                          (*default sort on input*)
wenzelm@16370:     types: (decl * stamp) NameSpace.table,  (*declared types*)
wenzelm@16370:     log_types: string list,                 (*logical types sorted by number of arguments*)
wenzelm@16370:     witness: (typ * sort) option};          (*witness for non-emptiness of strictest sort*)
wenzelm@14790: 
wenzelm@14790: fun rep_tsig (TSig comps) = comps;
wenzelm@14790: 
wenzelm@19642: fun make_tsig (classes, default, types, log_types, witness) =
wenzelm@19642:   TSig {classes = classes, default = default, types = types,
wenzelm@14790:     log_types = log_types, witness = witness};
wenzelm@14790: 
wenzelm@19642: fun build_tsig ((space, classes), default, types) =
wenzelm@14790:   let
wenzelm@14790:     val log_types =
wenzelm@17756:       Symtab.fold (fn (c, (LogicalType n, _)) => cons (c, n) | _ => I) (snd types) []
wenzelm@17756:       |> Library.sort (Library.int_ord o pairself snd) |> map fst;
wenzelm@14790:     val witness =
wenzelm@19642:       (case Sorts.witness_sorts classes log_types [] [Sorts.classes classes] of
skalberg@15531:         [w] => SOME w | _ => NONE);
wenzelm@19642:   in make_tsig ((space, classes), default, types, log_types, witness) end;
wenzelm@14790: 
wenzelm@19642: fun map_tsig f (TSig {classes, default, types, log_types = _, witness = _}) =
wenzelm@19642:   build_tsig (f (classes, default, types));
wenzelm@14790: 
wenzelm@16370: val empty_tsig =
wenzelm@19642:   build_tsig ((NameSpace.empty, Sorts.empty_algebra), [], NameSpace.empty_table);
wenzelm@14790: 
wenzelm@14790: 
wenzelm@14790: (* classes and sorts *)
wenzelm@14790: 
wenzelm@14790: fun defaultS (TSig {default, ...}) = default;
wenzelm@14790: fun logical_types (TSig {log_types, ...}) = log_types;
wenzelm@14790: fun universal_witness (TSig {witness, ...}) = witness;
wenzelm@14790: 
wenzelm@16370: fun eq_sort (TSig {classes, ...}) = Sorts.sort_eq (#2 classes);
wenzelm@16370: fun subsort (TSig {classes, ...}) = Sorts.sort_le (#2 classes);
wenzelm@19642: fun of_sort (TSig {classes, ...}) = Sorts.of_sort (#2 classes);
wenzelm@19464: fun inter_sort (TSig {classes, ...}) = Sorts.inter_sort (#2 classes);
wenzelm@14790: 
wenzelm@19642: fun cert_class (TSig {classes, ...}) = Sorts.certify_class (#2 classes);
wenzelm@19642: fun cert_sort (TSig {classes, ...}) = Sorts.certify_sort (#2 classes);
wenzelm@19515: 
wenzelm@19642: fun witness_sorts (tsig as TSig {classes, log_types, ...}) =
wenzelm@19642:   Sorts.witness_sorts (#2 classes) log_types;
wenzelm@14790: 
wenzelm@14790: 
wenzelm@14790: (* certified types *)
wenzelm@14790: 
wenzelm@14790: fun bad_nargs t = "Bad number of arguments for type constructor: " ^ quote t;
wenzelm@14830: fun undecl_type c = "Undeclared type constructor: " ^ quote c;
wenzelm@14830: 
wenzelm@14998: local
wenzelm@14998: 
wenzelm@14998: fun inst_typ env (Type (c, Ts)) = Type (c, map (inst_typ env) Ts)
wenzelm@18957:   | inst_typ env (T as TFree (x, _)) = the_default T (AList.lookup (op =) env x)
wenzelm@14998:   | inst_typ _ T = T;
wenzelm@14998: 
wenzelm@14790: fun certify_typ normalize syntax tsig ty =
wenzelm@14790:   let
wenzelm@19515:     val TSig {types = (_, types), ...} = tsig;
wenzelm@14790:     fun err msg = raise TYPE (msg, [ty], []);
wenzelm@14790: 
wenzelm@14989:     val check_syntax =
wenzelm@14989:       if syntax then K ()
wenzelm@14989:       else fn c => err ("Illegal occurrence of syntactic type: " ^ quote c);
wenzelm@14989: 
wenzelm@14989:     fun cert (T as Type (c, Ts)) =
wenzelm@14989:           let
wenzelm@14989:             val Ts' = map cert Ts;
wenzelm@14989:             fun nargs n = if length Ts <> n then err (bad_nargs c) else ();
wenzelm@14989:           in
wenzelm@17412:             (case Symtab.lookup types c of
skalberg@15531:               SOME (LogicalType n, _) => (nargs n; Type (c, Ts'))
skalberg@15531:             | SOME (Abbreviation (vs, U, syn), _) => (nargs (length vs);
wenzelm@14989:                 if syn then check_syntax c else ();
wenzelm@14993:                 if normalize then inst_typ (vs ~~ Ts') U
wenzelm@14989:                 else Type (c, Ts'))
skalberg@15531:             | SOME (Nonterminal, _) => (nargs 0; check_syntax c; T)
skalberg@15531:             | NONE => err (undecl_type c))
wenzelm@14790:           end
wenzelm@19515:       | cert (TFree (x, S)) = TFree (x, cert_sort tsig S)
wenzelm@14989:       | cert (TVar (xi as (_, i), S)) =
wenzelm@14993:           if i < 0 then
wenzelm@14993:             err ("Malformed type variable: " ^ quote (Term.string_of_vname xi))
wenzelm@19515:           else TVar (xi, cert_sort tsig S);
wenzelm@14790: 
wenzelm@14989:     val ty' = cert ty;
wenzelm@14993:   in if ty = ty' then ty else ty' end;  (*avoid copying of already normal type*)
wenzelm@14830: 
wenzelm@14998: in
wenzelm@14998: 
wenzelm@16340: val cert_typ        = certify_typ true false;
wenzelm@16340: val cert_typ_syntax = certify_typ true true;
wenzelm@16340: val cert_typ_abbrev = certify_typ false true;
wenzelm@14790: 
wenzelm@14998: end;
wenzelm@14998: 
wenzelm@14790: 
wenzelm@19464: (* type arities *)
wenzelm@19464: 
wenzelm@19464: fun arity_number (TSig {types = (_, types), ...}) a =
wenzelm@19464:   (case Symtab.lookup types a of
wenzelm@19464:     SOME (LogicalType n, _) => n
wenzelm@19464:   | _ => error (undecl_type a));
wenzelm@19464: 
wenzelm@19464: fun arity_sorts _ tsig a [] = replicate (arity_number tsig a) []
wenzelm@19642:   | arity_sorts pp (TSig {classes, ...}) a S = Sorts.mg_domain (#2 classes) a S
wenzelm@19642:       handle Sorts.CLASS_ERROR err => Sorts.class_error pp err;
wenzelm@19464: 
wenzelm@19464: 
wenzelm@14790: 
wenzelm@14790: (** special treatment of type vars **)
wenzelm@14790: 
wenzelm@14790: (* strip_sorts *)
wenzelm@14790: 
wenzelm@14790: fun strip_sorts (Type (a, Ts)) = Type (a, map strip_sorts Ts)
wenzelm@14790:   | strip_sorts (TFree (x, _)) = TFree (x, [])
wenzelm@14790:   | strip_sorts (TVar (xi, _)) = TVar (xi, []);
wenzelm@14790: 
wenzelm@14790: 
wenzelm@14790: (* no_tvars *)
wenzelm@621: 
wenzelm@621: fun no_tvars T =
wenzelm@12501:   (case typ_tvars T of [] => T
wenzelm@12501:   | vs => raise TYPE ("Illegal schematic type variable(s): " ^
wenzelm@14830:       commas_quote (map (Term.string_of_vname o #1) vs), [T], []));
wenzelm@621: 
wenzelm@7641: 
wenzelm@19806: (* varify *)
wenzelm@621: 
wenzelm@621: fun varify (t, fixed) =
wenzelm@621:   let
wenzelm@19305:     val fs = Term.fold_types (Term.fold_atyps
wenzelm@19305:       (fn TFree v => if member (op =) fixed v then I else insert (op =) v | _ => I)) t [];
wenzelm@621:     val ixns = add_term_tvar_ixns (t, []);
wenzelm@20071:     val fmap = fs ~~ map (rpair 0) (Name.variant_list (map #1 ixns) (map fst fs))
wenzelm@2964:     fun thaw (f as (a, S)) =
wenzelm@17184:       (case AList.lookup (op =) fmap f of
skalberg@15531:         NONE => TFree f
wenzelm@16946:       | SOME xi => TVar (xi, S));
wenzelm@20548:   in (map_types (map_type_tfree thaw) t, fmap) end;
wenzelm@2964: 
wenzelm@2964: 
wenzelm@7641: (* freeze_thaw: freeze TVars in a term; return the "thaw" inverse *)
paulson@3411: 
wenzelm@7641: local
wenzelm@7641: 
wenzelm@16289: fun new_name (ix, (pairs, used)) =
wenzelm@20071:   let val v = Name.variant used (string_of_indexname ix)
wenzelm@16289:   in ((ix, v) :: pairs, v :: used) end;
wenzelm@621: 
wenzelm@16289: fun freeze_one alist (ix, sort) =
wenzelm@17184:   TFree (the (AList.lookup (op =) alist ix), sort)
skalberg@15531:     handle Option =>
wenzelm@3790:       raise TYPE ("Failure during freezing of ?" ^ string_of_indexname ix, [], []);
wenzelm@2964: 
wenzelm@17184: fun thaw_one alist (a, sort) = TVar (the (AList.lookup (op =) alist a), sort)
wenzelm@16289:   handle Option => TFree (a, sort);
wenzelm@416: 
wenzelm@10495: in
wenzelm@10495: 
wenzelm@10495: (*this sort of code could replace unvarifyT*)
wenzelm@7641: fun freeze_thaw_type T =
wenzelm@7641:   let
wenzelm@7641:     val used = add_typ_tfree_names (T, [])
wenzelm@7641:     and tvars = map #1 (add_typ_tvars (T, []));
skalberg@15574:     val (alist, _) = foldr new_name ([], used) tvars;
wenzelm@7641:   in (map_type_tvar (freeze_one alist) T, map_type_tfree (thaw_one (map swap alist))) end;
wenzelm@7641: 
wenzelm@16289: val freeze_type = #1 o freeze_thaw_type;
wenzelm@16289: 
paulson@3411: fun freeze_thaw t =
wenzelm@7641:   let
wenzelm@7641:     val used = it_term_types add_typ_tfree_names (t, [])
wenzelm@7641:     and tvars = map #1 (it_term_types add_typ_tvars (t, []));
skalberg@15574:     val (alist, _) = foldr new_name ([], used) tvars;
wenzelm@7641:   in
wenzelm@7641:     (case alist of
wenzelm@7641:       [] => (t, fn x => x) (*nothing to do!*)
wenzelm@20548:     | _ => (map_types (map_type_tvar (freeze_one alist)) t,
wenzelm@20548:       map_types (map_type_tfree (thaw_one (map swap alist)))))
wenzelm@7641:   end;
wenzelm@7641: 
wenzelm@16289: val freeze = #1 o freeze_thaw;
wenzelm@16289: 
wenzelm@7641: end;
wenzelm@7641: 
wenzelm@256: 
wenzelm@256: 
wenzelm@14790: (** matching and unification of types **)
wenzelm@8899: 
berghofe@15797: type tyenv = (sort * typ) Vartab.table;
wenzelm@256: 
berghofe@15797: fun tvar_clash ixn S S' = raise TYPE ("Type variable " ^
berghofe@15797:   quote (Term.string_of_vname ixn) ^ " has two distinct sorts",
berghofe@15797:   [TVar (ixn, S), TVar (ixn, S')], []);
clasohm@0: 
wenzelm@16289: fun lookup (tye, (ixn, S)) =
wenzelm@17412:   (case Vartab.lookup tye ixn of
berghofe@15797:     NONE => NONE
wenzelm@16289:   | SOME (S', T) => if S = S' then SOME T else tvar_clash ixn S S');
wenzelm@16289: 
clasohm@0: 
wenzelm@14790: (* matching *)
clasohm@0: 
wenzelm@2964: exception TYPE_MATCH;
clasohm@0: 
wenzelm@16946: fun typ_match tsig =
wenzelm@2964:   let
wenzelm@16340:     fun match (TVar (v, S), T) subs =
berghofe@15797:           (case lookup (subs, (v, S)) of
skalberg@15531:             NONE =>
wenzelm@17412:               if of_sort tsig (T, S) then Vartab.update_new (v, (S, T)) subs
wenzelm@14993:               else raise TYPE_MATCH
skalberg@15531:           | SOME U => if U = T then subs else raise TYPE_MATCH)
wenzelm@16340:       | match (Type (a, Ts), Type (b, Us)) subs =
wenzelm@2964:           if a <> b then raise TYPE_MATCH
wenzelm@16885:           else matches (Ts, Us) subs
wenzelm@16340:       | match (TFree x, TFree y) subs =
wenzelm@2964:           if x = y then subs else raise TYPE_MATCH
wenzelm@16885:       | match _ _ = raise TYPE_MATCH
wenzelm@16885:     and matches (T :: Ts, U :: Us) subs = matches (Ts, Us) (match (T, U) subs)
wenzelm@16885:       | matches _ subs = subs;
wenzelm@16946:   in match end;
clasohm@0: 
wenzelm@14790: fun typ_instance tsig (T, U) =
wenzelm@16946:   (typ_match tsig (U, T) Vartab.empty; true) handle TYPE_MATCH => false;
wenzelm@16946: 
wenzelm@16946: (*purely structural matching*)
wenzelm@16946: fun raw_match (TVar (v, S), T) subs =
wenzelm@16946:       (case lookup (subs, (v, S)) of
wenzelm@17412:         NONE => Vartab.update_new (v, (S, T)) subs
wenzelm@16946:       | SOME U => if U = T then subs else raise TYPE_MATCH)
wenzelm@16946:   | raw_match (Type (a, Ts), Type (b, Us)) subs =
wenzelm@16946:       if a <> b then raise TYPE_MATCH
wenzelm@16946:       else raw_matches (Ts, Us) subs
wenzelm@16946:   | raw_match (TFree x, TFree y) subs =
wenzelm@16946:       if x = y then subs else raise TYPE_MATCH
wenzelm@16946:   | raw_match _ _ = raise TYPE_MATCH
wenzelm@16946: and raw_matches (T :: Ts, U :: Us) subs = raw_matches (Ts, Us) (raw_match (T, U) subs)
wenzelm@19694:   | raw_matches ([], []) subs = subs
wenzelm@19694:   | raw_matches _ _ = raise TYPE_MATCH;
wenzelm@16946: 
wenzelm@16946: fun raw_instance (T, U) =
wenzelm@16946:   (raw_match (U, T) Vartab.empty; true) handle TYPE_MATCH => false;
wenzelm@2964: 
clasohm@0: 
wenzelm@14790: (* unification *)
wenzelm@2964: 
clasohm@0: exception TUNIFY;
clasohm@0: 
wenzelm@14790: (*occurs_check*)
wenzelm@2964: fun occurs v tye =
wenzelm@2964:   let
wenzelm@2964:     fun occ (Type (_, Ts)) = exists occ Ts
wenzelm@2964:       | occ (TFree _) = false
berghofe@15797:       | occ (TVar (w, S)) =
wenzelm@2964:           eq_ix (v, w) orelse
berghofe@15797:             (case lookup (tye, (w, S)) of
skalberg@15531:               NONE => false
skalberg@15531:             | SOME U => occ U);
clasohm@0:   in occ end;
clasohm@0: 
wenzelm@14790: (*chase variable assignments; if devar returns a type var then it must be unassigned*)
wenzelm@16885: fun devar tye (T as TVar v) =
wenzelm@16885:       (case lookup (tye, v) of
wenzelm@16885:         SOME U => devar tye U
skalberg@15531:       | NONE => T)
wenzelm@16885:   | devar tye T = T;
clasohm@0: 
wenzelm@17804: (*order-sorted unification*)
wenzelm@19642: fun unify (tsig as TSig {classes = (_, classes), ...}) TU (tyenv, maxidx) =
wenzelm@2964:   let
wenzelm@2964:     val tyvar_count = ref maxidx;
wenzelm@2964:     fun gen_tyvar S = TVar (("'a", inc tyvar_count), S);
wenzelm@2964: 
wenzelm@19642:     fun mg_domain a S = Sorts.mg_domain classes a S
wenzelm@19642:       handle Sorts.CLASS_ERROR _ => raise TUNIFY;
wenzelm@2964: 
wenzelm@16885:     fun meet (_, []) tye = tye
wenzelm@16885:       | meet (TVar (xi, S'), S) tye =
wenzelm@14790:           if Sorts.sort_le classes (S', S) then tye
wenzelm@17412:           else Vartab.update_new
wenzelm@17221:             (xi, (S', gen_tyvar (Sorts.inter_sort classes (S', S)))) tye
wenzelm@16885:       | meet (TFree (_, S'), S) tye =
wenzelm@14790:           if Sorts.sort_le classes (S', S) then tye
wenzelm@2964:           else raise TUNIFY
wenzelm@16885:       | meet (Type (a, Ts), S) tye = meets (Ts, mg_domain a S) tye
wenzelm@16885:     and meets (T :: Ts, S :: Ss) tye = meets (Ts, Ss) (meet (devar tye T, S) tye)
wenzelm@16885:       | meets _ tye = tye;
wenzelm@2964: 
wenzelm@16885:     fun unif (ty1, ty2) tye =
wenzelm@16885:       (case (devar tye ty1, devar tye ty2) of
wenzelm@2964:         (T as TVar (v, S1), U as TVar (w, S2)) =>
berghofe@15797:           if eq_ix (v, w) then
berghofe@15797:             if S1 = S2 then tye else tvar_clash v S1 S2
wenzelm@14790:           else if Sorts.sort_le classes (S1, S2) then
wenzelm@17412:             Vartab.update_new (w, (S2, T)) tye
wenzelm@14790:           else if Sorts.sort_le classes (S2, S1) then
wenzelm@17412:             Vartab.update_new (v, (S1, U)) tye
wenzelm@2964:           else
wenzelm@14790:             let val S = gen_tyvar (Sorts.inter_sort classes (S1, S2)) in
wenzelm@17412:               Vartab.update_new (v, (S1, S)) (Vartab.update_new (w, (S2, S)) tye)
wenzelm@2964:             end
wenzelm@2964:       | (TVar (v, S), T) =>
wenzelm@2964:           if occurs v tye T then raise TUNIFY
wenzelm@17412:           else meet (T, S) (Vartab.update_new (v, (S, T)) tye)
wenzelm@2964:       | (T, TVar (v, S)) =>
wenzelm@2964:           if occurs v tye T then raise TUNIFY
wenzelm@17412:           else meet (T, S) (Vartab.update_new (v, (S, T)) tye)
wenzelm@2964:       | (Type (a, Ts), Type (b, Us)) =>
wenzelm@2964:           if a <> b then raise TUNIFY
wenzelm@16885:           else unifs (Ts, Us) tye
wenzelm@16885:       | (T, U) => if T = U then tye else raise TUNIFY)
wenzelm@16885:     and unifs (T :: Ts, U :: Us) tye = unifs (Ts, Us) (unif (T, U) tye)
wenzelm@16885:       | unifs _ tye = tye;
wenzelm@16885:   in (unif TU tyenv, ! tyvar_count) end;
clasohm@0: 
wenzelm@16946: (*purely structural unification*)
wenzelm@16946: fun raw_unify (ty1, ty2) tye =
wenzelm@16946:   (case (devar tye ty1, devar tye ty2) of
wenzelm@16946:     (T as TVar (v, S1), U as TVar (w, S2)) =>
wenzelm@16946:       if eq_ix (v, w) then
wenzelm@16946:         if S1 = S2 then tye else tvar_clash v S1 S2
wenzelm@17412:       else Vartab.update_new (w, (S2, T)) tye
wenzelm@16946:   | (TVar (v, S), T) =>
wenzelm@16946:       if occurs v tye T then raise TUNIFY
wenzelm@17412:       else Vartab.update_new (v, (S, T)) tye
wenzelm@16946:   | (T, TVar (v, S)) =>
wenzelm@16946:       if occurs v tye T then raise TUNIFY
wenzelm@17412:       else Vartab.update_new (v, (S, T)) tye
wenzelm@16946:   | (Type (a, Ts), Type (b, Us)) =>
wenzelm@16946:       if a <> b then raise TUNIFY
wenzelm@16946:       else raw_unifys (Ts, Us) tye
wenzelm@16946:   | (T, U) => if T = U then tye else raise TUNIFY)
wenzelm@16946: and raw_unifys (T :: Ts, U :: Us) tye = raw_unifys (Ts, Us) (raw_unify (T, U) tye)
wenzelm@19696:   | raw_unifys ([], []) tye = tye
wenzelm@19696:   | raw_unifys _ _ = raise TUNIFY;
wenzelm@16946: 
wenzelm@17804: (*fast unification filter*)
wenzelm@17804: fun could_unify (Type (a, Ts), Type (b, Us)) = a = b andalso could_unifys (Ts, Us)
wenzelm@17804:   | could_unify (TFree (a, _), TFree (b, _)) = a = b
wenzelm@17804:   | could_unify (TVar _, _) = true
wenzelm@17804:   | could_unify (_, TVar _) = true
wenzelm@17804:   | could_unify _ = false
wenzelm@17804: and could_unifys (T :: Ts, U :: Us) = could_unify (T, U) andalso could_unifys (Ts, Us)
wenzelm@19696:   | could_unifys ([], []) = true
wenzelm@19696:   | could_unifys _ = false;
wenzelm@450: 
wenzelm@17804: 
wenzelm@17804: (*equality with respect to a type environment*)
berghofe@16650: fun eq_type tye (T, T') =
wenzelm@16885:   (case (devar tye T, devar tye T') of
berghofe@16650:      (Type (s, Ts), Type (s', Ts')) =>
berghofe@16650:        s = s' andalso ListPair.all (eq_type tye) (Ts, Ts')
berghofe@16650:    | (U, U') => U = U');
berghofe@16650: 
wenzelm@450: 
clasohm@0: 
wenzelm@14790: (** extend and merge type signatures **)
wenzelm@14790: 
wenzelm@14790: (* classes *)
wenzelm@14790: 
wenzelm@16370: fun add_class pp naming (c, cs) tsig =
wenzelm@19642:   tsig |> map_tsig (fn ((space, classes), default, types) =>
wenzelm@16370:     let
wenzelm@16370:       val c' = NameSpace.full naming c;
wenzelm@16370:       val cs' = map (cert_class tsig) cs
wenzelm@16370:         handle TYPE (msg, _, _) => error msg;
wenzelm@16370:       val space' = space |> NameSpace.declare naming c';
wenzelm@19515:       val classes' = classes |> Sorts.add_class pp (c', cs');
wenzelm@19642:     in ((space', classes'), default, types) end);
wenzelm@14790: 
wenzelm@19642: fun hide_classes fully cs = map_tsig (fn ((space, classes), default, types) =>
wenzelm@19642:   ((fold (NameSpace.hide fully) cs space, classes), default, types));
wenzelm@16370: 
wenzelm@14790: 
wenzelm@19515: (* arities *)
wenzelm@19515: 
wenzelm@19642: fun add_arity pp (t, Ss, S) tsig = tsig |> map_tsig (fn ((space, classes), default, types) =>
wenzelm@19515:   let
wenzelm@19515:     val _ =
wenzelm@19515:       (case Symtab.lookup (#2 types) t of
wenzelm@19515:         SOME (LogicalType n, _) => if length Ss <> n then error (bad_nargs t) else ()
wenzelm@19515:       | SOME (decl, _) => error ("Illegal " ^ str_of_decl decl ^ ": " ^ quote t)
wenzelm@19515:       | NONE => error (undecl_type t));
wenzelm@19515:     val (Ss', S') = (map (cert_sort tsig) Ss, cert_sort tsig S)
wenzelm@19515:       handle TYPE (msg, _, _) => error msg;
wenzelm@19642:     val classes' = classes |> Sorts.add_arities pp ((t, map (fn c' => (c', Ss')) S'));
wenzelm@19642:   in ((space, classes'), default, types) end);
wenzelm@19515: 
wenzelm@19515: 
wenzelm@19515: (* classrel *)
wenzelm@19515: 
wenzelm@19515: fun add_classrel pp rel tsig =
wenzelm@19642:   tsig |> map_tsig (fn ((space, classes), default, types) =>
wenzelm@19515:     let
wenzelm@19515:       val rel' = pairself (cert_class tsig) rel
wenzelm@19515:         handle TYPE (msg, _, _) => error msg;
wenzelm@19515:       val classes' = classes |> Sorts.add_classrel pp rel;
wenzelm@19642:     in ((space, classes'), default, types) end);
wenzelm@19515: 
wenzelm@19515: 
wenzelm@14790: (* default sort *)
wenzelm@14790: 
wenzelm@19642: fun set_defsort S tsig = tsig |> map_tsig (fn (classes, _, types) =>
wenzelm@19642:   (classes, cert_sort tsig S handle TYPE (msg, _, _) => error msg, types));
clasohm@0: 
clasohm@0: 
wenzelm@14790: (* types *)
wenzelm@14790: 
wenzelm@14790: local
wenzelm@14790: 
wenzelm@14790: fun err_neg_args c =
wenzelm@14790:   error ("Negative number of arguments in type constructor declaration: " ^ quote c);
nipkow@949: 
wenzelm@14790: fun err_in_decls c decl decl' =
wenzelm@14906:   let val s = str_of_decl decl and s' = str_of_decl decl' in
wenzelm@14906:     if s = s' then error ("Duplicate declaration of " ^ s ^ ": " ^ quote c)
wenzelm@14830:     else error ("Conflict of " ^ s ^ " with " ^ s' ^ ": " ^ quote c)
wenzelm@14790:   end;
wenzelm@14790: 
wenzelm@16370: fun new_decl naming (c, decl) (space, types) =
wenzelm@16370:   let
wenzelm@16370:     val c' = NameSpace.full naming c;
wenzelm@16370:     val space' = NameSpace.declare naming c' space;
wenzelm@16370:     val types' =
wenzelm@17412:       (case Symtab.lookup types c' of
wenzelm@16370:         SOME (decl', _) => err_in_decls c' decl decl'
wenzelm@17412:       | NONE => Symtab.update (c', (decl, stamp ())) types);
wenzelm@16370:   in (space', types') end;
wenzelm@14790: 
wenzelm@17412: fun the_decl (_, types) = fst o the o Symtab.lookup types;
wenzelm@14790: 
wenzelm@19642: fun map_types f = map_tsig (fn (classes, default, types) =>
wenzelm@19579:   let
wenzelm@19579:     val (space', tab') = f types;
wenzelm@19579:     val _ = assert (NameSpace.intern space' "dummy" = "dummy") "Illegal declaration of dummy type";
wenzelm@19642:   in (classes, default, (space', tab')) end);
wenzelm@2964: 
wenzelm@14989: fun syntactic types (Type (c, Ts)) =
wenzelm@17412:       (case Symtab.lookup types c of SOME (Nonterminal, _) => true | _ => false)
wenzelm@14989:         orelse exists (syntactic types) Ts
wenzelm@14989:   | syntactic _ _ = false;
wenzelm@14989: 
wenzelm@19579: fun add_abbrev naming (a, vs, rhs) tsig = tsig |> map_types (fn types =>
wenzelm@14790:   let
wenzelm@19250:     fun err msg = cat_error msg ("The error(s) above occurred in type abbreviation: " ^ quote a);
wenzelm@16946:     val rhs' = strip_sorts (no_tvars (cert_typ_syntax tsig rhs))
wenzelm@14790:       handle TYPE (msg, _, _) => err msg;
wenzelm@14790:   in
wenzelm@18964:     (case duplicates (op =) vs of
wenzelm@14790:       [] => []
wenzelm@14790:     | dups => err ("Duplicate variables on lhs: " ^ commas_quote dups));
wenzelm@14790:     (case gen_rems (op =) (map (#1 o #1) (typ_tvars rhs'), vs) of
wenzelm@14790:       [] => []
wenzelm@14790:     | extras => err ("Extra variables on rhs: " ^ commas_quote extras));
wenzelm@16370:     types |> new_decl naming (a, Abbreviation (vs, rhs', syntactic (#2 types) rhs'))
wenzelm@14790:   end);
clasohm@0: 
wenzelm@14790: in
wenzelm@14790: 
wenzelm@19579: fun add_types naming ps = map_types (fold (new_decl naming) (ps |> map (fn (c, n) =>
wenzelm@14790:   if n < 0 then err_neg_args c else (c, LogicalType n))));
wenzelm@14790: 
wenzelm@16370: val add_abbrevs = fold o add_abbrev;
wenzelm@16370: 
wenzelm@19579: fun add_nonterminals naming = map_types o fold (new_decl naming) o map (rpair Nonterminal);
wenzelm@14790: 
wenzelm@14790: fun merge_types (types1, types2) =
haftmann@17496:   NameSpace.merge_tables (Library.eq_snd (op =)) (types1, types2) handle Symtab.DUPS (d :: _) =>
wenzelm@14790:     err_in_decls d (the_decl types1 d) (the_decl types2 d);
wenzelm@14790: 
wenzelm@14790: end;
clasohm@0: 
wenzelm@19642: fun hide_types fully cs = map_tsig (fn (classes, default, (space, types)) =>
wenzelm@19642:   (classes, default, (fold (NameSpace.hide fully) cs space, types)));
wenzelm@16370: 
wenzelm@3790: 
wenzelm@14790: (* merge type signatures *)
wenzelm@14790: 
wenzelm@14830: fun merge_tsigs pp (tsig1, tsig2) =
wenzelm@14790:   let
wenzelm@19515:     val (TSig {classes = (space1, classes1), default = default1, types = types1,
wenzelm@19642:       log_types = _, witness = _}) = tsig1;
wenzelm@19515:     val (TSig {classes = (space2, classes2), default = default2, types = types2,
wenzelm@19642:       log_types = _, witness = _}) = tsig2;
wenzelm@14790: 
wenzelm@19515:     val space' = NameSpace.merge (space1, space2);
wenzelm@19642:     val classes' = Sorts.merge_algebra pp (classes1, classes2);
wenzelm@19515:     val default' = Sorts.inter_sort classes' (default1, default2);
wenzelm@14790:     val types' = merge_types (types1, types2);
wenzelm@19642:   in build_tsig ((space', classes'), default', types') end;
wenzelm@14790: 
clasohm@0: end;