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@14790:    {classes: Sorts.classes,
wenzelm@14790:     default: sort,
wenzelm@14790:     types: (decl * stamp) Symtab.table,
wenzelm@14790:     arities: Sorts.arities,
wenzelm@14790:     log_types: string list,
wenzelm@14790:     witness: (typ * sort) option}
wenzelm@14790:   val empty_tsig: tsig
wenzelm@14790:   val classes: tsig -> class list
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@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@14993:   val cert_typ_raw: tsig -> typ -> typ
wenzelm@14790: 
wenzelm@14790:   (*special treatment of type vars*)
wenzelm@14790:   val strip_sorts: typ -> typ
wenzelm@621:   val no_tvars: typ -> typ
wenzelm@621:   val varifyT: typ -> typ
wenzelm@621:   val unvarifyT: 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
berghofe@15797:   val typ_match: tsig -> tyenv * (typ * typ) -> tyenv
wenzelm@14790:   val typ_instance: tsig -> typ * typ -> bool
wenzelm@2964:   exception TUNIFY
berghofe@15797:   val unify: tsig -> tyenv * int -> typ * typ -> tyenv * int
wenzelm@450:   val raw_unify: typ * typ -> bool
clasohm@0: 
wenzelm@14790:   (*extend and merge type signatures*)
wenzelm@14830:   val add_classes: Pretty.pp -> (class * class list) list -> tsig -> tsig
wenzelm@14830:   val add_classrel: Pretty.pp -> (class * class) list -> tsig -> tsig
wenzelm@14790:   val set_defsort: sort -> tsig -> tsig
wenzelm@14790:   val add_types: (string * int) list -> tsig -> tsig
wenzelm@14790:   val add_abbrs: (string * string list * typ) list -> tsig -> tsig
wenzelm@14790:   val add_nonterminals: string list -> tsig -> tsig
wenzelm@14830:   val add_arities: Pretty.pp -> arity list -> 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@14790:     classes: Sorts.classes,              (*declared classes with proper subclass relation*)
wenzelm@14790:     default: sort,                       (*default sort on input*)
wenzelm@14790:     types: (decl * stamp) Symtab.table,  (*declared types*)
wenzelm@14790:     arities: Sorts.arities,              (*image specification of types wrt. sorts*)
wenzelm@14790:     log_types: string list,              (*logical types sorted by number of arguments*)
wenzelm@14790:     witness: (typ * sort) option};       (*witness for non-emptiness of strictest sort*)
wenzelm@14790: 
wenzelm@14790: fun rep_tsig (TSig comps) = comps;
wenzelm@14790: 
wenzelm@14790: fun make_tsig (classes, default, types, arities, log_types, witness) =
wenzelm@14790:   TSig {classes = classes, default = default, types = types, arities = arities,
wenzelm@14790:     log_types = log_types, witness = witness};
wenzelm@14790: 
wenzelm@14790: fun map_tsig f (TSig {classes, default, types, arities, log_types, witness}) =
wenzelm@14790:   make_tsig (f (classes, default, types, arities, log_types, witness));
wenzelm@14790: 
wenzelm@14790: fun build_tsig (classes, default, types, arities) =
wenzelm@14790:   let
wenzelm@14790:     fun add_log_type (ts, (c, (LogicalType n, _))) = (c, n) :: ts
wenzelm@14790:       | add_log_type (ts, _) = ts;
wenzelm@14790:     val log_types =
wenzelm@14790:       Symtab.foldl add_log_type ([], types)
wenzelm@14790:       |> Library.sort (Library.int_ord o pairself #2) |> map #1;
wenzelm@14790:     val witness =
wenzelm@14790:       (case Sorts.witness_sorts (classes, arities) log_types [] [Graph.keys classes] of
skalberg@15531:         [w] => SOME w | _ => NONE);
wenzelm@14790:   in make_tsig (classes, default, types, arities, log_types, witness) end;
wenzelm@14790: 
wenzelm@14790: fun change_tsig f (TSig {classes, default, types, arities, log_types = _, witness = _}) =
wenzelm@14790:   build_tsig (f (classes, default, types, arities));
wenzelm@14790: 
wenzelm@14790: val empty_tsig = build_tsig (Graph.empty, [], Symtab.empty, Symtab.empty);
wenzelm@14790: 
wenzelm@14790: 
wenzelm@14790: (* classes and sorts *)
wenzelm@14790: 
wenzelm@14790: fun classes (TSig {classes = C, ...}) = Graph.keys C;
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@14790: fun eq_sort (TSig {classes, ...}) = Sorts.sort_eq classes;
wenzelm@14790: fun subsort (TSig {classes, ...}) = Sorts.sort_le classes;
wenzelm@14790: fun of_sort (TSig {classes, arities, ...}) = Sorts.of_sort (classes, arities);
wenzelm@14790: 
wenzelm@14989: fun cert_class (TSig {classes, ...}) = Sorts.certify_class classes;
wenzelm@14989: fun cert_sort (TSig {classes, ...}) = Sorts.certify_sort classes;
wenzelm@14790: 
wenzelm@14790: fun witness_sorts (tsig as TSig {classes, arities, log_types, ...}) =
wenzelm@14790:   Sorts.witness_sorts (classes, arities) 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@16289:   | inst_typ env (T as TFree (x, _)) = if_none (Library.assoc_string (env, x)) T
wenzelm@14998:   | inst_typ _ T = T;
wenzelm@14998: 
wenzelm@14790: fun certify_typ normalize syntax tsig ty =
wenzelm@14790:   let
wenzelm@14989:     val TSig {classes, 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@14790:             (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@14989:       | cert (TFree (x, S)) = TFree (x, Sorts.certify_sort classes 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@14989:           else TVar (xi, Sorts.certify_sort classes 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@14790: val cert_typ         = certify_typ true false;
wenzelm@14790: val cert_typ_syntax  = certify_typ true true;
wenzelm@14790: val cert_typ_raw     = certify_typ false true;
wenzelm@14790: 
wenzelm@14998: end;
wenzelm@14998: 
wenzelm@14790: 
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@2964: (* varify, unvarify *)
wenzelm@621: 
wenzelm@2964: val varifyT = map_type_tfree (fn (a, S) => TVar ((a, 0), S));
wenzelm@2964: 
wenzelm@621: fun unvarifyT (Type (a, Ts)) = Type (a, map unvarifyT Ts)
wenzelm@621:   | unvarifyT (TVar ((a, 0), S)) = TFree (a, S)
wenzelm@621:   | unvarifyT T = T;
wenzelm@621: 
wenzelm@621: fun varify (t, fixed) =
wenzelm@621:   let
berghofe@15797:     val fs = add_term_tfrees (t, []) \\ fixed;
wenzelm@621:     val ixns = add_term_tvar_ixns (t, []);
berghofe@15797:     val fmap = fs ~~ map (rpair 0) (variantlist (map fst fs, map #1 ixns))
wenzelm@2964:     fun thaw (f as (a, S)) =
berghofe@15797:       (case assoc (fmap, f) of
skalberg@15531:         NONE => TFree f
skalberg@15531:       | SOME b => TVar (b, S));
wenzelm@12501:   in (map_term_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@16289:   let val v = 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@16289:   TFree (the (assoc_string_int (alist, ix)), sort)
skalberg@15531:     handle Option =>
wenzelm@3790:       raise TYPE ("Failure during freezing of ?" ^ string_of_indexname ix, [], []);
wenzelm@2964: 
wenzelm@16289: fun thaw_one alist (a, sort) = TVar (the (assoc_string (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@7641:     | _ => (map_term_types (map_type_tvar (freeze_one alist)) t,
wenzelm@7641:       map_term_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@16289:   (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@2964: fun typ_match tsig =
wenzelm@2964:   let
wenzelm@2964:     fun match (subs, (TVar (v, S), T)) =
berghofe@15797:           (case lookup (subs, (v, S)) of
skalberg@15531:             NONE =>
berghofe@15797:               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@2964:       | match (subs, (Type (a, Ts), Type (b, Us))) =
wenzelm@2964:           if a <> b then raise TYPE_MATCH
skalberg@15570:           else Library.foldl match (subs, Ts ~~ Us)
wenzelm@2964:       | match (subs, (TFree x, TFree y)) =
wenzelm@2964:           if x = y then subs else raise TYPE_MATCH
wenzelm@2964:       | match _ = raise TYPE_MATCH;
wenzelm@2964:   in match end;
clasohm@0: 
wenzelm@14790: fun typ_instance tsig (T, U) =
berghofe@8406:   (typ_match tsig (Vartab.empty, (U, T)); 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*)
berghofe@15797: fun devar (T as TVar v, tye) =
berghofe@15797:       (case  lookup (tye, v) of
skalberg@15531:         SOME U => devar (U, tye)
skalberg@15531:       | NONE => T)
wenzelm@256:   | devar (T, tye) = T;
clasohm@0: 
wenzelm@14790: fun unify (tsig as TSig {classes, arities, ...}) (tyenv, maxidx) TU =
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@2964:     fun mg_domain a S =
wenzelm@14790:       Sorts.mg_domain (classes, arities) a S handle Sorts.DOMAIN _ => raise TUNIFY;
wenzelm@2964: 
wenzelm@2964:     fun meet ((_, []), tye) = tye
wenzelm@2964:       | meet ((TVar (xi, S'), S), tye) =
wenzelm@14790:           if Sorts.sort_le classes (S', S) then tye
berghofe@15797:           else Vartab.update_new ((xi, (S',
berghofe@15797:             gen_tyvar (Sorts.inter_sort classes (S', S)))), tye)
wenzelm@2964:       | meet ((TFree (_, S'), S), tye) =
wenzelm@14790:           if Sorts.sort_le classes (S', S) then tye
wenzelm@2964:           else raise TUNIFY
wenzelm@2964:       | meet ((Type (a, Ts), S), tye) = meets ((Ts, mg_domain a S), tye)
wenzelm@2964:     and meets (([], []), tye) = tye
wenzelm@2964:       | meets ((T :: Ts, S :: Ss), tye) =
wenzelm@2964:           meets ((Ts, Ss), meet ((devar (T, tye), S), tye))
wenzelm@2964:       | meets _ = sys_error "meets";
wenzelm@2964: 
wenzelm@2964:     fun unif ((ty1, ty2), tye) =
wenzelm@2964:       (case (devar (ty1, tye), devar (ty2, tye)) 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
berghofe@15797:             Vartab.update_new ((w, (S2, T)), tye)
wenzelm@14790:           else if Sorts.sort_le classes (S2, S1) then
berghofe@15797:             Vartab.update_new ((v, (S1, U)), tye)
wenzelm@2964:           else
wenzelm@14790:             let val S = gen_tyvar (Sorts.inter_sort classes (S1, S2)) in
berghofe@15797:               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
berghofe@15797:           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
berghofe@15797:           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
skalberg@15574:           else foldr unif tye (Ts ~~ Us)
wenzelm@2964:       | (T, U) => if T = U then tye else raise TUNIFY);
wenzelm@12528:   in (unif (TU, tyenv), ! tyvar_count) end;
clasohm@0: 
wenzelm@14790: (*purely structural unification *)
wenzelm@450: fun raw_unify (ty1, ty2) =
wenzelm@14790:   (unify empty_tsig (Vartab.empty, 0) (strip_sorts ty1, strip_sorts ty2); true)
wenzelm@450:     handle TUNIFY => false;
wenzelm@450: 
wenzelm@450: 
clasohm@0: 
wenzelm@14790: (** extend and merge type signatures **)
wenzelm@14790: 
wenzelm@14790: (* arities *)
wenzelm@14790: 
wenzelm@14790: local
nipkow@1435: 
wenzelm@14790: fun err_decl t decl = error ("Illegal " ^ str_of_decl decl ^ ": " ^ quote t);
wenzelm@14830: 
skalberg@15531: fun for_classes _ NONE = ""
skalberg@15531:   | for_classes pp (SOME (c1, c2)) =
wenzelm@14830:       " for classes " ^ Pretty.string_of_classrel pp [c1, c2];
wenzelm@3790: 
wenzelm@14830: fun err_conflict pp t cc (c, Ss) (c', Ss') =
wenzelm@14830:   error ("Conflict of type arities" ^ for_classes pp cc ^ ":\n  " ^
wenzelm@14830:     Pretty.string_of_arity pp (t, Ss, [c]) ^ " and\n  " ^
wenzelm@14830:     Pretty.string_of_arity pp (t, Ss', [c']));
wenzelm@14790: 
wenzelm@14830: fun coregular pp C t (c, Ss) ars =
wenzelm@3790:   let
wenzelm@14790:     fun conflict (c', Ss') =
wenzelm@14790:       if Sorts.class_le C (c, c') andalso not (Sorts.sorts_le C (Ss, Ss')) then
skalberg@15531:         SOME ((c, c'), (c', Ss'))
wenzelm@14790:       else if Sorts.class_le C (c', c) andalso not (Sorts.sorts_le C (Ss', Ss)) then
skalberg@15531:         SOME ((c', c), (c', Ss'))
skalberg@15531:       else NONE;
wenzelm@14790:   in
wenzelm@14790:     (case Library.get_first conflict ars of
skalberg@15531:       SOME ((c1, c2), (c', Ss')) => err_conflict pp t (SOME (c1, c2)) (c, Ss) (c', Ss')
skalberg@15531:     | NONE => (c, Ss) :: ars)
wenzelm@14790:   end;
wenzelm@3790: 
wenzelm@14830: fun insert pp C t ((c, Ss), ars) =
wenzelm@14790:   (case assoc_string (ars, c) of
skalberg@15531:     NONE => coregular pp C t (c, Ss) ars
skalberg@15531:   | SOME Ss' =>
wenzelm@14790:       if Sorts.sorts_le C (Ss, Ss') then ars
wenzelm@14790:       else if Sorts.sorts_le C (Ss', Ss)
wenzelm@14830:       then coregular pp C t (c, Ss) (ars \ (c, Ss'))
skalberg@15531:       else err_conflict pp t NONE (c, Ss) (c, Ss'));
wenzelm@2587: 
wenzelm@14790: fun complete C (c, Ss) = map (rpair Ss) (Graph.all_succs C [c]);
wenzelm@3790: 
wenzelm@14830: fun insert_arities pp classes (arities, (t, ars)) =
wenzelm@14790:   let val ars' =
wenzelm@14790:     Symtab.lookup_multi (arities, t)
skalberg@15570:     |> curry (Library.foldr (insert pp classes t)) (List.concat (map (complete classes) ars))
wenzelm@14790:   in Symtab.update ((t, ars'), arities) end;
wenzelm@3790: 
wenzelm@14830: fun insert_table pp classes = Symtab.foldl (fn (arities, (t, ars)) =>
wenzelm@14830:   insert_arities pp classes (arities, (t, map (apsnd (map (Sorts.norm_sort classes))) ars)));
wenzelm@14790: 
wenzelm@14790: in
wenzelm@2587: 
wenzelm@14830: fun add_arities pp decls tsig = tsig |> change_tsig (fn (classes, default, types, arities) =>
wenzelm@14790:   let
wenzelm@14790:     fun prep (t, Ss, S) =
wenzelm@14790:       (case Symtab.lookup (types, t) of
skalberg@15531:         SOME (LogicalType n, _) =>
wenzelm@14790:           if length Ss = n then
wenzelm@14790:             (t, map (cert_sort tsig) Ss, cert_sort tsig S)
wenzelm@14790:               handle TYPE (msg, _, _) => error msg
wenzelm@14790:           else error (bad_nargs t)
skalberg@15531:       | SOME (decl, _) => err_decl t decl
skalberg@15531:       | NONE => error (undecl_type t));
wenzelm@4603: 
wenzelm@14790:     val ars = decls |> map ((fn (t, Ss, S) => (t, map (fn c => (c, Ss)) S)) o prep);
skalberg@15570:     val arities' = Library.foldl (insert_arities pp classes) (arities, ars);
wenzelm@14790:   in (classes, default, types, arities') end);
wenzelm@12528: 
wenzelm@14830: fun rebuild_arities pp classes arities =
wenzelm@14830:   insert_table pp classes (Symtab.empty, arities);
wenzelm@14790: 
wenzelm@14830: fun merge_arities pp classes (arities1, arities2) =
wenzelm@14830:   insert_table pp classes (insert_table pp classes (Symtab.empty, arities1), arities2);
wenzelm@14790: 
wenzelm@14790: end;
wenzelm@4603: 
wenzelm@4603: 
wenzelm@14790: (* classes *)
wenzelm@14790: 
wenzelm@14790: local
clasohm@0: 
wenzelm@14790: fun err_dup_classes cs =
wenzelm@14790:   error ("Duplicate declaration of class(es): " ^ commas_quote cs);
wenzelm@14790: 
wenzelm@14830: fun err_cyclic_classes pp css =
wenzelm@14790:   error (cat_lines (map (fn cs =>
wenzelm@14830:     "Cycle in class relation: " ^ Pretty.string_of_classrel pp cs) css));
wenzelm@14790: 
wenzelm@14830: fun add_class pp (c, cs) tsig = tsig |> change_tsig (fn (classes, default, types, arities) =>
wenzelm@2964:   let
wenzelm@14790:     val cs' = map (cert_class tsig) cs
wenzelm@14790:       handle TYPE (msg, _, _) => error msg;
wenzelm@14790:     val classes' = classes |> Graph.new_node (c, stamp ())
wenzelm@14790:       handle Graph.DUP d => err_dup_classes [d];
wenzelm@14790:     val classes'' = classes' |> fold Graph.add_edge_trans_acyclic (map (pair c) cs')
wenzelm@14830:       handle Graph.CYCLES css => err_cyclic_classes pp css;
wenzelm@14790:   in (classes'', default, types, arities) end);
wenzelm@2964: 
wenzelm@14790: in
clasohm@0: 
wenzelm@14830: val add_classes = fold o add_class;
wenzelm@14790: 
wenzelm@14830: fun add_classrel pp ps tsig = tsig |> change_tsig (fn (classes, default, types, arities) =>
wenzelm@14790:   let
wenzelm@14790:     val ps' = map (pairself (cert_class tsig)) ps
wenzelm@14790:       handle TYPE (msg, _, _) => error msg;
wenzelm@14790:     val classes' = classes |> fold Graph.add_edge_trans_acyclic ps'
wenzelm@14830:       handle Graph.CYCLES css => err_cyclic_classes pp css;
wenzelm@14790:     val default' = default |> Sorts.norm_sort classes';
wenzelm@14830:     val arities' = arities |> rebuild_arities pp classes';
wenzelm@14790:   in (classes', default', types, arities') end);
wenzelm@14790: 
wenzelm@14830: fun merge_classes pp CC = Graph.merge_trans_acyclic (op =) CC
wenzelm@14790:   handle Graph.DUPS cs => err_dup_classes cs
wenzelm@14830:     | Graph.CYCLES css => err_cyclic_classes pp css;
wenzelm@14790: 
wenzelm@14790: end;
wenzelm@14790: 
wenzelm@14790: 
wenzelm@14790: (* default sort *)
wenzelm@14790: 
wenzelm@14790: fun set_defsort S tsig = tsig |> change_tsig (fn (classes, _, types, arities) =>
wenzelm@14790:   (classes, cert_sort tsig S handle TYPE (msg, _, _) => error msg, types, arities));
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@14790: fun new_decl (c, decl) types =
wenzelm@14790:   (case Symtab.lookup (types, c) of
skalberg@15531:     SOME (decl', _) => err_in_decls c decl decl'
skalberg@15531:   | NONE => Symtab.update ((c, (decl, stamp ())), types));
wenzelm@14790: 
wenzelm@16289: fun the_decl types c = fst (the (Symtab.lookup (types, c)));
wenzelm@14790: 
wenzelm@14790: fun change_types f = change_tsig (fn (classes, default, types, arities) =>
wenzelm@14790:   (classes, default, f types, arities));
wenzelm@2964: 
wenzelm@14989: fun syntactic types (Type (c, Ts)) =
skalberg@15531:       (case Symtab.lookup (types, c) of SOME (Nonterminal, _) => true | _ => false)
wenzelm@14989:         orelse exists (syntactic types) Ts
wenzelm@14989:   | syntactic _ _ = false;
wenzelm@14989: 
wenzelm@14790: fun add_abbr (a, vs, rhs) tsig = tsig |> change_types (fn types =>
wenzelm@14790:   let
wenzelm@14790:     fun err msg =
wenzelm@14906:       error (msg ^ "\nThe error(s) above occurred in type abbreviation: " ^ quote a);
wenzelm@14993:     val rhs' = strip_sorts (no_tvars (cert_typ_syntax tsig rhs))
wenzelm@14790:       handle TYPE (msg, _, _) => err msg;
wenzelm@14790:   in
wenzelm@14790:     (case duplicates 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@14989:     types |> new_decl (a, Abbreviation (vs, rhs', syntactic types rhs'))
wenzelm@14790:   end);
clasohm@0: 
wenzelm@14790: in
wenzelm@14790: 
wenzelm@14790: fun add_types ps = change_types (fold new_decl (ps |> map (fn (c, n) =>
wenzelm@14790:   if n < 0 then err_neg_args c else (c, LogicalType n))));
wenzelm@14790: 
wenzelm@14790: val add_abbrs = fold add_abbr;
wenzelm@14790: val add_nonterminals = change_types o fold new_decl o map (rpair Nonterminal);
wenzelm@14790: 
wenzelm@14790: fun merge_types (types1, types2) =
wenzelm@14790:   Symtab.merge Library.eq_snd (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@3790: 
wenzelm@14790: (* merge type signatures *)
wenzelm@14790: 
wenzelm@14830: fun merge_tsigs pp (tsig1, tsig2) =
wenzelm@14790:   let
wenzelm@14790:     val (TSig {classes = classes1, default = default1, types = types1, arities = arities1,
wenzelm@14790:       log_types = _, witness = _}) = tsig1;
wenzelm@14790:     val (TSig {classes = classes2, default = default2, types = types2, arities = arities2,
wenzelm@14790:       log_types = _, witness = _}) = tsig2;
wenzelm@14790: 
wenzelm@14830:     val classes' = merge_classes pp (classes1, classes2);
wenzelm@14790:     val default' = Sorts.inter_sort classes' (default1, default2);
wenzelm@14790:     val types' = merge_types (types1, types2);
wenzelm@14830:     val arities' = merge_arities pp classes' (arities1, arities2);
wenzelm@14790:   in build_tsig (classes', default', types', arities') end;
wenzelm@14790: 
clasohm@0: end;