src/HOL/Tools/typedef_package.ML
author wenzelm
Tue Dec 19 13:06:49 2000 +0100 (2000-12-19)
changeset 10697 ec197510165a
parent 10675 0b40c19f09f3
child 11426 f280d4b29a2c
permissions -rw-r--r--
improved errors;
     1 (*  Title:      HOL/Tools/typedef_package.ML
     2     ID:         $Id$
     3     Author:     Markus Wenzel, TU Muenchen
     4     License:    GPL (GNU GENERAL PUBLIC LICENSE)
     5 
     6 Gordon/HOL-style type definitions.
     7 *)
     8 
     9 signature TYPEDEF_PACKAGE =
    10 sig
    11   val quiet_mode: bool ref
    12   val add_typedecls: (bstring * string list * mixfix) list -> theory -> theory
    13   val add_typedef: string -> bstring * string list * mixfix ->
    14     string -> string list -> thm list -> tactic option -> theory -> theory
    15   val add_typedef_i: string -> bstring * string list * mixfix ->
    16     term -> string list -> thm list -> tactic option -> theory -> theory
    17   val add_typedef_i_no_def: string -> bstring * string list * mixfix ->
    18     term -> string list -> thm list -> tactic option -> theory -> theory
    19   val typedef_proof: (string * (bstring * string list * mixfix) * string) * Comment.text
    20     -> bool -> theory -> ProofHistory.T
    21   val typedef_proof_i: (string * (bstring * string list * mixfix) * term) * Comment.text
    22     -> bool -> theory -> ProofHistory.T
    23 end;
    24 
    25 structure TypedefPackage: TYPEDEF_PACKAGE =
    26 struct
    27 
    28 
    29 (** theory context references **)
    30 
    31 val type_definitionN = "subset.type_definition";
    32 val type_definition_def = thm "type_definition_def";
    33 
    34 val Rep = thm "Rep";
    35 val Rep_inverse = thm "Rep_inverse";
    36 val Abs_inverse = thm "Abs_inverse";
    37 val Rep_inject = thm "Rep_inject";
    38 val Abs_inject = thm "Abs_inject";
    39 val Rep_cases = thm "Rep_cases";
    40 val Abs_cases = thm "Abs_cases";
    41 val Rep_induct = thm "Rep_induct";
    42 val Abs_induct = thm "Abs_induct";
    43 
    44 
    45 
    46 (** type declarations **)
    47 
    48 fun add_typedecls decls thy =
    49   let
    50     val full = Sign.full_name (Theory.sign_of thy);
    51 
    52     fun arity_of (raw_name, args, mx) =
    53       (full (Syntax.type_name raw_name mx), replicate (length args) HOLogic.termS, HOLogic.termS);
    54   in
    55     if can (Theory.assert_super HOL.thy) thy then
    56       thy
    57       |> PureThy.add_typedecls decls
    58       |> Theory.add_arities_i (map arity_of decls)
    59     else thy |> PureThy.add_typedecls decls
    60   end;
    61 
    62 
    63 
    64 (** type definitions **)
    65 
    66 (* messages *)
    67 
    68 val quiet_mode = ref false;
    69 fun message s = if ! quiet_mode then () else writeln s;
    70 
    71 
    72 (* non-emptiness of set *)              (*exception ERROR*)
    73 
    74 fun check_nonempty cset thm =
    75   let
    76     val {t, sign, maxidx, ...} = Thm.rep_cterm cset;
    77     val {prop, ...} = Thm.rep_thm (Thm.transfer_sg sign (Drule.standard thm));
    78     val matches = Pattern.matches (Sign.tsig_of sign);
    79   in
    80     (case try (HOLogic.dest_mem o HOLogic.dest_Trueprop) prop of
    81       None => raise ERROR
    82     | Some (_, A) => if matches (Logic.incr_indexes ([], maxidx) A, t) then () else raise ERROR)
    83   end handle ERROR => error ("Bad non-emptiness theorem " ^ Display.string_of_thm thm ^
    84     "\nfor set " ^ quote (Display.string_of_cterm cset));
    85 
    86 fun goal_nonempty ex cset =
    87   let
    88     val {T = setT, t = A, maxidx, sign} = Thm.rep_cterm cset;
    89     val T = HOLogic.dest_setT setT;
    90     val tm =
    91       if ex then HOLogic.mk_exists ("x", T, HOLogic.mk_mem (Free ("x", T), A))
    92       else HOLogic.mk_mem (Var (("x", maxidx + 1), T), A);   (*old-style version*)
    93   in Thm.cterm_of sign (HOLogic.mk_Trueprop tm) end;
    94 
    95 fun prove_nonempty thy cset (witn_names, witn_thms, witn_tac) =
    96   let
    97     val is_def = Logic.is_equals o #prop o Thm.rep_thm;
    98     val thms = PureThy.get_thmss thy witn_names @ witn_thms;
    99     val tac =
   100       TRY (rewrite_goals_tac (filter is_def thms)) THEN
   101       TRY (REPEAT_FIRST (resolve_tac (filter_out is_def thms))) THEN
   102       if_none witn_tac (TRY (ALLGOALS (CLASET' blast_tac)));
   103   in
   104     message ("Proving non-emptiness of set " ^ quote (string_of_cterm cset) ^ " ...");
   105     prove_goalw_cterm [] (goal_nonempty false cset) (K [tac])
   106   end handle ERROR => error ("Failed to prove non-emptiness of " ^ quote (string_of_cterm cset));
   107 
   108 
   109 (* prepare_typedef *)
   110 
   111 fun read_term sg used s =
   112   #1 (Thm.read_def_cterm (sg, K None, K None) used true (s, HOLogic.termT));
   113 
   114 fun cert_term sg _ t = Thm.cterm_of sg t handle TERM (msg, _) => error msg;
   115 
   116 fun err_in_typedef name =
   117   error ("The error(s) above occurred in typedef " ^ quote name);
   118 
   119 fun prepare_typedef prep_term no_def name (t, vs, mx) raw_set thy =
   120   let
   121     val _ = Theory.requires thy "subset" "typedefs";
   122     val sign = Theory.sign_of thy;
   123     val full = Sign.full_name sign;
   124 
   125     (*rhs*)
   126     val full_name = full name;
   127     val cset = prep_term sign vs raw_set;
   128     val {T = setT, t = set, ...} = Thm.rep_cterm cset;
   129     val rhs_tfrees = term_tfrees set;
   130     val oldT = HOLogic.dest_setT setT handle TYPE _ =>
   131       error ("Not a set type: " ^ quote (Sign.string_of_typ sign setT));
   132     val cset_pat = Thm.cterm_of sign (Var ((name, 0), setT));
   133 
   134     (*lhs*)
   135     val lhs_tfrees = map (fn v => (v, if_none (assoc (rhs_tfrees, v)) HOLogic.termS)) vs;
   136     val tname = Syntax.type_name t mx;
   137     val full_tname = full tname;
   138     val newT = Type (full_tname, map TFree lhs_tfrees);
   139 
   140     val Rep_name = "Rep_" ^ name;
   141     val Abs_name = "Abs_" ^ name;
   142 
   143     val setC = Const (full_name, setT);
   144     val RepC = Const (full Rep_name, newT --> oldT);
   145     val AbsC = Const (full Abs_name, oldT --> newT);
   146     val x_new = Free ("x", newT);
   147     val y_old = Free ("y", oldT);
   148 
   149     val set' = if no_def then set else setC;
   150 
   151     val typedef_name = "type_definition_" ^ name;
   152     val typedefC =
   153       Const (type_definitionN, (newT --> oldT) --> (oldT --> newT) --> setT --> HOLogic.boolT);
   154     val typedef_prop = HOLogic.mk_Trueprop (typedefC $ RepC $ AbsC $ set');
   155 
   156     (*theory extender*)
   157     fun do_typedef super_theory theory =
   158       theory
   159       |> Theory.assert_super super_theory
   160       |> add_typedecls [(t, vs, mx)]
   161       |> Theory.add_consts_i
   162        ((if no_def then [] else [(name, setT, NoSyn)]) @
   163         [(Rep_name, newT --> oldT, NoSyn),
   164          (Abs_name, oldT --> newT, NoSyn)])
   165       |> (if no_def then I else (#1 oo (PureThy.add_defs_i false o map Thm.no_attributes))
   166        [Logic.mk_defpair (setC, set)])
   167       |> PureThy.add_axioms_i [((typedef_name, typedef_prop), [])]
   168       |> (fn (theory', typedef_ax) =>
   169         let fun make th = standard (th OF typedef_ax) in
   170           rpair (hd typedef_ax) (theory'
   171           |> (#1 oo PureThy.add_thms)
   172             ([((Rep_name, make Rep), []),
   173               ((Rep_name ^ "_inverse", make Rep_inverse), []),
   174               ((Abs_name ^ "_inverse", make Abs_inverse), []),
   175               ((Rep_name ^ "_inject", make Rep_inject), []),
   176               ((Abs_name ^ "_inject", make Abs_inject), []),
   177               ((Rep_name ^ "_cases", make Rep_cases),
   178                 [RuleCases.case_names [Rep_name], InductAttrib.cases_set_global full_name]),
   179               ((Abs_name ^ "_cases", make Abs_cases),
   180                 [RuleCases.case_names [Abs_name], InductAttrib.cases_type_global full_tname]),
   181               ((Rep_name ^ "_induct", make Rep_induct),
   182                 [RuleCases.case_names [Rep_name], InductAttrib.induct_set_global full_name]),
   183               ((Abs_name ^ "_induct", make Abs_induct),
   184                 [RuleCases.case_names [Abs_name], InductAttrib.induct_type_global full_tname])]))
   185         end)
   186       handle ERROR => err_in_typedef name;
   187 
   188 
   189     (* errors *)
   190 
   191     fun show_names pairs = commas_quote (map fst pairs);
   192 
   193     val illegal_vars =
   194       if null (term_vars set) andalso null (term_tvars set) then []
   195       else ["Illegal schematic variable(s) on rhs"];
   196 
   197     val dup_lhs_tfrees =
   198       (case duplicates lhs_tfrees of [] => []
   199       | dups => ["Duplicate type variables on lhs: " ^ show_names dups]);
   200 
   201     val extra_rhs_tfrees =
   202       (case gen_rems (op =) (rhs_tfrees, lhs_tfrees) of [] => []
   203       | extras => ["Extra type variables on rhs: " ^ show_names extras]);
   204 
   205     val illegal_frees =
   206       (case term_frees set of [] => []
   207       | xs => ["Illegal variables on rhs: " ^ show_names (map dest_Free xs)]);
   208 
   209     val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees;
   210   in
   211     if null errs then () else error (cat_lines errs);
   212     (cset, cset_pat, do_typedef)
   213   end handle ERROR => err_in_typedef name;
   214 
   215 
   216 (* add_typedef interfaces *)
   217 
   218 fun gen_add_typedef prep_term no_def name typ set names thms tac thy =
   219   let
   220     val (cset, _, do_typedef) = prepare_typedef prep_term no_def name typ set thy;
   221     val result = prove_nonempty thy cset (names, thms, tac);
   222   in check_nonempty cset result; thy |> do_typedef thy |> #1 end;
   223 
   224 val add_typedef = gen_add_typedef read_term false;
   225 val add_typedef_i = gen_add_typedef cert_term false;
   226 val add_typedef_i_no_def = gen_add_typedef cert_term true;
   227 
   228 
   229 (* typedef_proof interface *)
   230 
   231 fun typedef_attribute cset do_typedef (thy, thm) =
   232   (check_nonempty cset (thm RS (some_eq_ex RS iffD2)); (thy |> do_typedef));
   233 
   234 fun gen_typedef_proof prep_term ((name, typ, set), comment) int thy =
   235   let
   236     val (cset, cset_pat, do_typedef) = prepare_typedef prep_term false name typ set thy;
   237     val goal = Thm.term_of (goal_nonempty true cset);
   238     val goal_pat = Thm.term_of (goal_nonempty true cset_pat);
   239     val test_thy = Theory.copy thy;
   240   in
   241     test_thy |> do_typedef test_thy;  (*preview errors!*)
   242     thy |> IsarThy.theorem_i ((("", [typedef_attribute cset (do_typedef thy)]),
   243       (goal, ([goal_pat], []))), comment) int
   244   end;
   245 
   246 val typedef_proof = gen_typedef_proof read_term;
   247 val typedef_proof_i = gen_typedef_proof cert_term;
   248 
   249 
   250 
   251 (** outer syntax **)
   252 
   253 local structure P = OuterParse and K = OuterSyntax.Keyword in
   254 
   255 val typedeclP =
   256   OuterSyntax.command "typedecl" "HOL type declaration" K.thy_decl
   257     (P.type_args -- P.name -- P.opt_infix --| P.marg_comment >> (fn ((vs, t), mx) =>
   258       Toplevel.theory (add_typedecls [(t, vs, mx)])));
   259 
   260 
   261 val typedef_proof_decl =
   262   Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") --
   263     (P.type_args -- P.name) -- P.opt_infix -- (P.$$$ "=" |-- P.term) -- P.marg_comment;
   264 
   265 fun mk_typedef_proof ((((opt_name, (vs, t)), mx), A), comment) =
   266   typedef_proof ((if_none opt_name (Syntax.type_name t mx), (t, vs, mx), A), comment);
   267 
   268 val typedefP =
   269   OuterSyntax.command "typedef" "HOL type definition (requires non-emptiness proof)" K.thy_goal
   270     (typedef_proof_decl >> (Toplevel.print oo (Toplevel.theory_to_proof o mk_typedef_proof)));
   271 
   272 
   273 val _ = OuterSyntax.add_parsers [typedeclP, typedefP];
   274 
   275 end;
   276 
   277 
   278 end;