src/HOL/Tools/typedef_package.ML
author wenzelm
Sat Oct 13 20:31:34 2001 +0200 (2001-10-13)
changeset 11740 86ac4189a1c1
parent 11727 a27150cc8fa5
child 11744 3a4625eaead0
permissions -rw-r--r--
IsarThy.theorem_i Drule.internalK;
     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 = "Typedef.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 (* prove_nonempty -- tactical version *)        (*exception ERROR*)
    73 
    74 fun prove_nonempty thy cset goal (witn_names, witn_thms, witn_tac) =
    75   let
    76     val is_def = Logic.is_equals o #prop o Thm.rep_thm;
    77     val thms = PureThy.get_thmss thy witn_names @ witn_thms;
    78     val tac =
    79       rtac exI 1 THEN
    80       TRY (rewrite_goals_tac (filter is_def thms)) THEN
    81       TRY (REPEAT_FIRST (resolve_tac (filter_out is_def thms))) THEN
    82       if_none witn_tac (TRY (ALLGOALS (CLASET' blast_tac)));
    83   in
    84     message ("Proving non-emptiness of set " ^ quote (string_of_cterm cset) ^ " ...");
    85     prove_goalw_cterm [] (cterm_of (sign_of thy) goal) (K [tac])
    86   end handle ERROR => error ("Failed to prove non-emptiness of " ^ quote (string_of_cterm cset));
    87 
    88 
    89 (* prepare_typedef *)
    90 
    91 fun read_term sg used s =
    92   #1 (Thm.read_def_cterm (sg, K None, K None) used true (s, HOLogic.termT));
    93 
    94 fun cert_term sg _ t = Thm.cterm_of sg t handle TERM (msg, _) => error msg;
    95 
    96 fun err_in_typedef name =
    97   error ("The error(s) above occurred in typedef " ^ quote name);
    98 
    99 fun prepare_typedef prep_term no_def name (t, vs, mx) raw_set thy =
   100   let
   101     val _ = Theory.requires thy "Typedef" "typedefs";
   102     val sign = Theory.sign_of thy;
   103     val full = Sign.full_name sign;
   104 
   105     (*rhs*)
   106     val full_name = full name;
   107     val cset = prep_term sign vs raw_set;
   108     val {T = setT, t = set, ...} = Thm.rep_cterm cset;
   109     val rhs_tfrees = term_tfrees set;
   110     val oldT = HOLogic.dest_setT setT handle TYPE _ =>
   111       error ("Not a set type: " ^ quote (Sign.string_of_typ sign setT));
   112     fun mk_nonempty A =
   113       HOLogic.mk_Trueprop (HOLogic.mk_exists ("x", oldT, HOLogic.mk_mem (Free ("x", oldT), A)));
   114     val goal = mk_nonempty set;
   115     val goal_pat = mk_nonempty (Var ((name, 0), setT));
   116 
   117     (*lhs*)
   118     val lhs_tfrees = map (fn v => (v, if_none (assoc (rhs_tfrees, v)) HOLogic.termS)) vs;
   119     val tname = Syntax.type_name t mx;
   120     val full_tname = full tname;
   121     val newT = Type (full_tname, map TFree lhs_tfrees);
   122 
   123     val Rep_name = "Rep_" ^ name;
   124     val Abs_name = "Abs_" ^ name;
   125 
   126     val setC = Const (full_name, setT);
   127     val RepC = Const (full Rep_name, newT --> oldT);
   128     val AbsC = Const (full Abs_name, oldT --> newT);
   129     val x_new = Free ("x", newT);
   130     val y_old = Free ("y", oldT);
   131 
   132     val set' = if no_def then set else setC;
   133 
   134     val typedef_name = "type_definition_" ^ name;
   135     val typedefC =
   136       Const (type_definitionN, (newT --> oldT) --> (oldT --> newT) --> setT --> HOLogic.boolT);
   137     val typedef_prop =
   138       Logic.mk_implies (goal, HOLogic.mk_Trueprop (typedefC $ RepC $ AbsC $ set'));
   139 
   140     fun typedef_att (theory, nonempty) =
   141       theory
   142       |> add_typedecls [(t, vs, mx)]
   143       |> Theory.add_consts_i
   144        ((if no_def then [] else [(name, setT, NoSyn)]) @
   145         [(Rep_name, newT --> oldT, NoSyn),
   146          (Abs_name, oldT --> newT, NoSyn)])
   147       |> (if no_def then I else (#1 oo (PureThy.add_defs_i false o map Thm.no_attributes))
   148        [Logic.mk_defpair (setC, set)])
   149       |> PureThy.add_axioms_i [((typedef_name, typedef_prop),
   150           [apsnd (fn cond_axm => Drule.standard (nonempty RS cond_axm))])]
   151       |> (fn (theory', axm) =>
   152         let fun make th = Drule.standard (th OF axm) in
   153           rpair (hd axm) (theory'
   154           |> (#1 oo PureThy.add_thms)
   155             ([((Rep_name, make Rep), []),
   156               ((Rep_name ^ "_inverse", make Rep_inverse), []),
   157               ((Abs_name ^ "_inverse", make Abs_inverse), []),
   158               ((Rep_name ^ "_inject", make Rep_inject), []),
   159               ((Abs_name ^ "_inject", make Abs_inject), []),
   160               ((Rep_name ^ "_cases", make Rep_cases),
   161                 [RuleCases.case_names [Rep_name], InductAttrib.cases_set_global full_name]),
   162               ((Abs_name ^ "_cases", make Abs_cases),
   163                 [RuleCases.case_names [Abs_name], InductAttrib.cases_type_global full_tname]),
   164               ((Rep_name ^ "_induct", make Rep_induct),
   165                 [RuleCases.case_names [Rep_name], InductAttrib.induct_set_global full_name]),
   166               ((Abs_name ^ "_induct", make Abs_induct),
   167                 [RuleCases.case_names [Abs_name], InductAttrib.induct_type_global full_tname])]))
   168         end);
   169 
   170 
   171     (* errors *)
   172 
   173     fun show_names pairs = commas_quote (map fst pairs);
   174 
   175     val illegal_vars =
   176       if null (term_vars set) andalso null (term_tvars set) then []
   177       else ["Illegal schematic variable(s) on rhs"];
   178 
   179     val dup_lhs_tfrees =
   180       (case duplicates lhs_tfrees of [] => []
   181       | dups => ["Duplicate type variables on lhs: " ^ show_names dups]);
   182 
   183     val extra_rhs_tfrees =
   184       (case gen_rems (op =) (rhs_tfrees, lhs_tfrees) of [] => []
   185       | extras => ["Extra type variables on rhs: " ^ show_names extras]);
   186 
   187     val illegal_frees =
   188       (case term_frees set of [] => []
   189       | xs => ["Illegal variables on rhs: " ^ show_names (map dest_Free xs)]);
   190 
   191     val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees;
   192     val _ = if null errs then () else error (cat_lines errs);
   193 
   194     (*test theory errors now!*)
   195     val test_thy = Theory.copy thy;
   196     val _ = (test_thy,
   197       setmp quick_and_dirty true (SkipProof.make_thm test_thy) goal) |> typedef_att;
   198 
   199   in (cset, goal, goal_pat, typedef_att) end
   200   handle ERROR => err_in_typedef name;
   201 
   202 
   203 (* add_typedef interfaces *)
   204 
   205 fun gen_add_typedef prep_term no_def name typ set names thms tac thy =
   206   let
   207     val (cset, goal, _, typedef_att) = prepare_typedef prep_term no_def name typ set thy;
   208     val result = prove_nonempty thy cset goal (names, thms, tac);
   209   in (thy, result) |> typedef_att |> #1 end;
   210 
   211 val add_typedef = gen_add_typedef read_term false;
   212 val add_typedef_i = gen_add_typedef cert_term false;
   213 val add_typedef_i_no_def = gen_add_typedef cert_term true;
   214 
   215 
   216 (* typedef_proof interface *)
   217 
   218 fun gen_typedef_proof prep_term ((name, typ, set), comment) int thy =
   219   let val (_, goal, goal_pat, att) = prepare_typedef prep_term false name typ set thy in
   220     thy
   221     |> IsarThy.theorem_i Drule.internalK ((("", [att]), (goal, ([goal_pat], []))), comment) int
   222   end;
   223 
   224 val typedef_proof = gen_typedef_proof read_term;
   225 val typedef_proof_i = gen_typedef_proof cert_term;
   226 
   227 
   228 
   229 (** outer syntax **)
   230 
   231 local structure P = OuterParse and K = OuterSyntax.Keyword in
   232 
   233 val typedeclP =
   234   OuterSyntax.command "typedecl" "HOL type declaration" K.thy_decl
   235     (P.type_args -- P.name -- P.opt_infix --| P.marg_comment >> (fn ((vs, t), mx) =>
   236       Toplevel.theory (add_typedecls [(t, vs, mx)])));
   237 
   238 
   239 val typedef_proof_decl =
   240   Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") --
   241     (P.type_args -- P.name) -- P.opt_infix -- (P.$$$ "=" |-- P.term) -- P.marg_comment;
   242 
   243 fun mk_typedef_proof ((((opt_name, (vs, t)), mx), A), comment) =
   244   typedef_proof ((if_none opt_name (Syntax.type_name t mx), (t, vs, mx), A), comment);
   245 
   246 val typedefP =
   247   OuterSyntax.command "typedef" "HOL type definition (requires non-emptiness proof)" K.thy_goal
   248     (typedef_proof_decl >> (Toplevel.print oo (Toplevel.theory_to_proof o mk_typedef_proof)));
   249 
   250 
   251 val _ = OuterSyntax.add_parsers [typedeclP, typedefP];
   252 
   253 end;
   254 
   255 
   256 end;