src/HOL/Tools/typedef_package.ML
author wenzelm
Tue Oct 16 17:55:53 2001 +0200 (2001-10-16)
changeset 11807 50a36627e6d6
parent 11744 3a4625eaead0
child 11822 122834177ec1
permissions -rw-r--r--
typedef: export result;
     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 * thm
    15   val add_typedef_no_result: string -> bstring * string list * mixfix ->
    16     string -> string list -> thm list -> tactic option -> theory -> theory
    17   val add_typedef_i: string -> bstring * string list * mixfix ->
    18     term -> string list -> thm list -> tactic option -> theory -> theory * thm
    19   val add_typedef_i_no_def: string -> bstring * string list * mixfix ->
    20     term -> string list -> thm list -> tactic option -> theory -> theory * thm
    21   val typedef_proof:
    22     (string * (bstring * string list * mixfix) * string * (string * string) option) * Comment.text
    23     -> bool -> theory -> ProofHistory.T
    24   val typedef_proof_i:
    25     (string * (bstring * string list * mixfix) * term * (string * string) option) * Comment.text
    26     -> bool -> theory -> ProofHistory.T
    27 end;
    28 
    29 structure TypedefPackage: TYPEDEF_PACKAGE =
    30 struct
    31 
    32 
    33 (** theory context references **)
    34 
    35 val type_definitionN = "Typedef.type_definition";
    36 val type_definition_def = thm "type_definition_def";
    37 
    38 val Rep = thm "Rep";
    39 val Rep_inverse = thm "Rep_inverse";
    40 val Abs_inverse = thm "Abs_inverse";
    41 val Rep_inject = thm "Rep_inject";
    42 val Abs_inject = thm "Abs_inject";
    43 val Rep_cases = thm "Rep_cases";
    44 val Abs_cases = thm "Abs_cases";
    45 val Rep_induct = thm "Rep_induct";
    46 val Abs_induct = thm "Abs_induct";
    47 
    48 
    49 
    50 (** type declarations **)
    51 
    52 fun add_typedecls decls thy =
    53   let
    54     val full = Sign.full_name (Theory.sign_of thy);
    55 
    56     fun arity_of (raw_name, args, mx) =
    57       (full (Syntax.type_name raw_name mx), replicate (length args) HOLogic.termS, HOLogic.termS);
    58   in
    59     if can (Theory.assert_super HOL.thy) thy then
    60       thy
    61       |> PureThy.add_typedecls decls
    62       |> Theory.add_arities_i (map arity_of decls)
    63     else thy |> PureThy.add_typedecls decls
    64   end;
    65 
    66 
    67 
    68 (** type definitions **)
    69 
    70 (* messages *)
    71 
    72 val quiet_mode = ref false;
    73 fun message s = if ! quiet_mode then () else writeln s;
    74 
    75 
    76 (* prove_nonempty -- tactical version *)        (*exception ERROR*)
    77 
    78 fun prove_nonempty thy cset goal (witn_names, witn_thms, witn_tac) =
    79   let
    80     val is_def = Logic.is_equals o #prop o Thm.rep_thm;
    81     val thms = PureThy.get_thmss thy witn_names @ witn_thms;
    82     val tac =
    83       rtac exI 1 THEN
    84       TRY (rewrite_goals_tac (filter is_def thms)) THEN
    85       TRY (REPEAT_FIRST (resolve_tac (filter_out is_def thms))) THEN
    86       if_none witn_tac (TRY (ALLGOALS (CLASET' blast_tac)));
    87   in
    88     message ("Proving non-emptiness of set " ^ quote (string_of_cterm cset) ^ " ...");
    89     prove_goalw_cterm [] (cterm_of (sign_of thy) goal) (K [tac])
    90   end handle ERROR => error ("Failed to prove non-emptiness of " ^ quote (string_of_cterm cset));
    91 
    92 
    93 (* prepare_typedef *)
    94 
    95 fun read_term sg used s =
    96   #1 (Thm.read_def_cterm (sg, K None, K None) used true (s, HOLogic.termT));
    97 
    98 fun cert_term sg _ t = Thm.cterm_of sg t handle TERM (msg, _) => error msg;
    99 
   100 fun err_in_typedef name =
   101   error ("The error(s) above occurred in typedef " ^ quote name);
   102 
   103 fun prepare_typedef prep_term no_def name (t, vs, mx) raw_set opt_morphs thy =
   104   let
   105     val _ = Theory.requires thy "Typedef" "typedefs";
   106     val sign = Theory.sign_of thy;
   107     val full = Sign.full_name sign;
   108 
   109     (*rhs*)
   110     val full_name = full name;
   111     val cset = prep_term sign vs raw_set;
   112     val {T = setT, t = set, ...} = Thm.rep_cterm cset;
   113     val rhs_tfrees = term_tfrees set;
   114     val oldT = HOLogic.dest_setT setT handle TYPE _ =>
   115       error ("Not a set type: " ^ quote (Sign.string_of_typ sign setT));
   116     fun mk_nonempty A =
   117       HOLogic.mk_Trueprop (HOLogic.mk_exists ("x", oldT, HOLogic.mk_mem (Free ("x", oldT), A)));
   118     val goal = mk_nonempty set;
   119     val vname = take_suffix Symbol.is_digit (Symbol.explode name)
   120       |> apfst implode |> apsnd (#1 o Term.read_int);
   121     val goal_pat = mk_nonempty (Var (vname, setT));
   122 
   123     (*lhs*)
   124     val lhs_tfrees = map (fn v => (v, if_none (assoc (rhs_tfrees, v)) HOLogic.termS)) vs;
   125     val tname = Syntax.type_name t mx;
   126     val full_tname = full tname;
   127     val newT = Type (full_tname, map TFree lhs_tfrees);
   128 
   129     val (Rep_name, Abs_name) = if_none opt_morphs ("Rep_" ^ name, "Abs_" ^ name);
   130     val setC = Const (full_name, setT);
   131     val RepC = Const (full Rep_name, newT --> oldT);
   132     val AbsC = Const (full Abs_name, oldT --> newT);
   133     val x_new = Free ("x", newT);
   134     val y_old = Free ("y", oldT);
   135 
   136     val set' = if no_def then set else setC;
   137 
   138     val typedef_name = "type_definition_" ^ name;
   139     val typedefC =
   140       Const (type_definitionN, (newT --> oldT) --> (oldT --> newT) --> setT --> HOLogic.boolT);
   141     val typedef_prop =
   142       Logic.mk_implies (goal, HOLogic.mk_Trueprop (typedefC $ RepC $ AbsC $ set'));
   143 
   144     fun typedef_att (theory, nonempty) =
   145       theory
   146       |> add_typedecls [(t, vs, mx)]
   147       |> Theory.add_consts_i
   148        ((if no_def then [] else [(name, setT, NoSyn)]) @
   149         [(Rep_name, newT --> oldT, NoSyn),
   150          (Abs_name, oldT --> newT, NoSyn)])
   151       |> (if no_def then I else (#1 oo (PureThy.add_defs_i false o map Thm.no_attributes))
   152        [Logic.mk_defpair (setC, set)])
   153       |> PureThy.add_axioms_i [((typedef_name, typedef_prop),
   154           [apsnd (fn cond_axm => Drule.standard (nonempty RS cond_axm))])]
   155       |> (fn (theory', axm) =>
   156         let fun make th = Drule.standard (th OF axm) in
   157           rpair (hd axm) (theory'
   158           |> (#1 oo PureThy.add_thms)
   159             ([((Rep_name, make Rep), []),
   160               ((Rep_name ^ "_inverse", make Rep_inverse), []),
   161               ((Abs_name ^ "_inverse", make Abs_inverse), []),
   162               ((Rep_name ^ "_inject", make Rep_inject), []),
   163               ((Abs_name ^ "_inject", make Abs_inject), []),
   164               ((Rep_name ^ "_cases", make Rep_cases),
   165                 [RuleCases.case_names [Rep_name], InductAttrib.cases_set_global full_name]),
   166               ((Abs_name ^ "_cases", make Abs_cases),
   167                 [RuleCases.case_names [Abs_name], InductAttrib.cases_type_global full_tname]),
   168               ((Rep_name ^ "_induct", make Rep_induct),
   169                 [RuleCases.case_names [Rep_name], InductAttrib.induct_set_global full_name]),
   170               ((Abs_name ^ "_induct", make Abs_induct),
   171                 [RuleCases.case_names [Abs_name], InductAttrib.induct_type_global full_tname])]))
   172         end);
   173 
   174 
   175     (* errors *)
   176 
   177     fun show_names pairs = commas_quote (map fst pairs);
   178 
   179     val illegal_vars =
   180       if null (term_vars set) andalso null (term_tvars set) then []
   181       else ["Illegal schematic variable(s) on rhs"];
   182 
   183     val dup_lhs_tfrees =
   184       (case duplicates lhs_tfrees of [] => []
   185       | dups => ["Duplicate type variables on lhs: " ^ show_names dups]);
   186 
   187     val extra_rhs_tfrees =
   188       (case gen_rems (op =) (rhs_tfrees, lhs_tfrees) of [] => []
   189       | extras => ["Extra type variables on rhs: " ^ show_names extras]);
   190 
   191     val illegal_frees =
   192       (case term_frees set of [] => []
   193       | xs => ["Illegal variables on rhs: " ^ show_names (map dest_Free xs)]);
   194 
   195     val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees;
   196     val _ = if null errs then () else error (cat_lines errs);
   197 
   198     (*test theory errors now!*)
   199     val test_thy = Theory.copy thy;
   200     val _ = (test_thy,
   201       setmp quick_and_dirty true (SkipProof.make_thm test_thy) goal) |> typedef_att;
   202 
   203   in (cset, goal, goal_pat, typedef_att) end
   204   handle ERROR => err_in_typedef name;
   205 
   206 
   207 (* add_typedef interfaces *)
   208 
   209 fun gen_add_typedef prep_term no_def name typ set names thms tac thy =
   210   let
   211     val (cset, goal, _, typedef_att) = prepare_typedef prep_term no_def name typ set None thy;
   212     val result = prove_nonempty thy cset goal (names, thms, tac);
   213   in (thy, result) |> typedef_att end;
   214 
   215 val add_typedef = gen_add_typedef read_term false;
   216 val add_typedef_i = gen_add_typedef cert_term false;
   217 val add_typedef_i_no_def = gen_add_typedef cert_term true;
   218 fun add_typedef_no_result x y z = #1 oooo add_typedef x y z;
   219 
   220 
   221 (* typedef_proof interface *)
   222 
   223 fun gen_typedef_proof prep_term ((name, typ, set, opt_morphs), comment) int thy =
   224   let val (_, goal, goal_pat, att) = prepare_typedef prep_term false name typ set opt_morphs thy in
   225     thy |>
   226     IsarThy.theorem_i Drule.internalK ((("", [att]), (goal, ([goal_pat], []))), comment) int
   227   end;
   228 
   229 val typedef_proof = gen_typedef_proof read_term;
   230 val typedef_proof_i = gen_typedef_proof cert_term;
   231 
   232 
   233 
   234 (** outer syntax **)
   235 
   236 local structure P = OuterParse and K = OuterSyntax.Keyword in
   237 
   238 val typedeclP =
   239   OuterSyntax.command "typedecl" "HOL type declaration" K.thy_decl
   240     (P.type_args -- P.name -- P.opt_infix --| P.marg_comment >> (fn ((vs, t), mx) =>
   241       Toplevel.theory (add_typedecls [(t, vs, mx)])));
   242 
   243 
   244 val typedef_proof_decl =
   245   Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") --
   246     (P.type_args -- P.name) -- P.opt_infix -- (P.$$$ "=" |-- P.term) --
   247     Scan.option (P.$$$ "morphisms" |-- P.!!! (P.name -- P.name)) --
   248     P.marg_comment;
   249 
   250 fun mk_typedef_proof (((((opt_name, (vs, t)), mx), A), morphs), comment) =
   251   typedef_proof ((if_none opt_name (Syntax.type_name t mx), (t, vs, mx), A, morphs), comment);
   252 
   253 val typedefP =
   254   OuterSyntax.command "typedef" "HOL type definition (requires non-emptiness proof)" K.thy_goal
   255     (typedef_proof_decl >> (Toplevel.print oo (Toplevel.theory_to_proof o mk_typedef_proof)));
   256 
   257 
   258 val _ = OuterSyntax.add_keywords ["morphisms"];
   259 val _ = OuterSyntax.add_parsers [typedeclP, typedefP];
   260 
   261 end;
   262 
   263 
   264 end;