src/HOL/Tools/typedef_package.ML
author wenzelm
Mon Jun 20 22:13:59 2005 +0200 (2005-06-20)
changeset 16486 1a12cdb6ee6b
parent 16458 4c6fd0c01d28
child 16645 a152d6b21c31
permissions -rw-r--r--
get_thm(s): Name;
     1 (*  Title:      HOL/Tools/typedef_package.ML
     2     ID:         $Id$
     3     Author:     Markus Wenzel and Stefan Berghofer, TU Muenchen
     4 
     5 Gordon/HOL-style type definitions.
     6 *)
     7 
     8 signature TYPEDEF_PACKAGE =
     9 sig
    10   val quiet_mode: bool ref
    11   val add_typedecls: (bstring * string list * mixfix) list -> theory -> theory
    12   val add_typedef_x: string -> bstring * string list * mixfix ->
    13     string -> string list -> thm list -> tactic option -> theory -> theory
    14   val add_typedef: bool -> string option -> bstring * string list * mixfix ->
    15     string -> (bstring * bstring) option -> tactic -> theory -> theory *
    16     {type_definition: thm, set_def: thm option, Rep: thm, Rep_inverse: thm,
    17       Abs_inverse: thm, Rep_inject: thm, Abs_inject: thm, Rep_cases: thm, Abs_cases: thm,
    18       Rep_induct: thm, Abs_induct: thm}
    19   val add_typedef_i: bool -> string option -> bstring * string list * mixfix ->
    20     term -> (bstring * bstring) option -> tactic -> theory -> theory *
    21     {type_definition: thm, set_def: thm option, Rep: thm, Rep_inverse: thm,
    22       Abs_inverse: thm, Rep_inject: thm, Abs_inject: thm, Rep_cases: thm, Abs_cases: thm,
    23       Rep_induct: thm, Abs_induct: thm}
    24   val typedef_proof: (bool * string) * (bstring * string list * mixfix) * string
    25     * (string * string) option -> bool -> theory -> ProofHistory.T
    26   val typedef_proof_i: (bool * string) * (bstring * string list * mixfix) * term
    27     * (string * string) option -> bool -> theory -> ProofHistory.T
    28   val setup: (theory -> theory) list
    29 end;
    30 
    31 structure TypedefPackage: TYPEDEF_PACKAGE =
    32 struct
    33 
    34 
    35 (** theory context references **)
    36 
    37 val type_definitionN = "Typedef.type_definition";
    38 
    39 val Rep = thm "type_definition.Rep";
    40 val Rep_inverse = thm "type_definition.Rep_inverse";
    41 val Abs_inverse = thm "type_definition.Abs_inverse";
    42 val Rep_inject = thm "type_definition.Rep_inject";
    43 val Abs_inject = thm "type_definition.Abs_inject";
    44 val Rep_cases = thm "type_definition.Rep_cases";
    45 val Abs_cases = thm "type_definition.Abs_cases";
    46 val Rep_induct = thm "type_definition.Rep_induct";
    47 val Abs_induct = thm "type_definition.Abs_induct";
    48 
    49 
    50 
    51 (** theory data **)
    52 
    53 structure TypedefData = TheoryDataFun
    54 (struct
    55   val name = "HOL/typedef";
    56   type T = (typ * typ * string * string) Symtab.table;
    57   val empty = Symtab.empty;
    58   val copy = I;
    59   val extend = I;
    60   fun merge _ (tabs: T * T) = Symtab.merge (op =) tabs;
    61   fun print _ _ = ();
    62 end);
    63 
    64 fun put_typedef newT oldT Abs_name Rep_name thy =
    65   TypedefData.put (Symtab.update_new
    66     ((fst (dest_Type newT), (newT, oldT, Abs_name, Rep_name)),
    67      TypedefData.get thy)) thy;
    68 
    69 
    70 
    71 (** type declarations **)
    72 
    73 fun add_typedecls decls thy =
    74   let
    75     fun arity_of (raw_name, args, mx) =
    76       (Sign.full_name thy (Syntax.type_name raw_name mx),
    77         replicate (length args) HOLogic.typeS, HOLogic.typeS);
    78   in
    79     if can (Theory.assert_super HOL.thy) thy then
    80       thy |> Theory.add_typedecls decls
    81       |> Theory.add_arities_i (map arity_of decls)
    82     else thy |> Theory.add_typedecls decls
    83   end;
    84 
    85 
    86 
    87 (** type definitions **)
    88 
    89 (* messages *)
    90 
    91 val quiet_mode = ref false;
    92 fun message s = if ! quiet_mode then () else writeln s;
    93 
    94 
    95 (* prove_nonempty -- tactical version *)        (*exception ERROR*)
    96 
    97 fun prove_nonempty thy cset goal (witn1_tac, witn_names, witn_thms, witn2_tac) =
    98   let
    99     val is_def = Logic.is_equals o #prop o Thm.rep_thm;
   100     val thms = PureThy.get_thmss thy (map Name witn_names) @ witn_thms;
   101     val tac =
   102       witn1_tac THEN
   103       TRY (rewrite_goals_tac (List.filter is_def thms)) THEN
   104       TRY (REPEAT_FIRST (resolve_tac (filter_out is_def thms))) THEN
   105       getOpt (witn2_tac, TRY (ALLGOALS (CLASET' blast_tac)));
   106   in
   107     message ("Proving non-emptiness of set " ^ quote (string_of_cterm cset) ^ " ...");
   108     Tactic.prove thy [] [] goal (K tac)
   109   end
   110   handle ERROR => error ("Failed to prove non-emptiness of " ^ quote (string_of_cterm cset));
   111 
   112 
   113 (* prepare_typedef *)
   114 
   115 fun read_term thy used s =
   116   #1 (Thm.read_def_cterm (thy, K NONE, K NONE) used true (s, HOLogic.typeT));
   117 
   118 fun cert_term thy _ t = Thm.cterm_of thy t handle TERM (msg, _) => error msg;
   119 
   120 fun err_in_typedef name =
   121   error ("The error(s) above occurred in typedef " ^ quote name);
   122 
   123 fun prepare_typedef prep_term def name (t, vs, mx) raw_set opt_morphs thy =
   124   let
   125     val _ = Theory.requires thy "Typedef" "typedefs";
   126     val full = Sign.full_name thy;
   127 
   128     (*rhs*)
   129     val full_name = full name;
   130     val cset = prep_term thy vs raw_set;
   131     val {T = setT, t = set, ...} = Thm.rep_cterm cset;
   132     val rhs_tfrees = term_tfrees set;
   133     val oldT = HOLogic.dest_setT setT handle TYPE _ =>
   134       error ("Not a set type: " ^ quote (Sign.string_of_typ thy setT));
   135     fun mk_nonempty A =
   136       HOLogic.mk_Trueprop (HOLogic.mk_exists ("x", oldT, HOLogic.mk_mem (Free ("x", oldT), A)));
   137     val goal = mk_nonempty set;
   138     val vname = take_suffix Symbol.is_digit (Symbol.explode name)
   139       |> apfst implode |> apsnd (#1 o Library.read_int);
   140     val goal_pat = mk_nonempty (Var (vname, setT));
   141 
   142     (*lhs*)
   143     val lhs_tfrees = map (fn v => (v, getOpt (assoc (rhs_tfrees, v), HOLogic.typeS))) vs;
   144     val tname = Syntax.type_name t mx;
   145     val full_tname = full tname;
   146     val newT = Type (full_tname, map TFree lhs_tfrees);
   147 
   148     val (Rep_name, Abs_name) = getOpt (opt_morphs, ("Rep_" ^ name, "Abs_" ^ name));
   149     val setC = Const (full_name, setT);
   150     val RepC = Const (full Rep_name, newT --> oldT);
   151     val AbsC = Const (full Abs_name, oldT --> newT);
   152     val x_new = Free ("x", newT);
   153     val y_old = Free ("y", oldT);
   154 
   155     val set' = if def then setC else set;
   156 
   157     val typedef_name = "type_definition_" ^ name;
   158     val typedefC =
   159       Const (type_definitionN, (newT --> oldT) --> (oldT --> newT) --> setT --> HOLogic.boolT);
   160     val typedef_prop =
   161       Logic.mk_implies (goal, HOLogic.mk_Trueprop (typedefC $ RepC $ AbsC $ set'));
   162 
   163     fun typedef_result (theory, nonempty) =
   164       theory
   165       |> put_typedef newT oldT (full Abs_name) (full Rep_name)
   166       |> add_typedecls [(t, vs, mx)]
   167       |> Theory.add_consts_i
   168        ((if def then [(name, setT, NoSyn)] else []) @
   169         [(Rep_name, newT --> oldT, NoSyn),
   170          (Abs_name, oldT --> newT, NoSyn)])
   171       |> (if def then (apsnd (SOME o hd) oo (PureThy.add_defs_i false o map Thm.no_attributes))
   172            [Logic.mk_defpair (setC, set)]
   173           else rpair NONE)
   174       |>>> PureThy.add_axioms_i [((typedef_name, typedef_prop),
   175           [apsnd (fn cond_axm => Drule.standard (nonempty RS cond_axm))])]
   176       |>> Theory.add_finals_i false [RepC, AbsC]
   177       |> (fn (theory', (set_def, [type_definition])) =>
   178         let
   179           fun make th = Drule.standard (th OF [type_definition]);
   180           val (theory'', [Rep, Rep_inverse, Abs_inverse, Rep_inject, Abs_inject,
   181               Rep_cases, Abs_cases, Rep_induct, Abs_induct]) =
   182             theory'
   183             |> Theory.add_path name
   184             |> PureThy.add_thms
   185               ([((Rep_name, make Rep), []),
   186                 ((Rep_name ^ "_inverse", make Rep_inverse), []),
   187                 ((Abs_name ^ "_inverse", make Abs_inverse), []),
   188                 ((Rep_name ^ "_inject", make Rep_inject), []),
   189                 ((Abs_name ^ "_inject", make Abs_inject), []),
   190                 ((Rep_name ^ "_cases", make Rep_cases),
   191                   [RuleCases.case_names [Rep_name], InductAttrib.cases_set_global full_name]),
   192                 ((Abs_name ^ "_cases", make Abs_cases),
   193                   [RuleCases.case_names [Abs_name], InductAttrib.cases_type_global full_tname]),
   194                 ((Rep_name ^ "_induct", make Rep_induct),
   195                   [RuleCases.case_names [Rep_name], InductAttrib.induct_set_global full_name]),
   196                 ((Abs_name ^ "_induct", make Abs_induct),
   197                   [RuleCases.case_names [Abs_name], InductAttrib.induct_type_global full_tname])])
   198             |>> Theory.parent_path;
   199           val result = {type_definition = type_definition, set_def = set_def,
   200             Rep = Rep, Rep_inverse = Rep_inverse, Abs_inverse = Abs_inverse,
   201             Rep_inject = Rep_inject, Abs_inject = Abs_inject, Rep_cases = Rep_cases,
   202             Abs_cases = Abs_cases, Rep_induct = Rep_induct, Abs_induct = Abs_induct};
   203         in ((theory'', type_definition), result) end);
   204 
   205 
   206     (* errors *)
   207 
   208     fun show_names pairs = commas_quote (map fst pairs);
   209 
   210     val illegal_vars =
   211       if null (term_vars set) andalso null (term_tvars set) then []
   212       else ["Illegal schematic variable(s) on rhs"];
   213 
   214     val dup_lhs_tfrees =
   215       (case duplicates lhs_tfrees of [] => []
   216       | dups => ["Duplicate type variables on lhs: " ^ show_names dups]);
   217 
   218     val extra_rhs_tfrees =
   219       (case gen_rems (op =) (rhs_tfrees, lhs_tfrees) of [] => []
   220       | extras => ["Extra type variables on rhs: " ^ show_names extras]);
   221 
   222     val illegal_frees =
   223       (case term_frees set of [] => []
   224       | xs => ["Illegal variables on rhs: " ^ show_names (map dest_Free xs)]);
   225 
   226     val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees;
   227     val _ = if null errs then () else error (cat_lines errs);
   228 
   229     (*test theory errors now!*)
   230     val test_thy = Theory.copy thy;
   231     val _ = (test_thy,
   232       setmp quick_and_dirty true (SkipProof.make_thm test_thy) goal) |> typedef_result;
   233 
   234   in (cset, goal, goal_pat, typedef_result) end
   235   handle ERROR => err_in_typedef name;
   236 
   237 
   238 (* add_typedef interfaces *)
   239 
   240 fun gen_typedef prep_term def name typ set opt_morphs tac1 names thms tac2 thy =
   241   let
   242     val (cset, goal, _, typedef_result) =
   243       prepare_typedef prep_term def name typ set opt_morphs thy;
   244     val non_empty = prove_nonempty thy cset goal (tac1, names, thms, tac2);
   245     val ((thy', _), result) = (thy, non_empty) |> typedef_result;
   246   in (thy', result) end;
   247 
   248 fun sane_typedef prep_term def opt_name typ set opt_morphs tac =
   249   gen_typedef prep_term def
   250     (getOpt (opt_name, #1 typ)) typ set opt_morphs all_tac [] [] (SOME tac);
   251 
   252 fun add_typedef_x name typ set names thms tac =
   253   #1 o gen_typedef read_term true name typ set NONE (Tactic.rtac exI 1) names thms tac;
   254 
   255 val add_typedef = sane_typedef read_term;
   256 val add_typedef_i = sane_typedef cert_term;
   257 
   258 
   259 (* typedef_proof interface *)
   260 
   261 fun gen_typedef_proof prep_term ((def, name), typ, set, opt_morphs) int thy =
   262   let
   263     val (_, goal, goal_pat, att_result) =
   264       prepare_typedef prep_term def name typ set opt_morphs thy;
   265     val att = #1 o att_result;
   266   in thy |> IsarThy.theorem_i Drule.internalK (("", [att]), (goal, ([goal_pat], []))) int end;
   267 
   268 val typedef_proof = gen_typedef_proof read_term;
   269 val typedef_proof_i = gen_typedef_proof cert_term;
   270 
   271 
   272 
   273 (** trivial code generator **)
   274 
   275 fun typedef_codegen thy gr dep brack t =
   276   let
   277     fun mk_fun s T ts =
   278       let
   279         val (gr', _) = Codegen.invoke_tycodegen thy dep false (gr, T);
   280         val (gr'', ps) =
   281           foldl_map (Codegen.invoke_codegen thy dep true) (gr', ts);
   282         val id = Codegen.mk_const_id thy s
   283       in SOME (gr'', Codegen.mk_app brack (Pretty.str id) ps) end;
   284     fun get_name (Type (tname, _)) = tname
   285       | get_name _ = "";
   286     fun lookup f T = getOpt (Option.map f (Symtab.lookup
   287       (TypedefData.get thy, get_name T)), "")
   288   in
   289     (case strip_comb t of
   290        (Const (s, Type ("fun", [T, U])), ts) =>
   291          if lookup #4 T = s andalso
   292            is_none (Codegen.get_assoc_type thy (get_name T))
   293          then mk_fun s T ts
   294          else if lookup #3 U = s andalso
   295            is_none (Codegen.get_assoc_type thy (get_name U))
   296          then mk_fun s U ts
   297          else NONE
   298      | _ => NONE)
   299   end;
   300 
   301 fun mk_tyexpr [] s = Pretty.str s
   302   | mk_tyexpr [p] s = Pretty.block [p, Pretty.str (" " ^ s)]
   303   | mk_tyexpr ps s = Pretty.list "(" (") " ^ s) ps;
   304 
   305 fun typedef_tycodegen thy gr dep brack (Type (s, Ts)) =
   306       (case Symtab.lookup (TypedefData.get thy, s) of
   307          NONE => NONE
   308        | SOME (newT as Type (tname, Us), oldT, Abs_name, Rep_name) =>
   309            if isSome (Codegen.get_assoc_type thy tname) then NONE else
   310            let
   311              val Abs_id = Codegen.mk_const_id thy Abs_name;
   312              val Rep_id = Codegen.mk_const_id thy Rep_name;
   313              val ty_id = Codegen.mk_type_id thy s;
   314              val (gr', qs) = foldl_map
   315                (Codegen.invoke_tycodegen thy dep (length Ts = 1)) (gr, Ts);
   316              val gr'' = Graph.add_edge (Abs_id, dep) gr' handle Graph.UNDEF _ =>
   317                let
   318                  val (gr'', p :: ps) = foldl_map
   319                    (Codegen.invoke_tycodegen thy Abs_id false)
   320                    (Graph.add_edge (Abs_id, dep)
   321                       (Graph.new_node (Abs_id, (NONE, "")) gr'), oldT :: Us);
   322                  val s =
   323                    Pretty.string_of (Pretty.block [Pretty.str "datatype ",
   324                      mk_tyexpr ps ty_id,
   325                      Pretty.str " =", Pretty.brk 1, Pretty.str (Abs_id ^ " of"),
   326                      Pretty.brk 1, p, Pretty.str ";"]) ^ "\n\n" ^
   327                    Pretty.string_of (Pretty.block [Pretty.str ("fun " ^ Rep_id),
   328                      Pretty.brk 1, Pretty.str ("(" ^ Abs_id), Pretty.brk 1,
   329                      Pretty.str "x) = x;"]) ^ "\n\n" ^
   330                    (if "term_of" mem !Codegen.mode then
   331                       Pretty.string_of (Pretty.block [Pretty.str "fun ",
   332                         Codegen.mk_term_of thy false newT, Pretty.brk 1,
   333                         Pretty.str ("(" ^ Abs_id), Pretty.brk 1,
   334                         Pretty.str "x) =", Pretty.brk 1,
   335                         Pretty.block [Pretty.str ("Const (\"" ^ Abs_name ^ "\","),
   336                           Pretty.brk 1, Codegen.mk_type false (oldT --> newT),
   337                           Pretty.str ")"], Pretty.str " $", Pretty.brk 1,
   338                         Codegen.mk_term_of thy false oldT, Pretty.brk 1,
   339                         Pretty.str "x;"]) ^ "\n\n"
   340                     else "") ^
   341                    (if "test" mem !Codegen.mode then
   342                       Pretty.string_of (Pretty.block [Pretty.str "fun ",
   343                         Codegen.mk_gen thy false [] "" newT, Pretty.brk 1,
   344                         Pretty.str "i =", Pretty.brk 1,
   345                         Pretty.block [Pretty.str (Abs_id ^ " ("),
   346                           Codegen.mk_gen thy false [] "" oldT, Pretty.brk 1,
   347                           Pretty.str "i);"]]) ^ "\n\n"
   348                     else "")
   349                in Graph.map_node Abs_id (K (NONE, s)) gr'' end
   350            in
   351              SOME (gr'', mk_tyexpr qs ty_id)
   352            end)
   353   | typedef_tycodegen thy gr dep brack _ = NONE;
   354 
   355 val setup =
   356   [TypedefData.init,
   357    Codegen.add_codegen "typedef" typedef_codegen,
   358    Codegen.add_tycodegen "typedef" typedef_tycodegen];
   359 
   360 
   361 
   362 (** outer syntax **)
   363 
   364 local structure P = OuterParse and K = OuterSyntax.Keyword in
   365 
   366 val typedeclP =
   367   OuterSyntax.command "typedecl" "type declaration (HOL)" K.thy_decl
   368     (P.type_args -- P.name -- P.opt_infix >> (fn ((vs, t), mx) =>
   369       Toplevel.theory (add_typedecls [(t, vs, mx)])));
   370 
   371 
   372 val typedef_proof_decl =
   373   Scan.optional (P.$$$ "(" |--
   374       ((P.$$$ "open" >> K false) -- Scan.option P.name || P.name >> (fn s => (true, SOME s)))
   375         --| P.$$$ ")") (true, NONE) --
   376     (P.type_args -- P.name) -- P.opt_infix -- (P.$$$ "=" |-- P.term) --
   377     Scan.option (P.$$$ "morphisms" |-- P.!!! (P.name -- P.name));
   378 
   379 fun mk_typedef_proof ((((((def, opt_name), (vs, t)), mx), A), morphs)) =
   380   typedef_proof ((def, getOpt (opt_name, Syntax.type_name t mx)), (t, vs, mx), A, morphs);
   381 
   382 val typedefP =
   383   OuterSyntax.command "typedef" "HOL type definition (requires non-emptiness proof)" K.thy_goal
   384     (typedef_proof_decl >> (Toplevel.print oo (Toplevel.theory_to_proof o mk_typedef_proof)));
   385 
   386 
   387 val _ = OuterSyntax.add_keywords ["morphisms"];
   388 val _ = OuterSyntax.add_parsers [typedeclP, typedefP];
   389 
   390 end;
   391 
   392 end;