src/HOL/Tools/typedef_package.ML
author paulson
Fri Nov 24 16:38:42 2006 +0100 (2006-11-24)
changeset 21513 9e9fff87dc6c
parent 21434 944f80576be0
child 21565 bd28361f4c5b
permissions -rw-r--r--
Conversion of "equal" to "=" for TSTP format; big tidy-up
     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: create a new syntactic type
     6 represented by a non-empty subset.
     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   type info =
    14    {rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string,
    15     type_definition: thm, set_def: thm option, Rep: thm, Rep_inverse: thm,
    16     Abs_inverse: thm, Rep_inject: thm, Abs_inject: thm, Rep_cases: thm,
    17     Abs_cases: thm, Rep_induct: thm, Abs_induct: thm};
    18   val get_info: theory -> string -> info option
    19   val add_typedef: bool -> string option -> bstring * string list * mixfix ->
    20     string -> (bstring * bstring) option -> tactic -> theory -> (string * info) * theory
    21   val add_typedef_i: bool -> string option -> bstring * string list * mixfix ->
    22     term -> (bstring * bstring) option -> tactic -> theory -> (string * info) * theory
    23   val typedef: (bool * string) * (bstring * string list * mixfix) * string
    24     * (string * string) option -> theory -> Proof.state
    25   val typedef_i: (bool * string) * (bstring * string list * mixfix) * term
    26     * (string * string) option -> theory -> Proof.state
    27   val setup: theory -> theory
    28 end;
    29 
    30 structure TypedefPackage: TYPEDEF_PACKAGE =
    31 struct
    32 
    33 (** theory context references **)
    34 
    35 val type_definitionN = "Typedef.type_definition";
    36 
    37 val Rep = thm "type_definition.Rep";
    38 val Rep_inverse = thm "type_definition.Rep_inverse";
    39 val Abs_inverse = thm "type_definition.Abs_inverse";
    40 val Rep_inject = thm "type_definition.Rep_inject";
    41 val Abs_inject = thm "type_definition.Abs_inject";
    42 val Rep_cases = thm "type_definition.Rep_cases";
    43 val Abs_cases = thm "type_definition.Abs_cases";
    44 val Rep_induct = thm "type_definition.Rep_induct";
    45 val Abs_induct = thm "type_definition.Abs_induct";
    46 
    47 
    48 
    49 (** type declarations **)
    50 
    51 fun HOL_arity (raw_name, args, mx) thy =
    52   thy |> AxClass.axiomatize_arity_i
    53     (Sign.full_name thy (Syntax.type_name raw_name mx),
    54       replicate (length args) HOLogic.typeS, HOLogic.typeS);
    55 
    56 fun add_typedecls decls thy =
    57   thy
    58   |> Theory.add_typedecls decls
    59   |> can (Theory.assert_super HOL.thy) ? fold HOL_arity decls;
    60 
    61 
    62 
    63 (** type definitions **)
    64 
    65 (* messages *)
    66 
    67 val quiet_mode = ref false;
    68 fun message s = if ! quiet_mode then () else writeln s;
    69 
    70 
    71 (* theory data *)
    72 
    73 type info =
    74  {rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string,
    75   type_definition: thm, set_def: thm option, Rep: thm, Rep_inverse: thm,
    76   Abs_inverse: thm, Rep_inject: thm, Abs_inject: thm, Rep_cases: thm,
    77   Abs_cases: thm, Rep_induct: thm, Abs_induct: thm};
    78 
    79 structure TypedefData = TheoryDataFun
    80 (struct
    81   val name = "HOL/typedef";
    82   type T = info Symtab.table;
    83   val empty = Symtab.empty;
    84   val copy = I;
    85   val extend = I;
    86   fun merge _ tabs : T = Symtab.merge (K true) tabs;
    87   fun print _ _ = ();
    88 end);
    89 
    90 val get_info = Symtab.lookup o TypedefData.get;
    91 fun put_info name info = TypedefData.map (Symtab.update (name, info));
    92 
    93 
    94 (* prepare_typedef *)
    95 
    96 fun err_in_typedef msg name =
    97   cat_error msg ("The error(s) above occurred in typedef " ^ quote name);
    98 
    99 fun declare_type_name a = Variable.declare_constraints (Logic.mk_type (TFree (a, dummyS)));
   100 
   101 fun prepare_typedef prep_term def name (t, vs, mx) raw_set opt_morphs thy =
   102   let
   103     val _ = Theory.requires thy "Typedef" "typedefs";
   104     val ctxt = ProofContext.init thy;
   105     val full = Sign.full_name thy;
   106 
   107     (*rhs*)
   108     val full_name = full name;
   109     val set = prep_term (ctxt |> fold declare_type_name vs) raw_set;
   110     val setT = Term.fastype_of set;
   111     val rhs_tfrees = Term.add_tfrees set [];
   112     val rhs_tfreesT = Term.add_tfreesT setT [];
   113     val oldT = HOLogic.dest_setT setT handle TYPE _ =>
   114       error ("Not a set type: " ^ quote (ProofContext.string_of_typ ctxt setT));
   115     fun mk_nonempty A =
   116       HOLogic.mk_Trueprop (HOLogic.mk_exists ("x", oldT, HOLogic.mk_mem (Free ("x", oldT), A)));
   117     val goal = mk_nonempty set;
   118     val goal_pat = mk_nonempty (Var (the_default (name, 0) (Syntax.read_variable name), setT));
   119 
   120     (*lhs*)
   121     val defS = Sign.defaultS thy;
   122     val lhs_tfrees = map (fn v => (v, the_default defS (AList.lookup (op =) rhs_tfrees v))) vs;
   123     val args_setT = lhs_tfrees
   124       |> filter (member (op =) rhs_tfrees andf (not o member (op =) rhs_tfreesT))
   125       |> map TFree;
   126 
   127     val tname = Syntax.type_name t mx;
   128     val full_tname = full tname;
   129     val newT = Type (full_tname, map TFree lhs_tfrees);
   130 
   131     val (Rep_name, Abs_name) = the_default ("Rep_" ^ name, "Abs_" ^ name) opt_morphs;
   132     val setT' = map Term.itselfT args_setT ---> setT;
   133     val setC = Term.list_comb (Const (full_name, setT'), map Logic.mk_type args_setT);
   134     val RepC = Const (full Rep_name, newT --> oldT);
   135     val AbsC = Const (full Abs_name, oldT --> newT);
   136     val x_new = Free ("x", newT);
   137     val y_old = Free ("y", oldT);
   138 
   139     val set' = if def then setC else set;
   140 
   141     val typedef_name = "type_definition_" ^ name;
   142     val typedefC =
   143       Const (type_definitionN, (newT --> oldT) --> (oldT --> newT) --> setT --> HOLogic.boolT);
   144     val typedef_prop =
   145       Logic.mk_implies (goal, HOLogic.mk_Trueprop (typedefC $ RepC $ AbsC $ set'));
   146     val typedef_deps = Term.fold_aterms (fn Const c => insert (op =) c | _ => I) set' [];
   147 
   148     fun add_def eq thy =
   149       if def then
   150         thy
   151         |> PureThy.add_defs_i false [Thm.no_attributes eq]
   152         |-> (fn [th] => pair (SOME th))
   153       else (NONE, thy);
   154 
   155     fun typedef_result nonempty =
   156       add_typedecls [(t, vs, mx)]
   157       #> Theory.add_consts_i
   158        ((if def then [(name, setT', NoSyn)] else []) @
   159         [(Rep_name, newT --> oldT, NoSyn),
   160          (Abs_name, oldT --> newT, NoSyn)])
   161       #> add_def (Logic.mk_defpair (setC, set))
   162       ##>> PureThy.add_axioms_i [((typedef_name, typedef_prop),
   163           [apsnd (fn cond_axm => nonempty RS cond_axm)])]
   164       ##> Theory.add_deps "" (dest_Const RepC) typedef_deps
   165       ##> Theory.add_deps "" (dest_Const AbsC) typedef_deps
   166       #-> (fn (set_def, [type_definition]) => fn thy1 =>
   167         let
   168           fun make th = Drule.standard (th OF [type_definition]);
   169           val abs_inject = make Abs_inject;
   170           val abs_inverse = make Abs_inverse;
   171           val ([Rep, Rep_inverse, Abs_inverse, Rep_inject, Abs_inject,
   172               Rep_cases, Abs_cases, Rep_induct, Abs_induct], thy2) =
   173             thy1
   174             |> Theory.add_path name
   175             |> PureThy.add_thms
   176               ([((Rep_name, make Rep), []),
   177                 ((Rep_name ^ "_inverse", make Rep_inverse), []),
   178                 ((Abs_name ^ "_inverse", abs_inverse), []),
   179                 ((Rep_name ^ "_inject", make Rep_inject), []),
   180                 ((Abs_name ^ "_inject", abs_inject), []),
   181                 ((Rep_name ^ "_cases", make Rep_cases),
   182                   [RuleCases.case_names [Rep_name], InductAttrib.cases_set full_name]),
   183                 ((Abs_name ^ "_cases", make Abs_cases),
   184                   [RuleCases.case_names [Abs_name], InductAttrib.cases_type full_tname]),
   185                 ((Rep_name ^ "_induct", make Rep_induct),
   186                   [RuleCases.case_names [Rep_name], InductAttrib.induct_set full_name]),
   187                 ((Abs_name ^ "_induct", make Abs_induct),
   188                   [RuleCases.case_names [Abs_name], InductAttrib.induct_type full_tname])])
   189             ||> Theory.parent_path;
   190           val info = {rep_type = oldT, abs_type = newT,
   191             Rep_name = full Rep_name, Abs_name = full Abs_name,
   192               type_definition = type_definition, set_def = set_def,
   193               Rep = Rep, Rep_inverse = Rep_inverse, Abs_inverse = Abs_inverse,
   194               Rep_inject = Rep_inject, Abs_inject = Abs_inject, Rep_cases = Rep_cases,
   195             Abs_cases = Abs_cases, Rep_induct = Rep_induct, Abs_induct = Abs_induct};
   196           val thy3 = thy2 |> put_info full_tname info;
   197         in ((full_tname, info), thy3) end);
   198 
   199 
   200     (* errors *)
   201 
   202     fun show_names pairs = commas_quote (map fst pairs);
   203 
   204     val illegal_vars =
   205       if null (term_vars set) andalso null (term_tvars set) then []
   206       else ["Illegal schematic variable(s) on rhs"];
   207 
   208     val dup_lhs_tfrees =
   209       (case duplicates (op =) lhs_tfrees of [] => []
   210       | dups => ["Duplicate type variables on lhs: " ^ show_names dups]);
   211 
   212     val extra_rhs_tfrees =
   213       (case fold (remove (op =)) lhs_tfrees rhs_tfrees of [] => []
   214       | extras => ["Extra type variables on rhs: " ^ show_names extras]);
   215 
   216     val illegal_frees =
   217       (case term_frees set of [] => []
   218       | xs => ["Illegal variables on rhs: " ^ show_names (map dest_Free xs)]);
   219 
   220     val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees;
   221     val _ = if null errs then () else error (cat_lines errs);
   222 
   223     (*test theory errors now!*)
   224     val test_thy = Theory.copy thy;
   225     val _ = test_thy
   226       |> typedef_result (setmp quick_and_dirty true (SkipProof.make_thm test_thy) goal);
   227 
   228   in (set, goal, goal_pat, typedef_result) end
   229   handle ERROR msg => err_in_typedef msg name;
   230 
   231 
   232 (* add_typedef interfaces *)
   233 
   234 local
   235 
   236 fun gen_typedef prep_term def opt_name typ set opt_morphs tac thy =
   237   let
   238     val string_of_term = ProofContext.string_of_term (ProofContext.init thy);
   239     val name = the_default (#1 typ) opt_name;
   240     val (set, goal, _, typedef_result) =
   241       prepare_typedef prep_term def name typ set opt_morphs thy;
   242     val _ = message ("Proving non-emptiness of set " ^ quote (string_of_term set) ^ " ...");
   243     val non_empty = Goal.prove_global thy [] [] goal (K tac) handle ERROR msg =>
   244       cat_error msg ("Failed to prove non-emptiness of " ^ quote (string_of_term set));
   245   in typedef_result non_empty thy end;
   246 
   247 in
   248 
   249 val add_typedef = gen_typedef ProofContext.read_term;
   250 val add_typedef_i = gen_typedef ProofContext.cert_term;
   251 
   252 end;
   253 
   254 
   255 (* Isar typedef interface *)
   256 
   257 local
   258 
   259 fun gen_typedef prep_term ((def, name), typ, set, opt_morphs) thy =
   260   let
   261     val (_, goal, goal_pat, typedef_result) =
   262       prepare_typedef prep_term def name typ set opt_morphs thy;
   263     fun after_qed [[th]] = ProofContext.theory (snd o typedef_result th);
   264   in Proof.theorem_i NONE after_qed [[(goal, [goal_pat])]] (ProofContext.init thy) end;
   265 
   266 in
   267 
   268 val typedef = gen_typedef ProofContext.read_term;
   269 val typedef_i = gen_typedef ProofContext.cert_term;
   270 
   271 end;
   272 
   273 val setup = TypedefData.init;
   274 
   275 
   276 
   277 (** outer syntax **)
   278 
   279 local structure P = OuterParse and K = OuterKeyword in
   280 
   281 val typedeclP =
   282   OuterSyntax.command "typedecl" "type declaration (HOL)" K.thy_decl
   283     (P.type_args -- P.name -- P.opt_infix >> (fn ((vs, t), mx) =>
   284       Toplevel.theory (add_typedecls [(t, vs, mx)])));
   285 
   286 
   287 val typedef_decl =
   288   Scan.optional (P.$$$ "(" |--
   289       ((P.$$$ "open" >> K false) -- Scan.option P.name || P.name >> (fn s => (true, SOME s)))
   290         --| P.$$$ ")") (true, NONE) --
   291     (P.type_args -- P.name) -- P.opt_infix -- (P.$$$ "=" |-- P.term) --
   292     Scan.option (P.$$$ "morphisms" |-- P.!!! (P.name -- P.name));
   293 
   294 fun mk_typedef ((((((def, opt_name), (vs, t)), mx), A), morphs)) =
   295   typedef ((def, the_default (Syntax.type_name t mx) opt_name), (t, vs, mx), A, morphs);
   296 
   297 val typedefP =
   298   OuterSyntax.command "typedef" "HOL type definition (requires non-emptiness proof)" K.thy_goal
   299     (typedef_decl >> (Toplevel.print oo (Toplevel.theory_to_proof o mk_typedef)));
   300 
   301 
   302 val _ = OuterSyntax.add_keywords ["morphisms"];
   303 val _ = OuterSyntax.add_parsers [typedeclP, typedefP];
   304 
   305 end;
   306 
   307 end;