src/HOL/Tools/typedef_package.ML
author paulson
Thu Feb 09 12:20:31 2006 +0100 (2006-02-09)
changeset 18986 5060ca625e02
parent 18964 67f572e03236
child 19342 094a1c071c8e
permissions -rw-r--r--
tidying
     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: bool -> string option -> bstring * string list * mixfix ->
    13     string -> (bstring * bstring) option -> tactic -> theory -> theory *
    14     {type_definition: thm, set_def: thm option, Rep: thm, Rep_inverse: thm,
    15       Abs_inverse: thm, Rep_inject: thm, Abs_inject: thm, Rep_cases: thm, Abs_cases: thm,
    16       Rep_induct: thm, Abs_induct: thm}
    17   val add_typedef_i: bool -> string option -> bstring * string list * mixfix ->
    18     term -> (bstring * bstring) option -> tactic -> theory -> theory *
    19     {type_definition: thm, set_def: thm option, Rep: thm, Rep_inverse: thm,
    20       Abs_inverse: thm, Rep_inject: thm, Abs_inject: thm, Rep_cases: thm, Abs_cases: thm,
    21       Rep_induct: thm, Abs_induct: thm}
    22   val typedef: (bool * string) * (bstring * string list * mixfix) * string
    23     * (string * string) option -> theory -> Proof.state
    24   val typedef_i: (bool * string) * (bstring * string list * mixfix) * term
    25     * (string * string) option -> theory -> Proof.state
    26   val setup: theory -> theory
    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 
    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 add_typedecls decls thy =
    52   let
    53     fun arity_of (raw_name, args, mx) =
    54       (Sign.full_name thy (Syntax.type_name raw_name mx),
    55         replicate (length args) HOLogic.typeS, HOLogic.typeS);
    56   in
    57     thy
    58     |> Theory.add_typedecls decls
    59     |> can (Theory.assert_super HOL.thy) ? Theory.add_arities_i (map arity_of 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 (* theory data *)
    73 
    74 structure TypedefData = TheoryDataFun
    75 (struct
    76   val name = "HOL/typedef";
    77   type T = (typ * typ * string * string) Symtab.table;
    78   val empty = Symtab.empty;
    79   val copy = I;
    80   val extend = I;
    81   fun merge _ (tabs: T * T) = Symtab.merge (op =) tabs;
    82   fun print _ _ = ();
    83 end);
    84 
    85 fun put_typedef newT oldT Abs_name Rep_name =
    86   TypedefData.map (Symtab.update_new (fst (dest_Type newT), (newT, oldT, Abs_name, Rep_name)));
    87 
    88 
    89 (* prepare_typedef *)
    90 
    91 fun read_term thy used s =
    92   #1 (Thm.read_def_cterm (thy, K NONE, K NONE) used true (s, HOLogic.typeT));
    93 
    94 fun cert_term thy _ t = Thm.cterm_of thy t handle TERM (msg, _) => error msg;
    95 
    96 fun err_in_typedef msg name =
    97   cat_error msg ("The error(s) above occurred in typedef " ^ quote name);
    98 
    99 fun prepare_typedef prep_term def name (t, vs, mx) raw_set opt_morphs thy =
   100   let
   101     val _ = Theory.requires thy "Typedef" "typedefs";
   102     val full = Sign.full_name thy;
   103 
   104     (*rhs*)
   105     val full_name = full name;
   106     val cset = prep_term thy vs raw_set;
   107     val {T = setT, t = set, ...} = Thm.rep_cterm cset;
   108     val rhs_tfrees = Term.add_tfrees set [];
   109     val rhs_tfreesT = Term.add_tfreesT setT [];
   110     val oldT = HOLogic.dest_setT setT handle TYPE _ =>
   111       error ("Not a set type: " ^ quote (Sign.string_of_typ thy 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 (if_none (Syntax.read_variable name) (name, 0), setT));
   116 
   117     (*lhs*)
   118     val defS = Sign.defaultS thy;
   119     val lhs_tfrees = map (fn v => (v, if_none (AList.lookup (op =) rhs_tfrees v) defS)) vs;
   120     val args_setT = lhs_tfrees
   121       |> filter (member (op =) rhs_tfrees andf (not o member (op =) rhs_tfreesT))
   122       |> map TFree;
   123 
   124     val tname = Syntax.type_name t mx;
   125     val full_tname = full tname;
   126     val newT = Type (full_tname, map TFree lhs_tfrees);
   127 
   128     val (Rep_name, Abs_name) = if_none opt_morphs ("Rep_" ^ name, "Abs_" ^ name);
   129     val setT' = map itselfT args_setT ---> setT;
   130     val setC = Term.list_comb (Const (full_name, setT'), map Logic.mk_type args_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 def then setC else set;
   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 add_def def def' thy =
   145       if def
   146       then
   147         thy
   148         |> PureThy.add_defs_i false [Thm.no_attributes def']
   149         |-> (fn [def'] => pair (SOME def'))
   150       else
   151         (NONE, thy);
   152 
   153     fun typedef_result (context, nonempty) =
   154       Context.the_theory context
   155       |> put_typedef newT oldT (full Abs_name) (full Rep_name)
   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 def (Logic.mk_defpair (setC, set))
   162       ||>> PureThy.add_axioms_i [((typedef_name, typedef_prop),
   163           [apsnd (fn cond_axm => Drule.standard (nonempty RS cond_axm))])]
   164       ||> Theory.add_finals_i false [RepC, AbsC]
   165       |-> (fn (set_def, [type_definition]) => fn theory' =>
   166         let
   167           fun make th = Drule.standard (th OF [type_definition]);
   168           val ([Rep, Rep_inverse, Abs_inverse, Rep_inject, Abs_inject,
   169               Rep_cases, Abs_cases, Rep_induct, Abs_induct], theory'') =
   170             theory'
   171             |> Theory.add_path name
   172             |> PureThy.add_thms
   173               ([((Rep_name, make Rep), []),
   174                 ((Rep_name ^ "_inverse", make Rep_inverse), []),
   175                 ((Abs_name ^ "_inverse", make Abs_inverse), []),
   176                 ((Rep_name ^ "_inject", make Rep_inject), []),
   177                 ((Abs_name ^ "_inject", make Abs_inject), []),
   178                 ((Rep_name ^ "_cases", make Rep_cases),
   179                   [RuleCases.case_names [Rep_name], InductAttrib.cases_set full_name]),
   180                 ((Abs_name ^ "_cases", make Abs_cases),
   181                   [RuleCases.case_names [Abs_name], InductAttrib.cases_type full_tname]),
   182                 ((Rep_name ^ "_induct", make Rep_induct),
   183                   [RuleCases.case_names [Rep_name], InductAttrib.induct_set full_name]),
   184                 ((Abs_name ^ "_induct", make Abs_induct),
   185                   [RuleCases.case_names [Abs_name], InductAttrib.induct_type full_tname])])
   186             ||> Theory.parent_path;
   187           val result = {type_definition = type_definition, set_def = set_def,
   188             Rep = Rep, Rep_inverse = Rep_inverse, Abs_inverse = Abs_inverse,
   189             Rep_inject = Rep_inject, Abs_inject = Abs_inject, Rep_cases = Rep_cases,
   190             Abs_cases = Abs_cases, Rep_induct = Rep_induct, Abs_induct = Abs_induct};
   191         in ((Context.Theory theory'', type_definition), result) end);
   192 
   193 
   194     (* errors *)
   195 
   196     fun show_names pairs = commas_quote (map fst pairs);
   197 
   198     val illegal_vars =
   199       if null (term_vars set) andalso null (term_tvars set) then []
   200       else ["Illegal schematic variable(s) on rhs"];
   201 
   202     val dup_lhs_tfrees =
   203       (case duplicates (op =) lhs_tfrees of [] => []
   204       | dups => ["Duplicate type variables on lhs: " ^ show_names dups]);
   205 
   206     val extra_rhs_tfrees =
   207       (case fold (remove (op =)) lhs_tfrees rhs_tfrees of [] => []
   208       | extras => ["Extra type variables on rhs: " ^ show_names extras]);
   209 
   210     val illegal_frees =
   211       (case term_frees set of [] => []
   212       | xs => ["Illegal variables on rhs: " ^ show_names (map dest_Free xs)]);
   213 
   214     val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees;
   215     val _ = if null errs then () else error (cat_lines errs);
   216 
   217     (*test theory errors now!*)
   218     val test_thy = Theory.copy thy;
   219     val _ = (Context.Theory test_thy,
   220       setmp quick_and_dirty true (SkipProof.make_thm test_thy) goal) |> typedef_result;
   221 
   222   in (cset, goal, goal_pat, typedef_result) end
   223   handle ERROR msg => err_in_typedef msg name;
   224 
   225 
   226 (* add_typedef interfaces *)
   227 
   228 local
   229 
   230 fun gen_typedef prep_term def opt_name typ set opt_morphs tac thy =
   231   let
   232     val name = the_default (#1 typ) opt_name;
   233     val (cset, goal, _, typedef_result) =
   234       prepare_typedef prep_term def name typ set opt_morphs thy;
   235     val _ = message ("Proving non-emptiness of set " ^ quote (string_of_cterm cset) ^ " ...");
   236     val non_empty = Goal.prove thy [] [] goal (K tac) handle ERROR msg =>
   237       cat_error msg ("Failed to prove non-emptiness of " ^ quote (string_of_cterm cset));
   238     val (thy', result) =
   239       (Context.Theory thy, non_empty) |> typedef_result |>> (Context.the_theory o fst);
   240   in (thy', result) end;
   241 
   242 in
   243 
   244 val add_typedef = gen_typedef read_term;
   245 val add_typedef_i = gen_typedef cert_term;
   246 
   247 end;
   248 
   249 
   250 (* Isar typedef interface *)
   251 
   252 local
   253 
   254 fun gen_typedef prep_term ((def, name), typ, set, opt_morphs) thy =
   255   let
   256     val (_, goal, goal_pat, att_result) =
   257       prepare_typedef prep_term def name typ set opt_morphs thy;
   258     val att = #1 o att_result;
   259   in IsarThy.theorem_i PureThy.internalK ("", [att]) (goal, ([goal_pat], [])) thy end;
   260 
   261 in
   262 
   263 val typedef = gen_typedef read_term;
   264 val typedef_i = gen_typedef cert_term;
   265 
   266 end;
   267 
   268 
   269 
   270 (** trivial code generator **)
   271 
   272 fun typedef_codegen thy defs gr dep module brack t =
   273   let
   274     fun get_name (Type (tname, _)) = tname
   275       | get_name _ = "";
   276     fun mk_fun s T ts =
   277       let
   278         val (gr', _) = Codegen.invoke_tycodegen thy defs dep module false (gr, T);
   279         val (gr'', ps) =
   280           foldl_map (Codegen.invoke_codegen thy defs dep module true) (gr', ts);
   281         val id = Codegen.mk_qual_id module (Codegen.get_const_id s gr'')
   282       in SOME (gr'', Codegen.mk_app brack (Pretty.str id) ps) end;
   283     fun lookup f T =
   284       (case Symtab.lookup (TypedefData.get thy) (get_name T) of
   285         NONE => ""
   286       | SOME s => f s);
   287   in
   288     (case strip_comb t of
   289        (Const (s, Type ("fun", [T, U])), ts) =>
   290          if lookup #4 T = s andalso
   291            is_none (Codegen.get_assoc_type thy (get_name T))
   292          then mk_fun s T ts
   293          else if lookup #3 U = s andalso
   294            is_none (Codegen.get_assoc_type thy (get_name U))
   295          then mk_fun s U ts
   296          else NONE
   297      | _ => NONE)
   298   end;
   299 
   300 fun mk_tyexpr [] s = Pretty.str s
   301   | mk_tyexpr [p] s = Pretty.block [p, Pretty.str (" " ^ s)]
   302   | mk_tyexpr ps s = Pretty.list "(" (") " ^ s) ps;
   303 
   304 fun typedef_tycodegen thy defs gr dep module brack (Type (s, Ts)) =
   305       (case Symtab.lookup (TypedefData.get thy) s of
   306          NONE => NONE
   307        | SOME (newT as Type (tname, Us), oldT, Abs_name, Rep_name) =>
   308            if is_some (Codegen.get_assoc_type thy tname) then NONE else
   309            let
   310              val module' = Codegen.if_library
   311                (Codegen.thyname_of_type tname thy) module;
   312              val node_id = tname ^ " (type)";
   313              val (gr', (((qs, (_, Abs_id)), (_, Rep_id)), ty_id)) = foldl_map
   314                  (Codegen.invoke_tycodegen thy defs dep module (length Ts = 1))
   315                    (gr, Ts) |>>>
   316                Codegen.mk_const_id module' Abs_name |>>>
   317                Codegen.mk_const_id module' Rep_name |>>>
   318                Codegen.mk_type_id module' s;
   319              val tyexpr = mk_tyexpr qs (Codegen.mk_qual_id module ty_id)
   320            in SOME (case try (Codegen.get_node gr') node_id of
   321                NONE =>
   322                let
   323                  val (gr'', p :: ps) = foldl_map
   324                    (Codegen.invoke_tycodegen thy defs node_id module' false)
   325                    (Codegen.add_edge (node_id, dep)
   326                       (Codegen.new_node (node_id, (NONE, "", "")) gr'), oldT :: Us);
   327                  val s =
   328                    Pretty.string_of (Pretty.block [Pretty.str "datatype ",
   329                      mk_tyexpr ps (snd ty_id),
   330                      Pretty.str " =", Pretty.brk 1, Pretty.str (Abs_id ^ " of"),
   331                      Pretty.brk 1, p, Pretty.str ";"]) ^ "\n\n" ^
   332                    Pretty.string_of (Pretty.block [Pretty.str ("fun " ^ Rep_id),
   333                      Pretty.brk 1, Pretty.str ("(" ^ Abs_id), Pretty.brk 1,
   334                      Pretty.str "x) = x;"]) ^ "\n\n" ^
   335                    (if "term_of" mem !Codegen.mode then
   336                       Pretty.string_of (Pretty.block [Pretty.str "fun ",
   337                         Codegen.mk_term_of gr'' module' false newT, Pretty.brk 1,
   338                         Pretty.str ("(" ^ Abs_id), Pretty.brk 1,
   339                         Pretty.str "x) =", Pretty.brk 1,
   340                         Pretty.block [Pretty.str ("Const (\"" ^ Abs_name ^ "\","),
   341                           Pretty.brk 1, Codegen.mk_type false (oldT --> newT),
   342                           Pretty.str ")"], Pretty.str " $", Pretty.brk 1,
   343                         Codegen.mk_term_of gr'' module' false oldT, Pretty.brk 1,
   344                         Pretty.str "x;"]) ^ "\n\n"
   345                     else "") ^
   346                    (if "test" mem !Codegen.mode then
   347                       Pretty.string_of (Pretty.block [Pretty.str "fun ",
   348                         Codegen.mk_gen gr'' module' false [] "" newT, Pretty.brk 1,
   349                         Pretty.str "i =", Pretty.brk 1,
   350                         Pretty.block [Pretty.str (Abs_id ^ " ("),
   351                           Codegen.mk_gen gr'' module' false [] "" oldT, Pretty.brk 1,
   352                           Pretty.str "i);"]]) ^ "\n\n"
   353                     else "")
   354                in Codegen.map_node node_id (K (NONE, module', s)) gr'' end
   355              | SOME _ => Codegen.add_edge (node_id, dep) gr', tyexpr)
   356            end)
   357   | typedef_tycodegen thy defs gr dep module brack _ = NONE;
   358 
   359 val setup =
   360   TypedefData.init #>
   361   Codegen.add_codegen "typedef" typedef_codegen #>
   362   Codegen.add_tycodegen "typedef" typedef_tycodegen;
   363 
   364 
   365 
   366 (** outer syntax **)
   367 
   368 local structure P = OuterParse and K = OuterKeyword in
   369 
   370 val typedeclP =
   371   OuterSyntax.command "typedecl" "type declaration (HOL)" K.thy_decl
   372     (P.type_args -- P.name -- P.opt_infix >> (fn ((vs, t), mx) =>
   373       Toplevel.theory (add_typedecls [(t, vs, mx)])));
   374 
   375 
   376 val typedef_decl =
   377   Scan.optional (P.$$$ "(" |--
   378       ((P.$$$ "open" >> K false) -- Scan.option P.name || P.name >> (fn s => (true, SOME s)))
   379         --| P.$$$ ")") (true, NONE) --
   380     (P.type_args -- P.name) -- P.opt_infix -- (P.$$$ "=" |-- P.term) --
   381     Scan.option (P.$$$ "morphisms" |-- P.!!! (P.name -- P.name));
   382 
   383 fun mk_typedef ((((((def, opt_name), (vs, t)), mx), A), morphs)) =
   384   typedef ((def, if_none opt_name (Syntax.type_name t mx)), (t, vs, mx), A, morphs);
   385 
   386 val typedefP =
   387   OuterSyntax.command "typedef" "HOL type definition (requires non-emptiness proof)" K.thy_goal
   388     (typedef_decl >> (Toplevel.print oo (Toplevel.theory_to_proof o mk_typedef)));
   389 
   390 
   391 val _ = OuterSyntax.add_keywords ["morphisms"];
   392 val _ = OuterSyntax.add_parsers [typedeclP, typedefP];
   393 
   394 end;
   395 
   396 end;