src/HOL/Tools/typedef_package.ML
author wenzelm
Thu Jul 13 23:13:10 2000 +0200 (2000-07-13)
changeset 9315 f793f05024f6
parent 9230 17ae63f82ad8
child 9969 4753185f1dd2
permissions -rw-r--r--
adapted PureThy.add_defs_i;
     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 (** type declarations **)
    30 
    31 fun add_typedecls decls thy =
    32   let
    33     val full = Sign.full_name (Theory.sign_of thy);
    34 
    35     fun arity_of (raw_name, args, mx) =
    36       (full (Syntax.type_name raw_name mx), replicate (length args) HOLogic.termS, HOLogic.termS);
    37   in
    38     if can (Theory.assert_super HOL.thy) thy then
    39       thy
    40       |> PureThy.add_typedecls decls
    41       |> Theory.add_arities_i (map arity_of decls)
    42     else thy |> PureThy.add_typedecls decls
    43   end;
    44 
    45 
    46 
    47 (** type definitions **)
    48 
    49 (* messages *)
    50 
    51 val quiet_mode = ref false;
    52 fun message s = if ! quiet_mode then () else writeln s;
    53 
    54 
    55 (* non-emptiness of set *)              (*exception ERROR*)
    56 
    57 fun check_nonempty cset thm =
    58   let
    59     val {t, sign, maxidx, ...} = Thm.rep_cterm cset;
    60     val {prop, ...} = Thm.rep_thm (Thm.transfer_sg sign (Drule.standard thm));
    61     val matches = Pattern.matches (Sign.tsig_of sign);
    62   in
    63     (case try (HOLogic.dest_mem o HOLogic.dest_Trueprop) prop of
    64       None => raise ERROR
    65     | Some (_, A) => if matches (Logic.incr_indexes ([], maxidx) A, t) then () else raise ERROR)
    66   end handle ERROR => error ("Bad non-emptiness theorem " ^ Display.string_of_thm thm ^
    67     "\nfor set " ^ quote (Display.string_of_cterm cset));
    68 
    69 fun goal_nonempty ex cset =
    70   let
    71     val {T = setT, t = A, maxidx, sign} = Thm.rep_cterm cset;
    72     val T = HOLogic.dest_setT setT;
    73     val tm =
    74       if ex then HOLogic.mk_exists ("x", T, HOLogic.mk_mem (Free ("x", T), A))
    75       else HOLogic.mk_mem (Var (("x", maxidx + 1), T), A);   (*old-style version*)
    76   in Thm.cterm_of sign (HOLogic.mk_Trueprop tm) end;
    77 
    78 fun prove_nonempty thy cset (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       TRY (rewrite_goals_tac (filter is_def thms)) THEN
    84       TRY (REPEAT_FIRST (resolve_tac (filter_out is_def thms))) THEN
    85       if_none witn_tac (TRY (ALLGOALS (CLASET' blast_tac)));
    86   in
    87     message ("Proving non-emptiness of set " ^ quote (string_of_cterm cset) ^ " ...");
    88     prove_goalw_cterm [] (goal_nonempty false cset) (K [tac])
    89   end handle ERROR => error ("Failed to prove non-emptiness of " ^ quote (string_of_cterm cset));
    90 
    91 
    92 (* prepare_typedef *)
    93 
    94 fun read_term sg used s =
    95   #1 (Thm.read_def_cterm (sg, K None, K None) used true (s, HOLogic.termT));
    96 
    97 fun cert_term sg _ t = Thm.cterm_of sg t handle TERM (msg, _) => error msg;
    98 
    99 fun err_in_typedef name =
   100   error ("The error(s) above occurred in typedef " ^ quote name);
   101 
   102 fun prepare_typedef prep_term no_def name (t, vs, mx) raw_set thy =
   103   let
   104     val _ = Theory.requires thy "Set" "typedefs";
   105     val sign = Theory.sign_of thy;
   106     val full_name = Sign.full_name sign;
   107 
   108     (*rhs*)
   109     val cset = prep_term sign vs raw_set;
   110     val {T = setT, t = set, ...} = Thm.rep_cterm cset;
   111     val rhs_tfrees = term_tfrees set;
   112     val oldT = HOLogic.dest_setT setT handle TYPE _ =>
   113       error ("Not a set type: " ^ quote (Sign.string_of_typ sign setT));
   114 
   115     (*lhs*)
   116     val lhs_tfrees = map (fn v => (v, if_none (assoc (rhs_tfrees, v)) HOLogic.termS)) vs;
   117     val tname = Syntax.type_name t mx;
   118     val newT = Type (full_name tname, map TFree lhs_tfrees);
   119 
   120     val Rep_name = "Rep_" ^ name;
   121     val Abs_name = "Abs_" ^ name;
   122     val setC = Const (full_name name, setT);
   123     val RepC = Const (full_name Rep_name, newT --> oldT);
   124     val AbsC = Const (full_name Abs_name, oldT --> newT);
   125     val x_new = Free ("x", newT);
   126     val y_old = Free ("y", oldT);
   127     val set' = if no_def then set else setC;
   128 
   129     (*axioms*)
   130     val rep_type = HOLogic.mk_Trueprop (HOLogic.mk_mem (RepC $ x_new, set'));
   131     val rep_type_inv = HOLogic.mk_Trueprop (HOLogic.mk_eq (AbsC $ (RepC $ x_new), x_new));
   132     val abs_type_inv = Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (y_old, set')),
   133       HOLogic.mk_Trueprop (HOLogic.mk_eq (RepC $ (AbsC $ y_old), y_old)));
   134 
   135     (*theory extender*)
   136     fun do_typedef theory =
   137       theory
   138       |> Theory.assert_super thy
   139       |> add_typedecls [(t, vs, mx)]
   140       |> Theory.add_consts_i
   141        ((if no_def then [] else [(name, setT, NoSyn)]) @
   142         [(Rep_name, newT --> oldT, NoSyn),
   143          (Abs_name, oldT --> newT, NoSyn)])
   144       |> (if no_def then I else (#1 oo (PureThy.add_defs_i false o map Thm.no_attributes))
   145        [Logic.mk_defpair (setC, set)])
   146       |> (#1 oo (PureThy.add_axioms_i o map Thm.no_attributes))
   147        [(Rep_name, rep_type),
   148         (Rep_name ^ "_inverse", rep_type_inv),
   149         (Abs_name ^ "_inverse", abs_type_inv)]
   150       handle ERROR => err_in_typedef name;
   151 
   152 
   153     (* errors *)
   154 
   155     fun show_names pairs = commas_quote (map fst pairs);
   156 
   157     val illegal_vars =
   158       if null (term_vars set) andalso null (term_tvars set) then []
   159       else ["Illegal schematic variable(s) on rhs"];
   160 
   161     val dup_lhs_tfrees =
   162       (case duplicates lhs_tfrees of [] => []
   163       | dups => ["Duplicate type variables on lhs: " ^ show_names dups]);
   164 
   165     val extra_rhs_tfrees =
   166       (case gen_rems (op =) (rhs_tfrees, lhs_tfrees) of [] => []
   167       | extras => ["Extra type variables on rhs: " ^ show_names extras]);
   168 
   169     val illegal_frees =
   170       (case term_frees set of [] => []
   171       | xs => ["Illegal variables on rhs: " ^ show_names (map dest_Free xs)]);
   172 
   173     val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees;
   174   in
   175     if null errs then () else error (cat_lines errs);
   176     (cset, do_typedef)
   177   end handle ERROR => err_in_typedef name;
   178 
   179 
   180 (* add_typedef interfaces *)
   181 
   182 fun gen_add_typedef prep_term no_def name typ set names thms tac thy =
   183   let
   184     val (cset, do_typedef) = prepare_typedef prep_term no_def name typ set thy;
   185     val result = prove_nonempty thy cset (names, thms, tac);
   186   in check_nonempty cset result; thy |> do_typedef end;
   187 
   188 val add_typedef = gen_add_typedef read_term false;
   189 val add_typedef_i = gen_add_typedef cert_term false;
   190 val add_typedef_i_no_def = gen_add_typedef cert_term true;
   191 
   192 
   193 (* typedef_proof interface *)
   194 
   195 fun typedef_attribute cset do_typedef (thy, thm) =
   196   (check_nonempty cset (thm RS (select_eq_Ex RS iffD2)); (thy |> do_typedef, thm));
   197 
   198 fun gen_typedef_proof prep_term ((name, typ, set), comment) int thy =
   199   let
   200     val (cset, do_typedef) = prepare_typedef prep_term false name typ set thy;
   201     val goal = Thm.term_of (goal_nonempty true cset);
   202   in
   203     thy
   204     |> IsarThy.theorem_i (("", [typedef_attribute cset do_typedef], (goal, ([], []))), comment) int
   205   end;
   206 
   207 val typedef_proof = gen_typedef_proof read_term;
   208 val typedef_proof_i = gen_typedef_proof cert_term;
   209 
   210 
   211 
   212 (** outer syntax **)
   213 
   214 local structure P = OuterParse and K = OuterSyntax.Keyword in
   215 
   216 val typedeclP =
   217   OuterSyntax.command "typedecl" "HOL type declaration" K.thy_decl
   218     (P.type_args -- P.name -- P.opt_infix --| P.marg_comment >> (fn ((vs, t), mx) =>
   219       Toplevel.theory (add_typedecls [(t, vs, mx)])));
   220 
   221 
   222 val typedef_proof_decl =
   223   Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") --
   224     (P.type_args -- P.name) -- P.opt_infix -- (P.$$$ "=" |-- P.term) -- P.marg_comment;
   225 
   226 fun mk_typedef_proof ((((opt_name, (vs, t)), mx), A), comment) =
   227   typedef_proof ((if_none opt_name (Syntax.type_name t mx), (t, vs, mx), A), comment);
   228 
   229 val typedefP =
   230   OuterSyntax.command "typedef" "HOL type definition (requires non-emptiness proof)" K.thy_goal
   231     (typedef_proof_decl >> (Toplevel.print oo (Toplevel.theory_to_proof o mk_typedef_proof)));
   232 
   233 
   234 val _ = OuterSyntax.add_parsers [typedeclP, typedefP];
   235 
   236 end;
   237 
   238 
   239 end;