src/HOL/Tools/typedef_package.ML
author wenzelm
Fri May 15 11:34:12 1998 +0200 (1998-05-15)
changeset 4932 c90411dde8e8
parent 4866 72a46bd00c8d
child 4970 8b65444edbb0
permissions -rw-r--r--
PureThy.add_typedecls;
     1 (*  Title:      HOL/Tools/typedef_package.ML
     2     ID:         $Id$
     3     Author:     Markus Wenzel, TU Muenchen
     4 
     5 Gordon/HOL style type definitions.
     6 *)
     7 
     8 signature TYPEDEF_PACKAGE =
     9 sig
    10   val prove_nonempty: cterm -> thm list -> tactic option -> thm
    11   val add_typedef: string -> bstring * string list * mixfix ->
    12     string -> string list -> thm list -> tactic option -> theory -> theory
    13   val add_typedef_i: string -> bstring * string list * mixfix ->
    14     term -> string list -> thm list -> tactic option -> theory -> theory
    15 end;
    16 
    17 structure TypedefPackage: TYPEDEF_PACKAGE =
    18 struct
    19 
    20 
    21 (* prove non-emptyness of a set *)   (*exception ERROR*)
    22 
    23 val is_def = Logic.is_equals o #prop o rep_thm;
    24 
    25 fun prove_nonempty cset thms usr_tac =
    26   let
    27     val {T = setT, t = set, maxidx, sign} = rep_cterm cset;
    28     val T = HOLogic.dest_setT setT;
    29     val goal = cterm_of sign
    30       (HOLogic.mk_Trueprop (HOLogic.mk_mem (Var (("x", maxidx + 1), T), set)));
    31     val tac =
    32       TRY (rewrite_goals_tac (filter is_def thms)) THEN
    33       TRY (REPEAT_FIRST (resolve_tac (filter_out is_def thms))) THEN
    34       if_none usr_tac (TRY (ALLGOALS (CLASET' blast_tac)));
    35   in
    36     prove_goalw_cterm [] goal (K [tac])
    37   end
    38   handle ERROR =>
    39     error ("Failed to prove nonemptiness of " ^ quote (string_of_cterm cset));
    40 
    41 
    42 (* gen_add_typedef *)
    43 
    44 fun gen_add_typedef prep_term name (t, vs, mx) raw_set axms thms usr_tac thy =
    45   let
    46     val _ = Theory.require thy "Set" "typedefs";
    47     val sign = sign_of thy;
    48     val full_name = Sign.full_name sign;
    49 
    50     (*rhs*)
    51     val cset = prep_term sign raw_set;
    52     val {T = setT, t = set, ...} = rep_cterm cset;
    53     val rhs_tfrees = term_tfrees set;
    54     val oldT = HOLogic.dest_setT setT handle TYPE _ =>
    55       error ("Not a set type: " ^ quote (Sign.string_of_typ sign setT));
    56 
    57     (*lhs*)
    58     val lhs_tfrees =
    59       map (fn v => (v, if_none (assoc (rhs_tfrees, v)) HOLogic.termS)) vs;
    60 
    61     val tname = Syntax.type_name t mx;
    62     val newT = Type (full_name tname, map TFree lhs_tfrees);
    63 
    64     val Rep_name = "Rep_" ^ name;
    65     val Abs_name = "Abs_" ^ name;
    66     val setC = Const (full_name name, setT);
    67     val RepC = Const (full_name Rep_name, newT --> oldT);
    68     val AbsC = Const (full_name Abs_name, oldT --> newT);
    69     val x_new = Free ("x", newT);
    70     val y_old = Free ("y", oldT);
    71 
    72     (*axioms*)
    73     val rep_type = HOLogic.mk_Trueprop (HOLogic.mk_mem (RepC $ x_new, setC));
    74     val rep_type_inv = HOLogic.mk_Trueprop (HOLogic.mk_eq (AbsC $ (RepC $ x_new), x_new));
    75     val abs_type_inv = Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (y_old, setC)),
    76       HOLogic.mk_Trueprop (HOLogic.mk_eq (RepC $ (AbsC $ y_old), y_old)));
    77 
    78 
    79     (* errors *)
    80 
    81     fun show_names pairs = commas_quote (map fst pairs);
    82 
    83     val illegal_vars =
    84       if null (term_vars set) andalso null (term_tvars set) then []
    85       else ["Illegal schematic variable(s) on rhs"];
    86 
    87     val dup_lhs_tfrees =
    88       (case duplicates lhs_tfrees of [] => []
    89       | dups => ["Duplicate type variables on lhs: " ^ show_names dups]);
    90 
    91     val extra_rhs_tfrees =
    92       (case gen_rems (op =) (rhs_tfrees, lhs_tfrees) of [] => []
    93       | extras => ["Extra type variables on rhs: " ^ show_names extras]);
    94 
    95     val illegal_frees =
    96       (case term_frees set of [] => []
    97       | xs => ["Illegal variables on rhs: " ^ show_names (map dest_Free xs)]);
    98 
    99     val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees;
   100   in
   101     if null errs then ()
   102     else error (cat_lines errs);
   103 
   104     writeln("Proving nonemptiness of " ^ quote name ^ " ...");
   105     prove_nonempty cset (map (get_axiom thy) axms @ thms) usr_tac;
   106 
   107     thy
   108     |> PureThy.add_typedecls [(t, vs, mx)]
   109     |> Theory.add_arities_i
   110      [(full_name tname, replicate (length vs) HOLogic.termS, HOLogic.termS)]
   111     |> Theory.add_consts_i
   112      [(name, setT, NoSyn),
   113       (Rep_name, newT --> oldT, NoSyn),
   114       (Abs_name, oldT --> newT, NoSyn)]
   115     |> (PureThy.add_defs_i o map Attribute.none)
   116      [(name ^ "_def", Logic.mk_equals (setC, set))]
   117     |> (PureThy.add_axioms_i o map Attribute.none)
   118      [(Rep_name, rep_type),
   119       (Rep_name ^ "_inverse", rep_type_inv),
   120       (Abs_name ^ "_inverse", abs_type_inv)]
   121   end
   122   handle ERROR =>
   123     error ("The error(s) above occurred in typedef " ^ quote name);
   124 
   125 
   126 (* external interfaces *)
   127 
   128 fun read_term sg str =
   129   read_cterm sg (str, HOLogic.termTVar);
   130 
   131 fun cert_term sg tm =
   132   cterm_of sg tm handle TERM (msg, _) => error msg;
   133 
   134 val add_typedef = gen_add_typedef read_term;
   135 val add_typedef_i = gen_add_typedef cert_term;
   136 
   137 
   138 end;