src/HOL/Tools/typedef_package.ML
author wenzelm
Wed Apr 29 11:39:52 1998 +0200 (1998-04-29)
changeset 4866 72a46bd00c8d
child 4932 c90411dde8e8
permissions -rw-r--r--
renamed from typedef.ML;
     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 tlen = length vs;
    63     val newT = Type (full_name tname, map TFree lhs_tfrees);
    64 
    65     val Rep_name = "Rep_" ^ name;
    66     val Abs_name = "Abs_" ^ name;
    67     val setC = Const (full_name name, setT);
    68     val RepC = Const (full_name Rep_name, newT --> oldT);
    69     val AbsC = Const (full_name Abs_name, oldT --> newT);
    70     val x_new = Free ("x", newT);
    71     val y_old = Free ("y", oldT);
    72 
    73     (*axioms*)
    74     val rep_type = HOLogic.mk_Trueprop (HOLogic.mk_mem (RepC $ x_new, setC));
    75     val rep_type_inv = HOLogic.mk_Trueprop (HOLogic.mk_eq (AbsC $ (RepC $ x_new), x_new));
    76     val abs_type_inv = Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (y_old, setC)),
    77       HOLogic.mk_Trueprop (HOLogic.mk_eq (RepC $ (AbsC $ y_old), y_old)));
    78 
    79 
    80     (* errors *)
    81 
    82     fun show_names pairs = commas_quote (map fst pairs);
    83 
    84     val illegal_vars =
    85       if null (term_vars set) andalso null (term_tvars set) then []
    86       else ["Illegal schematic variable(s) on rhs"];
    87 
    88     val dup_lhs_tfrees =
    89       (case duplicates lhs_tfrees of [] => []
    90       | dups => ["Duplicate type variables on lhs: " ^ show_names dups]);
    91 
    92     val extra_rhs_tfrees =
    93       (case gen_rems (op =) (rhs_tfrees, lhs_tfrees) of [] => []
    94       | extras => ["Extra type variables on rhs: " ^ show_names extras]);
    95 
    96     val illegal_frees =
    97       (case term_frees set of [] => []
    98       | xs => ["Illegal variables on rhs: " ^ show_names (map dest_Free xs)]);
    99 
   100     val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees;
   101   in
   102     if null errs then ()
   103     else error (cat_lines errs);
   104 
   105     writeln("Proving nonemptiness of " ^ quote name ^ " ...");
   106     prove_nonempty cset (map (get_axiom thy) axms @ thms) usr_tac;
   107 
   108     thy
   109     |> Theory.add_types [(t, tlen, mx)]
   110     |> Theory.add_arities_i
   111      [(full_name tname, replicate tlen logicS, logicS),
   112       (full_name tname, replicate tlen HOLogic.termS, HOLogic.termS)]
   113     |> Theory.add_consts_i
   114      [(name, setT, NoSyn),
   115       (Rep_name, newT --> oldT, NoSyn),
   116       (Abs_name, oldT --> newT, NoSyn)]
   117     |> (PureThy.add_defs_i o map Attribute.none)
   118      [(name ^ "_def", Logic.mk_equals (setC, set))]
   119     |> (PureThy.add_axioms_i o map Attribute.none)
   120      [(Rep_name, rep_type),
   121       (Rep_name ^ "_inverse", rep_type_inv),
   122       (Abs_name ^ "_inverse", abs_type_inv)]
   123   end
   124   handle ERROR =>
   125     error ("The error(s) above occurred in typedef " ^ quote name);
   126 
   127 
   128 (* external interfaces *)
   129 
   130 fun read_term sg str =
   131   read_cterm sg (str, HOLogic.termTVar);
   132 
   133 fun cert_term sg tm =
   134   cterm_of sg tm handle TERM (msg, _) => error msg;
   135 
   136 val add_typedef = gen_add_typedef read_term;
   137 val add_typedef_i = gen_add_typedef cert_term;
   138 
   139 
   140 end;