src/HOL/Tools/typedef_package.ML
author wenzelm
Wed, 29 Apr 1998 11:39:52 +0200
changeset 4866 72a46bd00c8d
child 4932 c90411dde8e8
permissions -rw-r--r--
renamed from typedef.ML;
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
4866
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
     1
(*  Title:      HOL/Tools/typedef_package.ML
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
     2
    ID:         $Id$
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
     3
    Author:     Markus Wenzel, TU Muenchen
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
     4
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
     5
Gordon/HOL style type definitions.
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
     6
*)
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
     7
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
     8
signature TYPEDEF_PACKAGE =
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
     9
sig
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    10
  val prove_nonempty: cterm -> thm list -> tactic option -> thm
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    11
  val add_typedef: string -> bstring * string list * mixfix ->
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    12
    string -> string list -> thm list -> tactic option -> theory -> theory
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    13
  val add_typedef_i: string -> bstring * string list * mixfix ->
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    14
    term -> string list -> thm list -> tactic option -> theory -> theory
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    15
end;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    16
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    17
structure TypedefPackage: TYPEDEF_PACKAGE =
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    18
struct
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    19
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    20
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    21
(* prove non-emptyness of a set *)   (*exception ERROR*)
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    22
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    23
val is_def = Logic.is_equals o #prop o rep_thm;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    24
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    25
fun prove_nonempty cset thms usr_tac =
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    26
  let
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    27
    val {T = setT, t = set, maxidx, sign} = rep_cterm cset;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    28
    val T = HOLogic.dest_setT setT;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    29
    val goal = cterm_of sign
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    30
      (HOLogic.mk_Trueprop (HOLogic.mk_mem (Var (("x", maxidx + 1), T), set)));
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    31
    val tac =
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    32
      TRY (rewrite_goals_tac (filter is_def thms)) THEN
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    33
      TRY (REPEAT_FIRST (resolve_tac (filter_out is_def thms))) THEN
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    34
      if_none usr_tac (TRY (ALLGOALS (CLASET' blast_tac)));
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    35
  in
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    36
    prove_goalw_cterm [] goal (K [tac])
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    37
  end
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    38
  handle ERROR =>
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    39
    error ("Failed to prove nonemptiness of " ^ quote (string_of_cterm cset));
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    40
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    41
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    42
(* gen_add_typedef *)
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    43
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    44
fun gen_add_typedef prep_term name (t, vs, mx) raw_set axms thms usr_tac thy =
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    45
  let
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    46
    val _ = Theory.require thy "Set" "typedefs";
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    47
    val sign = sign_of thy;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    48
    val full_name = Sign.full_name sign;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    49
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    50
    (*rhs*)
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    51
    val cset = prep_term sign raw_set;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    52
    val {T = setT, t = set, ...} = rep_cterm cset;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    53
    val rhs_tfrees = term_tfrees set;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    54
    val oldT = HOLogic.dest_setT setT handle TYPE _ =>
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    55
      error ("Not a set type: " ^ quote (Sign.string_of_typ sign setT));
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    56
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    57
    (*lhs*)
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    58
    val lhs_tfrees =
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    59
      map (fn v => (v, if_none (assoc (rhs_tfrees, v)) HOLogic.termS)) vs;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    60
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    61
    val tname = Syntax.type_name t mx;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    62
    val tlen = length vs;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    63
    val newT = Type (full_name tname, map TFree lhs_tfrees);
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    64
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    65
    val Rep_name = "Rep_" ^ name;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    66
    val Abs_name = "Abs_" ^ name;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    67
    val setC = Const (full_name name, setT);
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    68
    val RepC = Const (full_name Rep_name, newT --> oldT);
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    69
    val AbsC = Const (full_name Abs_name, oldT --> newT);
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    70
    val x_new = Free ("x", newT);
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    71
    val y_old = Free ("y", oldT);
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    72
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    73
    (*axioms*)
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    74
    val rep_type = HOLogic.mk_Trueprop (HOLogic.mk_mem (RepC $ x_new, setC));
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    75
    val rep_type_inv = HOLogic.mk_Trueprop (HOLogic.mk_eq (AbsC $ (RepC $ x_new), x_new));
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    76
    val abs_type_inv = Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (y_old, setC)),
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    77
      HOLogic.mk_Trueprop (HOLogic.mk_eq (RepC $ (AbsC $ y_old), y_old)));
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    78
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    79
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    80
    (* errors *)
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    81
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    82
    fun show_names pairs = commas_quote (map fst pairs);
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    83
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    84
    val illegal_vars =
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    85
      if null (term_vars set) andalso null (term_tvars set) then []
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    86
      else ["Illegal schematic variable(s) on rhs"];
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    87
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    88
    val dup_lhs_tfrees =
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    89
      (case duplicates lhs_tfrees of [] => []
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    90
      | dups => ["Duplicate type variables on lhs: " ^ show_names dups]);
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    91
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    92
    val extra_rhs_tfrees =
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    93
      (case gen_rems (op =) (rhs_tfrees, lhs_tfrees) of [] => []
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    94
      | extras => ["Extra type variables on rhs: " ^ show_names extras]);
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    95
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    96
    val illegal_frees =
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    97
      (case term_frees set of [] => []
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    98
      | xs => ["Illegal variables on rhs: " ^ show_names (map dest_Free xs)]);
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
    99
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   100
    val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   101
  in
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   102
    if null errs then ()
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   103
    else error (cat_lines errs);
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   104
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   105
    writeln("Proving nonemptiness of " ^ quote name ^ " ...");
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   106
    prove_nonempty cset (map (get_axiom thy) axms @ thms) usr_tac;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   107
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   108
    thy
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   109
    |> Theory.add_types [(t, tlen, mx)]
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   110
    |> Theory.add_arities_i
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   111
     [(full_name tname, replicate tlen logicS, logicS),
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   112
      (full_name tname, replicate tlen HOLogic.termS, HOLogic.termS)]
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   113
    |> Theory.add_consts_i
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   114
     [(name, setT, NoSyn),
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   115
      (Rep_name, newT --> oldT, NoSyn),
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   116
      (Abs_name, oldT --> newT, NoSyn)]
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   117
    |> (PureThy.add_defs_i o map Attribute.none)
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   118
     [(name ^ "_def", Logic.mk_equals (setC, set))]
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   119
    |> (PureThy.add_axioms_i o map Attribute.none)
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   120
     [(Rep_name, rep_type),
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   121
      (Rep_name ^ "_inverse", rep_type_inv),
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   122
      (Abs_name ^ "_inverse", abs_type_inv)]
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   123
  end
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   124
  handle ERROR =>
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   125
    error ("The error(s) above occurred in typedef " ^ quote name);
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   126
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   127
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   128
(* external interfaces *)
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   129
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   130
fun read_term sg str =
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   131
  read_cterm sg (str, HOLogic.termTVar);
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   132
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   133
fun cert_term sg tm =
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   134
  cterm_of sg tm handle TERM (msg, _) => error msg;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   135
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   136
val add_typedef = gen_add_typedef read_term;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   137
val add_typedef_i = gen_add_typedef cert_term;
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   138
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   139
72a46bd00c8d renamed from typedef.ML;
wenzelm
parents:
diff changeset
   140
end;