src/HOL/typedef.ML
author clasohm
Wed Mar 13 11:55:25 1996 +0100 (1996-03-13 ago)
changeset 1574 5a63ab90ee8a
parent 1475 7f5a4cd08209
child 2238 c72a23bbe762
permissions -rw-r--r--
modified primrec so it can be used in MiniML/Type.thy
     1 (*  Title:      HOL/typedef.ML
     2     ID:         $Id$
     3     Author:     Markus Wenzel, TU Muenchen
     4 
     5 Internal interface for typedef definitions.
     6 *)
     7 
     8 signature TYPEDEF =
     9 sig
    10   val prove_nonempty: cterm -> thm list -> tactic option -> thm
    11   val add_typedef: string -> string * string list * mixfix ->
    12     string -> string list -> thm list -> tactic option -> theory -> theory
    13   val add_typedef_i: string -> string * string list * mixfix ->
    14     term -> string list -> thm list -> tactic option -> theory -> theory
    15 end;
    16 
    17 structure Typedef: TYPEDEF =
    18 struct
    19 
    20 open Syntax Logic HOLogic;
    21 
    22 
    23 (* prove non-emptyness of a set *)   (*exception ERROR*)
    24 
    25 val is_def = is_equals o #prop o rep_thm;
    26 
    27 fun prove_nonempty cset thms usr_tac =
    28   let
    29     val {T = setT, t = set, maxidx, sign} = rep_cterm cset;
    30     val T = dest_setT setT;
    31     val goal =
    32       cterm_of sign (mk_Trueprop (mk_mem (Var (("x", maxidx + 1), T), set)));
    33     val tac =
    34       TRY (rewrite_goals_tac (filter is_def thms)) THEN
    35       TRY (REPEAT_FIRST (resolve_tac (filter_out is_def thms))) THEN
    36       if_none usr_tac (TRY (ALLGOALS (fast_tac set_cs)));
    37   in
    38     prove_goalw_cterm [] goal (K [tac])
    39   end
    40   handle ERROR =>
    41     error ("Failed to prove non-emptyness of " ^ quote (string_of_cterm cset));
    42 
    43 
    44 (* ext_typedef *)
    45 
    46 fun ext_typedef prep_term name (t, vs, mx) raw_set axms thms usr_tac thy =
    47   let
    48     val dummy = require_thy thy "Set" "typedef definitions";
    49     val sign = sign_of thy;
    50 
    51     (*rhs*)
    52     val cset = prep_term sign raw_set;
    53     val {T = setT, t = set, ...} = rep_cterm cset;
    54     val rhs_tfrees = term_tfrees set;
    55     val oldT = dest_setT setT handle TYPE _ =>
    56       error ("Not a set type: " ^ quote (Sign.string_of_typ sign setT));
    57 
    58     (*lhs*)
    59     val lhs_tfrees =
    60       map (fn v => (v, if_none (assoc (rhs_tfrees, v)) termS)) vs;
    61 
    62     val tname = type_name t mx;
    63     val tlen = length vs;
    64     val newT = Type (tname, map TFree lhs_tfrees);
    65 
    66     val Rep_name = "Rep_" ^ name;
    67     val Abs_name = "Abs_" ^ name;
    68     val setC = Const (name, setT);
    69     val RepC = Const (Rep_name, newT --> oldT);
    70     val AbsC = Const (Abs_name, oldT --> newT);
    71     val x_new = Free ("x", newT);
    72     val y_old = Free ("y", oldT);
    73 
    74     (*axioms*)
    75     val rep_type = mk_Trueprop (mk_mem (RepC $ x_new, setC));
    76     val rep_type_inv = mk_Trueprop (mk_eq (AbsC $ (RepC $ x_new), x_new));
    77     val abs_type_inv = mk_implies (mk_Trueprop (mk_mem (y_old, setC)),
    78       mk_Trueprop (mk_eq (RepC $ (AbsC $ y_old), y_old)));
    79 
    80 
    81     (* errors *)
    82 
    83     val show_names = commas_quote o map fst;
    84 
    85     val illegal_vars =
    86       if null (term_vars set) andalso null (term_tvars set) then []
    87       else ["Illegal schematic variable(s) on rhs"];
    88 
    89     val dup_lhs_tfrees =
    90       (case duplicates lhs_tfrees of [] => []
    91       | dups => ["Duplicate type variables on lhs: " ^ show_names dups]);
    92 
    93     val extra_rhs_tfrees =
    94       (case gen_rems (op =) (rhs_tfrees, lhs_tfrees) of [] => []
    95       | extras => ["Extra type variables on rhs: " ^ show_names extras]);
    96 
    97     val illegal_frees =
    98       (case term_frees set of [] => []
    99       | xs => ["Illegal variables on rhs: " ^ show_names (map dest_Free xs)]);
   100 
   101     val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees;
   102   in
   103     if null errs then ()
   104     else error (cat_lines errs);
   105 
   106     prove_nonempty cset (map (get_axiom thy) axms @ thms) usr_tac;
   107 
   108     thy
   109     |> add_types [(t, tlen, mx)]
   110     |> add_arities
   111      [(tname, replicate tlen logicS, logicS),
   112       (tname, replicate tlen termS, termS)]
   113     |> add_consts_i
   114      [(name, setT, NoSyn),
   115       (Rep_name, newT --> oldT, NoSyn),
   116       (Abs_name, oldT --> newT, NoSyn)]
   117     |> add_defs_i
   118      [(name ^ "_def", mk_equals (setC, set))]
   119     |> add_axioms_i
   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 definition " ^ quote name);
   126 
   127 
   128 (* external interfaces *)
   129 
   130 fun cert_term sg tm =
   131   cterm_of sg tm handle TERM (msg, _) => error msg;
   132 
   133 fun read_term sg str =
   134   read_cterm sg (str, termTVar);
   135 
   136 val add_typedef = ext_typedef read_term;
   137 val add_typedef_i = ext_typedef cert_term;
   138 
   139 
   140 end;
   141