src/HOL/Tools/typedef_package.ML
author wenzelm
Tue Jan 12 13:54:51 1999 +0100 (1999-01-12)
changeset 6092 d9db67970c73
parent 5697 e816c4f1a396
child 6357 12448b8f92fb
permissions -rw-r--r--
eliminated tthm type and Attribute structure;
     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 quiet_mode: bool ref
    11   val add_typedecls: (bstring * string list * mixfix) list -> theory -> theory
    12   val prove_nonempty: cterm -> thm list -> tactic option -> thm
    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 end;
    20 
    21 structure TypedefPackage: TYPEDEF_PACKAGE =
    22 struct
    23 
    24 
    25 (** type declarations **)
    26 
    27 fun add_typedecls decls thy =
    28   let
    29     val full = Sign.full_name (Theory.sign_of thy);
    30 
    31     fun arity_of (raw_name, args, mx) =
    32       (full (Syntax.type_name raw_name mx), replicate (length args) HOLogic.termS, HOLogic.termS);
    33   in
    34     thy
    35     |> PureThy.add_typedecls decls
    36     |> Theory.add_arities_i (map arity_of decls)
    37   end;
    38 
    39 
    40 
    41 (** type definitions **)
    42 
    43 (* messages *)
    44 
    45 val quiet_mode = ref false;
    46 fun message s = if ! quiet_mode then () else writeln s;
    47 
    48 
    49 (* prove non-emptyness of a set *)   (*exception ERROR*)
    50 
    51 val is_def = Logic.is_equals o #prop o rep_thm;
    52 
    53 fun prove_nonempty cset thms usr_tac =
    54   let
    55     val {T = setT, t = set, maxidx, sign} = rep_cterm cset;
    56     val T = HOLogic.dest_setT setT;
    57     val goal = cterm_of sign
    58       (HOLogic.mk_Trueprop (HOLogic.mk_mem (Var (("x", maxidx + 1), T), set)));
    59     val tac =
    60       TRY (rewrite_goals_tac (filter is_def thms)) THEN
    61       TRY (REPEAT_FIRST (resolve_tac (filter_out is_def thms))) THEN
    62       if_none usr_tac (TRY (ALLGOALS (CLASET' blast_tac)));
    63   in
    64     prove_goalw_cterm [] goal (K [tac])
    65   end
    66   handle ERROR =>
    67     error ("Failed to prove nonemptiness of " ^ quote (string_of_cterm cset));
    68 
    69 
    70 (* gen_add_typedef *)
    71 
    72 fun gen_add_typedef prep_term no_def name (t, vs, mx) raw_set axms thms usr_tac thy =
    73   let
    74     val _ = Theory.requires thy "Set" "typedefs";
    75     val sign = sign_of thy;
    76     val full_name = Sign.full_name sign;
    77 
    78     (*rhs*)
    79     val cset = prep_term sign raw_set;
    80     val {T = setT, t = set, ...} = rep_cterm cset;
    81     val rhs_tfrees = term_tfrees set;
    82     val oldT = HOLogic.dest_setT setT handle TYPE _ =>
    83       error ("Not a set type: " ^ quote (Sign.string_of_typ sign setT));
    84 
    85     (*lhs*)
    86     val lhs_tfrees =
    87       map (fn v => (v, if_none (assoc (rhs_tfrees, v)) HOLogic.termS)) vs;
    88 
    89     val tname = Syntax.type_name t mx;
    90     val newT = Type (full_name tname, map TFree lhs_tfrees);
    91 
    92     val Rep_name = "Rep_" ^ name;
    93     val Abs_name = "Abs_" ^ name;
    94     val setC = Const (full_name name, setT);
    95     val RepC = Const (full_name Rep_name, newT --> oldT);
    96     val AbsC = Const (full_name Abs_name, oldT --> newT);
    97     val x_new = Free ("x", newT);
    98     val y_old = Free ("y", oldT);
    99     val set' = if no_def then set else setC;
   100 
   101     (*axioms*)
   102     val rep_type = HOLogic.mk_Trueprop (HOLogic.mk_mem (RepC $ x_new, set'));
   103     val rep_type_inv = HOLogic.mk_Trueprop (HOLogic.mk_eq (AbsC $ (RepC $ x_new), x_new));
   104     val abs_type_inv = Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (y_old, set')),
   105       HOLogic.mk_Trueprop (HOLogic.mk_eq (RepC $ (AbsC $ y_old), y_old)));
   106 
   107 
   108     (* errors *)
   109 
   110     fun show_names pairs = commas_quote (map fst pairs);
   111 
   112     val illegal_vars =
   113       if null (term_vars set) andalso null (term_tvars set) then []
   114       else ["Illegal schematic variable(s) on rhs"];
   115 
   116     val dup_lhs_tfrees =
   117       (case duplicates lhs_tfrees of [] => []
   118       | dups => ["Duplicate type variables on lhs: " ^ show_names dups]);
   119 
   120     val extra_rhs_tfrees =
   121       (case gen_rems (op =) (rhs_tfrees, lhs_tfrees) of [] => []
   122       | extras => ["Extra type variables on rhs: " ^ show_names extras]);
   123 
   124     val illegal_frees =
   125       (case term_frees set of [] => []
   126       | xs => ["Illegal variables on rhs: " ^ show_names (map dest_Free xs)]);
   127 
   128     val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees;
   129   in
   130     if null errs then ()
   131     else error (cat_lines errs);
   132 
   133     message ("Proving nonemptiness of " ^ quote name ^ " ...");
   134     prove_nonempty cset (map (get_axiom thy) axms @ thms) usr_tac;
   135 
   136     thy
   137     |> PureThy.add_typedecls [(t, vs, mx)]
   138     |> Theory.add_arities_i
   139      [(full_name tname, replicate (length vs) HOLogic.termS, HOLogic.termS)]
   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 (PureThy.add_defs_i o map Thm.no_attributes)
   145      [(name ^ "_def", Logic.mk_equals (setC, set))])
   146     |> (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   end
   151   handle ERROR =>
   152     error ("The error(s) above occurred in typedef " ^ quote name);
   153 
   154 
   155 (* external interfaces *)
   156 
   157 fun read_term sg str =
   158   read_cterm sg (str, HOLogic.termTVar);
   159 
   160 fun cert_term sg tm =
   161   cterm_of sg tm handle TERM (msg, _) => error msg;
   162 
   163 val add_typedef = gen_add_typedef read_term false;
   164 val add_typedef_i = gen_add_typedef cert_term false;
   165 val add_typedef_i_no_def = gen_add_typedef cert_term true;
   166 
   167 
   168 end;