src/HOL/Tools/typedef_package.ML
author wenzelm
Thu, 19 Oct 2000 21:25:15 +0200
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provide more theorems (see subset.thy); tuned;
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(*  Title:      HOL/Tools/typedef_package.ML
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    ID:         $Id$
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    Author:     Markus Wenzel, TU Muenchen
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    License:    GPL (GNU GENERAL PUBLIC LICENSE)
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Gordon/HOL-style type definitions.
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*)
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signature TYPEDEF_PACKAGE =
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sig
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  val quiet_mode: bool ref
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  val add_typedecls: (bstring * string list * mixfix) list -> theory -> theory
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  val add_typedef: string -> bstring * string list * mixfix ->
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    string -> string list -> thm list -> tactic option -> theory -> theory
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  val add_typedef_i: string -> bstring * string list * mixfix ->
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    term -> string list -> thm list -> tactic option -> theory -> theory
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  val add_typedef_i_no_def: string -> bstring * string list * mixfix ->
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    term -> string list -> thm list -> tactic option -> theory -> theory
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  val typedef_proof: (string * (bstring * string list * mixfix) * string) * Comment.text
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    -> bool -> theory -> ProofHistory.T
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  val typedef_proof_i: (string * (bstring * string list * mixfix) * term) * Comment.text
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    -> bool -> theory -> ProofHistory.T
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end;
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structure TypedefPackage: TYPEDEF_PACKAGE =
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struct
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(** theory context references **)
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val type_definitionN = "subset.type_definition";
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val type_definition_def = thm "type_definition_def";
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val Rep = thm "Rep";
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val Rep_inverse = thm "Rep_inverse";
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val Abs_inverse = thm "Abs_inverse";
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val Rep_inject = thm "Rep_inject";
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val Abs_inject = thm "Abs_inject";
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val Rep_cases = thm "Rep_cases";
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val Abs_cases = thm "Abs_cases";
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val Rep_induct = thm "Rep_induct";
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val Abs_induct = thm "Abs_induct";
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(** type declarations **)
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fun add_typedecls decls thy =
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  let
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    val full = Sign.full_name (Theory.sign_of thy);
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    fun arity_of (raw_name, args, mx) =
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      (full (Syntax.type_name raw_name mx), replicate (length args) HOLogic.termS, HOLogic.termS);
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  in
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    if can (Theory.assert_super HOL.thy) thy then
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      thy
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      |> PureThy.add_typedecls decls
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      |> Theory.add_arities_i (map arity_of decls)
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    else thy |> PureThy.add_typedecls decls
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  end;
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(** type definitions **)
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(* messages *)
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val quiet_mode = ref false;
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fun message s = if ! quiet_mode then () else writeln s;
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(* non-emptiness of set *)              (*exception ERROR*)
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fun check_nonempty cset thm =
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  let
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    val {t, sign, maxidx, ...} = Thm.rep_cterm cset;
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    val {prop, ...} = Thm.rep_thm (Thm.transfer_sg sign (Drule.standard thm));
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    val matches = Pattern.matches (Sign.tsig_of sign);
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  in
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    (case try (HOLogic.dest_mem o HOLogic.dest_Trueprop) prop of
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      None => raise ERROR
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    | Some (_, A) => if matches (Logic.incr_indexes ([], maxidx) A, t) then () else raise ERROR)
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  end handle ERROR => error ("Bad non-emptiness theorem " ^ Display.string_of_thm thm ^
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    "\nfor set " ^ quote (Display.string_of_cterm cset));
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fun goal_nonempty ex cset =
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  let
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    val {T = setT, t = A, maxidx, sign} = Thm.rep_cterm cset;
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    val T = HOLogic.dest_setT setT;
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    val tm =
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      if ex then HOLogic.mk_exists ("x", T, HOLogic.mk_mem (Free ("x", T), A))
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      else HOLogic.mk_mem (Var (("x", maxidx + 1), T), A);   (*old-style version*)
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  in Thm.cterm_of sign (HOLogic.mk_Trueprop tm) end;
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fun prove_nonempty thy cset (witn_names, witn_thms, witn_tac) =
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  let
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    val is_def = Logic.is_equals o #prop o Thm.rep_thm;
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    val thms = PureThy.get_thmss thy witn_names @ witn_thms;
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    val tac =
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      TRY (rewrite_goals_tac (filter is_def thms)) THEN
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      TRY (REPEAT_FIRST (resolve_tac (filter_out is_def thms))) THEN
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      if_none witn_tac (TRY (ALLGOALS (CLASET' blast_tac)));
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  in
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    message ("Proving non-emptiness of set " ^ quote (string_of_cterm cset) ^ " ...");
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    prove_goalw_cterm [] (goal_nonempty false cset) (K [tac])
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  end handle ERROR => error ("Failed to prove non-emptiness of " ^ quote (string_of_cterm cset));
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(* prepare_typedef *)
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fun read_term sg used s =
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  #1 (Thm.read_def_cterm (sg, K None, K None) used true (s, HOLogic.termT));
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fun cert_term sg _ t = Thm.cterm_of sg t handle TERM (msg, _) => error msg;
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fun err_in_typedef name =
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  error ("The error(s) above occurred in typedef " ^ quote name);
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fun prepare_typedef prep_term no_def name (t, vs, mx) raw_set thy =
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  let
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    val _ = Theory.requires thy "subset" "typedefs";
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    val sign = Theory.sign_of thy;
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    val full = Sign.full_name sign;
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    (*rhs*)
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    val full_name = full name;
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    val cset = prep_term sign vs raw_set;
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    val {T = setT, t = set, ...} = Thm.rep_cterm cset;
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    val rhs_tfrees = term_tfrees set;
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    val oldT = HOLogic.dest_setT setT handle TYPE _ =>
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      error ("Not a set type: " ^ quote (Sign.string_of_typ sign setT));
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    val cset_pat = Thm.cterm_of sign (Var ((name, 0), setT));
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    (*lhs*)
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    val lhs_tfrees = map (fn v => (v, if_none (assoc (rhs_tfrees, v)) HOLogic.termS)) vs;
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    val tname = Syntax.type_name t mx;
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    val full_tname = full tname;
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    val newT = Type (full_tname, map TFree lhs_tfrees);
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    val Rep_name = "Rep_" ^ name;
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    val Abs_name = "Abs_" ^ name;
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    val setC = Const (full_name, setT);
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    val RepC = Const (full Rep_name, newT --> oldT);
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    val AbsC = Const (full Abs_name, oldT --> newT);
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    val x_new = Free ("x", newT);
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    val y_old = Free ("y", oldT);
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    val set' = if no_def then set else setC;    (* FIXME !?? *)
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    val typedef_name = "type_definition_" ^ name;
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    val typedefC =
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      Const (type_definitionN, (newT --> oldT) --> (oldT --> newT) --> setT --> HOLogic.boolT);
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    val typedef_prop = HOLogic.mk_Trueprop (typedefC $ RepC $ AbsC $ set');
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    (*theory extender*)
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    fun do_typedef theory =
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      theory
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      |> Theory.assert_super thy
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      |> add_typedecls [(t, vs, mx)]
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      |> Theory.add_consts_i
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       ((if no_def then [] else [(name, setT, NoSyn)]) @
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        [(Rep_name, newT --> oldT, NoSyn),
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         (Abs_name, oldT --> newT, NoSyn)])
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      |> (if no_def then I else (#1 oo (PureThy.add_defs_i false o map Thm.no_attributes))
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       [Logic.mk_defpair (setC, set)])
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      |> PureThy.add_axioms_i [((typedef_name, typedef_prop), [])]
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      |> (fn (theory', typedef_ax) =>
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        let fun make th = standard (th OF typedef_ax) in
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          theory'
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          |> (#1 oo PureThy.add_thms)
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            ([((Rep_name, make Rep), []),
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              ((Rep_name ^ "_inverse", make Rep_inverse), []),
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              ((Abs_name ^ "_inverse", make Abs_inverse), [])] @
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            (if no_def then [] else
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             [((Rep_name ^ "_inject", make Rep_inject), []),
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              ((Abs_name ^ "_inject", make Abs_inject), []),
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              ((Rep_name ^ "_cases", make Rep_cases),
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                [RuleCases.case_names [Rep_name], InductAttrib.cases_set_global full_name]),
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              ((Abs_name ^ "_cases", make Abs_cases),
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                [RuleCases.case_names [Abs_name], InductAttrib.cases_type_global full_tname]),
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              ((Rep_name ^ "_induct", make Rep_induct),
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                [RuleCases.case_names [Rep_name], InductAttrib.induct_set_global full_name]),
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              ((Abs_name ^ "_induct", make Abs_induct),
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                [RuleCases.case_names [Abs_name], InductAttrib.induct_type_global full_tname])]))
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        end)
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      handle ERROR => err_in_typedef name;
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    (* errors *)
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    fun show_names pairs = commas_quote (map fst pairs);
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    val illegal_vars =
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      if null (term_vars set) andalso null (term_tvars set) then []
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      else ["Illegal schematic variable(s) on rhs"];
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    val dup_lhs_tfrees =
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      (case duplicates lhs_tfrees of [] => []
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      | dups => ["Duplicate type variables on lhs: " ^ show_names dups]);
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    val extra_rhs_tfrees =
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      (case gen_rems (op =) (rhs_tfrees, lhs_tfrees) of [] => []
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      | extras => ["Extra type variables on rhs: " ^ show_names extras]);
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    val illegal_frees =
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      (case term_frees set of [] => []
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      | xs => ["Illegal variables on rhs: " ^ show_names (map dest_Free xs)]);
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    val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees;
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  in
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    if null errs then () else error (cat_lines errs);
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    (cset, cset_pat, do_typedef)
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  end handle ERROR => err_in_typedef name;
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(* add_typedef interfaces *)
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fun gen_add_typedef prep_term no_def name typ set names thms tac thy =
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  let
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    val (cset, _, do_typedef) = prepare_typedef prep_term no_def name typ set thy;
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    val result = prove_nonempty thy cset (names, thms, tac);
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  in check_nonempty cset result; thy |> do_typedef end;
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val add_typedef = gen_add_typedef read_term false;
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val add_typedef_i = gen_add_typedef cert_term false;
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val add_typedef_i_no_def = gen_add_typedef cert_term true;
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(* typedef_proof interface *)
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fun typedef_attribute cset do_typedef (thy, thm) =
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  (check_nonempty cset (thm RS (some_eq_ex RS iffD2)); (thy |> do_typedef, thm));
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fun gen_typedef_proof prep_term ((name, typ, set), comment) int thy =
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  let
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    val (cset, cset_pat, do_typedef) = prepare_typedef prep_term false name typ set thy;
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    val goal = Thm.term_of (goal_nonempty true cset);
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    val goal_pat = Thm.term_of (goal_nonempty true cset_pat);
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  in
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    thy
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    |> IsarThy.theorem_i (("", [typedef_attribute cset do_typedef],
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      (goal, ([goal_pat], []))), comment) int
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  end;
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val typedef_proof = gen_typedef_proof read_term;
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val typedef_proof_i = gen_typedef_proof cert_term;
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(** outer syntax **)
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local structure P = OuterParse and K = OuterSyntax.Keyword in
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val typedeclP =
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  OuterSyntax.command "typedecl" "HOL type declaration" K.thy_decl
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    (P.type_args -- P.name -- P.opt_infix --| P.marg_comment >> (fn ((vs, t), mx) =>
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      Toplevel.theory (add_typedecls [(t, vs, mx)])));
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val typedef_proof_decl =
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  Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") --
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    (P.type_args -- P.name) -- P.opt_infix -- (P.$$$ "=" |-- P.term) -- P.marg_comment;
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fun mk_typedef_proof ((((opt_name, (vs, t)), mx), A), comment) =
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  typedef_proof ((if_none opt_name (Syntax.type_name t mx), (t, vs, mx), A), comment);
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val typedefP =
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  OuterSyntax.command "typedef" "HOL type definition (requires non-emptiness proof)" K.thy_goal
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    (typedef_proof_decl >> (Toplevel.print oo (Toplevel.theory_to_proof o mk_typedef_proof)));
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val _ = OuterSyntax.add_parsers [typedeclP, typedefP];
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end;
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end;