src/HOL/Tools/typedef_package.ML
author berghofe
Wed, 13 Nov 2002 15:28:41 +0100
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child 14570 0bf4e84bf51d
permissions -rw-r--r--
prove_goal' -> Goal.simple_prove_goal_cterm
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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_x: 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: bool -> string option -> bstring * string list * mixfix ->
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    string -> (bstring * bstring) option -> tactic -> theory -> theory *
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    {type_definition: thm, set_def: thm option, Rep: thm, Rep_inverse: thm,
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      Abs_inverse: thm, Rep_inject: thm, Abs_inject: thm, Rep_cases: thm, Abs_cases: thm,
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      Rep_induct: thm, Abs_induct: thm}
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  val add_typedef_i: bool -> string option -> bstring * string list * mixfix ->
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    term -> (bstring * bstring) option -> tactic -> theory -> theory *
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    {type_definition: thm, set_def: thm option, Rep: thm, Rep_inverse: thm,
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      Abs_inverse: thm, Rep_inject: thm, Abs_inject: thm, Rep_cases: thm, Abs_cases: thm,
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      Rep_induct: thm, Abs_induct: thm}
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  val typedef_proof: (bool * string) * (bstring * string list * mixfix) * string
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    * (string * string) option -> bool -> theory -> ProofHistory.T
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  val typedef_proof_i: (bool * string) * (bstring * string list * mixfix) * term
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    * (string * string) option -> 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 = "Typedef.type_definition";
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val Rep = thm "type_definition.Rep";
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val Rep_inverse = thm "type_definition.Rep_inverse";
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val Abs_inverse = thm "type_definition.Abs_inverse";
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val Rep_inject = thm "type_definition.Rep_inject";
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val Abs_inject = thm "type_definition.Abs_inject";
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val Rep_cases = thm "type_definition.Rep_cases";
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val Abs_cases = thm "type_definition.Abs_cases";
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val Rep_induct = thm "type_definition.Rep_induct";
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val Abs_induct = thm "type_definition.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.typeS, HOLogic.typeS);
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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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(* prove_nonempty -- tactical version *)        (*exception ERROR*)
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fun prove_nonempty thy cset goal (witn1_tac, witn_names, witn_thms, witn2_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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      witn1_tac THEN
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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 witn2_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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    Tactic.prove (Theory.sign_of thy) [] [] goal (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.typeT));
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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 def name (t, vs, mx) raw_set opt_morphs thy =
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  let
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    val _ = Theory.requires thy "Typedef" "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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    fun mk_nonempty A =
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      HOLogic.mk_Trueprop (HOLogic.mk_exists ("x", oldT, HOLogic.mk_mem (Free ("x", oldT), A)));
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    val goal = mk_nonempty set;
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    val vname = take_suffix Symbol.is_digit (Symbol.explode name)
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      |> apfst implode |> apsnd (#1 o Term.read_int);
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    val goal_pat = mk_nonempty (Var (vname, setT));
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    (*lhs*)
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    val lhs_tfrees = map (fn v => (v, if_none (assoc (rhs_tfrees, v)) HOLogic.typeS)) 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, Abs_name) = if_none opt_morphs ("Rep_" ^ 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 def then setC else set;
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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 =
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      Logic.mk_implies (goal, HOLogic.mk_Trueprop (typedefC $ RepC $ AbsC $ set'));
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    fun typedef_result (theory, nonempty) =
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      theory
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      |> add_typedecls [(t, vs, mx)]
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      |> Theory.add_consts_i
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       ((if def then [(name, setT, NoSyn)] else []) @
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        [(Rep_name, newT --> oldT, NoSyn),
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         (Abs_name, oldT --> newT, NoSyn)])
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      |> (if def then (apsnd (Some o hd) oo (PureThy.add_defs_i false o map Thm.no_attributes))
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           [Logic.mk_defpair (setC, set)]
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          else rpair None)
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      |>> PureThy.add_axioms_i [((typedef_name, typedef_prop),
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          [apsnd (fn cond_axm => Drule.standard (nonempty RS cond_axm))])]
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      |> (fn ((theory', [type_definition]), set_def) =>
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        let
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          fun make th = Drule.standard (th OF [type_definition]);
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          val (theory'', [Rep, Rep_inverse, Abs_inverse, Rep_inject, Abs_inject,
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              Rep_cases, Abs_cases, Rep_induct, Abs_induct]) =
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            theory'
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            |> Theory.add_path name
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            |> 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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                ((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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            |>> Theory.parent_path;
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          val result = {type_definition = type_definition, set_def = set_def,
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            Rep = Rep, Rep_inverse = Rep_inverse, Abs_inverse = Abs_inverse,
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            Rep_inject = Rep_inject, Abs_inject = Abs_inject, Rep_cases = Rep_cases,
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            Abs_cases = Abs_cases, Rep_induct = Rep_induct, Abs_induct = Abs_induct};
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        in ((theory'', type_definition), result) end);
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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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    val _ = if null errs then () else error (cat_lines errs);
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    (*test theory errors now!*)
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    val test_thy = Theory.copy thy;
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    val _ = (test_thy,
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      setmp quick_and_dirty true (SkipProof.make_thm test_thy) goal) |> typedef_result;
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  in (cset, goal, goal_pat, typedef_result) end
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  handle ERROR => err_in_typedef name;
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(* add_typedef interfaces *)
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fun gen_typedef prep_term def name typ set opt_morphs tac1 names thms tac2 thy =
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  let
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    val (cset, goal, _, typedef_result) =
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      prepare_typedef prep_term def name typ set opt_morphs thy;
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    val non_empty = prove_nonempty thy cset goal (tac1, names, thms, tac2);
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    val ((thy', _), result) = (thy, non_empty) |> typedef_result;
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  in (thy', result) end;
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fun sane_typedef prep_term def opt_name typ set opt_morphs tac =
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  gen_typedef prep_term def
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    (if_none opt_name (#1 typ)) typ set opt_morphs all_tac [] [] (Some tac);
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fun add_typedef_x name typ set names thms tac =
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  #1 o gen_typedef read_term true name typ set None (Tactic.rtac exI 1) names thms tac;
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val add_typedef = sane_typedef read_term;
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val add_typedef_i = sane_typedef cert_term;
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(* typedef_proof interface *)
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fun gen_typedef_proof prep_term ((def, name), typ, set, opt_morphs) int thy =
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  let
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    val (_, goal, goal_pat, att_result) =
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      prepare_typedef prep_term def name typ set opt_morphs thy;
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    val att = #1 o att_result;
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  in thy |> IsarThy.theorem_i Drule.internalK (("", [att]), (goal, ([goal_pat], []))) int 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" "type declaration (HOL)" K.thy_decl
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    (P.type_args -- P.name -- P.opt_infix >> (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.optional (P.$$$ "(" |-- P.!!!
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      (((P.$$$ "open" >> K false) -- Scan.option P.name || P.name >> (fn s => (true, Some s)))
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        --| P.$$$ ")")) (true, None) --
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    (P.type_args -- P.name) -- P.opt_infix -- (P.$$$ "=" |-- P.term) --
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    Scan.option (P.$$$ "morphisms" |-- P.!!! (P.name -- P.name));
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fun mk_typedef_proof ((((((def, opt_name), (vs, t)), mx), A), morphs)) =
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  typedef_proof ((def, if_none opt_name (Syntax.type_name t mx)), (t, vs, mx), A, morphs);
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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_keywords ["morphisms"];
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val _ = OuterSyntax.add_parsers [typedeclP, typedefP];
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end;
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end;