src/HOL/Nominal/nominal_package.ML
author berghofe
Wed Feb 07 17:51:38 2007 +0100 (2007-02-07)
changeset 22274 ce1459004c8d
parent 22245 1b8f4ef50c48
child 22311 ebcd44cb8d61
permissions -rw-r--r--
Adapted to changes in Finite_Set theory.
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(*  Title:      HOL/Nominal/nominal_package.ML
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    ID:         $Id$
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    Author:     Stefan Berghofer and Christian Urban, TU Muenchen
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Nominal datatype package for Isabelle/HOL.
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*)
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signature NOMINAL_PACKAGE =
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sig
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  val add_nominal_datatype : bool -> string list -> (string list * bstring * mixfix *
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    (bstring * string list * mixfix) list) list -> theory -> theory
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  type nominal_datatype_info
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  val get_nominal_datatypes : theory -> nominal_datatype_info Symtab.table
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  val get_nominal_datatype : theory -> string -> nominal_datatype_info option
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  val setup: theory -> theory
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end
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structure NominalPackage : NOMINAL_PACKAGE =
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struct
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val finite_emptyI = thm "finite.emptyI";
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val finite_Diff = thm "finite_Diff";
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val finite_Un = thm "finite_Un";
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val Un_iff = thm "Un_iff";
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val In0_eq = thm "In0_eq";
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val In1_eq = thm "In1_eq";
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val In0_not_In1 = thm "In0_not_In1";
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val In1_not_In0 = thm "In1_not_In0";
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val Un_assoc = thm "Un_assoc";
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val Collect_disj_eq = thm "Collect_disj_eq";
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val empty_def = thm "empty_def";
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open DatatypeAux;
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open NominalAtoms;
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(** FIXME: DatatypePackage should export this function **)
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local
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fun dt_recs (DtTFree _) = []
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  | dt_recs (DtType (_, dts)) = List.concat (map dt_recs dts)
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  | dt_recs (DtRec i) = [i];
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fun dt_cases (descr: descr) (_, args, constrs) =
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  let
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    fun the_bname i = Sign.base_name (#1 (valOf (AList.lookup (op =) descr i)));
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    val bnames = map the_bname (distinct op = (List.concat (map dt_recs args)));
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  in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end;
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fun induct_cases descr =
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  DatatypeProp.indexify_names (List.concat (map (dt_cases descr) (map #2 descr)));
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fun exhaust_cases descr i = dt_cases descr (valOf (AList.lookup (op =) descr i));
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in
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fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr);
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fun mk_case_names_exhausts descr new =
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  map (RuleCases.case_names o exhaust_cases descr o #1)
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    (List.filter (fn ((_, (name, _, _))) => name mem_string new) descr);
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end;
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(* data kind 'HOL/nominal_datatypes' *)
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type nominal_datatype_info =
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  {index : int,
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   descr : descr,
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   sorts : (string * sort) list,
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   rec_names : string list,
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   rec_rewrites : thm list,
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   induction : thm,
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   distinct : thm list,
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   inject : thm list};
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structure NominalDatatypesData = TheoryDataFun
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(struct
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  val name = "HOL/nominal_datatypes";
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  type T = nominal_datatype_info Symtab.table;
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  val empty = Symtab.empty;
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  val copy = I;
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  val extend = I;
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  fun merge _ tabs : T = Symtab.merge (K true) tabs;
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  fun print sg tab =
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    Pretty.writeln (Pretty.strs ("nominal datatypes:" ::
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      map #1 (NameSpace.extern_table (Sign.type_space sg, tab))));
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end);
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val get_nominal_datatypes = NominalDatatypesData.get;
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val put_nominal_datatypes = NominalDatatypesData.put;
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val map_nominal_datatypes = NominalDatatypesData.map;
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val get_nominal_datatype = Symtab.lookup o get_nominal_datatypes;
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val setup = NominalDatatypesData.init;
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(**** make datatype info ****)
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fun make_dt_info descr sorts induct reccomb_names rec_thms
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    (((i, (_, (tname, _, _))), distinct), inject) =
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  (tname,
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   {index = i,
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    descr = descr,
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    sorts = sorts,
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    rec_names = reccomb_names,
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    rec_rewrites = rec_thms,
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    induction = induct,
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    distinct = distinct,
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    inject = inject});
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(*******************************)
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val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma);
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fun read_typ sign ((Ts, sorts), str) =
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  let
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    val T = Type.no_tvars (Sign.read_typ (sign, (AList.lookup op =)
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      (map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg
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  in (Ts @ [T], add_typ_tfrees (T, sorts)) end;
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(** taken from HOL/Tools/datatype_aux.ML **)
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fun indtac indrule indnames i st =
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  let
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    val ts = HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule));
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    val ts' = HOLogic.dest_conj (HOLogic.dest_Trueprop
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      (Logic.strip_imp_concl (List.nth (prems_of st, i - 1))));
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    val getP = if can HOLogic.dest_imp (hd ts) then
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      (apfst SOME) o HOLogic.dest_imp else pair NONE;
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    fun abstr (t1, t2) = (case t1 of
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        NONE => (case filter (fn Free (s, _) => s mem indnames | _ => false)
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              (term_frees t2) of
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            [Free (s, T)] => absfree (s, T, t2)
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          | _ => sys_error "indtac")
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      | SOME (_ $ t') => Abs ("x", fastype_of t', abstract_over (t', t2)))
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    val cert = cterm_of (Thm.sign_of_thm st);
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    val Ps = map (cert o head_of o snd o getP) ts;
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    val indrule' = cterm_instantiate (Ps ~~
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      (map (cert o abstr o getP) ts')) indrule
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  in
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    rtac indrule' i st
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  end;
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fun mk_subgoal i f st =
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  let
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    val cg = List.nth (cprems_of st, i - 1);
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    val g = term_of cg;
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    val revcut_rl' = Thm.lift_rule cg revcut_rl;
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    val v = head_of (Logic.strip_assums_concl (hd (prems_of revcut_rl')));
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    val ps = Logic.strip_params g;
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    val cert = cterm_of (sign_of_thm st);
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  in
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    compose_tac (false,
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      Thm.instantiate ([], [(cert v, cert (list_abs (ps,
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        f (rev ps) (Logic.strip_assums_hyp g) (Logic.strip_assums_concl g))))])
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      revcut_rl', 2) i st
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  end;
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(** simplification procedure for sorting permutations **)
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val dj_cp = thm "dj_cp";
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fun dest_permT (Type ("fun", [Type ("List.list", [Type ("*", [T, _])]),
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      Type ("fun", [_, U])])) = (T, U);
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fun permTs_of (Const ("Nominal.perm", T) $ t $ u) = fst (dest_permT T) :: permTs_of u
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  | permTs_of _ = [];
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fun perm_simproc' thy ss (Const ("Nominal.perm", T) $ t $ (u as Const ("Nominal.perm", U) $ r $ s)) =
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      let
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        val (aT as Type (a, []), S) = dest_permT T;
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        val (bT as Type (b, []), _) = dest_permT U
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      in if aT mem permTs_of u andalso aT <> bT then
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          let
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            val a' = Sign.base_name a;
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            val b' = Sign.base_name b;
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            val cp = PureThy.get_thm thy (Name ("cp_" ^ a' ^ "_" ^ b' ^ "_inst"));
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            val dj = PureThy.get_thm thy (Name ("dj_" ^ b' ^ "_" ^ a'));
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            val dj_cp' = [cp, dj] MRS dj_cp;
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            val cert = SOME o cterm_of thy
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          in
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            SOME (mk_meta_eq (Drule.instantiate' [SOME (ctyp_of thy S)]
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              [cert t, cert r, cert s] dj_cp'))
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          end
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        else NONE
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      end
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  | perm_simproc' thy ss _ = NONE;
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val perm_simproc =
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  Simplifier.simproc (the_context ()) "perm_simp" ["pi1 \\<bullet> (pi2 \\<bullet> x)"] perm_simproc';
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val allE_Nil = read_instantiate_sg (the_context()) [("x", "[]")] allE;
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val meta_spec = thm "meta_spec";
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fun projections rule =
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  ProjectRule.projections (ProofContext.init (Thm.theory_of_thm rule)) rule
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  |> map (standard #> RuleCases.save rule);
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val supp_prod = thm "supp_prod";
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val fresh_prod = thm "fresh_prod";
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val supports_fresh = thm "supports_fresh";
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val supports_def = thm "Nominal.op supports_def";
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val fresh_def = thm "fresh_def";
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val supp_def = thm "supp_def";
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val rev_simps = thms "rev.simps";
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val app_simps = thms "op @.simps";
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val collect_simp = rewrite_rule [mk_meta_eq mem_Collect_eq];
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fun gen_add_nominal_datatype prep_typ err flat_names new_type_names dts thy =
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  let
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    (* this theory is used just for parsing *)
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    val tmp_thy = thy |>
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      Theory.copy |>
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      Theory.add_types (map (fn (tvs, tname, mx, _) =>
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        (tname, length tvs, mx)) dts);
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    val sign = Theory.sign_of tmp_thy;
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    val atoms = atoms_of thy;
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    val classes = map (NameSpace.map_base (fn s => "pt_" ^ s)) atoms;
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    val cp_classes = List.concat (map (fn atom1 => map (fn atom2 =>
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      Sign.intern_class thy ("cp_" ^ Sign.base_name atom1 ^ "_" ^
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        Sign.base_name atom2)) atoms) atoms);
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    fun augment_sort S = S union classes;
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    val augment_sort_typ = map_type_tfree (fn (s, S) => TFree (s, augment_sort S));
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    fun prep_constr ((constrs, sorts), (cname, cargs, mx)) =
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      let val (cargs', sorts') = Library.foldl (prep_typ sign) (([], sorts), cargs)
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      in (constrs @ [(cname, cargs', mx)], sorts') end
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    fun prep_dt_spec ((dts, sorts), (tvs, tname, mx, constrs)) =
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      let val (constrs', sorts') = Library.foldl prep_constr (([], sorts), constrs)
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      in (dts @ [(tvs, tname, mx, constrs')], sorts') end
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    val (dts', sorts) = Library.foldl prep_dt_spec (([], []), dts);
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    val sorts' = map (apsnd augment_sort) sorts;
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    val tyvars = map #1 dts';
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    val types_syntax = map (fn (tvs, tname, mx, constrs) => (tname, mx)) dts';
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    val constr_syntax = map (fn (tvs, tname, mx, constrs) =>
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      map (fn (cname, cargs, mx) => (cname, mx)) constrs) dts';
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    val ps = map (fn (_, n, _, _) =>
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      (Sign.full_name sign n, Sign.full_name sign (n ^ "_Rep"))) dts;
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    val rps = map Library.swap ps;
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    fun replace_types (Type ("Nominal.ABS", [T, U])) =
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          Type ("fun", [T, Type ("Nominal.noption", [replace_types U])])
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      | replace_types (Type (s, Ts)) =
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          Type (getOpt (AList.lookup op = ps s, s), map replace_types Ts)
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      | replace_types T = T;
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    val dts'' = map (fn (tvs, tname, mx, constrs) => (tvs, tname ^ "_Rep", NoSyn,
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      map (fn (cname, cargs, mx) => (cname ^ "_Rep",
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        map (augment_sort_typ o replace_types) cargs, NoSyn)) constrs)) dts';
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    val new_type_names' = map (fn n => n ^ "_Rep") new_type_names;
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    val full_new_type_names' = map (Sign.full_name (sign_of thy)) new_type_names';
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    val ({induction, ...},thy1) =
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      DatatypePackage.add_datatype_i err flat_names new_type_names' dts'' thy;
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    val SOME {descr, ...} = Symtab.lookup
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      (DatatypePackage.get_datatypes thy1) (hd full_new_type_names');
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    fun nth_dtyp i = typ_of_dtyp descr sorts' (DtRec i);
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    (**** define permutation functions ****)
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    val permT = mk_permT (TFree ("'x", HOLogic.typeS));
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    val pi = Free ("pi", permT);
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    val perm_types = map (fn (i, _) =>
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      let val T = nth_dtyp i
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      in permT --> T --> T end) descr;
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    val perm_names = replicate (length new_type_names) "Nominal.perm" @
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      DatatypeProp.indexify_names (map (fn i => Sign.full_name (sign_of thy1)
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        ("perm_" ^ name_of_typ (nth_dtyp i)))
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          (length new_type_names upto length descr - 1));
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    val perm_names_types = perm_names ~~ perm_types;
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    val perm_eqs = List.concat (map (fn (i, (_, _, constrs)) =>
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      let val T = nth_dtyp i
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      in map (fn (cname, dts) =>
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        let
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          val Ts = map (typ_of_dtyp descr sorts') dts;
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          val names = DatatypeProp.make_tnames Ts;
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          val args = map Free (names ~~ Ts);
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          val c = Const (cname, Ts ---> T);
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          fun perm_arg (dt, x) =
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            let val T = type_of x
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            in if is_rec_type dt then
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                let val (Us, _) = strip_type T
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                in list_abs (map (pair "x") Us,
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                  Const (List.nth (perm_names_types, body_index dt)) $ pi $
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                    list_comb (x, map (fn (i, U) =>
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                      Const ("Nominal.perm", permT --> U --> U) $
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                        (Const ("List.rev", permT --> permT) $ pi) $
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                        Bound i) ((length Us - 1 downto 0) ~~ Us)))
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                end
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              else Const ("Nominal.perm", permT --> T --> T) $ pi $ x
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            end;
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        in
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          (("", HOLogic.mk_Trueprop (HOLogic.mk_eq
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            (Const (List.nth (perm_names_types, i)) $
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               Free ("pi", mk_permT (TFree ("'x", HOLogic.typeS))) $
berghofe@17870
   310
               list_comb (c, args),
berghofe@17870
   311
             list_comb (c, map perm_arg (dts ~~ args))))), [])
berghofe@17870
   312
        end) constrs
berghofe@17870
   313
      end) descr);
berghofe@17870
   314
haftmann@20179
   315
    val (perm_simps, thy2) = thy1 |>
berghofe@17870
   316
      Theory.add_consts_i (map (fn (s, T) => (Sign.base_name s, T, NoSyn))
berghofe@17870
   317
        (List.drop (perm_names_types, length new_type_names))) |>
wenzelm@19635
   318
      PrimrecPackage.add_primrec_unchecked_i "" perm_eqs;
berghofe@17870
   319
berghofe@17870
   320
    (**** prove that permutation functions introduced by unfolding are ****)
berghofe@17870
   321
    (**** equivalent to already existing permutation functions         ****)
berghofe@17870
   322
berghofe@17870
   323
    val _ = warning ("length descr: " ^ string_of_int (length descr));
berghofe@17870
   324
    val _ = warning ("length new_type_names: " ^ string_of_int (length new_type_names));
berghofe@17870
   325
berghofe@17870
   326
    val perm_indnames = DatatypeProp.make_tnames (map body_type perm_types);
berghofe@17870
   327
    val perm_fun_def = PureThy.get_thm thy2 (Name "perm_fun_def");
berghofe@17870
   328
berghofe@17870
   329
    val unfolded_perm_eq_thms =
berghofe@17870
   330
      if length descr = length new_type_names then []
berghofe@17870
   331
      else map standard (List.drop (split_conj_thm
wenzelm@20046
   332
        (Goal.prove_global thy2 [] []
berghofe@17870
   333
          (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@17870
   334
            (map (fn (c as (s, T), x) =>
berghofe@17870
   335
               let val [T1, T2] = binder_types T
berghofe@17870
   336
               in HOLogic.mk_eq (Const c $ pi $ Free (x, T2),
berghofe@19494
   337
                 Const ("Nominal.perm", T) $ pi $ Free (x, T2))
berghofe@17870
   338
               end)
berghofe@18010
   339
             (perm_names_types ~~ perm_indnames))))
berghofe@18010
   340
          (fn _ => EVERY [indtac induction perm_indnames 1,
berghofe@17870
   341
            ALLGOALS (asm_full_simp_tac
berghofe@17870
   342
              (simpset_of thy2 addsimps [perm_fun_def]))])),
berghofe@17870
   343
        length new_type_names));
berghofe@17870
   344
berghofe@17870
   345
    (**** prove [] \<bullet> t = t ****)
berghofe@17870
   346
berghofe@17870
   347
    val _ = warning "perm_empty_thms";
berghofe@17870
   348
berghofe@17870
   349
    val perm_empty_thms = List.concat (map (fn a =>
berghofe@17870
   350
      let val permT = mk_permT (Type (a, []))
berghofe@17870
   351
      in map standard (List.take (split_conj_thm
wenzelm@20046
   352
        (Goal.prove_global thy2 [] []
berghofe@17870
   353
          (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@17870
   354
            (map (fn ((s, T), x) => HOLogic.mk_eq
berghofe@17870
   355
                (Const (s, permT --> T --> T) $
berghofe@17870
   356
                   Const ("List.list.Nil", permT) $ Free (x, T),
berghofe@17870
   357
                 Free (x, T)))
berghofe@17870
   358
             (perm_names ~~
berghofe@18010
   359
              map body_type perm_types ~~ perm_indnames))))
berghofe@18010
   360
          (fn _ => EVERY [indtac induction perm_indnames 1,
berghofe@17870
   361
            ALLGOALS (asm_full_simp_tac (simpset_of thy2))])),
berghofe@17870
   362
        length new_type_names))
berghofe@17870
   363
      end)
berghofe@17870
   364
      atoms);
berghofe@17870
   365
berghofe@17870
   366
    (**** prove (pi1 @ pi2) \<bullet> t = pi1 \<bullet> (pi2 \<bullet> t) ****)
berghofe@17870
   367
berghofe@17870
   368
    val _ = warning "perm_append_thms";
berghofe@17870
   369
berghofe@17870
   370
    (*FIXME: these should be looked up statically*)
berghofe@17870
   371
    val at_pt_inst = PureThy.get_thm thy2 (Name "at_pt_inst");
berghofe@17870
   372
    val pt2 = PureThy.get_thm thy2 (Name "pt2");
berghofe@17870
   373
berghofe@17870
   374
    val perm_append_thms = List.concat (map (fn a =>
berghofe@17870
   375
      let
berghofe@17870
   376
        val permT = mk_permT (Type (a, []));
berghofe@17870
   377
        val pi1 = Free ("pi1", permT);
berghofe@17870
   378
        val pi2 = Free ("pi2", permT);
berghofe@17870
   379
        val pt_inst = PureThy.get_thm thy2 (Name ("pt_" ^ Sign.base_name a ^ "_inst"));
berghofe@17870
   380
        val pt2' = pt_inst RS pt2;
berghofe@17870
   381
        val pt2_ax = PureThy.get_thm thy2
berghofe@17870
   382
          (Name (NameSpace.map_base (fn s => "pt_" ^ s ^ "2") a));
berghofe@17870
   383
      in List.take (map standard (split_conj_thm
wenzelm@20046
   384
        (Goal.prove_global thy2 [] []
berghofe@17870
   385
             (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@17870
   386
                (map (fn ((s, T), x) =>
berghofe@17870
   387
                    let val perm = Const (s, permT --> T --> T)
berghofe@17870
   388
                    in HOLogic.mk_eq
berghofe@17870
   389
                      (perm $ (Const ("List.op @", permT --> permT --> permT) $
berghofe@17870
   390
                         pi1 $ pi2) $ Free (x, T),
berghofe@17870
   391
                       perm $ pi1 $ (perm $ pi2 $ Free (x, T)))
berghofe@17870
   392
                    end)
berghofe@17870
   393
                  (perm_names ~~
berghofe@18010
   394
                   map body_type perm_types ~~ perm_indnames))))
berghofe@18010
   395
           (fn _ => EVERY [indtac induction perm_indnames 1,
berghofe@17870
   396
              ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt2', pt2_ax]))]))),
berghofe@17870
   397
         length new_type_names)
berghofe@17870
   398
      end) atoms);
berghofe@17870
   399
berghofe@17870
   400
    (**** prove pi1 ~ pi2 ==> pi1 \<bullet> t = pi2 \<bullet> t ****)
berghofe@17870
   401
berghofe@17870
   402
    val _ = warning "perm_eq_thms";
berghofe@17870
   403
berghofe@17870
   404
    val pt3 = PureThy.get_thm thy2 (Name "pt3");
berghofe@17870
   405
    val pt3_rev = PureThy.get_thm thy2 (Name "pt3_rev");
berghofe@17870
   406
berghofe@17870
   407
    val perm_eq_thms = List.concat (map (fn a =>
berghofe@17870
   408
      let
berghofe@17870
   409
        val permT = mk_permT (Type (a, []));
berghofe@17870
   410
        val pi1 = Free ("pi1", permT);
berghofe@17870
   411
        val pi2 = Free ("pi2", permT);
berghofe@17870
   412
        (*FIXME: not robust - better access these theorems using NominalData?*)
berghofe@17870
   413
        val at_inst = PureThy.get_thm thy2 (Name ("at_" ^ Sign.base_name a ^ "_inst"));
berghofe@17870
   414
        val pt_inst = PureThy.get_thm thy2 (Name ("pt_" ^ Sign.base_name a ^ "_inst"));
berghofe@17870
   415
        val pt3' = pt_inst RS pt3;
berghofe@17870
   416
        val pt3_rev' = at_inst RS (pt_inst RS pt3_rev);
berghofe@17870
   417
        val pt3_ax = PureThy.get_thm thy2
berghofe@17870
   418
          (Name (NameSpace.map_base (fn s => "pt_" ^ s ^ "3") a));
berghofe@17870
   419
      in List.take (map standard (split_conj_thm
wenzelm@20046
   420
        (Goal.prove_global thy2 [] [] (Logic.mk_implies
berghofe@19494
   421
             (HOLogic.mk_Trueprop (Const ("Nominal.prm_eq",
berghofe@17870
   422
                permT --> permT --> HOLogic.boolT) $ pi1 $ pi2),
berghofe@17870
   423
              HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@17870
   424
                (map (fn ((s, T), x) =>
berghofe@17870
   425
                    let val perm = Const (s, permT --> T --> T)
berghofe@17870
   426
                    in HOLogic.mk_eq
berghofe@17870
   427
                      (perm $ pi1 $ Free (x, T),
berghofe@17870
   428
                       perm $ pi2 $ Free (x, T))
berghofe@17870
   429
                    end)
berghofe@17870
   430
                  (perm_names ~~
berghofe@18010
   431
                   map body_type perm_types ~~ perm_indnames)))))
berghofe@18010
   432
           (fn _ => EVERY [indtac induction perm_indnames 1,
berghofe@17870
   433
              ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt3', pt3_rev', pt3_ax]))]))),
berghofe@17870
   434
         length new_type_names)
berghofe@17870
   435
      end) atoms);
berghofe@17870
   436
berghofe@17870
   437
    (**** prove pi1 \<bullet> (pi2 \<bullet> t) = (pi1 \<bullet> pi2) \<bullet> (pi1 \<bullet> t) ****)
berghofe@17870
   438
berghofe@17870
   439
    val cp1 = PureThy.get_thm thy2 (Name "cp1");
berghofe@17870
   440
    val dj_cp = PureThy.get_thm thy2 (Name "dj_cp");
berghofe@17870
   441
    val pt_perm_compose = PureThy.get_thm thy2 (Name "pt_perm_compose");
berghofe@17870
   442
    val pt_perm_compose_rev = PureThy.get_thm thy2 (Name "pt_perm_compose_rev");
berghofe@17870
   443
    val dj_perm_perm_forget = PureThy.get_thm thy2 (Name "dj_perm_perm_forget");
berghofe@17870
   444
berghofe@17870
   445
    fun composition_instance name1 name2 thy =
berghofe@17870
   446
      let
berghofe@17870
   447
        val name1' = Sign.base_name name1;
berghofe@17870
   448
        val name2' = Sign.base_name name2;
berghofe@17870
   449
        val cp_class = Sign.intern_class thy ("cp_" ^ name1' ^ "_" ^ name2');
berghofe@17870
   450
        val permT1 = mk_permT (Type (name1, []));
berghofe@17870
   451
        val permT2 = mk_permT (Type (name2, []));
berghofe@17870
   452
        val augment = map_type_tfree
berghofe@17870
   453
          (fn (x, S) => TFree (x, cp_class :: S));
berghofe@17870
   454
        val Ts = map (augment o body_type) perm_types;
berghofe@17870
   455
        val cp_inst = PureThy.get_thm thy
berghofe@17870
   456
          (Name ("cp_" ^ name1' ^ "_" ^ name2' ^ "_inst"));
berghofe@17870
   457
        val simps = simpset_of thy addsimps (perm_fun_def ::
berghofe@17870
   458
          (if name1 <> name2 then
berghofe@17870
   459
             let val dj = PureThy.get_thm thy (Name ("dj_" ^ name2' ^ "_" ^ name1'))
berghofe@17870
   460
             in [dj RS (cp_inst RS dj_cp), dj RS dj_perm_perm_forget] end
berghofe@17870
   461
           else
berghofe@17870
   462
             let
berghofe@17870
   463
               val at_inst = PureThy.get_thm thy (Name ("at_" ^ name1' ^ "_inst"));
berghofe@17870
   464
               val pt_inst = PureThy.get_thm thy (Name ("pt_" ^ name1' ^ "_inst"))
berghofe@17870
   465
             in
berghofe@17870
   466
               [cp_inst RS cp1 RS sym,
berghofe@17870
   467
                at_inst RS (pt_inst RS pt_perm_compose) RS sym,
berghofe@17870
   468
                at_inst RS (pt_inst RS pt_perm_compose_rev) RS sym]
berghofe@17870
   469
            end))
wenzelm@20046
   470
        val thms = split_conj_thm (Goal.prove_global thy [] []
berghofe@17870
   471
            (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@17870
   472
              (map (fn ((s, T), x) =>
berghofe@17870
   473
                  let
berghofe@17870
   474
                    val pi1 = Free ("pi1", permT1);
berghofe@17870
   475
                    val pi2 = Free ("pi2", permT2);
berghofe@17870
   476
                    val perm1 = Const (s, permT1 --> T --> T);
berghofe@17870
   477
                    val perm2 = Const (s, permT2 --> T --> T);
berghofe@19494
   478
                    val perm3 = Const ("Nominal.perm", permT1 --> permT2 --> permT2)
berghofe@17870
   479
                  in HOLogic.mk_eq
berghofe@17870
   480
                    (perm1 $ pi1 $ (perm2 $ pi2 $ Free (x, T)),
berghofe@17870
   481
                     perm2 $ (perm3 $ pi1 $ pi2) $ (perm1 $ pi1 $ Free (x, T)))
berghofe@17870
   482
                  end)
berghofe@18010
   483
                (perm_names ~~ Ts ~~ perm_indnames))))
berghofe@18010
   484
          (fn _ => EVERY [indtac induction perm_indnames 1,
wenzelm@20046
   485
             ALLGOALS (asm_full_simp_tac simps)]))
berghofe@17870
   486
      in
berghofe@19275
   487
        foldl (fn ((s, tvs), thy) => AxClass.prove_arity
berghofe@17870
   488
            (s, replicate (length tvs) (cp_class :: classes), [cp_class])
berghofe@19133
   489
            (ClassPackage.intro_classes_tac [] THEN ALLGOALS (resolve_tac thms)) thy)
berghofe@17870
   490
          thy (full_new_type_names' ~~ tyvars)
berghofe@17870
   491
      end;
berghofe@17870
   492
urbanc@18381
   493
    val (perm_thmss,thy3) = thy2 |>
berghofe@17870
   494
      fold (fn name1 => fold (composition_instance name1) atoms) atoms |>
berghofe@17870
   495
      curry (Library.foldr (fn ((i, (tyname, args, _)), thy) =>
berghofe@19275
   496
        AxClass.prove_arity (tyname, replicate (length args) classes, classes)
berghofe@19133
   497
        (ClassPackage.intro_classes_tac [] THEN REPEAT (EVERY
berghofe@17870
   498
           [resolve_tac perm_empty_thms 1,
berghofe@17870
   499
            resolve_tac perm_append_thms 1,
berghofe@17870
   500
            resolve_tac perm_eq_thms 1, assume_tac 1])) thy))
berghofe@17870
   501
        (List.take (descr, length new_type_names)) |>
berghofe@17870
   502
      PureThy.add_thmss
berghofe@17870
   503
        [((space_implode "_" new_type_names ^ "_unfolded_perm_eq",
krauss@18759
   504
          unfolded_perm_eq_thms), [Simplifier.simp_add]),
berghofe@17870
   505
         ((space_implode "_" new_type_names ^ "_perm_empty",
krauss@18759
   506
          perm_empty_thms), [Simplifier.simp_add]),
berghofe@17870
   507
         ((space_implode "_" new_type_names ^ "_perm_append",
krauss@18759
   508
          perm_append_thms), [Simplifier.simp_add]),
berghofe@17870
   509
         ((space_implode "_" new_type_names ^ "_perm_eq",
krauss@18759
   510
          perm_eq_thms), [Simplifier.simp_add])];
wenzelm@21365
   511
berghofe@17870
   512
    (**** Define representing sets ****)
berghofe@17870
   513
berghofe@17870
   514
    val _ = warning "representing sets";
berghofe@17870
   515
berghofe@21021
   516
    val rep_set_names = DatatypeProp.indexify_names
berghofe@21021
   517
      (map (fn (i, _) => name_of_typ (nth_dtyp i) ^ "_set") descr);
berghofe@17870
   518
    val big_rep_name =
berghofe@17870
   519
      space_implode "_" (DatatypeProp.indexify_names (List.mapPartial
berghofe@19494
   520
        (fn (i, ("Nominal.noption", _, _)) => NONE
berghofe@17870
   521
          | (i, _) => SOME (name_of_typ (nth_dtyp i))) descr)) ^ "_set";
berghofe@17870
   522
    val _ = warning ("big_rep_name: " ^ big_rep_name);
berghofe@17870
   523
berghofe@17870
   524
    fun strip_option (dtf as DtType ("fun", [dt, DtRec i])) =
berghofe@17870
   525
          (case AList.lookup op = descr i of
berghofe@19494
   526
             SOME ("Nominal.noption", _, [(_, [dt']), _]) =>
berghofe@17870
   527
               apfst (cons dt) (strip_option dt')
berghofe@17870
   528
           | _ => ([], dtf))
berghofe@19494
   529
      | strip_option (DtType ("fun", [dt, DtType ("Nominal.noption", [dt'])])) =
berghofe@18261
   530
          apfst (cons dt) (strip_option dt')
berghofe@17870
   531
      | strip_option dt = ([], dt);
berghofe@17870
   532
berghofe@19133
   533
    val dt_atomTs = distinct op = (map (typ_of_dtyp descr sorts')
berghofe@18280
   534
      (List.concat (map (fn (_, (_, _, cs)) => List.concat
berghofe@18280
   535
        (map (List.concat o map (fst o strip_option) o snd) cs)) descr)));
berghofe@18280
   536
berghofe@17870
   537
    fun make_intr s T (cname, cargs) =
berghofe@17870
   538
      let
wenzelm@21365
   539
        fun mk_prem (dt, (j, j', prems, ts)) =
berghofe@17870
   540
          let
berghofe@17870
   541
            val (dts, dt') = strip_option dt;
berghofe@17870
   542
            val (dts', dt'') = strip_dtyp dt';
berghofe@18107
   543
            val Ts = map (typ_of_dtyp descr sorts') dts;
berghofe@18107
   544
            val Us = map (typ_of_dtyp descr sorts') dts';
berghofe@18107
   545
            val T = typ_of_dtyp descr sorts' dt'';
berghofe@17870
   546
            val free = mk_Free "x" (Us ---> T) j;
berghofe@17870
   547
            val free' = app_bnds free (length Us);
berghofe@17870
   548
            fun mk_abs_fun (T, (i, t)) =
berghofe@17870
   549
              let val U = fastype_of t
berghofe@19494
   550
              in (i + 1, Const ("Nominal.abs_fun", [T, U, T] --->
berghofe@19494
   551
                Type ("Nominal.noption", [U])) $ mk_Free "y" T i $ t)
berghofe@17870
   552
              end
berghofe@17870
   553
          in (j + 1, j' + length Ts,
berghofe@17870
   554
            case dt'' of
berghofe@17870
   555
                DtRec k => list_all (map (pair "x") Us,
berghofe@21021
   556
                  HOLogic.mk_Trueprop (Free (List.nth (rep_set_names, k),
berghofe@21021
   557
                    T --> HOLogic.boolT) $ free')) :: prems
berghofe@17870
   558
              | _ => prems,
berghofe@17870
   559
            snd (foldr mk_abs_fun (j', free) Ts) :: ts)
berghofe@17870
   560
          end;
berghofe@17870
   561
berghofe@17870
   562
        val (_, _, prems, ts) = foldr mk_prem (1, 1, [], []) cargs;
berghofe@21021
   563
        val concl = HOLogic.mk_Trueprop (Free (s, T --> HOLogic.boolT) $
berghofe@21021
   564
          list_comb (Const (cname, map fastype_of ts ---> T), ts))
berghofe@17870
   565
      in Logic.list_implies (prems, concl)
berghofe@17870
   566
      end;
berghofe@17870
   567
berghofe@21021
   568
    val (intr_ts, (rep_set_names', recTs')) =
berghofe@21021
   569
      apfst List.concat (apsnd ListPair.unzip (ListPair.unzip (List.mapPartial
berghofe@19494
   570
        (fn ((_, ("Nominal.noption", _, _)), _) => NONE
berghofe@17870
   571
          | ((i, (_, _, constrs)), rep_set_name) =>
berghofe@17870
   572
              let val T = nth_dtyp i
berghofe@17870
   573
              in SOME (map (make_intr rep_set_name T) constrs,
berghofe@21021
   574
                (rep_set_name, T))
berghofe@17870
   575
              end)
berghofe@21021
   576
                (descr ~~ rep_set_names))));
berghofe@21021
   577
    val rep_set_names'' = map (Sign.full_name thy3) rep_set_names';
berghofe@17870
   578
wenzelm@21365
   579
    val ({raw_induct = rep_induct, intrs = rep_intrs, ...}, thy4) =
berghofe@17870
   580
      setmp InductivePackage.quiet_mode false
berghofe@21021
   581
        (TheoryTarget.init NONE #>
berghofe@21021
   582
         InductivePackage.add_inductive_i false big_rep_name false true false
berghofe@21021
   583
           (map (fn (s, T) => (s, SOME (T --> HOLogic.boolT), NoSyn))
berghofe@21021
   584
              (rep_set_names' ~~ recTs'))
berghofe@21021
   585
           [] (map (fn x => (("", []), x)) intr_ts) [] #>
wenzelm@21365
   586
         apsnd (ProofContext.theory_of o LocalTheory.exit)) thy3;
berghofe@17870
   587
berghofe@17870
   588
    (**** Prove that representing set is closed under permutation ****)
berghofe@17870
   589
berghofe@17870
   590
    val _ = warning "proving closure under permutation...";
berghofe@17870
   591
berghofe@17870
   592
    val perm_indnames' = List.mapPartial
berghofe@19494
   593
      (fn (x, (_, ("Nominal.noption", _, _))) => NONE | (x, _) => SOME x)
berghofe@17870
   594
      (perm_indnames ~~ descr);
berghofe@17870
   595
berghofe@17870
   596
    fun mk_perm_closed name = map (fn th => standard (th RS mp))
wenzelm@20046
   597
      (List.take (split_conj_thm (Goal.prove_global thy4 [] []
berghofe@17870
   598
        (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map
berghofe@21021
   599
           (fn ((s, T), x) =>
berghofe@17870
   600
              let
berghofe@21021
   601
                val T = map_type_tfree
berghofe@21021
   602
                  (fn (s, cs) => TFree (s, cs union cp_classes)) T;
berghofe@21021
   603
                val S = Const (s, T --> HOLogic.boolT);
berghofe@17870
   604
                val permT = mk_permT (Type (name, []))
berghofe@21021
   605
              in HOLogic.mk_imp (S $ Free (x, T),
berghofe@21021
   606
                S $ (Const ("Nominal.perm", permT --> T --> T) $
berghofe@21021
   607
                  Free ("pi", permT) $ Free (x, T)))
berghofe@21021
   608
              end) (rep_set_names'' ~~ recTs' ~~ perm_indnames'))))
berghofe@18010
   609
        (fn _ => EVERY (* CU: added perm_fun_def in the final tactic in order to deal with funs *)
berghofe@17870
   610
           [indtac rep_induct [] 1,
berghofe@17870
   611
            ALLGOALS (simp_tac (simpset_of thy4 addsimps
berghofe@17870
   612
              (symmetric perm_fun_def :: PureThy.get_thms thy4 (Name ("abs_perm"))))),
wenzelm@21365
   613
            ALLGOALS (resolve_tac rep_intrs
berghofe@17870
   614
               THEN_ALL_NEW (asm_full_simp_tac (simpset_of thy4 addsimps [perm_fun_def])))])),
berghofe@17870
   615
        length new_type_names));
berghofe@17870
   616
berghofe@17870
   617
    (* FIXME: theorems are stored in database for testing only *)
berghofe@17870
   618
    val perm_closed_thmss = map mk_perm_closed atoms;
haftmann@20483
   619
    val (_, thy5) = PureThy.add_thmss [(("perm_closed", List.concat perm_closed_thmss), [])] thy4;
berghofe@17870
   620
berghofe@17870
   621
    (**** typedef ****)
berghofe@17870
   622
berghofe@17870
   623
    val _ = warning "defining type...";
berghofe@17870
   624
berghofe@18366
   625
    val (typedefs, thy6) =
haftmann@20483
   626
      thy5
berghofe@21021
   627
      |> fold_map (fn ((((name, mx), tvs), (cname, U)), name') => fn thy =>
berghofe@17870
   628
        setmp TypedefPackage.quiet_mode true
berghofe@21021
   629
          (TypedefPackage.add_typedef_i false (SOME name') (name, tvs, mx)
berghofe@21021
   630
            (Const ("Collect", (U --> HOLogic.boolT) --> HOLogic.mk_setT U) $
berghofe@21021
   631
               Const (cname, U --> HOLogic.boolT)) NONE
berghofe@21021
   632
            (rtac exI 1 THEN rtac CollectI 1 THEN
berghofe@17870
   633
              QUIET_BREADTH_FIRST (has_fewer_prems 1)
haftmann@20483
   634
              (resolve_tac rep_intrs 1))) thy |> (fn ((_, r), thy) =>
berghofe@17870
   635
        let
wenzelm@20071
   636
          val permT = mk_permT (TFree (Name.variant tvs "'a", HOLogic.typeS));
berghofe@17870
   637
          val pi = Free ("pi", permT);
berghofe@17870
   638
          val tvs' = map (fn s => TFree (s, the (AList.lookup op = sorts' s))) tvs;
berghofe@17870
   639
          val T = Type (Sign.intern_type thy name, tvs');
berghofe@18366
   640
        in apfst (pair r o hd)
wenzelm@19635
   641
          (PureThy.add_defs_unchecked_i true [(("prm_" ^ name ^ "_def", Logic.mk_equals
berghofe@19494
   642
            (Const ("Nominal.perm", permT --> T --> T) $ pi $ Free ("x", T),
berghofe@17870
   643
             Const (Sign.intern_const thy ("Abs_" ^ name), U --> T) $
berghofe@19494
   644
               (Const ("Nominal.perm", permT --> U --> U) $ pi $
berghofe@17870
   645
                 (Const (Sign.intern_const thy ("Rep_" ^ name), T --> U) $
berghofe@17870
   646
                   Free ("x", T))))), [])] thy)
berghofe@17870
   647
        end))
berghofe@18366
   648
          (types_syntax ~~ tyvars ~~
berghofe@21021
   649
            List.take (rep_set_names'' ~~ recTs', length new_type_names) ~~
berghofe@21021
   650
            new_type_names);
berghofe@17870
   651
berghofe@17870
   652
    val perm_defs = map snd typedefs;
berghofe@21021
   653
    val Abs_inverse_thms = map (collect_simp o #Abs_inverse o fst) typedefs;
berghofe@18016
   654
    val Rep_inverse_thms = map (#Rep_inverse o fst) typedefs;
berghofe@21021
   655
    val Rep_thms = map (collect_simp o #Rep o fst) typedefs;
berghofe@17870
   656
berghofe@18016
   657
    val big_name = space_implode "_" new_type_names;
berghofe@18016
   658
berghofe@18016
   659
berghofe@17870
   660
    (** prove that new types are in class pt_<name> **)
berghofe@17870
   661
berghofe@17870
   662
    val _ = warning "prove that new types are in class pt_<name> ...";
berghofe@17870
   663
berghofe@17870
   664
    fun pt_instance ((class, atom), perm_closed_thms) =
berghofe@21021
   665
      fold (fn ((((((Abs_inverse, Rep_inverse), Rep),
berghofe@17870
   666
        perm_def), name), tvs), perm_closed) => fn thy =>
berghofe@19275
   667
          AxClass.prove_arity
berghofe@17870
   668
            (Sign.intern_type thy name,
berghofe@17870
   669
              replicate (length tvs) (classes @ cp_classes), [class])
berghofe@19133
   670
            (EVERY [ClassPackage.intro_classes_tac [],
berghofe@17870
   671
              rewrite_goals_tac [perm_def],
berghofe@17870
   672
              asm_full_simp_tac (simpset_of thy addsimps [Rep_inverse]) 1,
berghofe@17870
   673
              asm_full_simp_tac (simpset_of thy addsimps
berghofe@17870
   674
                [Rep RS perm_closed RS Abs_inverse]) 1,
berghofe@17870
   675
              asm_full_simp_tac (HOL_basic_ss addsimps [PureThy.get_thm thy
berghofe@17870
   676
                (Name ("pt_" ^ Sign.base_name atom ^ "3"))]) 1]) thy)
berghofe@21021
   677
        (Abs_inverse_thms ~~ Rep_inverse_thms ~~ Rep_thms ~~ perm_defs ~~
berghofe@21021
   678
           new_type_names ~~ tyvars ~~ perm_closed_thms);
berghofe@17870
   679
berghofe@17870
   680
berghofe@17870
   681
    (** prove that new types are in class cp_<name1>_<name2> **)
berghofe@17870
   682
berghofe@17870
   683
    val _ = warning "prove that new types are in class cp_<name1>_<name2> ...";
berghofe@17870
   684
berghofe@17870
   685
    fun cp_instance (atom1, perm_closed_thms1) (atom2, perm_closed_thms2) thy =
berghofe@17870
   686
      let
berghofe@17870
   687
        val name = "cp_" ^ Sign.base_name atom1 ^ "_" ^ Sign.base_name atom2;
berghofe@17870
   688
        val class = Sign.intern_class thy name;
berghofe@17870
   689
        val cp1' = PureThy.get_thm thy (Name (name ^ "_inst")) RS cp1
berghofe@21021
   690
      in fold (fn ((((((Abs_inverse, Rep),
berghofe@17870
   691
        perm_def), name), tvs), perm_closed1), perm_closed2) => fn thy =>
berghofe@19275
   692
          AxClass.prove_arity
berghofe@17870
   693
            (Sign.intern_type thy name,
berghofe@17870
   694
              replicate (length tvs) (classes @ cp_classes), [class])
berghofe@19133
   695
            (EVERY [ClassPackage.intro_classes_tac [],
berghofe@17870
   696
              rewrite_goals_tac [perm_def],
berghofe@17870
   697
              asm_full_simp_tac (simpset_of thy addsimps
berghofe@17870
   698
                ((Rep RS perm_closed1 RS Abs_inverse) ::
berghofe@17870
   699
                 (if atom1 = atom2 then []
berghofe@17870
   700
                  else [Rep RS perm_closed2 RS Abs_inverse]))) 1,
berghofe@18016
   701
              cong_tac 1,
berghofe@17870
   702
              rtac refl 1,
berghofe@17870
   703
              rtac cp1' 1]) thy)
berghofe@21021
   704
        (Abs_inverse_thms ~~ Rep_thms ~~ perm_defs ~~ new_type_names ~~
berghofe@21021
   705
           tyvars ~~ perm_closed_thms1 ~~ perm_closed_thms2) thy
berghofe@17870
   706
      end;
berghofe@17870
   707
berghofe@17870
   708
    val thy7 = fold (fn x => fn thy => thy |>
berghofe@17870
   709
      pt_instance x |>
berghofe@17870
   710
      fold (cp_instance (apfst snd x)) (atoms ~~ perm_closed_thmss))
berghofe@17870
   711
        (classes ~~ atoms ~~ perm_closed_thmss) thy6;
berghofe@17870
   712
berghofe@17870
   713
    (**** constructors ****)
berghofe@17870
   714
berghofe@17870
   715
    fun mk_abs_fun (x, t) =
berghofe@17870
   716
      let
berghofe@17870
   717
        val T = fastype_of x;
berghofe@17870
   718
        val U = fastype_of t
berghofe@17870
   719
      in
berghofe@19494
   720
        Const ("Nominal.abs_fun", T --> U --> T -->
berghofe@19494
   721
          Type ("Nominal.noption", [U])) $ x $ t
berghofe@17870
   722
      end;
berghofe@17870
   723
berghofe@18016
   724
    val (ty_idxs, _) = foldl
berghofe@19494
   725
      (fn ((i, ("Nominal.noption", _, _)), p) => p
berghofe@18016
   726
        | ((i, _), (ty_idxs, j)) => (ty_idxs @ [(i, j)], j + 1)) ([], 0) descr;
berghofe@18016
   727
berghofe@18016
   728
    fun reindex (DtType (s, dts)) = DtType (s, map reindex dts)
berghofe@18016
   729
      | reindex (DtRec i) = DtRec (the (AList.lookup op = ty_idxs i))
berghofe@18016
   730
      | reindex dt = dt;
berghofe@18016
   731
berghofe@18016
   732
    fun strip_suffix i s = implode (List.take (explode s, size s - i));
berghofe@18016
   733
berghofe@18016
   734
    (** strips the "_Rep" in type names *)
wenzelm@21365
   735
    fun strip_nth_name i s =
wenzelm@21858
   736
      let val xs = NameSpace.explode s;
wenzelm@21858
   737
      in NameSpace.implode (Library.nth_map (length xs - i) (strip_suffix 4) xs) end;
berghofe@18016
   738
berghofe@18107
   739
    val (descr'', ndescr) = ListPair.unzip (List.mapPartial
berghofe@19494
   740
      (fn (i, ("Nominal.noption", _, _)) => NONE
berghofe@18107
   741
        | (i, (s, dts, constrs)) =>
berghofe@18107
   742
             let
berghofe@18107
   743
               val SOME index = AList.lookup op = ty_idxs i;
berghofe@18107
   744
               val (constrs1, constrs2) = ListPair.unzip
berghofe@19833
   745
                 (map (fn (cname, cargs) => apfst (pair (strip_nth_name 2 (strip_nth_name 1 cname)))
berghofe@18107
   746
                   (foldl_map (fn (dts, dt) =>
berghofe@18107
   747
                     let val (dts', dt') = strip_option dt
berghofe@18107
   748
                     in (dts @ dts' @ [reindex dt'], (length dts, length dts')) end)
berghofe@18107
   749
                       ([], cargs))) constrs)
berghofe@18107
   750
             in SOME ((index, (strip_nth_name 1 s,  map reindex dts, constrs1)),
berghofe@18107
   751
               (index, constrs2))
berghofe@18107
   752
             end) descr);
urbanc@18045
   753
berghofe@19489
   754
    val (descr1, descr2) = chop (length new_type_names) descr'';
berghofe@18016
   755
    val descr' = [descr1, descr2];
berghofe@18016
   756
berghofe@19710
   757
    fun partition_cargs idxs xs = map (fn (i, j) =>
berghofe@19710
   758
      (List.take (List.drop (xs, i), j), List.nth (xs, i + j))) idxs;
berghofe@19710
   759
berghofe@19833
   760
    val pdescr = map (fn ((i, (s, dts, constrs)), (_, idxss)) => (i, (s, dts,
berghofe@19833
   761
      map (fn ((cname, cargs), idxs) => (cname, partition_cargs idxs cargs))
berghofe@19833
   762
        (constrs ~~ idxss)))) (descr'' ~~ ndescr);
berghofe@19833
   763
berghofe@19833
   764
    fun nth_dtyp' i = typ_of_dtyp descr'' sorts' (DtRec i);
berghofe@17870
   765
berghofe@17870
   766
    val rep_names = map (fn s =>
berghofe@17870
   767
      Sign.intern_const thy7 ("Rep_" ^ s)) new_type_names;
berghofe@17870
   768
    val abs_names = map (fn s =>
berghofe@17870
   769
      Sign.intern_const thy7 ("Abs_" ^ s)) new_type_names;
berghofe@17870
   770
berghofe@18107
   771
    val recTs = get_rec_types descr'' sorts';
berghofe@18016
   772
    val newTs' = Library.take (length new_type_names, recTs');
berghofe@18016
   773
    val newTs = Library.take (length new_type_names, recTs);
berghofe@17870
   774
berghofe@17870
   775
    val full_new_type_names = map (Sign.full_name (sign_of thy)) new_type_names;
berghofe@17870
   776
berghofe@19833
   777
    fun make_constr_def tname T T' ((thy, defs, eqns),
berghofe@19833
   778
        (((cname_rep, _), (cname, cargs)), (cname', mx))) =
berghofe@17870
   779
      let
berghofe@19833
   780
        fun constr_arg ((dts, dt), (j, l_args, r_args)) =
berghofe@17870
   781
          let
berghofe@19833
   782
            val xs = map (fn (dt, i) => mk_Free "x" (typ_of_dtyp descr'' sorts' dt) i)
berghofe@17870
   783
              (dts ~~ (j upto j + length dts - 1))
berghofe@19833
   784
            val x = mk_Free "x" (typ_of_dtyp descr'' sorts' dt) (j + length dts)
berghofe@18261
   785
          in
berghofe@18261
   786
            (j + length dts + 1,
berghofe@18261
   787
             xs @ x :: l_args,
berghofe@18261
   788
             foldr mk_abs_fun
berghofe@19833
   789
               (case dt of
berghofe@18261
   790
                  DtRec k => if k < length new_type_names then
berghofe@19833
   791
                      Const (List.nth (rep_names, k), typ_of_dtyp descr'' sorts' dt -->
berghofe@19833
   792
                        typ_of_dtyp descr sorts' dt) $ x
berghofe@18261
   793
                    else error "nested recursion not (yet) supported"
berghofe@18261
   794
                | _ => x) xs :: r_args)
berghofe@17870
   795
          end
berghofe@17870
   796
berghofe@17870
   797
        val (_, l_args, r_args) = foldr constr_arg (1, [], []) cargs;
berghofe@17870
   798
        val abs_name = Sign.intern_const (Theory.sign_of thy) ("Abs_" ^ tname);
berghofe@17870
   799
        val rep_name = Sign.intern_const (Theory.sign_of thy) ("Rep_" ^ tname);
berghofe@17870
   800
        val constrT = map fastype_of l_args ---> T;
berghofe@19833
   801
        val lhs = list_comb (Const (cname, constrT), l_args);
berghofe@19833
   802
        val rhs = list_comb (Const (cname_rep, map fastype_of r_args ---> T'), r_args);
berghofe@17870
   803
        val def = Logic.mk_equals (lhs, Const (abs_name, T' --> T) $ rhs);
berghofe@17870
   804
        val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17870
   805
          (Const (rep_name, T --> T') $ lhs, rhs));
berghofe@17870
   806
        val def_name = (Sign.base_name cname) ^ "_def";
berghofe@18366
   807
        val ([def_thm], thy') = thy |>
berghofe@17870
   808
          Theory.add_consts_i [(cname', constrT, mx)] |>
berghofe@17870
   809
          (PureThy.add_defs_i false o map Thm.no_attributes) [(def_name, def)]
berghofe@17870
   810
      in (thy', defs @ [def_thm], eqns @ [eqn]) end;
berghofe@17870
   811
berghofe@19833
   812
    fun dt_constr_defs ((thy, defs, eqns, dist_lemmas), ((((((_, (_, _, constrs)),
berghofe@19833
   813
        (_, (_, _, constrs'))), tname), T), T'), constr_syntax)) =
berghofe@17870
   814
      let
berghofe@17870
   815
        val rep_const = cterm_of thy
berghofe@17870
   816
          (Const (Sign.intern_const thy ("Rep_" ^ tname), T --> T'));
berghofe@17870
   817
        val dist = standard (cterm_instantiate [(cterm_of thy distinct_f, rep_const)] distinct_lemma);
berghofe@17870
   818
        val (thy', defs', eqns') = Library.foldl (make_constr_def tname T T')
berghofe@19833
   819
          ((Theory.add_path tname thy, defs, []), constrs ~~ constrs' ~~ constr_syntax)
berghofe@17870
   820
      in
berghofe@17870
   821
        (parent_path flat_names thy', defs', eqns @ [eqns'], dist_lemmas @ [dist])
berghofe@17870
   822
      end;
berghofe@17870
   823
berghofe@17870
   824
    val (thy8, constr_defs, constr_rep_eqns, dist_lemmas) = Library.foldl dt_constr_defs
berghofe@17870
   825
      ((thy7, [], [], []), List.take (descr, length new_type_names) ~~
berghofe@19833
   826
        List.take (pdescr, length new_type_names) ~~
berghofe@17870
   827
        new_type_names ~~ newTs ~~ newTs' ~~ constr_syntax);
berghofe@17870
   828
berghofe@21021
   829
    val abs_inject_thms = map (collect_simp o #Abs_inject o fst) typedefs
berghofe@21021
   830
    val rep_inject_thms = map (#Rep_inject o fst) typedefs
berghofe@17870
   831
berghofe@17870
   832
    (* prove theorem  Rep_i (Constr_j ...) = Constr'_j ...  *)
wenzelm@21365
   833
berghofe@17870
   834
    fun prove_constr_rep_thm eqn =
berghofe@17870
   835
      let
berghofe@17870
   836
        val inj_thms = map (fn r => r RS iffD1) abs_inject_thms;
berghofe@21021
   837
        val rewrites = constr_defs @ map mk_meta_eq Rep_inverse_thms
wenzelm@20046
   838
      in Goal.prove_global thy8 [] [] eqn (fn _ => EVERY
berghofe@17870
   839
        [resolve_tac inj_thms 1,
berghofe@17870
   840
         rewrite_goals_tac rewrites,
berghofe@17870
   841
         rtac refl 3,
berghofe@17870
   842
         resolve_tac rep_intrs 2,
berghofe@21021
   843
         REPEAT (resolve_tac Rep_thms 1)])
berghofe@17870
   844
      end;
berghofe@17870
   845
berghofe@17870
   846
    val constr_rep_thmss = map (map prove_constr_rep_thm) constr_rep_eqns;
berghofe@17870
   847
berghofe@17870
   848
    (* prove theorem  pi \<bullet> Rep_i x = Rep_i (pi \<bullet> x) *)
berghofe@17870
   849
berghofe@17870
   850
    fun prove_perm_rep_perm (atom, perm_closed_thms) = map (fn th =>
berghofe@17870
   851
      let
berghofe@21021
   852
        val _ $ (_ $ (Rep $ x)) = Logic.unvarify (prop_of th);
berghofe@17870
   853
        val Type ("fun", [T, U]) = fastype_of Rep;
berghofe@17870
   854
        val permT = mk_permT (Type (atom, []));
berghofe@17870
   855
        val pi = Free ("pi", permT);
berghofe@17870
   856
      in
wenzelm@20046
   857
        Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@19494
   858
            (Const ("Nominal.perm", permT --> U --> U) $ pi $ (Rep $ x),
berghofe@19494
   859
             Rep $ (Const ("Nominal.perm", permT --> T --> T) $ pi $ x))))
berghofe@18010
   860
          (fn _ => simp_tac (HOL_basic_ss addsimps (perm_defs @ Abs_inverse_thms @
wenzelm@20046
   861
            perm_closed_thms @ Rep_thms)) 1)
berghofe@17870
   862
      end) Rep_thms;
berghofe@17870
   863
berghofe@17870
   864
    val perm_rep_perm_thms = List.concat (map prove_perm_rep_perm
berghofe@17870
   865
      (atoms ~~ perm_closed_thmss));
berghofe@17870
   866
berghofe@17870
   867
    (* prove distinctness theorems *)
berghofe@17870
   868
berghofe@18016
   869
    val distinct_props = setmp DatatypeProp.dtK 1000
berghofe@18016
   870
      (DatatypeProp.make_distincts new_type_names descr' sorts') thy8;
berghofe@17870
   871
berghofe@17870
   872
    val dist_rewrites = map (fn (rep_thms, dist_lemma) =>
berghofe@17870
   873
      dist_lemma::(rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0]))
berghofe@17870
   874
        (constr_rep_thmss ~~ dist_lemmas);
berghofe@17870
   875
berghofe@17870
   876
    fun prove_distinct_thms (_, []) = []
berghofe@17870
   877
      | prove_distinct_thms (p as (rep_thms, dist_lemma), t::ts) =
berghofe@17870
   878
          let
wenzelm@20046
   879
            val dist_thm = Goal.prove_global thy8 [] [] t (fn _ =>
wenzelm@20046
   880
              simp_tac (simpset_of thy8 addsimps (dist_lemma :: rep_thms)) 1)
berghofe@17870
   881
          in dist_thm::(standard (dist_thm RS not_sym))::
berghofe@17870
   882
            (prove_distinct_thms (p, ts))
berghofe@17870
   883
          end;
berghofe@17870
   884
berghofe@17870
   885
    val distinct_thms = map prove_distinct_thms
berghofe@17870
   886
      (constr_rep_thmss ~~ dist_lemmas ~~ distinct_props);
berghofe@17870
   887
berghofe@17870
   888
    (** prove equations for permutation functions **)
berghofe@17870
   889
berghofe@17870
   890
    val abs_perm = PureThy.get_thms thy8 (Name "abs_perm"); (* FIXME *)
berghofe@17870
   891
berghofe@17870
   892
    val perm_simps' = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) =>
berghofe@19833
   893
      let val T = nth_dtyp' i
berghofe@17870
   894
      in List.concat (map (fn (atom, perm_closed_thms) =>
wenzelm@21365
   895
          map (fn ((cname, dts), constr_rep_thm) =>
berghofe@17870
   896
        let
berghofe@17870
   897
          val cname = Sign.intern_const thy8
berghofe@17870
   898
            (NameSpace.append tname (Sign.base_name cname));
berghofe@17870
   899
          val permT = mk_permT (Type (atom, []));
berghofe@17870
   900
          val pi = Free ("pi", permT);
berghofe@17870
   901
berghofe@17870
   902
          fun perm t =
berghofe@17870
   903
            let val T = fastype_of t
berghofe@19494
   904
            in Const ("Nominal.perm", permT --> T --> T) $ pi $ t end;
berghofe@17870
   905
berghofe@19833
   906
          fun constr_arg ((dts, dt), (j, l_args, r_args)) =
berghofe@17870
   907
            let
berghofe@19833
   908
              val Ts = map (typ_of_dtyp descr'' sorts') dts;
berghofe@17870
   909
              val xs = map (fn (T, i) => mk_Free "x" T i)
berghofe@17870
   910
                (Ts ~~ (j upto j + length dts - 1))
berghofe@19833
   911
              val x = mk_Free "x" (typ_of_dtyp descr'' sorts' dt) (j + length dts)
berghofe@18261
   912
            in
berghofe@18261
   913
              (j + length dts + 1,
berghofe@18261
   914
               xs @ x :: l_args,
berghofe@18261
   915
               map perm (xs @ [x]) @ r_args)
berghofe@17870
   916
            end
berghofe@17870
   917
berghofe@17870
   918
          val (_, l_args, r_args) = foldr constr_arg (1, [], []) dts;
berghofe@17870
   919
          val c = Const (cname, map fastype_of l_args ---> T)
berghofe@17870
   920
        in
wenzelm@20046
   921
          Goal.prove_global thy8 [] []
berghofe@17870
   922
            (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@18010
   923
              (perm (list_comb (c, l_args)), list_comb (c, r_args))))
berghofe@18010
   924
            (fn _ => EVERY
berghofe@17870
   925
              [simp_tac (simpset_of thy8 addsimps (constr_rep_thm :: perm_defs)) 1,
berghofe@17870
   926
               simp_tac (HOL_basic_ss addsimps (Rep_thms @ Abs_inverse_thms @
berghofe@17870
   927
                 constr_defs @ perm_closed_thms)) 1,
berghofe@17870
   928
               TRY (simp_tac (HOL_basic_ss addsimps
berghofe@17870
   929
                 (symmetric perm_fun_def :: abs_perm)) 1),
berghofe@17870
   930
               TRY (simp_tac (HOL_basic_ss addsimps
berghofe@17870
   931
                 (perm_fun_def :: perm_defs @ Rep_thms @ Abs_inverse_thms @
wenzelm@20046
   932
                    perm_closed_thms)) 1)])
berghofe@17870
   933
        end) (constrs ~~ constr_rep_thms)) (atoms ~~ perm_closed_thmss))
berghofe@19833
   934
      end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
berghofe@17870
   935
berghofe@17870
   936
    (** prove injectivity of constructors **)
berghofe@17870
   937
berghofe@17870
   938
    val rep_inject_thms' = map (fn th => th RS sym) rep_inject_thms;
berghofe@17870
   939
    val alpha = PureThy.get_thms thy8 (Name "alpha");
berghofe@17870
   940
    val abs_fresh = PureThy.get_thms thy8 (Name "abs_fresh");
berghofe@17870
   941
berghofe@17870
   942
    val inject_thms = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) =>
berghofe@19833
   943
      let val T = nth_dtyp' i
berghofe@17870
   944
      in List.mapPartial (fn ((cname, dts), constr_rep_thm) =>
berghofe@17870
   945
        if null dts then NONE else SOME
berghofe@17870
   946
        let
berghofe@17870
   947
          val cname = Sign.intern_const thy8
berghofe@17870
   948
            (NameSpace.append tname (Sign.base_name cname));
berghofe@17870
   949
berghofe@19833
   950
          fun make_inj ((dts, dt), (j, args1, args2, eqs)) =
berghofe@17870
   951
            let
berghofe@19833
   952
              val Ts_idx = map (typ_of_dtyp descr'' sorts') dts ~~ (j upto j + length dts - 1);
berghofe@17870
   953
              val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
berghofe@17870
   954
              val ys = map (fn (T, i) => mk_Free "y" T i) Ts_idx;
berghofe@19833
   955
              val x = mk_Free "x" (typ_of_dtyp descr'' sorts' dt) (j + length dts);
berghofe@19833
   956
              val y = mk_Free "y" (typ_of_dtyp descr'' sorts' dt) (j + length dts)
berghofe@18261
   957
            in
berghofe@18261
   958
              (j + length dts + 1,
berghofe@18261
   959
               xs @ (x :: args1), ys @ (y :: args2),
berghofe@18261
   960
               HOLogic.mk_eq
berghofe@18261
   961
                 (foldr mk_abs_fun x xs, foldr mk_abs_fun y ys) :: eqs)
berghofe@17870
   962
            end;
berghofe@17870
   963
berghofe@17870
   964
          val (_, args1, args2, eqs) = foldr make_inj (1, [], [], []) dts;
berghofe@17870
   965
          val Ts = map fastype_of args1;
berghofe@17870
   966
          val c = Const (cname, Ts ---> T)
berghofe@17870
   967
        in
wenzelm@20046
   968
          Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17870
   969
              (HOLogic.mk_eq (list_comb (c, args1), list_comb (c, args2)),
berghofe@18010
   970
               foldr1 HOLogic.mk_conj eqs)))
berghofe@18010
   971
            (fn _ => EVERY
berghofe@17870
   972
               [asm_full_simp_tac (simpset_of thy8 addsimps (constr_rep_thm ::
berghofe@17870
   973
                  rep_inject_thms')) 1,
berghofe@17870
   974
                TRY (asm_full_simp_tac (HOL_basic_ss addsimps (fresh_def :: supp_def ::
berghofe@17870
   975
                  alpha @ abs_perm @ abs_fresh @ rep_inject_thms @
berghofe@17874
   976
                  perm_rep_perm_thms)) 1),
berghofe@17874
   977
                TRY (asm_full_simp_tac (HOL_basic_ss addsimps (perm_fun_def ::
wenzelm@20046
   978
                  expand_fun_eq :: rep_inject_thms @ perm_rep_perm_thms)) 1)])
berghofe@17870
   979
        end) (constrs ~~ constr_rep_thms)
berghofe@19833
   980
      end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
berghofe@17870
   981
berghofe@17872
   982
    (** equations for support and freshness **)
berghofe@17872
   983
berghofe@17872
   984
    val (supp_thms, fresh_thms) = ListPair.unzip (map ListPair.unzip
berghofe@17872
   985
      (map (fn ((((i, (_, _, constrs)), tname), inject_thms'), perm_thms') =>
berghofe@19833
   986
      let val T = nth_dtyp' i
berghofe@17872
   987
      in List.concat (map (fn (cname, dts) => map (fn atom =>
berghofe@17872
   988
        let
berghofe@17872
   989
          val cname = Sign.intern_const thy8
berghofe@17872
   990
            (NameSpace.append tname (Sign.base_name cname));
berghofe@17872
   991
          val atomT = Type (atom, []);
berghofe@17872
   992
berghofe@19833
   993
          fun process_constr ((dts, dt), (j, args1, args2)) =
berghofe@17872
   994
            let
berghofe@19833
   995
              val Ts_idx = map (typ_of_dtyp descr'' sorts') dts ~~ (j upto j + length dts - 1);
berghofe@17872
   996
              val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
berghofe@19833
   997
              val x = mk_Free "x" (typ_of_dtyp descr'' sorts' dt) (j + length dts)
berghofe@18261
   998
            in
berghofe@18261
   999
              (j + length dts + 1,
berghofe@18261
  1000
               xs @ (x :: args1), foldr mk_abs_fun x xs :: args2)
berghofe@17872
  1001
            end;
berghofe@17872
  1002
berghofe@17872
  1003
          val (_, args1, args2) = foldr process_constr (1, [], []) dts;
berghofe@17872
  1004
          val Ts = map fastype_of args1;
berghofe@17872
  1005
          val c = list_comb (Const (cname, Ts ---> T), args1);
berghofe@17872
  1006
          fun supp t =
berghofe@19494
  1007
            Const ("Nominal.supp", fastype_of t --> HOLogic.mk_setT atomT) $ t;
berghofe@17872
  1008
          fun fresh t =
berghofe@19494
  1009
            Const ("Nominal.fresh", atomT --> fastype_of t --> HOLogic.boolT) $
berghofe@17872
  1010
              Free ("a", atomT) $ t;
wenzelm@20046
  1011
          val supp_thm = Goal.prove_global thy8 [] []
berghofe@17872
  1012
              (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17872
  1013
                (supp c,
berghofe@17872
  1014
                 if null dts then Const ("{}", HOLogic.mk_setT atomT)
berghofe@18010
  1015
                 else foldr1 (HOLogic.mk_binop "op Un") (map supp args2))))
berghofe@17872
  1016
            (fn _ =>
berghofe@18010
  1017
              simp_tac (HOL_basic_ss addsimps (supp_def ::
berghofe@17872
  1018
                 Un_assoc :: de_Morgan_conj :: Collect_disj_eq :: finite_Un ::
berghofe@22274
  1019
                 symmetric empty_def :: finite_emptyI :: simp_thms @
wenzelm@20046
  1020
                 abs_perm @ abs_fresh @ inject_thms' @ perm_thms')) 1)
berghofe@17872
  1021
        in
berghofe@17872
  1022
          (supp_thm,
wenzelm@20046
  1023
           Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17872
  1024
              (fresh c,
berghofe@17872
  1025
               if null dts then HOLogic.true_const
berghofe@18010
  1026
               else foldr1 HOLogic.mk_conj (map fresh args2))))
berghofe@17872
  1027
             (fn _ =>
wenzelm@20046
  1028
               simp_tac (simpset_of thy8 addsimps [fresh_def, supp_thm]) 1))
berghofe@17872
  1029
        end) atoms) constrs)
berghofe@19833
  1030
      end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ inject_thms ~~ perm_simps')));
berghofe@17872
  1031
berghofe@18107
  1032
    (**** weak induction theorem ****)
berghofe@18016
  1033
berghofe@18016
  1034
    fun mk_indrule_lemma ((prems, concls), (((i, _), T), U)) =
berghofe@18016
  1035
      let
berghofe@18016
  1036
        val Rep_t = Const (List.nth (rep_names, i), T --> U) $
berghofe@18016
  1037
          mk_Free "x" T i;
berghofe@18016
  1038
berghofe@18016
  1039
        val Abs_t =  Const (List.nth (abs_names, i), U --> T)
berghofe@18016
  1040
berghofe@21021
  1041
      in (prems @ [HOLogic.imp $
berghofe@21021
  1042
            (Const (List.nth (rep_set_names'', i), U --> HOLogic.boolT) $ Rep_t) $
berghofe@18016
  1043
              (mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))],
berghofe@18016
  1044
          concls @ [mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ mk_Free "x" T i])
berghofe@18016
  1045
      end;
berghofe@18016
  1046
berghofe@18016
  1047
    val (indrule_lemma_prems, indrule_lemma_concls) =
berghofe@18107
  1048
      Library.foldl mk_indrule_lemma (([], []), (descr'' ~~ recTs ~~ recTs'));
berghofe@18016
  1049
wenzelm@20046
  1050
    val indrule_lemma = Goal.prove_global thy8 [] []
berghofe@18016
  1051
      (Logic.mk_implies
berghofe@18016
  1052
        (HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems),
berghofe@18016
  1053
         HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls))) (fn _ => EVERY
berghofe@18016
  1054
           [REPEAT (etac conjE 1),
berghofe@18016
  1055
            REPEAT (EVERY
berghofe@18016
  1056
              [TRY (rtac conjI 1), full_simp_tac (HOL_basic_ss addsimps Rep_inverse_thms) 1,
wenzelm@20046
  1057
               etac mp 1, resolve_tac Rep_thms 1])]);
berghofe@18016
  1058
berghofe@18016
  1059
    val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma)));
berghofe@18016
  1060
    val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else
berghofe@18016
  1061
      map (Free o apfst fst o dest_Var) Ps;
berghofe@18016
  1062
    val indrule_lemma' = cterm_instantiate
berghofe@18016
  1063
      (map (cterm_of thy8) Ps ~~ map (cterm_of thy8) frees) indrule_lemma;
berghofe@18016
  1064
berghofe@19833
  1065
    val Abs_inverse_thms' = map (fn r => r RS subst) Abs_inverse_thms;
berghofe@18016
  1066
berghofe@18016
  1067
    val dt_induct_prop = DatatypeProp.make_ind descr' sorts';
wenzelm@20046
  1068
    val dt_induct = Goal.prove_global thy8 []
berghofe@18016
  1069
      (Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop)
berghofe@18016
  1070
      (fn prems => EVERY
berghofe@18016
  1071
        [rtac indrule_lemma' 1,
berghofe@18016
  1072
         (DatatypeAux.indtac rep_induct THEN_ALL_NEW ObjectLogic.atomize_tac) 1,
berghofe@18016
  1073
         EVERY (map (fn (prem, r) => (EVERY
berghofe@18016
  1074
           [REPEAT (eresolve_tac Abs_inverse_thms' 1),
berghofe@18016
  1075
            simp_tac (HOL_basic_ss addsimps [symmetric r]) 1,
berghofe@18016
  1076
            DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)]))
wenzelm@20046
  1077
                (prems ~~ constr_defs))]);
berghofe@18016
  1078
berghofe@18107
  1079
    val case_names_induct = mk_case_names_induct descr'';
berghofe@18016
  1080
berghofe@18066
  1081
    (**** prove that new datatypes have finite support ****)
berghofe@18066
  1082
urbanc@18246
  1083
    val _ = warning "proving finite support for the new datatype";
urbanc@18246
  1084
berghofe@18066
  1085
    val indnames = DatatypeProp.make_tnames recTs;
berghofe@18066
  1086
berghofe@18066
  1087
    val abs_supp = PureThy.get_thms thy8 (Name "abs_supp");
urbanc@18067
  1088
    val supp_atm = PureThy.get_thms thy8 (Name "supp_atm");
berghofe@18066
  1089
berghofe@18066
  1090
    val finite_supp_thms = map (fn atom =>
berghofe@18066
  1091
      let val atomT = Type (atom, [])
berghofe@18066
  1092
      in map standard (List.take
wenzelm@20046
  1093
        (split_conj_thm (Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop
berghofe@22274
  1094
           (foldr1 HOLogic.mk_conj (map (fn (s, T) =>
berghofe@22274
  1095
             Const ("Finite_Set.finite", HOLogic.mk_setT atomT --> HOLogic.boolT) $
berghofe@22274
  1096
               (Const ("Nominal.supp", T --> HOLogic.mk_setT atomT) $ Free (s, T)))
berghofe@18066
  1097
               (indnames ~~ recTs))))
berghofe@18066
  1098
           (fn _ => indtac dt_induct indnames 1 THEN
berghofe@18066
  1099
            ALLGOALS (asm_full_simp_tac (simpset_of thy8 addsimps
urbanc@18067
  1100
              (abs_supp @ supp_atm @
berghofe@18066
  1101
               PureThy.get_thms thy8 (Name ("fs_" ^ Sign.base_name atom ^ "1")) @
berghofe@18066
  1102
               List.concat supp_thms))))),
berghofe@18066
  1103
         length new_type_names))
berghofe@18066
  1104
      end) atoms;
berghofe@18066
  1105
krauss@18759
  1106
    val simp_atts = replicate (length new_type_names) [Simplifier.simp_add];
berghofe@18658
  1107
urbanc@22245
  1108
	(* Function to add both the simp and eqvt attributes *)
urbanc@22245
  1109
        (* These two attributes are duplicated on all the types in the mutual nominal datatypes *)
urbanc@22245
  1110
urbanc@22245
  1111
    val simp_eqvt_atts = replicate (length new_type_names) [Simplifier.simp_add, NominalThmDecls.eqvt_add];
urbanc@22245
  1112
 
berghofe@18658
  1113
    val (_, thy9) = thy8 |>
berghofe@18658
  1114
      Theory.add_path big_name |>
berghofe@18658
  1115
      PureThy.add_thms [(("induct_weak", dt_induct), [case_names_induct])] ||>>
berghofe@18658
  1116
      PureThy.add_thmss [(("inducts_weak", projections dt_induct), [case_names_induct])] ||>
berghofe@18658
  1117
      Theory.parent_path ||>>
berghofe@18658
  1118
      DatatypeAux.store_thmss_atts "distinct" new_type_names simp_atts distinct_thms ||>>
berghofe@18658
  1119
      DatatypeAux.store_thmss "constr_rep" new_type_names constr_rep_thmss ||>>
urbanc@22231
  1120
      DatatypeAux.store_thmss_atts "perm" new_type_names simp_eqvt_atts perm_simps' ||>>
berghofe@18658
  1121
      DatatypeAux.store_thmss "inject" new_type_names inject_thms ||>>
berghofe@18658
  1122
      DatatypeAux.store_thmss "supp" new_type_names supp_thms ||>>
berghofe@18658
  1123
      DatatypeAux.store_thmss_atts "fresh" new_type_names simp_atts fresh_thms ||>
berghofe@18658
  1124
      fold (fn (atom, ths) => fn thy =>
berghofe@18658
  1125
        let val class = Sign.intern_class thy ("fs_" ^ Sign.base_name atom)
berghofe@19275
  1126
        in fold (fn T => AxClass.prove_arity
berghofe@18658
  1127
            (fst (dest_Type T),
berghofe@18658
  1128
              replicate (length sorts) [class], [class])
berghofe@19133
  1129
            (ClassPackage.intro_classes_tac [] THEN resolve_tac ths 1)) newTs thy
berghofe@18658
  1130
        end) (atoms ~~ finite_supp_thms);
berghofe@18658
  1131
berghofe@18107
  1132
    (**** strong induction theorem ****)
berghofe@18107
  1133
berghofe@18107
  1134
    val pnames = if length descr'' = 1 then ["P"]
berghofe@18107
  1135
      else map (fn i => "P" ^ string_of_int i) (1 upto length descr'');
berghofe@18245
  1136
    val ind_sort = if null dt_atomTs then HOLogic.typeS
wenzelm@19649
  1137
      else Sign.certify_sort thy9 (map (fn T => Sign.intern_class thy9 ("fs_" ^
berghofe@18658
  1138
        Sign.base_name (fst (dest_Type T)))) dt_atomTs);
berghofe@18107
  1139
    val fsT = TFree ("'n", ind_sort);
berghofe@18658
  1140
    val fsT' = TFree ("'n", HOLogic.typeS);
berghofe@18107
  1141
berghofe@18658
  1142
    val fresh_fs = map (fn (s, T) => (T, Free (s, fsT' --> HOLogic.mk_setT T)))
berghofe@18658
  1143
      (DatatypeProp.indexify_names (replicate (length dt_atomTs) "f") ~~ dt_atomTs);
berghofe@18658
  1144
berghofe@18658
  1145
    fun make_pred fsT i T =
berghofe@18302
  1146
      Free (List.nth (pnames, i), fsT --> T --> HOLogic.boolT);
berghofe@18107
  1147
berghofe@19851
  1148
    fun mk_fresh1 xs [] = []
berghofe@19851
  1149
      | mk_fresh1 xs ((y as (_, T)) :: ys) = map (fn x => HOLogic.mk_Trueprop
berghofe@19851
  1150
            (HOLogic.mk_not (HOLogic.mk_eq (Free y, Free x))))
berghofe@19851
  1151
              (filter (fn (_, U) => T = U) (rev xs)) @
berghofe@19851
  1152
          mk_fresh1 (y :: xs) ys;
berghofe@19851
  1153
berghofe@19851
  1154
    fun mk_fresh2 xss [] = []
berghofe@19851
  1155
      | mk_fresh2 xss ((p as (ys, _)) :: yss) = List.concat (map (fn y as (_, T) =>
berghofe@19851
  1156
            map (fn (_, x as (_, U)) => HOLogic.mk_Trueprop
berghofe@19851
  1157
              (Const ("Nominal.fresh", T --> U --> HOLogic.boolT) $ Free y $ Free x))
berghofe@19851
  1158
                (rev xss @ yss)) ys) @
berghofe@19851
  1159
          mk_fresh2 (p :: xss) yss;
berghofe@19851
  1160
berghofe@18658
  1161
    fun make_ind_prem fsT f k T ((cname, cargs), idxs) =
berghofe@18107
  1162
      let
berghofe@18107
  1163
        val recs = List.filter is_rec_type cargs;
berghofe@18107
  1164
        val Ts = map (typ_of_dtyp descr'' sorts') cargs;
berghofe@18107
  1165
        val recTs' = map (typ_of_dtyp descr'' sorts') recs;
wenzelm@20071
  1166
        val tnames = Name.variant_list pnames (DatatypeProp.make_tnames Ts);
berghofe@18107
  1167
        val rec_tnames = map fst (List.filter (is_rec_type o snd) (tnames ~~ cargs));
berghofe@18107
  1168
        val frees = tnames ~~ Ts;
berghofe@19710
  1169
        val frees' = partition_cargs idxs frees;
wenzelm@20071
  1170
        val z = (Name.variant tnames "z", fsT);
berghofe@18107
  1171
berghofe@18107
  1172
        fun mk_prem ((dt, s), T) =
berghofe@18107
  1173
          let
berghofe@18107
  1174
            val (Us, U) = strip_type T;
berghofe@18107
  1175
            val l = length Us
berghofe@18107
  1176
          in list_all (z :: map (pair "x") Us, HOLogic.mk_Trueprop
berghofe@18658
  1177
            (make_pred fsT (body_index dt) U $ Bound l $ app_bnds (Free (s, T)) l))
berghofe@18107
  1178
          end;
berghofe@18107
  1179
berghofe@18107
  1180
        val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs');
berghofe@18107
  1181
        val prems' = map (fn p as (_, T) => HOLogic.mk_Trueprop
berghofe@19710
  1182
            (f T (Free p) (Free z))) (List.concat (map fst frees')) @
berghofe@19710
  1183
          mk_fresh1 [] (List.concat (map fst frees')) @
berghofe@19710
  1184
          mk_fresh2 [] frees'
berghofe@18107
  1185
berghofe@18302
  1186
      in list_all_free (frees @ [z], Logic.list_implies (prems' @ prems,
berghofe@18658
  1187
        HOLogic.mk_Trueprop (make_pred fsT k T $ Free z $
berghofe@18302
  1188
          list_comb (Const (cname, Ts ---> T), map Free frees))))
berghofe@18107
  1189
      end;
berghofe@18107
  1190
berghofe@18107
  1191
    val ind_prems = List.concat (map (fn (((i, (_, _, constrs)), (_, idxss)), T) =>
berghofe@18658
  1192
      map (make_ind_prem fsT (fn T => fn t => fn u =>
berghofe@19494
  1193
        Const ("Nominal.fresh", T --> fsT --> HOLogic.boolT) $ t $ u) i T)
berghofe@18658
  1194
          (constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs));
berghofe@18107
  1195
    val tnames = DatatypeProp.make_tnames recTs;
wenzelm@20071
  1196
    val zs = Name.variant_list tnames (replicate (length descr'') "z");
berghofe@18107
  1197
    val ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
berghofe@18658
  1198
      (map (fn ((((i, _), T), tname), z) =>
berghofe@18658
  1199
        make_pred fsT i T $ Free (z, fsT) $ Free (tname, T))
berghofe@18658
  1200
        (descr'' ~~ recTs ~~ tnames ~~ zs)));
berghofe@18107
  1201
    val induct = Logic.list_implies (ind_prems, ind_concl);
berghofe@18107
  1202
berghofe@18658
  1203
    val ind_prems' =
berghofe@18658
  1204
      map (fn (_, f as Free (_, T)) => list_all_free ([("x", fsT')],
berghofe@22274
  1205
        HOLogic.mk_Trueprop (Const ("Finite_Set.finite", body_type T -->
berghofe@22274
  1206
          HOLogic.boolT) $ (f $ Free ("x", fsT'))))) fresh_fs @
berghofe@18658
  1207
      List.concat (map (fn (((i, (_, _, constrs)), (_, idxss)), T) =>
berghofe@18658
  1208
        map (make_ind_prem fsT' (fn T => fn t => fn u => HOLogic.Not $
berghofe@18658
  1209
          HOLogic.mk_mem (t, the (AList.lookup op = fresh_fs T) $ u)) i T)
berghofe@18658
  1210
            (constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs));
berghofe@18658
  1211
    val ind_concl' = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
berghofe@18658
  1212
      (map (fn ((((i, _), T), tname), z) =>
berghofe@18658
  1213
        make_pred fsT' i T $ Free (z, fsT') $ Free (tname, T))
berghofe@18658
  1214
        (descr'' ~~ recTs ~~ tnames ~~ zs)));
berghofe@18658
  1215
    val induct' = Logic.list_implies (ind_prems', ind_concl');
berghofe@18658
  1216
berghofe@18658
  1217
    fun mk_perm Ts (t, u) =
berghofe@18658
  1218
      let
berghofe@18658
  1219
        val T = fastype_of1 (Ts, t);
berghofe@18658
  1220
        val U = fastype_of1 (Ts, u)
berghofe@19494
  1221
      in Const ("Nominal.perm", T --> U --> U) $ t $ u end;
berghofe@18658
  1222
berghofe@18658
  1223
    val aux_ind_vars =
berghofe@18658
  1224
      (DatatypeProp.indexify_names (replicate (length dt_atomTs) "pi") ~~
berghofe@18658
  1225
       map mk_permT dt_atomTs) @ [("z", fsT')];
berghofe@18658
  1226
    val aux_ind_Ts = rev (map snd aux_ind_vars);
berghofe@18658
  1227
    val aux_ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
berghofe@18658
  1228
      (map (fn (((i, _), T), tname) =>
berghofe@18658
  1229
        HOLogic.list_all (aux_ind_vars, make_pred fsT' i T $ Bound 0 $
berghofe@18658
  1230
          foldr (mk_perm aux_ind_Ts) (Free (tname, T))
berghofe@18658
  1231
            (map Bound (length dt_atomTs downto 1))))
berghofe@18658
  1232
        (descr'' ~~ recTs ~~ tnames)));
berghofe@18658
  1233
berghofe@18658
  1234
    fun mk_ind_perm i k p l vs j =
berghofe@18658
  1235
      let
berghofe@18658
  1236
        val n = length vs;
berghofe@18658
  1237
        val Ts = map snd vs;
berghofe@18658
  1238
        val T = List.nth (Ts, i - j);
berghofe@18658
  1239
        val pT = NominalAtoms.mk_permT T
berghofe@18658
  1240
      in
berghofe@18658
  1241
        Const ("List.list.Cons", HOLogic.mk_prodT (T, T) --> pT --> pT) $
berghofe@18658
  1242
          (HOLogic.pair_const T T $ Bound (l - j) $ foldr (mk_perm Ts)
berghofe@18658
  1243
            (Bound (i - j))
berghofe@18658
  1244
            (map (mk_ind_perm i k p l vs) (j - 1 downto 0) @
berghofe@18658
  1245
             map Bound (n - k - 1 downto n - k - p))) $
berghofe@18658
  1246
          Const ("List.list.Nil", pT)
berghofe@18658
  1247
      end;
berghofe@18658
  1248
berghofe@19710
  1249
    fun mk_fresh i i' j k p l is vs _ _ =
berghofe@18658
  1250
      let
berghofe@18658
  1251
        val n = length vs;
berghofe@18658
  1252
        val Ts = map snd vs;
berghofe@18658
  1253
        val T = List.nth (Ts, n - i - 1 - j);
berghofe@18658
  1254
        val f = the (AList.lookup op = fresh_fs T);
berghofe@18658
  1255
        val U = List.nth (Ts, n - i' - 1);
berghofe@18658
  1256
        val S = HOLogic.mk_setT T;
berghofe@19710
  1257
        val prms' = map Bound (n - k downto n - k - p + 1);
berghofe@18658
  1258
        val prms = map (mk_ind_perm (n - i) k p (n - l) (("a", T) :: vs))
berghofe@19710
  1259
            (j - 1 downto 0) @ prms';
berghofe@19710
  1260
        val bs = rev (List.mapPartial
berghofe@19710
  1261
          (fn ((_, T'), i) => if T = T' then SOME (Bound i) else NONE)
berghofe@19710
  1262
          (List.take (vs, n - k - p - 1) ~~ (1 upto n - k - p - 1)));
berghofe@19710
  1263
        val ts = map (fn i =>
berghofe@19710
  1264
          Const ("Nominal.supp", List.nth (Ts, n - i - 1) --> S) $
berghofe@19710
  1265
            foldr (mk_perm (T :: Ts)) (Bound (n - i)) prms') is
berghofe@18658
  1266
      in
berghofe@18658
  1267
        HOLogic.mk_Trueprop (Const ("Ex", (T --> HOLogic.boolT) --> HOLogic.boolT) $
berghofe@18658
  1268
          Abs ("a", T, HOLogic.Not $
berghofe@18658
  1269
            (Const ("op :", T --> S --> HOLogic.boolT) $ Bound 0 $
berghofe@19710
  1270
              (foldr (fn (t, u) => Const ("insert", T --> S --> S) $ t $ u)
berghofe@19710
  1271
                (foldl (fn (t, u) => Const ("op Un", S --> S --> S) $ u $ t)
berghofe@19710
  1272
                  (f $ Bound (n - k - p))
berghofe@19710
  1273
                  (Const ("Nominal.supp", U --> S) $
berghofe@19710
  1274
                     foldr (mk_perm (T :: Ts)) (Bound (n - i')) prms :: ts))
berghofe@19710
  1275
                (foldr (mk_perm (T :: Ts)) (Bound (n - i - j)) prms :: bs)))))
berghofe@18658
  1276
      end;
urbanc@18104
  1277
berghofe@18658
  1278
    fun mk_fresh_constr is p vs _ concl =
berghofe@18658
  1279
      let
berghofe@18658
  1280
        val n = length vs;
berghofe@18658
  1281
        val Ts = map snd vs;
berghofe@18658
  1282
        val _ $ (_ $ _ $ t) = concl;
berghofe@18658
  1283
        val c = head_of t;
berghofe@18658
  1284
        val T = body_type (fastype_of c);
berghofe@18658
  1285
        val k = foldr op + 0 (map (fn (_, i) => i + 1) is);
berghofe@18658
  1286
        val ps = map Bound (n - k - 1 downto n - k - p);
berghofe@18658
  1287
        val (_, _, ts, us) = foldl (fn ((_, i), (m, n, ts, us)) =>
berghofe@18658
  1288
          (m - i - 1, n - i,
berghofe@18658
  1289
           ts @ map Bound (n downto n - i + 1) @
berghofe@18658
  1290
             [foldr (mk_perm Ts) (Bound (m - i))
berghofe@18658
  1291
                (map (mk_ind_perm m k p n vs) (i - 1 downto 0) @ ps)],
berghofe@18658
  1292
           us @ map (fn j => foldr (mk_perm Ts) (Bound j) ps) (m downto m - i)))
berghofe@18658
  1293
          (n - 1, n - k - p - 2, [], []) is
berghofe@18658
  1294
      in
berghofe@18658
  1295
        HOLogic.mk_Trueprop (HOLogic.eq_const T $ list_comb (c, ts) $ list_comb (c, us))
berghofe@18658
  1296
      end;
berghofe@18658
  1297
berghofe@18658
  1298
    val abs_fun_finite_supp = PureThy.get_thm thy9 (Name "abs_fun_finite_supp");
berghofe@18658
  1299
berghofe@18658
  1300
    val at_finite_select = PureThy.get_thm thy9 (Name "at_finite_select");
berghofe@18658
  1301
berghofe@18658
  1302
    val induct_aux_lemmas = List.concat (map (fn Type (s, _) =>
berghofe@18658
  1303
      [PureThy.get_thm thy9 (Name ("pt_" ^ Sign.base_name s ^ "_inst")),
berghofe@18658
  1304
       PureThy.get_thm thy9 (Name ("fs_" ^ Sign.base_name s ^ "1")),
berghofe@18658
  1305
       PureThy.get_thm thy9 (Name ("at_" ^ Sign.base_name s ^ "_inst"))]) dt_atomTs);
berghofe@18658
  1306
berghofe@18658
  1307
    val induct_aux_lemmas' = map (fn Type (s, _) =>
berghofe@18658
  1308
      PureThy.get_thm thy9 (Name ("pt_" ^ Sign.base_name s ^ "2")) RS sym) dt_atomTs;
berghofe@18658
  1309
berghofe@19710
  1310
    val fresh_aux = PureThy.get_thms thy9 (Name "fresh_aux");
berghofe@19710
  1311
berghofe@19710
  1312
    (**********************************************************************
berghofe@19710
  1313
      The subgoals occurring in the proof of induct_aux have the
berghofe@19710
  1314
      following parameters:
berghofe@19710
  1315
berghofe@19710
  1316
        x_1 ... x_k p_1 ... p_m z b_1 ... b_n
berghofe@19710
  1317
berghofe@19710
  1318
      where
berghofe@19710
  1319
berghofe@19710
  1320
        x_i : constructor arguments (introduced by weak induction rule)
berghofe@19710
  1321
        p_i : permutations (one for each atom type in the data type)
berghofe@19710
  1322
        z   : freshness context
berghofe@19710
  1323
        b_i : newly introduced names for binders (sufficiently fresh)
berghofe@19710
  1324
    ***********************************************************************)
berghofe@19710
  1325
berghofe@19710
  1326
    val _ = warning "proving strong induction theorem ...";
berghofe@19710
  1327
wenzelm@20046
  1328
    val induct_aux = Goal.prove_global thy9 [] ind_prems' ind_concl'
berghofe@18658
  1329
      (fn prems => EVERY
berghofe@18658
  1330
        ([mk_subgoal 1 (K (K (K aux_ind_concl))),
berghofe@18658
  1331
          indtac dt_induct tnames 1] @
berghofe@18658
  1332
         List.concat (map (fn ((_, (_, _, constrs)), (_, constrs')) =>
berghofe@18658
  1333
           List.concat (map (fn ((cname, cargs), is) =>
berghofe@18658
  1334
             [simp_tac (HOL_basic_ss addsimps List.concat perm_simps') 1,
berghofe@18658
  1335
              REPEAT (rtac allI 1)] @
berghofe@18658
  1336
             List.concat (map
berghofe@18658
  1337
               (fn ((_, 0), _) => []
berghofe@18658
  1338
                 | ((i, j), k) => List.concat (map (fn j' =>
berghofe@18658
  1339
                     let
berghofe@18658
  1340
                       val DtType (tname, _) = List.nth (cargs, i + j');
berghofe@18658
  1341
                       val atom = Sign.base_name tname
berghofe@18658
  1342
                     in
berghofe@18658
  1343
                       [mk_subgoal 1 (mk_fresh i (i + j) j'
berghofe@18658
  1344
                          (length cargs) (length dt_atomTs)
berghofe@19710
  1345
                          (length cargs + length dt_atomTs + 1 + i - k)
berghofe@19710
  1346
                          (List.mapPartial (fn (i', j) =>
berghofe@19710
  1347
                             if i = i' then NONE else SOME (i' + j)) is)),
berghofe@18658
  1348
                        rtac at_finite_select 1,
berghofe@18658
  1349
                        rtac (PureThy.get_thm thy9 (Name ("at_" ^ atom ^ "_inst"))) 1,
berghofe@18658
  1350
                        asm_full_simp_tac (simpset_of thy9 addsimps
berghofe@18658
  1351
                          [PureThy.get_thm thy9 (Name ("fs_" ^ atom ^ "1"))]) 1,
berghofe@18658
  1352
                        resolve_tac prems 1,
berghofe@18658
  1353
                        etac exE 1,
berghofe@18658
  1354
                        asm_full_simp_tac (simpset_of thy9 addsimps
berghofe@18658
  1355
                          [symmetric fresh_def]) 1]
berghofe@18658
  1356
                     end) (0 upto j - 1))) (is ~~ (0 upto length is - 1))) @
berghofe@18658
  1357
             (if exists (not o equal 0 o snd) is then
berghofe@18658
  1358
                [mk_subgoal 1 (mk_fresh_constr is (length dt_atomTs)),
berghofe@18658
  1359
                 asm_full_simp_tac (simpset_of thy9 addsimps
berghofe@18658
  1360
                   (List.concat inject_thms @
berghofe@18658
  1361
                    alpha @ abs_perm @ abs_fresh @ [abs_fun_finite_supp] @
berghofe@18658
  1362
                    induct_aux_lemmas)) 1,
berghofe@18658
  1363
                 dtac sym 1,
berghofe@19710
  1364
                 asm_full_simp_tac (simpset_of thy9) 1,
berghofe@18658
  1365
                 REPEAT (etac conjE 1)]
berghofe@18658
  1366
              else
berghofe@18658
  1367
                []) @
berghofe@18658
  1368
             [(resolve_tac prems THEN_ALL_NEW
berghofe@19710
  1369
                (atac ORELSE'
berghofe@19710
  1370
                  SUBGOAL (fn (t, i) => case Logic.strip_assums_concl t of
berghofe@19710
  1371
                      _ $ (Const ("Nominal.fresh", _) $ _ $ _) =>
berghofe@19710
  1372
                        asm_simp_tac (simpset_of thy9 addsimps fresh_aux) i
berghofe@19710
  1373
                    | _ =>
berghofe@19710
  1374
                        asm_simp_tac (simpset_of thy9
berghofe@19710
  1375
                        addsimps induct_aux_lemmas'
berghofe@19710
  1376
                        addsimprocs [perm_simproc]) i))) 1])
berghofe@18658
  1377
               (constrs ~~ constrs'))) (descr'' ~~ ndescr)) @
berghofe@18658
  1378
         [REPEAT (eresolve_tac [conjE, allE_Nil] 1),
berghofe@18658
  1379
          REPEAT (etac allE 1),
wenzelm@20046
  1380
          REPEAT (TRY (rtac conjI 1) THEN asm_full_simp_tac (simpset_of thy9) 1)]));
berghofe@18658
  1381
berghofe@18658
  1382
    val induct_aux' = Thm.instantiate ([],
berghofe@18658
  1383
      map (fn (s, T) =>
berghofe@18658
  1384
        let val pT = TVar (("'n", 0), HOLogic.typeS) --> T --> HOLogic.boolT
berghofe@18658
  1385
        in (cterm_of thy9 (Var ((s, 0), pT)), cterm_of thy9 (Free (s, pT))) end)
berghofe@18658
  1386
          (pnames ~~ recTs) @
berghofe@18658
  1387
      map (fn (_, f) =>
berghofe@18658
  1388
        let val f' = Logic.varify f
berghofe@18658
  1389
        in (cterm_of thy9 f',
berghofe@19494
  1390
          cterm_of thy9 (Const ("Nominal.supp", fastype_of f')))
berghofe@18658
  1391
        end) fresh_fs) induct_aux;
berghofe@18658
  1392
wenzelm@20046
  1393
    val induct = Goal.prove_global thy9 [] ind_prems ind_concl
berghofe@18658
  1394
      (fn prems => EVERY
berghofe@18658
  1395
         [rtac induct_aux' 1,
berghofe@18658
  1396
          REPEAT (resolve_tac induct_aux_lemmas 1),
berghofe@18658
  1397
          REPEAT ((resolve_tac prems THEN_ALL_NEW
wenzelm@20046
  1398
            (etac meta_spec ORELSE' full_simp_tac (HOL_basic_ss addsimps [fresh_def]))) 1)])
berghofe@18658
  1399
berghofe@18658
  1400
    val (_, thy10) = thy9 |>
berghofe@18016
  1401
      Theory.add_path big_name |>
berghofe@18658
  1402
      PureThy.add_thms [(("induct'", induct_aux), [])] ||>>
berghofe@18658
  1403
      PureThy.add_thms [(("induct", induct), [case_names_induct])] ||>>
berghofe@20397
  1404
      PureThy.add_thmss [(("inducts", projections induct), [case_names_induct])];
berghofe@18658
  1405
berghofe@19322
  1406
    (**** recursion combinator ****)
berghofe@19251
  1407
berghofe@19322
  1408
    val _ = warning "defining recursion combinator ...";
berghofe@19251
  1409
berghofe@19251
  1410
    val used = foldr add_typ_tfree_names [] recTs;
berghofe@19251
  1411
berghofe@19985
  1412
    val (rec_result_Ts', rec_fn_Ts') = DatatypeProp.make_primrec_Ts descr' sorts' used;
berghofe@19985
  1413
wenzelm@21365
  1414
    val rec_sort = if null dt_atomTs then HOLogic.typeS else
berghofe@19985
  1415
      let val names = map (Sign.base_name o fst o dest_Type) dt_atomTs
berghofe@19985
  1416
      in Sign.certify_sort thy10 (map (Sign.intern_class thy10)
berghofe@19985
  1417
        (map (fn s => "pt_" ^ s) names @
berghofe@19985
  1418
         List.concat (map (fn s => List.mapPartial (fn s' =>
berghofe@19985
  1419
           if s = s' then NONE
berghofe@19985
  1420
           else SOME ("cp_" ^ s ^ "_" ^ s')) names) names)))
berghofe@19985
  1421
      end;
berghofe@19985
  1422
berghofe@19985
  1423
    val rec_result_Ts = map (fn TFree (s, _) => TFree (s, rec_sort)) rec_result_Ts';
berghofe@19985
  1424
    val rec_fn_Ts = map (typ_subst_atomic (rec_result_Ts' ~~ rec_result_Ts)) rec_fn_Ts';
berghofe@19251
  1425
berghofe@21021
  1426
    val rec_set_Ts = map (fn (T1, T2) =>
berghofe@21021
  1427
      rec_fn_Ts @ [T1, T2] ---> HOLogic.boolT) (recTs ~~ rec_result_Ts);
berghofe@19251
  1428
berghofe@19322
  1429
    val big_rec_name = big_name ^ "_rec_set";
berghofe@21021
  1430
    val rec_set_names' =
berghofe@21021
  1431
      if length descr'' = 1 then [big_rec_name] else
berghofe@21021
  1432
        map ((curry (op ^) (big_rec_name ^ "_")) o string_of_int)
berghofe@21021
  1433
          (1 upto (length descr''));
berghofe@21021
  1434
    val rec_set_names =  map (Sign.full_name (Theory.sign_of thy10)) rec_set_names';
berghofe@19251
  1435
berghofe@19322
  1436
    val rec_fns = map (uncurry (mk_Free "f"))
berghofe@19322
  1437
      (rec_fn_Ts ~~ (1 upto (length rec_fn_Ts)));
berghofe@21021
  1438
    val rec_sets' = map (fn c => list_comb (Free c, rec_fns))
berghofe@21021
  1439
      (rec_set_names' ~~ rec_set_Ts);
berghofe@19322
  1440
    val rec_sets = map (fn c => list_comb (Const c, rec_fns))
berghofe@19322
  1441
      (rec_set_names ~~ rec_set_Ts);
berghofe@19251
  1442
berghofe@19322
  1443
    (* introduction rules for graph of recursion function *)
berghofe@19251
  1444
berghofe@20145
  1445
    val rec_preds = map (fn (a, T) =>
berghofe@20145
  1446
      Free (a, T --> HOLogic.boolT)) (pnames ~~ rec_result_Ts);
berghofe@20145
  1447
berghofe@20267
  1448
    fun mk_fresh3 rs [] = []
berghofe@20267
  1449
      | mk_fresh3 rs ((p as (ys, z)) :: yss) = List.concat (map (fn y as (_, T) =>
berghofe@20267
  1450
            List.mapPartial (fn ((_, (_, x)), r as (_, U)) => if z = x then NONE
berghofe@20267
  1451
              else SOME (HOLogic.mk_Trueprop
berghofe@20267
  1452
                (Const ("Nominal.fresh", T --> U --> HOLogic.boolT) $ Free y $ Free r)))
berghofe@20267
  1453
                  rs) ys) @
berghofe@20267
  1454
          mk_fresh3 rs yss;
berghofe@20267
  1455
berghofe@21088
  1456
    (* FIXME: avoid collisions with other variable names? *)
berghofe@21088
  1457
    val rec_ctxt = Free ("z", fsT');
berghofe@21088
  1458
berghofe@20397
  1459
    fun make_rec_intr T p rec_set ((rec_intr_ts, rec_prems, rec_prems',
berghofe@20397
  1460
          rec_eq_prems, l), ((cname, cargs), idxs)) =
berghofe@19251
  1461
      let
berghofe@19251
  1462
        val Ts = map (typ_of_dtyp descr'' sorts') cargs;
berghofe@19851
  1463
        val frees = map (fn i => "x" ^ string_of_int i) (1 upto length Ts) ~~ Ts;
berghofe@19851
  1464
        val frees' = partition_cargs idxs frees;
berghofe@21088
  1465
        val binders = List.concat (map fst frees');
berghofe@20411
  1466
        val atomTs = distinct op = (maps (map snd o fst) frees');
berghofe@19851
  1467
        val recs = List.mapPartial
berghofe@20145
  1468
          (fn ((_, DtRec i), p) => SOME (i, p) | _ => NONE)
berghofe@19851
  1469
          (partition_cargs idxs cargs ~~ frees');
berghofe@19851
  1470
        val frees'' = map (fn i => "y" ^ string_of_int i) (1 upto length recs) ~~
berghofe@19851
  1471
          map (fn (i, _) => List.nth (rec_result_Ts, i)) recs;
berghofe@20145
  1472
        val prems1 = map (fn ((i, (_, x)), y) => HOLogic.mk_Trueprop
berghofe@21021
  1473
          (List.nth (rec_sets', i) $ Free x $ Free y)) (recs ~~ frees'');
berghofe@20145
  1474
        val prems2 =
berghofe@20145
  1475
          map (fn f => map (fn p as (_, T) => HOLogic.mk_Trueprop
berghofe@19851
  1476
            (Const ("Nominal.fresh", T --> fastype_of f --> HOLogic.boolT) $
berghofe@21088
  1477
              Free p $ f)) binders) rec_fns;
berghofe@21088
  1478
        val prems3 = mk_fresh1 [] binders @ mk_fresh2 [] frees';
berghofe@20145
  1479
        val prems4 = map (fn ((i, _), y) =>
berghofe@20145
  1480
          HOLogic.mk_Trueprop (List.nth (rec_preds, i) $ Free y)) (recs ~~ frees'');
berghofe@20267
  1481
        val prems5 = mk_fresh3 (recs ~~ frees'') frees';
berghofe@20411
  1482
        val prems6 = maps (fn aT => map (fn y as (_, T) => HOLogic.mk_Trueprop
berghofe@22274
  1483
          (Const ("Finite_Set.finite", HOLogic.mk_setT aT --> HOLogic.boolT) $
berghofe@22274
  1484
             (Const ("Nominal.supp", T --> HOLogic.mk_setT aT) $ Free y)))
berghofe@20411
  1485
               frees'') atomTs;
berghofe@21088
  1486
        val prems7 = map (fn x as (_, T) => HOLogic.mk_Trueprop
berghofe@21088
  1487
          (Const ("Nominal.fresh", T --> fsT' --> HOLogic.boolT) $
berghofe@21088
  1488
             Free x $ rec_ctxt)) binders;
berghofe@20145
  1489
        val result = list_comb (List.nth (rec_fns, l), map Free (frees @ frees''));
berghofe@20376
  1490
        val result_freshs = map (fn p as (_, T) =>
berghofe@20145
  1491
          Const ("Nominal.fresh", T --> fastype_of result --> HOLogic.boolT) $
berghofe@21088
  1492
            Free p $ result) binders;
berghofe@20145
  1493
        val P = HOLogic.mk_Trueprop (p $ result)
berghofe@20145
  1494
      in
berghofe@20145
  1495
        (rec_intr_ts @ [Logic.list_implies (List.concat prems2 @ prems3 @ prems1,
berghofe@21021
  1496
           HOLogic.mk_Trueprop (rec_set $
berghofe@21021
  1497
             list_comb (Const (cname, Ts ---> T), map Free frees) $ result))],
berghofe@20145
  1498
         rec_prems @ [list_all_free (frees @ frees'', Logic.list_implies (prems4, P))],
berghofe@21054
  1499
         rec_prems' @ map (fn fr => list_all_free (frees @ frees'',
berghofe@21088
  1500
           Logic.list_implies (List.nth (prems2, l) @ prems3 @ prems5 @ prems7 @ prems6 @ [P],
berghofe@21054
  1501
             HOLogic.mk_Trueprop fr))) result_freshs,
berghofe@20397
  1502
         rec_eq_prems @ [List.concat prems2 @ prems3],
berghofe@20145
  1503
         l + 1)
berghofe@19251
  1504
      end;
berghofe@19251
  1505
berghofe@20397
  1506
    val (rec_intr_ts, rec_prems, rec_prems', rec_eq_prems, _) =
berghofe@20145
  1507
      Library.foldl (fn (x, ((((d, d'), T), p), rec_set)) =>
berghofe@20145
  1508
        Library.foldl (make_rec_intr T p rec_set) (x, #3 (snd d) ~~ snd d'))
berghofe@21021
  1509
          (([], [], [], [], 0), descr'' ~~ ndescr ~~ recTs ~~ rec_preds ~~ rec_sets');
berghofe@19251
  1510
wenzelm@21365
  1511
    val ({intrs = rec_intrs, elims = rec_elims, raw_induct = rec_induct, ...}, thy11) =
berghofe@21055
  1512
      thy10 |>
berghofe@19251
  1513
      setmp InductivePackage.quiet_mode (!quiet_mode)
berghofe@21021
  1514
        (TheoryTarget.init NONE #>
berghofe@21021
  1515
         InductivePackage.add_inductive_i false big_rec_name false false false
berghofe@21021
  1516
           (map (fn (s, T) => (s, SOME T, NoSyn)) (rec_set_names' ~~ rec_set_Ts))
berghofe@21021
  1517
           (map (apsnd SOME o dest_Free) rec_fns)
berghofe@21021
  1518
           (map (fn x => (("", []), x)) rec_intr_ts) [] #>
wenzelm@21365
  1519
         apsnd (ProofContext.theory_of o LocalTheory.exit)) ||>
berghofe@21055
  1520
      PureThy.hide_thms true [NameSpace.append
berghofe@21055
  1521
        (Sign.full_name thy10 big_rec_name) "induct"];
berghofe@19251
  1522
berghofe@19985
  1523
    (** equivariance **)
berghofe@19985
  1524
berghofe@19985
  1525
    val fresh_bij = PureThy.get_thms thy11 (Name "fresh_bij");
berghofe@19985
  1526
    val perm_bij = PureThy.get_thms thy11 (Name "perm_bij");
berghofe@19985
  1527
berghofe@19985
  1528
    val (rec_equiv_thms, rec_equiv_thms') = ListPair.unzip (map (fn aT =>
berghofe@19985
  1529
      let
berghofe@19985
  1530
        val permT = mk_permT aT;
berghofe@19985
  1531
        val pi = Free ("pi", permT);
berghofe@19985
  1532
        val rec_fns_pi = map (curry (mk_perm []) pi o uncurry (mk_Free "f"))
berghofe@19985
  1533
          (rec_fn_Ts ~~ (1 upto (length rec_fn_Ts)));
berghofe@19985
  1534
        val rec_sets_pi = map (fn c => list_comb (Const c, rec_fns_pi))
berghofe@19985
  1535
          (rec_set_names ~~ rec_set_Ts);
berghofe@19985
  1536
        val ps = map (fn ((((T, U), R), R'), i) =>
berghofe@19985
  1537
          let
berghofe@19985
  1538
            val x = Free ("x" ^ string_of_int i, T);
berghofe@19985
  1539
            val y = Free ("y" ^ string_of_int i, U)
berghofe@19985
  1540
          in
berghofe@21021
  1541
            (R $ x $ y, R' $ mk_perm [] (pi, x) $ mk_perm [] (pi, y))
berghofe@19985
  1542
          end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~ rec_sets_pi ~~ (1 upto length recTs));
berghofe@19985
  1543
        val ths = map (fn th => standard (th RS mp)) (split_conj_thm
wenzelm@20046
  1544
          (Goal.prove_global thy11 [] []
berghofe@19985
  1545
            (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map HOLogic.mk_imp ps)))
berghofe@19985
  1546
            (fn _ => rtac rec_induct 1 THEN REPEAT
berghofe@19985
  1547
               (NominalPermeq.perm_simp_tac (simpset_of thy11) 1 THEN
berghofe@19985
  1548
                (resolve_tac rec_intrs THEN_ALL_NEW
berghofe@19985
  1549
                 asm_simp_tac (HOL_ss addsimps (fresh_bij @ perm_bij))) 1))))
wenzelm@20046
  1550
        val ths' = map (fn ((P, Q), th) =>
wenzelm@20046
  1551
          Goal.prove_global thy11 [] []
berghofe@19985
  1552
            (Logic.mk_implies (HOLogic.mk_Trueprop Q, HOLogic.mk_Trueprop P))
berghofe@19985
  1553
            (fn _ => dtac (Thm.instantiate ([],
berghofe@19985
  1554
                 [(cterm_of thy11 (Var (("pi", 0), permT)),
berghofe@19985
  1555
                   cterm_of thy11 (Const ("List.rev", permT --> permT) $ pi))]) th) 1 THEN
wenzelm@20046
  1556
               NominalPermeq.perm_simp_tac HOL_ss 1)) (ps ~~ ths)
berghofe@19985
  1557
      in (ths, ths') end) dt_atomTs);
berghofe@19985
  1558
berghofe@19985
  1559
    (** finite support **)
berghofe@19985
  1560
berghofe@19985
  1561
    val rec_fin_supp_thms = map (fn aT =>
berghofe@19985
  1562
      let
berghofe@19985
  1563
        val name = Sign.base_name (fst (dest_Type aT));
berghofe@19985
  1564
        val fs_name = PureThy.get_thm thy11 (Name ("fs_" ^ name ^ "1"));
berghofe@19985
  1565
        val aset = HOLogic.mk_setT aT;
berghofe@22274
  1566
        val finite = Const ("Finite_Set.finite", aset --> HOLogic.boolT);
berghofe@22274
  1567
        val fins = map (fn (f, T) => HOLogic.mk_Trueprop
berghofe@22274
  1568
          (finite $ (Const ("Nominal.supp", T --> aset) $ f)))
berghofe@19985
  1569
            (rec_fns ~~ rec_fn_Ts)
berghofe@19985
  1570
      in
berghofe@19985
  1571
        map (fn th => standard (th RS mp)) (split_conj_thm
wenzelm@20046
  1572
          (Goal.prove_global thy11 [] fins
berghofe@19985
  1573
            (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@19985
  1574
              (map (fn (((T, U), R), i) =>
berghofe@19985
  1575
                 let
berghofe@19985
  1576
                   val x = Free ("x" ^ string_of_int i, T);
berghofe@19985
  1577
                   val y = Free ("y" ^ string_of_int i, U)
berghofe@19985
  1578
                 in
berghofe@21021
  1579
                   HOLogic.mk_imp (R $ x $ y,
berghofe@22274
  1580
                     finite $ (Const ("Nominal.supp", U --> aset) $ y))
berghofe@19985
  1581
                 end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~ (1 upto length recTs)))))
berghofe@19985
  1582
            (fn fins => (rtac rec_induct THEN_ALL_NEW cut_facts_tac fins) 1 THEN REPEAT
berghofe@19985
  1583
               (NominalPermeq.finite_guess_tac (HOL_ss addsimps [fs_name]) 1))))
berghofe@19985
  1584
      end) dt_atomTs;
berghofe@19985
  1585
berghofe@20376
  1586
    (** freshness **)
berghofe@20376
  1587
berghofe@20376
  1588
    val perm_fresh_fresh = PureThy.get_thms thy11 (Name "perm_fresh_fresh");
berghofe@20376
  1589
    val perm_swap = PureThy.get_thms thy11 (Name "perm_swap");
berghofe@20145
  1590
berghofe@20376
  1591
    fun perm_of_pair (x, y) =
berghofe@20376
  1592
      let
berghofe@20376
  1593
        val T = fastype_of x;
berghofe@20376
  1594
        val pT = mk_permT T
berghofe@20376
  1595
      in Const ("List.list.Cons", HOLogic.mk_prodT (T, T) --> pT --> pT) $
berghofe@20376
  1596
        HOLogic.mk_prod (x, y) $ Const ("List.list.Nil", pT)
berghofe@20376
  1597
      end;
berghofe@20376
  1598
berghofe@20376
  1599
    val finite_premss = map (fn aT =>
berghofe@22274
  1600
      map (fn (f, T) => HOLogic.mk_Trueprop
berghofe@22274
  1601
        (Const ("Finite_Set.finite", HOLogic.mk_setT aT --> HOLogic.boolT) $
berghofe@22274
  1602
           (Const ("Nominal.supp", T --> HOLogic.mk_setT aT) $ f)))
berghofe@20376
  1603
           (rec_fns ~~ rec_fn_Ts)) dt_atomTs;
berghofe@20376
  1604
berghofe@20376
  1605
    val rec_fresh_thms = map (fn ((aT, eqvt_ths), finite_prems) =>
berghofe@20376
  1606
      let
berghofe@20376
  1607
        val name = Sign.base_name (fst (dest_Type aT));
berghofe@20376
  1608
        val fs_name = PureThy.get_thm thy11 (Name ("fs_" ^ name ^ "1"));
berghofe@20376
  1609
        val a = Free ("a", aT);
berghofe@20376
  1610
        val freshs = map (fn (f, fT) => HOLogic.mk_Trueprop
berghofe@20376
  1611
            (Const ("Nominal.fresh", aT --> fT --> HOLogic.boolT) $ a $ f))
berghofe@20376
  1612
          (rec_fns ~~ rec_fn_Ts)
berghofe@20376
  1613
      in
berghofe@20376
  1614
        map (fn (((T, U), R), eqvt_th) =>
berghofe@20376
  1615
          let
berghofe@20376
  1616
            val x = Free ("x", T);
berghofe@20376
  1617
            val y = Free ("y", U);
berghofe@20376
  1618
            val y' = Free ("y'", U)
berghofe@20376
  1619
          in
wenzelm@21516
  1620
            standard (Goal.prove (ProofContext.init thy11) [] (finite_prems @
berghofe@21021
  1621
                [HOLogic.mk_Trueprop (R $ x $ y),
berghofe@20376
  1622
                 HOLogic.mk_Trueprop (HOLogic.mk_all ("y'", U,
berghofe@21021
  1623
                   HOLogic.mk_imp (R $ x $ y', HOLogic.mk_eq (y', y)))),
berghofe@20376
  1624
                 HOLogic.mk_Trueprop (Const ("Nominal.fresh",
berghofe@20376
  1625
                   aT --> T --> HOLogic.boolT) $ a $ x)] @
berghofe@20376
  1626
              freshs)
berghofe@20376
  1627
              (HOLogic.mk_Trueprop (Const ("Nominal.fresh",
berghofe@20376
  1628
                 aT --> U --> HOLogic.boolT) $ a $ y))
berghofe@20376
  1629
              (fn {prems, context} =>
berghofe@20376
  1630
                 let
berghofe@20376
  1631
                   val (finite_prems, rec_prem :: unique_prem ::
berghofe@20376
  1632
                     fresh_prems) = chop (length finite_prems) prems;
berghofe@20376
  1633
                   val unique_prem' = unique_prem RS spec RS mp;
berghofe@20376
  1634
                   val unique = [unique_prem', unique_prem' RS sym] MRS trans;
berghofe@20376
  1635
                   val _ $ (_ $ (_ $ S $ _)) $ _ = prop_of supports_fresh;
berghofe@20376
  1636
                   val tuple = foldr1 HOLogic.mk_prod (x :: rec_fns)
berghofe@20376
  1637
                 in EVERY
berghofe@20376
  1638
                   [rtac (Drule.cterm_instantiate
berghofe@20376
  1639
                      [(cterm_of thy11 S,
berghofe@20376
  1640
                        cterm_of thy11 (Const ("Nominal.supp",
berghofe@20376
  1641
                          fastype_of tuple --> HOLogic.mk_setT aT) $ tuple))]
berghofe@20376
  1642
                      supports_fresh) 1,
berghofe@20376
  1643
                    simp_tac (HOL_basic_ss addsimps
berghofe@20376
  1644
                      [supports_def, symmetric fresh_def, fresh_prod]) 1,
berghofe@20376
  1645
                    REPEAT_DETERM (resolve_tac [allI, impI] 1),
berghofe@20376
  1646
                    REPEAT_DETERM (etac conjE 1),
berghofe@20376
  1647
                    rtac unique 1,
berghofe@20376
  1648
                    SUBPROOF (fn {prems = prems', params = [a, b], ...} => EVERY
berghofe@20376
  1649
                      [cut_facts_tac [rec_prem] 1,
berghofe@20376
  1650
                       rtac (Thm.instantiate ([],
berghofe@20376
  1651
                         [(cterm_of thy11 (Var (("pi", 0), mk_permT aT)),
berghofe@20376
  1652
                           cterm_of thy11 (perm_of_pair (term_of a, term_of b)))]) eqvt_th) 1,
berghofe@20376
  1653
                       asm_simp_tac (HOL_ss addsimps
berghofe@20376
  1654
                         (prems' @ perm_swap @ perm_fresh_fresh)) 1]) context 1,
berghofe@20376
  1655
                    rtac rec_prem 1,
berghofe@20376
  1656
                    simp_tac (HOL_ss addsimps (fs_name ::
berghofe@20376
  1657
                      supp_prod :: finite_Un :: finite_prems)) 1,
berghofe@20376
  1658
                    simp_tac (HOL_ss addsimps (symmetric fresh_def ::
berghofe@20376
  1659
                      fresh_prod :: fresh_prems)) 1]
berghofe@20376
  1660
                 end))
berghofe@20376
  1661
          end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~ eqvt_ths)
berghofe@20376
  1662
      end) (dt_atomTs ~~ rec_equiv_thms' ~~ finite_premss);
berghofe@20376
  1663
berghofe@20376
  1664
    (** uniqueness **)
berghofe@20376
  1665
urbanc@21377
  1666
    val exists_fresh' = PureThy.get_thms thy11 (Name "exists_fresh'");
berghofe@20376
  1667
    val fs_atoms = map (fn Type (s, _) => PureThy.get_thm thy11
berghofe@20376
  1668
      (Name ("fs_" ^ Sign.base_name s ^ "1"))) dt_atomTs;
berghofe@20376
  1669
    val fresh_atm = PureThy.get_thms thy11 (Name "fresh_atm");
berghofe@20376
  1670
    val calc_atm = PureThy.get_thms thy11 (Name "calc_atm");
berghofe@20376
  1671
    val fresh_left = PureThy.get_thms thy11 (Name "fresh_left");
berghofe@20145
  1672
berghofe@21088
  1673
    val fun_tuple = foldr1 HOLogic.mk_prod (rec_ctxt :: rec_fns);
berghofe@20145
  1674
    val fun_tupleT = fastype_of fun_tuple;
berghofe@20145
  1675
    val rec_unique_frees =
berghofe@20145
  1676
      DatatypeProp.indexify_names (replicate (length recTs) "x") ~~ recTs;
berghofe@20397
  1677
    val rec_unique_frees'' = map (fn (s, T) => (s ^ "'", T)) rec_unique_frees;
berghofe@20267
  1678
    val rec_unique_frees' =
berghofe@20267
  1679
      DatatypeProp.indexify_names (replicate (length recTs) "y") ~~ rec_result_Ts;
berghofe@21021
  1680
    val rec_unique_concls = map (fn ((x, U), R) =>
berghofe@20145
  1681
        Const ("Ex1", (U --> HOLogic.boolT) --> HOLogic.boolT) $
berghofe@21021
  1682
          Abs ("y", U, R $ Free x $ Bound 0))
berghofe@20145
  1683
      (rec_unique_frees ~~ rec_result_Ts ~~ rec_sets);
berghofe@20376
  1684
berghofe@20145
  1685
    val induct_aux_rec = Drule.cterm_instantiate
berghofe@20145
  1686
      (map (pairself (cterm_of thy11))
berghofe@20145
  1687
         (map (fn (aT, f) => (Logic.varify f, Abs ("z", HOLogic.unitT,
berghofe@20145
  1688
            Const ("Nominal.supp", fun_tupleT --> HOLogic.mk_setT aT) $ fun_tuple)))
berghofe@20145
  1689
              fresh_fs @
berghofe@20145
  1690
          map (fn (((P, T), (x, U)), Q) =>
berghofe@20145
  1691
           (Var ((P, 0), HOLogic.unitT --> Logic.varifyT T --> HOLogic.boolT),
berghofe@20145
  1692
            Abs ("z", HOLogic.unitT, absfree (x, U, Q))))
berghofe@20145
  1693
              (pnames ~~ recTs ~~ rec_unique_frees ~~ rec_unique_concls) @
berghofe@20145
  1694
          map (fn (s, T) => (Var ((s, 0), Logic.varifyT T), Free (s, T)))
berghofe@20145
  1695
            rec_unique_frees)) induct_aux;
berghofe@20145
  1696
berghofe@20376
  1697
    fun obtain_fresh_name vs ths rec_fin_supp T (freshs1, freshs2, ctxt) =
berghofe@20376
  1698
      let
berghofe@20376
  1699
        val p = foldr1 HOLogic.mk_prod (vs @ freshs1);
berghofe@20376
  1700
        val ex = Goal.prove ctxt [] [] (HOLogic.mk_Trueprop
berghofe@20376
  1701
            (HOLogic.exists_const T $ Abs ("x", T,
berghofe@20376
  1702
              Const ("Nominal.fresh", T --> fastype_of p --> HOLogic.boolT) $
berghofe@20376
  1703
                Bound 0 $ p)))
berghofe@20376
  1704
          (fn _ => EVERY
berghofe@20376
  1705
            [cut_facts_tac ths 1,
berghofe@20376
  1706
             REPEAT_DETERM (dresolve_tac (the (AList.lookup op = rec_fin_supp T)) 1),
urbanc@21377
  1707
             resolve_tac exists_fresh' 1,
berghofe@20376
  1708
             asm_simp_tac (HOL_ss addsimps (supp_prod :: finite_Un :: fs_atoms)) 1]);
berghofe@20376
  1709
        val (([cx], ths), ctxt') = Obtain.result
berghofe@20376
  1710
          (fn _ => EVERY
berghofe@20376
  1711
            [etac exE 1,
berghofe@20376
  1712
             full_simp_tac (HOL_ss addsimps (fresh_prod :: fresh_atm)) 1,
berghofe@20376
  1713
             REPEAT (etac conjE 1)])
berghofe@20376
  1714
          [ex] ctxt
berghofe@20376
  1715
      in (freshs1 @ [term_of cx], freshs2 @ ths, ctxt') end;
berghofe@20376
  1716
berghofe@21088
  1717
    val finite_ctxt_prems = map (fn aT =>
berghofe@22274
  1718
      HOLogic.mk_Trueprop
berghofe@22274
  1719
        (Const ("Finite_Set.finite", HOLogic.mk_setT aT --> HOLogic.boolT) $
berghofe@22274
  1720
           (Const ("Nominal.supp", fsT' --> HOLogic.mk_setT aT) $ rec_ctxt))) dt_atomTs;
berghofe@21088
  1721
berghofe@20397
  1722
    val rec_unique_thms = split_conj_thm (Goal.prove
wenzelm@21516
  1723
      (ProofContext.init thy11) (map fst rec_unique_frees)
berghofe@21088
  1724
      (List.concat finite_premss @ finite_ctxt_prems @ rec_prems @ rec_prems')
berghofe@20145
  1725
      (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj rec_unique_concls))
berghofe@20376
  1726
      (fn {prems, context} =>
berghofe@20267
  1727
         let
berghofe@20267
  1728
           val k = length rec_fns;
berghofe@20376
  1729
           val (finite_thss, ths1) = fold_map (fn T => fn xs =>
berghofe@20376
  1730
             apfst (pair T) (chop k xs)) dt_atomTs prems;
berghofe@21088
  1731
           val (finite_ctxt_ths, ths2) = chop (length dt_atomTs) ths1;
berghofe@21088
  1732
           val (P_ind_ths, fcbs) = chop k ths2;
berghofe@20267
  1733
           val P_ths = map (fn th => th RS mp) (split_conj_thm
berghofe@20376
  1734
             (Goal.prove context
berghofe@20397
  1735
               (map fst (rec_unique_frees'' @ rec_unique_frees')) []
berghofe@20267
  1736
               (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@21021
  1737
                  (map (fn (((x, y), S), P) => HOLogic.mk_imp
berghofe@21021
  1738
                    (S $ Free x $ Free y, P $ (Free y)))
berghofe@20397
  1739
                      (rec_unique_frees'' ~~ rec_unique_frees' ~~ rec_sets ~~ rec_preds))))
berghofe@20267
  1740
               (fn _ =>
berghofe@20267
  1741
                  rtac rec_induct 1 THEN
berghofe@20376
  1742
                  REPEAT ((resolve_tac P_ind_ths THEN_ALL_NEW assume_tac) 1))));
berghofe@20376
  1743
           val rec_fin_supp_thms' = map
berghofe@20376
  1744
             (fn (ths, (T, fin_ths)) => (T, map (curry op MRS fin_ths) ths))
berghofe@20376
  1745
             (rec_fin_supp_thms ~~ finite_thss);
berghofe@20267
  1746
         in EVERY
berghofe@20267
  1747
           ([rtac induct_aux_rec 1] @
berghofe@21088
  1748
            maps (fn ((_, finite_ths), finite_th) =>
berghofe@21088
  1749
              [cut_facts_tac (finite_th :: finite_ths) 1,
berghofe@21088
  1750
               asm_simp_tac (HOL_ss addsimps [supp_prod, finite_Un]) 1])
berghofe@21088
  1751
                (finite_thss ~~ finite_ctxt_ths) @
berghofe@20397
  1752
            maps (fn ((_, idxss), elim) => maps (fn idxs =>
berghofe@20397
  1753
              [full_simp_tac (HOL_ss addsimps [symmetric fresh_def, supp_prod, Un_iff]) 1,
berghofe@20397
  1754
               REPEAT_DETERM (eresolve_tac [conjE, ex1E] 1),
berghofe@20397
  1755
               rtac ex1I 1,
berghofe@20397
  1756
               (resolve_tac rec_intrs THEN_ALL_NEW atac) 1,
berghofe@20397
  1757
               rotate_tac ~1 1,
berghofe@20397
  1758
               ((DETERM o etac elim) THEN_ALL_NEW full_simp_tac
berghofe@21021
  1759
                  (HOL_ss addsimps List.concat distinct_thms)) 1] @
berghofe@21021
  1760
               (if null idxs then [] else [hyp_subst_tac 1,
berghofe@20397
  1761
                SUBPROOF (fn {asms, concl, prems = prems', params, context = context', ...} =>
berghofe@20376
  1762
                  let
berghofe@21021
  1763
                    val SOME prem = find_first (can (HOLogic.dest_eq o
berghofe@21021
  1764
                      HOLogic.dest_Trueprop o prop_of)) prems';
berghofe@20376
  1765
                    val _ $ (_ $ lhs $ rhs) = prop_of prem;
berghofe@20376
  1766
                    val _ $ (_ $ lhs' $ rhs') = term_of concl;
berghofe@20376
  1767
                    val rT = fastype_of lhs';
berghofe@20376
  1768
                    val (c, cargsl) = strip_comb lhs;
berghofe@20376
  1769
                    val cargsl' = partition_cargs idxs cargsl;
berghofe@20376
  1770
                    val boundsl = List.concat (map fst cargsl');
berghofe@20376
  1771
                    val (_, cargsr) = strip_comb rhs;
berghofe@20376
  1772
                    val cargsr' = partition_cargs idxs cargsr;
berghofe@20376
  1773
                    val boundsr = List.concat (map fst cargsr');
berghofe@20376
  1774
                    val (params1, _ :: params2) =
berghofe@20376
  1775
                      chop (length params div 2) (map term_of params);
berghofe@20376
  1776
                    val params' = params1 @ params2;
berghofe@20376
  1777
                    val rec_prems = filter (fn th => case prop_of th of
berghofe@21021
  1778
                      _ $ (S $ _ $ _) => S mem rec_sets | _ => false) prems';
berghofe@20376
  1779
                    val fresh_prems = filter (fn th => case prop_of th of
berghofe@20376
  1780
                        _ $ (Const ("Nominal.fresh", _) $ _ $ _) => true
berghofe@20376
  1781
                      | _ $ (Const ("Not", _) $ _) => true
berghofe@20376
  1782
                      | _ => false) prems';
berghofe@20376
  1783
                    val Ts = map fastype_of boundsl;
berghofe@20376
  1784
berghofe@20376
  1785
                    val _ = warning "step 1: obtaining fresh names";
berghofe@20376
  1786
                    val (freshs1, freshs2, context'') = fold
berghofe@21088
  1787
                      (obtain_fresh_name (rec_ctxt :: rec_fns @ params')
berghofe@21088
  1788
                         (List.concat (map snd finite_thss) @
berghofe@21088
  1789
                            finite_ctxt_ths @ rec_prems)
berghofe@20376
  1790
                         rec_fin_supp_thms')
berghofe@20376
  1791
                      Ts ([], [], context');
berghofe@20376
  1792
                    val pi1 = map perm_of_pair (boundsl ~~ freshs1);
berghofe@20376
  1793
                    val rpi1 = rev pi1;
berghofe@20376
  1794
                    val pi2 = map perm_of_pair (boundsr ~~ freshs1);
berghofe@21073
  1795
                    val rpi2 = rev pi2;
berghofe@20376
  1796
berghofe@20376
  1797
                    fun mk_not_sym ths = List.concat (map (fn th =>
berghofe@20376
  1798
                      case prop_of th of
berghofe@20376
  1799
                          _ $ (Const ("Not", _) $ _) => [th, th RS not_sym]
berghofe@20376
  1800
                        | _ => [th]) ths);
berghofe@20376
  1801
                    val fresh_prems' = mk_not_sym fresh_prems;
berghofe@20376
  1802
                    val freshs2' = mk_not_sym freshs2;
berghofe@20376
  1803
berghofe@20376
  1804
                    (** as, bs, cs # K as ts, K bs us **)
berghofe@20376
  1805
                    val _ = warning "step 2: as, bs, cs # K as ts, K bs us";
berghofe@20376
  1806
                    val prove_fresh_ss = HOL_ss addsimps
berghofe@20376
  1807
                      (finite_Diff :: List.concat fresh_thms @
berghofe@20376
  1808
                       fs_atoms @ abs_fresh @ abs_supp @ fresh_atm);
berghofe@20376
  1809
                    (* FIXME: avoid asm_full_simp_tac ? *)
berghofe@20376
  1810
                    fun prove_fresh ths y x = Goal.prove context'' [] []
berghofe@20376
  1811
                      (HOLogic.mk_Trueprop (Const ("Nominal.fresh",
berghofe@20376
  1812
                         fastype_of x --> fastype_of y --> HOLogic.boolT) $ x $ y))
berghofe@20376
  1813
                      (fn _ => cut_facts_tac ths 1 THEN asm_full_simp_tac prove_fresh_ss 1);
berghofe@20376
  1814
                    val constr_fresh_thms =
berghofe@20376
  1815
                      map (prove_fresh fresh_prems lhs) boundsl @
berghofe@20376
  1816
                      map (prove_fresh fresh_prems rhs) boundsr @
berghofe@20376
  1817
                      map (prove_fresh freshs2 lhs) freshs1 @
berghofe@20376
  1818
                      map (prove_fresh freshs2 rhs) freshs1;
berghofe@20376
  1819
berghofe@20376
  1820
                    (** pi1 o (K as ts) = pi2 o (K bs us) **)
berghofe@20376
  1821
                    val _ = warning "step 3: pi1 o (K as ts) = pi2 o (K bs us)";
berghofe@20376
  1822
                    val pi1_pi2_eq = Goal.prove context'' [] []
berghofe@20376
  1823
                      (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@20376
  1824
                        (foldr (mk_perm []) lhs pi1, foldr (mk_perm []) rhs pi2)))
berghofe@20376
  1825
                      (fn _ => EVERY
berghofe@20376
  1826
                         [cut_facts_tac constr_fresh_thms 1,
berghofe@20376
  1827
                          asm_simp_tac (HOL_basic_ss addsimps perm_fresh_fresh) 1,
berghofe@20376
  1828
                          rtac prem 1]);
berghofe@20376
  1829
berghofe@20376
  1830
                    (** pi1 o ts = pi2 o us **)
berghofe@20376
  1831
                    val _ = warning "step 4: pi1 o ts = pi2 o us";
berghofe@20376
  1832
                    val pi1_pi2_eqs = map (fn (t, u) =>
berghofe@20376
  1833
                      Goal.prove context'' [] []
berghofe@20376
  1834
                        (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@20376
  1835
                          (foldr (mk_perm []) t pi1, foldr (mk_perm []) u pi2)))
berghofe@20376
  1836
                        (fn _ => EVERY
berghofe@20376
  1837
                           [cut_facts_tac [pi1_pi2_eq] 1,
berghofe@20376
  1838
                            asm_full_simp_tac (HOL_ss addsimps
berghofe@20376
  1839
                              (calc_atm @ List.concat perm_simps' @
berghofe@20376
  1840
                               fresh_prems' @ freshs2' @ abs_perm @
berghofe@20376
  1841
                               alpha @ List.concat inject_thms)) 1]))
berghofe@20376
  1842
                        (map snd cargsl' ~~ map snd cargsr');
berghofe@20376
  1843
berghofe@20376
  1844
                    (** pi1^-1 o pi2 o us = ts **)
berghofe@20376
  1845
                    val _ = warning "step 5: pi1^-1 o pi2 o us = ts";
berghofe@20376
  1846
                    val rpi1_pi2_eqs = map (fn ((t, u), eq) =>
berghofe@20376
  1847
                      Goal.prove context'' [] []
berghofe@20376
  1848
                        (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@20376
  1849
                          (foldr (mk_perm []) u (rpi1 @ pi2), t)))
berghofe@20376
  1850
                        (fn _ => simp_tac (HOL_ss addsimps
berghofe@20376
  1851
                           ((eq RS sym) :: perm_swap)) 1))
berghofe@20376
  1852
                        (map snd cargsl' ~~ map snd cargsr' ~~ pi1_pi2_eqs);
berghofe@20376
  1853
berghofe@20376
  1854
                    val (rec_prems1, rec_prems2) =
berghofe@20376
  1855
                      chop (length rec_prems div 2) rec_prems;
berghofe@20376
  1856
berghofe@20376
  1857
                    (** (ts, pi1^-1 o pi2 o vs) in rec_set **)
berghofe@20376
  1858
                    val _ = warning "step 6: (ts, pi1^-1 o pi2 o vs) in rec_set";
berghofe@20376
  1859
                    val rec_prems' = map (fn th =>
berghofe@20376
  1860
                      let
berghofe@21021
  1861
                        val _ $ (S $ x $ y) = prop_of th;
berghofe@20376
  1862
                        val k = find_index (equal S) rec_sets;
berghofe@20376
  1863
                        val pi = rpi1 @ pi2;
berghofe@20376
  1864
                        fun mk_pi z = foldr (mk_perm []) z pi;
berghofe@20376
  1865
                        fun eqvt_tac p =
berghofe@20376
  1866
                          let
berghofe@20376
  1867
                            val U as Type (_, [Type (_, [T, _])]) = fastype_of p;
berghofe@20376
  1868
                            val l = find_index (equal T) dt_atomTs;
berghofe@20376
  1869
                            val th = List.nth (List.nth (rec_equiv_thms', l), k);
berghofe@20376
  1870
                            val th' = Thm.instantiate ([],
berghofe@20376
  1871
                              [(cterm_of thy11 (Var (("pi", 0), U)),
berghofe@20376
  1872
                                cterm_of thy11 p)]) th;
berghofe@20376
  1873
                          in rtac th' 1 end;
berghofe@20376
  1874
                        val th' = Goal.prove context'' [] []
berghofe@21021
  1875
                          (HOLogic.mk_Trueprop (S $ mk_pi x $ mk_pi y))
berghofe@20376
  1876
                          (fn _ => EVERY
berghofe@20376
  1877
                             (map eqvt_tac pi @
berghofe@20376
  1878
                              [simp_tac (HOL_ss addsimps (fresh_prems' @ freshs2' @
berghofe@20376
  1879
                                 perm_swap @ perm_fresh_fresh)) 1,
berghofe@20376
  1880
                               rtac th 1]))
berghofe@20376
  1881
                      in
berghofe@20376
  1882
                        Simplifier.simplify
berghofe@20376
  1883
                          (HOL_basic_ss addsimps rpi1_pi2_eqs) th'
berghofe@20376
  1884
                      end) rec_prems2;
berghofe@20376
  1885
berghofe@20376
  1886
                    val ihs = filter (fn th => case prop_of th of
berghofe@20376
  1887
                      _ $ (Const ("All", _) $ _) => true | _ => false) prems';
berghofe@20376
  1888
berghofe@21073
  1889
                    (** pi1 o rs = pi2 o vs , rs = pi1^-1 o pi2 o vs **)
berghofe@21073
  1890
                    val _ = warning "step 7: pi1 o rs = pi2 o vs , rs = pi1^-1 o pi2 o vs";
berghofe@21073
  1891
                    val rec_eqns = map (fn (th, ih) =>
berghofe@20376
  1892
                      let
berghofe@20376
  1893
                        val th' = th RS (ih RS spec RS mp) RS sym;
berghofe@20376
  1894
                        val _ $ (_ $ lhs $ rhs) = prop_of th';
berghofe@20376
  1895
                        fun strip_perm (_ $ _ $ t) = strip_perm t
berghofe@20376
  1896
                          | strip_perm t = t;
berghofe@20376
  1897
                      in
berghofe@21073
  1898
                        Goal.prove context'' [] []
berghofe@20376
  1899
                           (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@20376
  1900
                              (foldr (mk_perm []) lhs pi1,
berghofe@20376
  1901
                               foldr (mk_perm []) (strip_perm rhs) pi2)))
berghofe@20376
  1902
                           (fn _ => simp_tac (HOL_basic_ss addsimps
berghofe@21073
  1903
                              (th' :: perm_swap)) 1)
berghofe@21073
  1904
                      end) (rec_prems' ~~ ihs);
berghofe@20376
  1905
berghofe@21073
  1906
                    (** as # rs **)
berghofe@21073
  1907
                    val _ = warning "step 8: as # rs";
berghofe@21073
  1908
                    val rec_freshs = List.concat
berghofe@21073
  1909
                      (map (fn (rec_prem, ih) =>
berghofe@20376
  1910
                        let
berghofe@21021
  1911
                          val _ $ (S $ x $ (y as Free (_, T))) =
berghofe@20376
  1912
                            prop_of rec_prem;
berghofe@20376
  1913
                          val k = find_index (equal S) rec_sets;
berghofe@21073
  1914
                          val atoms = List.concat (List.mapPartial (fn (bs, z) =>
berghofe@21073
  1915
                            if z = x then NONE else SOME bs) cargsl')
berghofe@20376
  1916
                        in
berghofe@21073
  1917
                          map (fn a as Free (_, aT) =>
berghofe@21073
  1918
                            let val l = find_index (equal aT) dt_atomTs;
berghofe@21073
  1919
                            in
berghofe@21073
  1920
                              Goal.prove context'' [] []
berghofe@20376
  1921
                                (HOLogic.mk_Trueprop (Const ("Nominal.fresh",
berghofe@20376
  1922
                                  aT --> T --> HOLogic.boolT) $ a $ y))
berghofe@20376
  1923
                                (fn _ => EVERY
berghofe@20376
  1924
                                   (rtac (List.nth (List.nth (rec_fresh_thms, l), k)) 1 ::
berghofe@20376
  1925
                                    map (fn th => rtac th 1)
berghofe@20376
  1926
                                      (snd (List.nth (finite_thss, l))) @
berghofe@20376
  1927
                                    [rtac rec_prem 1, rtac ih 1,
berghofe@21073
  1928
                                     REPEAT_DETERM (resolve_tac fresh_prems 1)]))
berghofe@21073
  1929
                            end) atoms
berghofe@21073
  1930
                        end) (rec_prems1 ~~ ihs));
berghofe@20376
  1931
berghofe@20376
  1932
                    (** as # fK as ts rs , bs # fK bs us vs **)
berghofe@20376
  1933
                    val _ = warning "step 9: as # fK as ts rs , bs # fK bs us vs";
berghofe@21073
  1934
                    fun prove_fresh_result (a as Free (_, aT)) =
berghofe@20376
  1935
                      Goal.prove context'' [] []
berghofe@20376
  1936
                        (HOLogic.mk_Trueprop (Const ("Nominal.fresh",
berghofe@21073
  1937
                          aT --> rT --> HOLogic.boolT) $ a $ rhs'))
berghofe@20376
  1938
                        (fn _ => EVERY
berghofe@20376
  1939
                           [resolve_tac fcbs 1,
berghofe@20376
  1940
                            REPEAT_DETERM (resolve_tac
berghofe@21073
  1941
                              (fresh_prems @ rec_freshs) 1),
berghofe@20411
  1942
                            REPEAT_DETERM (resolve_tac (maps snd rec_fin_supp_thms') 1
berghofe@20411
  1943
                              THEN resolve_tac rec_prems 1),
berghofe@20376
  1944
                            resolve_tac P_ind_ths 1,
berghofe@20376
  1945
                            REPEAT_DETERM (resolve_tac (P_ths @ rec_prems) 1)]);
wenzelm@21365
  1946
berghofe@21073
  1947
                    val fresh_results'' = map prove_fresh_result boundsl;
berghofe@21073
  1948
berghofe@21073
  1949
                    fun prove_fresh_result'' ((a as Free (_, aT), b), th) =
berghofe@21073
  1950
                      let val th' = Goal.prove context'' [] []
berghofe@21073
  1951
                        (HOLogic.mk_Trueprop (Const ("Nominal.fresh",
berghofe@21073
  1952
                          aT --> rT --> HOLogic.boolT) $
berghofe@21073
  1953
                            foldr (mk_perm []) a (rpi2 @ pi1) $
berghofe@21073
  1954
                            foldr (mk_perm []) rhs' (rpi2 @ pi1)))
berghofe@21073
  1955
                        (fn _ => simp_tac (HOL_ss addsimps fresh_bij) 1 THEN
berghofe@21073
  1956
                           rtac th 1)
berghofe@21073
  1957
                      in
berghofe@21073
  1958
                        Goal.prove context'' [] []
berghofe@21073
  1959
                          (HOLogic.mk_Trueprop (Const ("Nominal.fresh",
berghofe@21073
  1960
                            aT --> rT --> HOLogic.boolT) $ b $ lhs'))
berghofe@21073
  1961
                          (fn _ => EVERY
berghofe@21073
  1962
                             [cut_facts_tac [th'] 1,
berghofe@21073
  1963
                              NominalPermeq.perm_simp_tac (HOL_ss addsimps
berghofe@21073
  1964
                                (rec_eqns @ pi1_pi2_eqs @ perm_swap)) 1,
berghofe@21073
  1965
                              full_simp_tac (HOL_ss addsimps (calc_atm @
berghofe@21073
  1966
                                fresh_prems' @ freshs2' @ perm_fresh_fresh)) 1])
berghofe@21073
  1967
                      end;
berghofe@21073
  1968
berghofe@21073
  1969
                    val fresh_results = fresh_results'' @ map prove_fresh_result''
berghofe@21073
  1970
                      (boundsl ~~ boundsr ~~ fresh_results'');
berghofe@20376
  1971
berghofe@20376
  1972
                    (** cs # fK as ts rs , cs # fK bs us vs **)
berghofe@20376
  1973
                    val _ = warning "step 10: cs # fK as ts rs , cs # fK bs us vs";
berghofe@20376
  1974
                    fun prove_fresh_result' recs t (a as Free (_, aT)) =
berghofe@20376
  1975
                      Goal.prove context'' [] []
berghofe@20376
  1976
                        (HOLogic.mk_Trueprop (Const ("Nominal.fresh",
berghofe@20376
  1977
                          aT --> rT --> HOLogic.boolT) $ a $ t))
berghofe@20376
  1978
                        (fn _ => EVERY
berghofe@20376
  1979
                          [cut_facts_tac recs 1,
berghofe@20376
  1980
                           REPEAT_DETERM (dresolve_tac
berghofe@20376
  1981
                             (the (AList.lookup op = rec_fin_supp_thms' aT)) 1),
berghofe@20376
  1982
                           NominalPermeq.fresh_guess_tac
berghofe@20376
  1983
                             (HOL_ss addsimps (freshs2 @
berghofe@20376
  1984
                                fs_atoms @ fresh_atm @
berghofe@20376
  1985
                                List.concat (map snd finite_thss))) 1]);
berghofe@20376
  1986
berghofe@20376
  1987
                    val fresh_results' =
berghofe@20376
  1988
                      map (prove_fresh_result' rec_prems1 rhs') freshs1 @
berghofe@20376
  1989
                      map (prove_fresh_result' rec_prems2 lhs') freshs1;
berghofe@20376
  1990
berghofe@20376
  1991
                    (** pi1 o (fK as ts rs) = pi2 o (fK bs us vs) **)
berghofe@20376
  1992
                    val _ = warning "step 11: pi1 o (fK as ts rs) = pi2 o (fK bs us vs)";
berghofe@20376
  1993
                    val pi1_pi2_result = Goal.prove context'' [] []
berghofe@20376
  1994
                      (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@20376
  1995
                        (foldr (mk_perm []) rhs' pi1, foldr (mk_perm []) lhs' pi2)))
berghofe@20376
  1996
                      (fn _ => NominalPermeq.perm_simp_tac (HOL_ss addsimps
berghofe@21073
  1997
                           pi1_pi2_eqs @ rec_eqns) 1 THEN
berghofe@20376
  1998
                         TRY (simp_tac (HOL_ss addsimps
berghofe@20376
  1999
                           (fresh_prems' @ freshs2' @ calc_atm @ perm_fresh_fresh)) 1));
berghofe@20376
  2000
berghofe@20376
  2001
                    val _ = warning "final result";
berghofe@20376
  2002
                    val final = Goal.prove context'' [] [] (term_of concl)
berghofe@20376
  2003
                      (fn _ => cut_facts_tac [pi1_pi2_result RS sym] 1 THEN
berghofe@20376
  2004
                        full_simp_tac (HOL_basic_ss addsimps perm_fresh_fresh @
berghofe@20376
  2005
                          fresh_results @ fresh_results') 1);
berghofe@20376
  2006
                    val final' = ProofContext.export context'' context' [final];
berghofe@20376
  2007
                    val _ = warning "finished!"
berghofe@20376
  2008
                  in
berghofe@20376
  2009
                    resolve_tac final' 1
berghofe@20397
  2010
                  end) context 1])) idxss) (ndescr ~~ rec_elims))
berghofe@20397
  2011
         end));
berghofe@20397
  2012
berghofe@20397
  2013
    val rec_total_thms = map (fn r => r RS theI') rec_unique_thms;
berghofe@20397
  2014
berghofe@20397
  2015
    (* define primrec combinators *)
berghofe@20397
  2016
berghofe@20397
  2017
    val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
berghofe@20397
  2018
    val reccomb_names = map (Sign.full_name thy11)
berghofe@20397
  2019
      (if length descr'' = 1 then [big_reccomb_name] else
berghofe@20397
  2020
        (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
berghofe@20397
  2021
          (1 upto (length descr''))));
berghofe@20397
  2022
    val reccombs = map (fn ((name, T), T') => list_comb
berghofe@20397
  2023
      (Const (name, rec_fn_Ts @ [T] ---> T'), rec_fns))
berghofe@20397
  2024
        (reccomb_names ~~ recTs ~~ rec_result_Ts);
berghofe@20397
  2025
berghofe@20397
  2026
    val (reccomb_defs, thy12) =
berghofe@20397
  2027
      thy11
berghofe@20397
  2028
      |> Theory.add_consts_i (map (fn ((name, T), T') =>
berghofe@20397
  2029
          (Sign.base_name name, rec_fn_Ts @ [T] ---> T', NoSyn))
berghofe@20397
  2030
          (reccomb_names ~~ recTs ~~ rec_result_Ts))
berghofe@20397
  2031
      |> (PureThy.add_defs_i false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') =>
berghofe@20397
  2032
          ((Sign.base_name name) ^ "_def", Logic.mk_equals (comb, absfree ("x", T,
berghofe@20397
  2033
           Const ("The", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T',
berghofe@21021
  2034
             set $ Free ("x", T) $ Free ("y", T'))))))
berghofe@20397
  2035
               (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts));
berghofe@20397
  2036
berghofe@20397
  2037
    (* prove characteristic equations for primrec combinators *)
berghofe@20397
  2038
berghofe@20397
  2039
    val rec_thms = map (fn (prems, concl) =>
berghofe@20397
  2040
      let
berghofe@20397
  2041
        val _ $ (_ $ (_ $ x) $ _) = concl;
berghofe@20397
  2042
        val (_, cargs) = strip_comb x;
berghofe@20397
  2043
        val ps = map (fn (x as Free (_, T), i) =>
berghofe@20397
  2044
          (Free ("x" ^ string_of_int i, T), x)) (cargs ~~ (1 upto length cargs));
berghofe@20397
  2045
        val concl' = subst_atomic_types (rec_result_Ts' ~~ rec_result_Ts) concl;
berghofe@21088
  2046
        val prems' = List.concat finite_premss @ finite_ctxt_prems @
berghofe@21088
  2047
          rec_prems @ rec_prems' @ map (subst_atomic ps) prems;
berghofe@20397
  2048
        fun solve rules prems = resolve_tac rules THEN_ALL_NEW
berghofe@20397
  2049
          (resolve_tac prems THEN_ALL_NEW atac)
berghofe@20397
  2050
      in
berghofe@20397
  2051
        Goal.prove_global thy12 [] prems' concl'
berghofe@20397
  2052
          (fn prems => EVERY
berghofe@20397
  2053
            [rewrite_goals_tac reccomb_defs,
berghofe@20397
  2054
             rtac the1_equality 1,
berghofe@20397
  2055
             solve rec_unique_thms prems 1,
berghofe@20397
  2056
             resolve_tac rec_intrs 1,
berghofe@20397
  2057
             REPEAT (solve (prems @ rec_total_thms) prems 1)])
berghofe@20397
  2058
      end) (rec_eq_prems ~~
berghofe@20397
  2059
        DatatypeProp.make_primrecs new_type_names descr' sorts' thy12);
wenzelm@21365
  2060
berghofe@21540
  2061
    val dt_infos = map (make_dt_info descr'' sorts induct reccomb_names rec_thms)
berghofe@21540
  2062
      ((0 upto length descr1 - 1) ~~ descr1 ~~ distinct_thms ~~ inject_thms);
berghofe@21540
  2063
berghofe@19985
  2064
    (* FIXME: theorems are stored in database for testing only *)
berghofe@20397
  2065
    val (_, thy13) = thy12 |>
berghofe@20145
  2066
      PureThy.add_thmss
berghofe@20145
  2067
        [(("rec_equiv", List.concat rec_equiv_thms), []),
berghofe@20145
  2068
         (("rec_equiv'", List.concat rec_equiv_thms'), []),
berghofe@20145
  2069
         (("rec_fin_supp", List.concat rec_fin_supp_thms), []),
berghofe@20376
  2070
         (("rec_fresh", List.concat rec_fresh_thms), []),
berghofe@20397
  2071
         (("rec_unique", map standard rec_unique_thms), []),
berghofe@20397
  2072
         (("recs", rec_thms), [])] ||>
berghofe@21540
  2073
      Theory.parent_path ||>
berghofe@21540
  2074
      map_nominal_datatypes (fold Symtab.update dt_infos);
berghofe@19985
  2075
berghofe@17870
  2076
  in
berghofe@20397
  2077
    thy13
berghofe@17870
  2078
  end;
berghofe@17870
  2079
berghofe@17870
  2080
val add_nominal_datatype = gen_add_nominal_datatype read_typ true;
berghofe@17870
  2081
berghofe@17870
  2082
berghofe@17870
  2083
(* FIXME: The following stuff should be exported by DatatypePackage *)
berghofe@17870
  2084
berghofe@17870
  2085
local structure P = OuterParse and K = OuterKeyword in
berghofe@17870
  2086
berghofe@17870
  2087
val datatype_decl =
berghofe@17870
  2088
  Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --
berghofe@17870
  2089
    (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix));
berghofe@17870
  2090
berghofe@17870
  2091
fun mk_datatype args =
berghofe@17870
  2092
  let
berghofe@17870
  2093
    val names = map (fn ((((NONE, _), t), _), _) => t | ((((SOME t, _), _), _), _) => t) args;
berghofe@17870
  2094
    val specs = map (fn ((((_, vs), t), mx), cons) =>
berghofe@17870
  2095
      (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;
berghofe@18068
  2096
  in add_nominal_datatype false names specs end;
berghofe@17870
  2097
berghofe@17870
  2098
val nominal_datatypeP =
berghofe@17870
  2099
  OuterSyntax.command "nominal_datatype" "define inductive datatypes" K.thy_decl
berghofe@17870
  2100
    (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));
berghofe@17870
  2101
berghofe@17870
  2102
val _ = OuterSyntax.add_parsers [nominal_datatypeP];
berghofe@17870
  2103
berghofe@17870
  2104
end;
berghofe@17870
  2105
berghofe@18261
  2106
end