src/HOL/Nominal/nominal_datatype.ML
author wenzelm
Fri Oct 12 21:22:35 2012 +0200 (2012-10-12)
changeset 49835 31f32ec4d766
parent 49833 1d80798e8d8a
child 51122 386a117925db
permissions -rw-r--r--
discontinued typedef with alternative name;
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(*  Title:      HOL/Nominal/nominal_datatype.ML
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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_DATATYPE =
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sig
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  val nominal_datatype : Datatype.config -> Datatype.spec list -> theory -> theory
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  val nominal_datatype_cmd : Datatype.config -> Datatype.spec_cmd list -> theory -> theory
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  type descr
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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 mk_perm: typ list -> term -> term -> term
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  val perm_of_pair: term * term -> term
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  val mk_not_sym: thm list -> thm list
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  val perm_simproc: simproc
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  val fresh_const: typ -> typ -> term
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  val fresh_star_const: typ -> typ -> term
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end
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structure NominalDatatype : NOMINAL_DATATYPE =
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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 Collect_False_empty = @{thm empty_def [THEN sym, THEN eq_reflection]};
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val empty_iff = @{thm empty_iff};
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open NominalAtoms;
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(* theory data *)
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type descr =
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  (int * (string * Datatype.dtyp list *
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      (string * (Datatype.dtyp list * Datatype.dtyp) list) list)) list;
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type nominal_datatype_info =
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  {index : int,
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   descr : descr,
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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 = Theory_Data
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(
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  type T = nominal_datatype_info Symtab.table;
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  val empty = Symtab.empty;
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  val extend = I;
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  fun merge data = Symtab.merge (K true) data;
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);
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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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(**** make datatype info ****)
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fun make_dt_info descr 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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    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 Datatype.distinct_lemma);
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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 (@{type_name Product_Type.prod}, [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 member (op =) (permTs_of u) aT andalso aT <> bT then
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          let
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            val cp = cp_inst_of thy a b;
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            val dj = dj_thm_of thy 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_global @{theory} "perm_simp" ["pi1 \<bullet> (pi2 \<bullet> x)"] perm_simproc';
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fun projections rule =
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  Project_Rule.projections (Proof_Context.init_global (Thm.theory_of_thm rule)) rule
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  |> map (Drule.export_without_context #> Rule_Cases.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 = Simpdata.mk_eq @{thm Nominal.supports_def};
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val fresh_def = Simpdata.mk_eq @{thm fresh_def};
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val supp_def = Simpdata.mk_eq @{thm supp_def};
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val rev_simps = @{thms rev.simps};
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val app_simps = @{thms append.simps};
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val at_fin_set_supp = @{thm at_fin_set_supp};
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val at_fin_set_fresh = @{thm at_fin_set_fresh};
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val abs_fun_eq1 = @{thm abs_fun_eq1};
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val collect_simp = rewrite_rule [mk_meta_eq mem_Collect_eq];
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fun mk_perm Ts t u =
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  let
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    val T = fastype_of1 (Ts, t);
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    val U = fastype_of1 (Ts, u)
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  in Const ("Nominal.perm", T --> U --> U) $ t $ u end;
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fun perm_of_pair (x, y) =
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  let
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    val T = fastype_of x;
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    val pT = mk_permT T
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  in Const ("List.list.Cons", HOLogic.mk_prodT (T, T) --> pT --> pT) $
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    HOLogic.mk_prod (x, y) $ Const ("List.list.Nil", pT)
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  end;
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fun mk_not_sym ths = maps (fn th => case prop_of th of
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    _ $ (Const (@{const_name Not}, _) $ (Const (@{const_name HOL.eq}, _) $ _ $ _)) => [th, th RS not_sym]
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  | _ => [th]) ths;
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fun fresh_const T U = Const ("Nominal.fresh", T --> U --> HOLogic.boolT);
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fun fresh_star_const T U =
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  Const ("Nominal.fresh_star", HOLogic.mk_setT T --> U --> HOLogic.boolT);
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fun gen_nominal_datatype prep_specs config dts thy =
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  let
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    val new_type_names = map (fn ((tname, _, _), _) => Binding.name_of tname) dts;
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    val (dts', _) = prep_specs dts thy;
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    val atoms = atoms_of thy;
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    val tyvars = map (fn ((_, tvs, _), _) => tvs) dts';
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    val sorts = flat tyvars;
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    fun inter_sort thy S S' = Sign.inter_sort thy (S, S');
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    fun augment_sort_typ thy S =
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      let val S = Sign.minimize_sort thy (Sign.certify_sort thy S)
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      in map_type_tfree (fn (s, S') => TFree (s,
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        if member (op = o apsnd fst) sorts s then inter_sort thy S S' else S'))
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      end;
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    fun augment_sort thy S = map_types (augment_sort_typ thy S);
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    val types_syntax = map (fn ((tname, tvs, mx), constrs) => (tname, mx)) dts';
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    val constr_syntax = map (fn (_, 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 thy n, Sign.full_name thy (Binding.suffix_name "_Rep" n))) 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 (the_default s (AList.lookup op = ps s), map replace_types Ts)
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      | replace_types T = T;
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    val dts'' = map (fn ((tname, tvs, mx), constrs) =>
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      ((Binding.suffix_name "_Rep" tname, tvs, NoSyn),
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        map (fn (cname, cargs, mx) => (Binding.suffix_name "_Rep" cname,
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          map 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',thy1) = Datatype.add_datatype config dts'' thy;
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    val {descr, induct, ...} = Datatype.the_info thy1 (hd full_new_type_names');
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    fun nth_dtyp i = Datatype_Aux.typ_of_dtyp descr (Datatype.DtRec i);
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    val big_name = space_implode "_" new_type_names;
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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' = Datatype_Prop.indexify_names (map (fn (i, _) =>
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      "perm_" ^ Datatype_Aux.name_of_typ (nth_dtyp i)) descr);
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    val perm_names = replicate (length new_type_names) "Nominal.perm" @
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      map (Sign.full_bname thy1) (List.drop (perm_names', length new_type_names));
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    val perm_names_types = perm_names ~~ perm_types;
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    val perm_names_types' = perm_names' ~~ perm_types;
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    val perm_eqs = maps (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 (Datatype_Aux.typ_of_dtyp descr) dts;
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          val names = Name.variant_list ["pi"] (Datatype_Prop.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 Datatype_Aux.is_rec_type dt then
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                let val Us = binder_types T
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                in
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                  fold_rev (Term.abs o pair "x") Us
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                    (Free (nth perm_names_types' (Datatype_Aux.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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          (Attrib.empty_binding, HOLogic.mk_Trueprop (HOLogic.mk_eq
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            (Free (nth perm_names_types' i) $
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               Free ("pi", mk_permT (TFree ("'x", HOLogic.typeS))) $
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               list_comb (c, args),
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             list_comb (c, map perm_arg (dts ~~ args)))))
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        end) constrs
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      end) descr;
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    val (perm_simps, thy2) =
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      Primrec.add_primrec_overloaded
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        (map (fn (s, sT) => (s, sT, false))
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           (List.take (perm_names' ~~ perm_names_types, length new_type_names)))
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        (map (fn s => (Binding.name s, NONE, NoSyn)) perm_names') perm_eqs thy1;
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    (**** prove that permutation functions introduced by unfolding are ****)
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    (**** equivalent to already existing permutation functions         ****)
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    val _ = warning ("length descr: " ^ string_of_int (length descr));
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    val _ = warning ("length new_type_names: " ^ string_of_int (length new_type_names));
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    val perm_indnames = Datatype_Prop.make_tnames (map body_type perm_types);
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    val perm_fun_def = Simpdata.mk_eq @{thm perm_fun_def};
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    val unfolded_perm_eq_thms =
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      if length descr = length new_type_names then []
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      else map Drule.export_without_context (List.drop (Datatype_Aux.split_conj_thm
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        (Goal.prove_global thy2 [] []
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          (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
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            (map (fn (c as (s, T), x) =>
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               let val [T1, T2] = binder_types T
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               in HOLogic.mk_eq (Const c $ pi $ Free (x, T2),
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                 Const ("Nominal.perm", T) $ pi $ Free (x, T2))
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               end)
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             (perm_names_types ~~ perm_indnames))))
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          (fn _ => EVERY [Datatype_Aux.ind_tac induct perm_indnames 1,
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            ALLGOALS (asm_full_simp_tac
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              (global_simpset_of thy2 addsimps [perm_fun_def]))])),
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        length new_type_names));
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    (**** prove [] \<bullet> t = t ****)
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    val _ = warning "perm_empty_thms";
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    val perm_empty_thms = maps (fn a =>
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      let val permT = mk_permT (Type (a, []))
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      in map Drule.export_without_context (List.take (Datatype_Aux.split_conj_thm
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        (Goal.prove_global thy2 [] []
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          (augment_sort thy2 [pt_class_of thy2 a]
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            (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
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              (map (fn ((s, T), x) => HOLogic.mk_eq
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                  (Const (s, permT --> T --> T) $
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                     Const ("List.list.Nil", permT) $ Free (x, T),
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                   Free (x, T)))
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               (perm_names ~~
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                map body_type perm_types ~~ perm_indnames)))))
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          (fn _ => EVERY [Datatype_Aux.ind_tac induct perm_indnames 1,
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            ALLGOALS (asm_full_simp_tac (global_simpset_of thy2))])),
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        length new_type_names))
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      end)
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      atoms;
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    (**** prove (pi1 @ pi2) \<bullet> t = pi1 \<bullet> (pi2 \<bullet> t) ****)
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    val _ = warning "perm_append_thms";
berghofe@17870
   309
berghofe@17870
   310
    (*FIXME: these should be looked up statically*)
wenzelm@39557
   311
    val at_pt_inst = Global_Theory.get_thm thy2 "at_pt_inst";
wenzelm@39557
   312
    val pt2 = Global_Theory.get_thm thy2 "pt2";
berghofe@17870
   313
wenzelm@32952
   314
    val perm_append_thms = maps (fn a =>
berghofe@17870
   315
      let
berghofe@17870
   316
        val permT = mk_permT (Type (a, []));
berghofe@17870
   317
        val pi1 = Free ("pi1", permT);
berghofe@17870
   318
        val pi2 = Free ("pi2", permT);
berghofe@28731
   319
        val pt_inst = pt_inst_of thy2 a;
berghofe@17870
   320
        val pt2' = pt_inst RS pt2;
wenzelm@39557
   321
        val pt2_ax = Global_Theory.get_thm thy2 (Long_Name.map_base_name (fn s => "pt_" ^ s ^ "2") a);
wenzelm@45838
   322
      in List.take (map Drule.export_without_context (Datatype_Aux.split_conj_thm
wenzelm@20046
   323
        (Goal.prove_global thy2 [] []
berghofe@28731
   324
           (augment_sort thy2 [pt_class_of thy2 a]
berghofe@17870
   325
             (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@17870
   326
                (map (fn ((s, T), x) =>
berghofe@17870
   327
                    let val perm = Const (s, permT --> T --> T)
berghofe@17870
   328
                    in HOLogic.mk_eq
haftmann@23029
   329
                      (perm $ (Const ("List.append", permT --> permT --> permT) $
berghofe@17870
   330
                         pi1 $ pi2) $ Free (x, T),
berghofe@17870
   331
                       perm $ pi1 $ (perm $ pi2 $ Free (x, T)))
berghofe@17870
   332
                    end)
berghofe@17870
   333
                  (perm_names ~~
berghofe@28731
   334
                   map body_type perm_types ~~ perm_indnames)))))
wenzelm@45735
   335
           (fn _ => EVERY [Datatype_Aux.ind_tac induct perm_indnames 1,
wenzelm@32149
   336
              ALLGOALS (asm_full_simp_tac (global_simpset_of thy2 addsimps [pt2', pt2_ax]))]))),
berghofe@17870
   337
         length new_type_names)
wenzelm@32952
   338
      end) atoms;
berghofe@17870
   339
berghofe@17870
   340
    (**** prove pi1 ~ pi2 ==> pi1 \<bullet> t = pi2 \<bullet> t ****)
berghofe@17870
   341
berghofe@17870
   342
    val _ = warning "perm_eq_thms";
berghofe@17870
   343
wenzelm@39557
   344
    val pt3 = Global_Theory.get_thm thy2 "pt3";
wenzelm@39557
   345
    val pt3_rev = Global_Theory.get_thm thy2 "pt3_rev";
berghofe@17870
   346
wenzelm@32952
   347
    val perm_eq_thms = maps (fn a =>
berghofe@17870
   348
      let
berghofe@17870
   349
        val permT = mk_permT (Type (a, []));
berghofe@17870
   350
        val pi1 = Free ("pi1", permT);
berghofe@17870
   351
        val pi2 = Free ("pi2", permT);
berghofe@28731
   352
        val at_inst = at_inst_of thy2 a;
berghofe@28731
   353
        val pt_inst = pt_inst_of thy2 a;
berghofe@17870
   354
        val pt3' = pt_inst RS pt3;
berghofe@17870
   355
        val pt3_rev' = at_inst RS (pt_inst RS pt3_rev);
wenzelm@39557
   356
        val pt3_ax = Global_Theory.get_thm thy2 (Long_Name.map_base_name (fn s => "pt_" ^ s ^ "3") a);
wenzelm@45838
   357
      in List.take (map Drule.export_without_context (Datatype_Aux.split_conj_thm
berghofe@28731
   358
        (Goal.prove_global thy2 [] []
berghofe@28731
   359
          (augment_sort thy2 [pt_class_of thy2 a] (Logic.mk_implies
berghofe@19494
   360
             (HOLogic.mk_Trueprop (Const ("Nominal.prm_eq",
berghofe@17870
   361
                permT --> permT --> HOLogic.boolT) $ pi1 $ pi2),
berghofe@17870
   362
              HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@17870
   363
                (map (fn ((s, T), x) =>
berghofe@17870
   364
                    let val perm = Const (s, permT --> T --> T)
berghofe@17870
   365
                    in HOLogic.mk_eq
berghofe@17870
   366
                      (perm $ pi1 $ Free (x, T),
berghofe@17870
   367
                       perm $ pi2 $ Free (x, T))
berghofe@17870
   368
                    end)
berghofe@17870
   369
                  (perm_names ~~
berghofe@28731
   370
                   map body_type perm_types ~~ perm_indnames))))))
wenzelm@45735
   371
           (fn _ => EVERY [Datatype_Aux.ind_tac induct perm_indnames 1,
wenzelm@32149
   372
              ALLGOALS (asm_full_simp_tac (global_simpset_of thy2 addsimps [pt3', pt3_rev', pt3_ax]))]))),
berghofe@17870
   373
         length new_type_names)
wenzelm@32952
   374
      end) atoms;
berghofe@17870
   375
berghofe@17870
   376
    (**** prove pi1 \<bullet> (pi2 \<bullet> t) = (pi1 \<bullet> pi2) \<bullet> (pi1 \<bullet> t) ****)
berghofe@17870
   377
wenzelm@39557
   378
    val cp1 = Global_Theory.get_thm thy2 "cp1";
wenzelm@39557
   379
    val dj_cp = Global_Theory.get_thm thy2 "dj_cp";
wenzelm@39557
   380
    val pt_perm_compose = Global_Theory.get_thm thy2 "pt_perm_compose";
wenzelm@39557
   381
    val pt_perm_compose_rev = Global_Theory.get_thm thy2 "pt_perm_compose_rev";
wenzelm@39557
   382
    val dj_perm_perm_forget = Global_Theory.get_thm thy2 "dj_perm_perm_forget";
berghofe@17870
   383
berghofe@17870
   384
    fun composition_instance name1 name2 thy =
berghofe@17870
   385
      let
berghofe@28731
   386
        val cp_class = cp_class_of thy name1 name2;
berghofe@28731
   387
        val pt_class =
berghofe@28731
   388
          if name1 = name2 then [pt_class_of thy name1]
berghofe@28731
   389
          else [];
berghofe@17870
   390
        val permT1 = mk_permT (Type (name1, []));
berghofe@17870
   391
        val permT2 = mk_permT (Type (name2, []));
berghofe@28731
   392
        val Ts = map body_type perm_types;
berghofe@28731
   393
        val cp_inst = cp_inst_of thy name1 name2;
wenzelm@32149
   394
        val simps = global_simpset_of thy addsimps (perm_fun_def ::
berghofe@17870
   395
          (if name1 <> name2 then
berghofe@28731
   396
             let val dj = dj_thm_of thy name2 name1
berghofe@17870
   397
             in [dj RS (cp_inst RS dj_cp), dj RS dj_perm_perm_forget] end
berghofe@17870
   398
           else
berghofe@17870
   399
             let
berghofe@28731
   400
               val at_inst = at_inst_of thy name1;
berghofe@28731
   401
               val pt_inst = pt_inst_of thy name1;
berghofe@17870
   402
             in
berghofe@17870
   403
               [cp_inst RS cp1 RS sym,
berghofe@17870
   404
                at_inst RS (pt_inst RS pt_perm_compose) RS sym,
berghofe@17870
   405
                at_inst RS (pt_inst RS pt_perm_compose_rev) RS sym]
berghofe@17870
   406
            end))
wenzelm@36428
   407
        val sort = Sign.minimize_sort thy (Sign.certify_sort thy (cp_class :: pt_class));
wenzelm@45838
   408
        val thms = Datatype_Aux.split_conj_thm (Goal.prove_global thy [] []
berghofe@28736
   409
          (augment_sort thy sort
berghofe@17870
   410
            (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@17870
   411
              (map (fn ((s, T), x) =>
berghofe@17870
   412
                  let
berghofe@17870
   413
                    val pi1 = Free ("pi1", permT1);
berghofe@17870
   414
                    val pi2 = Free ("pi2", permT2);
berghofe@17870
   415
                    val perm1 = Const (s, permT1 --> T --> T);
berghofe@17870
   416
                    val perm2 = Const (s, permT2 --> T --> T);
berghofe@19494
   417
                    val perm3 = Const ("Nominal.perm", permT1 --> permT2 --> permT2)
berghofe@17870
   418
                  in HOLogic.mk_eq
berghofe@17870
   419
                    (perm1 $ pi1 $ (perm2 $ pi2 $ Free (x, T)),
berghofe@17870
   420
                     perm2 $ (perm3 $ pi1 $ pi2) $ (perm1 $ pi1 $ Free (x, T)))
berghofe@17870
   421
                  end)
berghofe@28731
   422
                (perm_names ~~ Ts ~~ perm_indnames)))))
wenzelm@45735
   423
          (fn _ => EVERY [Datatype_Aux.ind_tac induct perm_indnames 1,
wenzelm@20046
   424
             ALLGOALS (asm_full_simp_tac simps)]))
berghofe@17870
   425
      in
berghofe@28736
   426
        fold (fn (s, tvs) => fn thy => AxClass.prove_arity
berghofe@28736
   427
            (s, map (inter_sort thy sort o snd) tvs, [cp_class])
haftmann@24218
   428
            (Class.intro_classes_tac [] THEN ALLGOALS (resolve_tac thms)) thy)
berghofe@28736
   429
          (full_new_type_names' ~~ tyvars) thy
berghofe@17870
   430
      end;
berghofe@17870
   431
urbanc@18381
   432
    val (perm_thmss,thy3) = thy2 |>
berghofe@17870
   433
      fold (fn name1 => fold (composition_instance name1) atoms) atoms |>
berghofe@28731
   434
      fold (fn atom => fn thy =>
berghofe@28731
   435
        let val pt_name = pt_class_of thy atom
berghofe@28731
   436
        in
berghofe@28736
   437
          fold (fn (s, tvs) => fn thy => AxClass.prove_arity
berghofe@28736
   438
              (s, map (inter_sort thy [pt_name] o snd) tvs, [pt_name])
berghofe@28731
   439
              (EVERY
berghofe@28731
   440
                [Class.intro_classes_tac [],
berghofe@28731
   441
                 resolve_tac perm_empty_thms 1,
berghofe@28731
   442
                 resolve_tac perm_append_thms 1,
berghofe@28736
   443
                 resolve_tac perm_eq_thms 1, assume_tac 1]) thy)
berghofe@28736
   444
            (full_new_type_names' ~~ tyvars) thy
berghofe@28731
   445
        end) atoms |>
wenzelm@39557
   446
      Global_Theory.add_thmss
haftmann@29585
   447
        [((Binding.name (space_implode "_" new_type_names ^ "_unfolded_perm_eq"),
krauss@18759
   448
          unfolded_perm_eq_thms), [Simplifier.simp_add]),
haftmann@29585
   449
         ((Binding.name (space_implode "_" new_type_names ^ "_perm_empty"),
krauss@18759
   450
          perm_empty_thms), [Simplifier.simp_add]),
haftmann@29585
   451
         ((Binding.name (space_implode "_" new_type_names ^ "_perm_append"),
krauss@18759
   452
          perm_append_thms), [Simplifier.simp_add]),
haftmann@29585
   453
         ((Binding.name (space_implode "_" new_type_names ^ "_perm_eq"),
krauss@18759
   454
          perm_eq_thms), [Simplifier.simp_add])];
wenzelm@21365
   455
berghofe@17870
   456
    (**** Define representing sets ****)
berghofe@17870
   457
berghofe@17870
   458
    val _ = warning "representing sets";
berghofe@17870
   459
wenzelm@45838
   460
    val rep_set_names =
wenzelm@45838
   461
      Datatype_Prop.indexify_names
wenzelm@45838
   462
        (map (fn (i, _) => Datatype_Aux.name_of_typ (nth_dtyp i) ^ "_set") descr);
berghofe@17870
   463
    val big_rep_name =
haftmann@33968
   464
      space_implode "_" (Datatype_Prop.indexify_names (map_filter
berghofe@19494
   465
        (fn (i, ("Nominal.noption", _, _)) => NONE
wenzelm@45838
   466
          | (i, _) => SOME (Datatype_Aux.name_of_typ (nth_dtyp i))) descr)) ^ "_set";
berghofe@17870
   467
    val _ = warning ("big_rep_name: " ^ big_rep_name);
berghofe@17870
   468
wenzelm@45896
   469
    fun strip_option (dtf as Datatype.DtType ("fun", [dt, Datatype.DtRec i])) =
berghofe@17870
   470
          (case AList.lookup op = descr i of
berghofe@19494
   471
             SOME ("Nominal.noption", _, [(_, [dt']), _]) =>
berghofe@17870
   472
               apfst (cons dt) (strip_option dt')
berghofe@17870
   473
           | _ => ([], dtf))
wenzelm@45896
   474
      | strip_option (Datatype.DtType ("fun",
wenzelm@45896
   475
            [dt, Datatype.DtType ("Nominal.noption", [dt'])])) =
berghofe@18261
   476
          apfst (cons dt) (strip_option dt')
berghofe@17870
   477
      | strip_option dt = ([], dt);
berghofe@17870
   478
wenzelm@45838
   479
    val dt_atomTs = distinct op = (map (Datatype_Aux.typ_of_dtyp descr)
wenzelm@32952
   480
      (maps (fn (_, (_, _, cs)) => maps (maps (fst o strip_option) o snd) cs) descr));
berghofe@28731
   481
    val dt_atoms = map (fst o dest_Type) dt_atomTs;
berghofe@18280
   482
berghofe@17870
   483
    fun make_intr s T (cname, cargs) =
berghofe@17870
   484
      let
wenzelm@33338
   485
        fun mk_prem dt (j, j', prems, ts) =
berghofe@17870
   486
          let
berghofe@17870
   487
            val (dts, dt') = strip_option dt;
wenzelm@45838
   488
            val (dts', dt'') = Datatype_Aux.strip_dtyp dt';
wenzelm@45838
   489
            val Ts = map (Datatype_Aux.typ_of_dtyp descr) dts;
wenzelm@45838
   490
            val Us = map (Datatype_Aux.typ_of_dtyp descr) dts';
wenzelm@45838
   491
            val T = Datatype_Aux.typ_of_dtyp descr dt'';
wenzelm@45838
   492
            val free = Datatype_Aux.mk_Free "x" (Us ---> T) j;
wenzelm@45838
   493
            val free' = Datatype_Aux.app_bnds free (length Us);
wenzelm@33338
   494
            fun mk_abs_fun T (i, t) =
berghofe@17870
   495
              let val U = fastype_of t
berghofe@19494
   496
              in (i + 1, Const ("Nominal.abs_fun", [T, U, T] --->
wenzelm@45838
   497
                Type ("Nominal.noption", [U])) $ Datatype_Aux.mk_Free "y" T i $ t)
berghofe@17870
   498
              end
berghofe@17870
   499
          in (j + 1, j' + length Ts,
berghofe@17870
   500
            case dt'' of
wenzelm@46218
   501
                Datatype.DtRec k => Logic.list_all (map (pair "x") Us,
wenzelm@42364
   502
                  HOLogic.mk_Trueprop (Free (nth rep_set_names k,
berghofe@21021
   503
                    T --> HOLogic.boolT) $ free')) :: prems
berghofe@17870
   504
              | _ => prems,
wenzelm@33338
   505
            snd (fold_rev mk_abs_fun Ts (j', free)) :: ts)
berghofe@17870
   506
          end;
berghofe@17870
   507
wenzelm@33338
   508
        val (_, _, prems, ts) = fold_rev mk_prem cargs (1, 1, [], []);
berghofe@21021
   509
        val concl = HOLogic.mk_Trueprop (Free (s, T --> HOLogic.boolT) $
berghofe@21021
   510
          list_comb (Const (cname, map fastype_of ts ---> T), ts))
berghofe@17870
   511
      in Logic.list_implies (prems, concl)
berghofe@17870
   512
      end;
berghofe@17870
   513
berghofe@21021
   514
    val (intr_ts, (rep_set_names', recTs')) =
wenzelm@32952
   515
      apfst flat (apsnd ListPair.unzip (ListPair.unzip (map_filter
berghofe@19494
   516
        (fn ((_, ("Nominal.noption", _, _)), _) => NONE
berghofe@17870
   517
          | ((i, (_, _, constrs)), rep_set_name) =>
berghofe@17870
   518
              let val T = nth_dtyp i
berghofe@17870
   519
              in SOME (map (make_intr rep_set_name T) constrs,
berghofe@21021
   520
                (rep_set_name, T))
berghofe@17870
   521
              end)
berghofe@21021
   522
                (descr ~~ rep_set_names))));
haftmann@28965
   523
    val rep_set_names'' = map (Sign.full_bname thy3) rep_set_names';
berghofe@17870
   524
wenzelm@21365
   525
    val ({raw_induct = rep_induct, intrs = rep_intrs, ...}, thy4) =
wenzelm@33278
   526
      thy3
wenzelm@33278
   527
      |> Sign.map_naming Name_Space.conceal
wenzelm@33726
   528
      |> Inductive.add_inductive_global
wenzelm@33669
   529
          {quiet_mode = false, verbose = false, alt_name = Binding.name big_rep_name,
wenzelm@49170
   530
           coind = false, no_elim = true, no_ind = false, skip_mono = true}
haftmann@28965
   531
          (map (fn (s, T) => ((Binding.name s, T --> HOLogic.boolT), NoSyn))
wenzelm@26128
   532
             (rep_set_names' ~~ recTs'))
wenzelm@33278
   533
          [] (map (fn x => (Attrib.empty_binding, x)) intr_ts) []
wenzelm@33278
   534
      ||> Sign.restore_naming thy3;
berghofe@17870
   535
berghofe@17870
   536
    (**** Prove that representing set is closed under permutation ****)
berghofe@17870
   537
berghofe@17870
   538
    val _ = warning "proving closure under permutation...";
berghofe@17870
   539
wenzelm@39557
   540
    val abs_perm = Global_Theory.get_thms thy4 "abs_perm";
berghofe@25951
   541
wenzelm@32952
   542
    val perm_indnames' = map_filter
berghofe@19494
   543
      (fn (x, (_, ("Nominal.noption", _, _))) => NONE | (x, _) => SOME x)
berghofe@17870
   544
      (perm_indnames ~~ descr);
berghofe@17870
   545
wenzelm@35021
   546
    fun mk_perm_closed name = map (fn th => Drule.export_without_context (th RS mp))
wenzelm@45838
   547
      (List.take (Datatype_Aux.split_conj_thm (Goal.prove_global thy4 [] []
berghofe@28731
   548
        (augment_sort thy4
haftmann@33040
   549
          (pt_class_of thy4 name :: map (cp_class_of thy4 name) (remove (op =) name dt_atoms))
berghofe@28731
   550
          (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map
berghofe@28731
   551
            (fn ((s, T), x) =>
berghofe@28731
   552
               let
berghofe@28731
   553
                 val S = Const (s, T --> HOLogic.boolT);
berghofe@28731
   554
                 val permT = mk_permT (Type (name, []))
berghofe@28731
   555
               in HOLogic.mk_imp (S $ Free (x, T),
berghofe@28731
   556
                 S $ (Const ("Nominal.perm", permT --> T --> T) $
berghofe@28731
   557
                   Free ("pi", permT) $ Free (x, T)))
berghofe@28731
   558
               end) (rep_set_names'' ~~ recTs' ~~ perm_indnames')))))
berghofe@28731
   559
        (fn _ => EVERY
wenzelm@45735
   560
           [Datatype_Aux.ind_tac rep_induct [] 1,
wenzelm@32149
   561
            ALLGOALS (simp_tac (global_simpset_of thy4 addsimps
wenzelm@36945
   562
              (Thm.symmetric perm_fun_def :: abs_perm))),
berghofe@28731
   563
            ALLGOALS (resolve_tac rep_intrs THEN_ALL_NEW assume_tac)])),
berghofe@17870
   564
        length new_type_names));
berghofe@17870
   565
berghofe@17870
   566
    val perm_closed_thmss = map mk_perm_closed atoms;
berghofe@17870
   567
berghofe@17870
   568
    (**** typedef ****)
berghofe@17870
   569
berghofe@17870
   570
    val _ = warning "defining type...";
berghofe@17870
   571
berghofe@18366
   572
    val (typedefs, thy6) =
wenzelm@26651
   573
      thy4
wenzelm@45701
   574
      |> fold_map (fn (((name, mx), tvs), (cname, U)) => fn thy =>
wenzelm@49835
   575
          Typedef.add_typedef_global
wenzelm@45701
   576
            (name, map (fn (v, _) => (v, dummyS)) tvs, mx)  (* FIXME keep constraints!? *)
haftmann@37677
   577
            (Const (@{const_name Collect}, (U --> HOLogic.boolT) --> HOLogic.mk_setT U) $
berghofe@21021
   578
               Const (cname, U --> HOLogic.boolT)) NONE
berghofe@21021
   579
            (rtac exI 1 THEN rtac CollectI 1 THEN
berghofe@17870
   580
              QUIET_BREADTH_FIRST (has_fewer_prems 1)
wenzelm@26475
   581
              (resolve_tac rep_intrs 1)) thy |> (fn ((_, r), thy) =>
berghofe@17870
   582
        let
berghofe@28736
   583
          val permT = mk_permT
wenzelm@43324
   584
            (TFree (singleton (Name.variant_list (map fst tvs)) "'a", HOLogic.typeS));
berghofe@17870
   585
          val pi = Free ("pi", permT);
wenzelm@45701
   586
          val T = Type (Sign.full_name thy name, map TFree tvs);
berghofe@18366
   587
        in apfst (pair r o hd)
wenzelm@45701
   588
          (Global_Theory.add_defs_unchecked true
wenzelm@45701
   589
            [((Binding.map_name (fn n => "prm_" ^ n ^ "_def") name, Logic.mk_equals
wenzelm@45701
   590
              (Const ("Nominal.perm", permT --> T --> T) $ pi $ Free ("x", T),
wenzelm@45701
   591
               Const (Sign.intern_const thy ("Abs_" ^ Binding.name_of name), U --> T) $
wenzelm@45701
   592
                 (Const ("Nominal.perm", permT --> U --> U) $ pi $
wenzelm@45701
   593
                   (Const (Sign.intern_const thy ("Rep_" ^ Binding.name_of name), T --> U) $
wenzelm@45701
   594
                     Free ("x", T))))), [])] thy)
berghofe@17870
   595
        end))
wenzelm@45701
   596
        (types_syntax ~~ tyvars ~~ List.take (rep_set_names'' ~~ recTs', length new_type_names));
berghofe@17870
   597
berghofe@17870
   598
    val perm_defs = map snd typedefs;
wenzelm@35994
   599
    val Abs_inverse_thms = map (collect_simp o #Abs_inverse o snd o fst) typedefs;
wenzelm@35994
   600
    val Rep_inverse_thms = map (#Rep_inverse o snd o fst) typedefs;
wenzelm@35994
   601
    val Rep_thms = map (collect_simp o #Rep o snd o fst) typedefs;
berghofe@17870
   602
berghofe@18016
   603
berghofe@17870
   604
    (** prove that new types are in class pt_<name> **)
berghofe@17870
   605
berghofe@17870
   606
    val _ = warning "prove that new types are in class pt_<name> ...";
berghofe@17870
   607
berghofe@28731
   608
    fun pt_instance (atom, perm_closed_thms) =
berghofe@21021
   609
      fold (fn ((((((Abs_inverse, Rep_inverse), Rep),
berghofe@17870
   610
        perm_def), name), tvs), perm_closed) => fn thy =>
berghofe@28731
   611
          let
berghofe@28731
   612
            val pt_class = pt_class_of thy atom;
wenzelm@36428
   613
            val sort = Sign.minimize_sort thy (Sign.certify_sort thy
wenzelm@36428
   614
              (pt_class :: map (cp_class_of thy atom) (remove (op =) atom dt_atoms)))
berghofe@28731
   615
          in AxClass.prove_arity
berghofe@17870
   616
            (Sign.intern_type thy name,
berghofe@28736
   617
              map (inter_sort thy sort o snd) tvs, [pt_class])
haftmann@24218
   618
            (EVERY [Class.intro_classes_tac [],
berghofe@17870
   619
              rewrite_goals_tac [perm_def],
wenzelm@32149
   620
              asm_full_simp_tac (global_simpset_of thy addsimps [Rep_inverse]) 1,
wenzelm@32149
   621
              asm_full_simp_tac (global_simpset_of thy addsimps
berghofe@17870
   622
                [Rep RS perm_closed RS Abs_inverse]) 1,
wenzelm@39557
   623
              asm_full_simp_tac (HOL_basic_ss addsimps [Global_Theory.get_thm thy
wenzelm@30364
   624
                ("pt_" ^ Long_Name.base_name atom ^ "3")]) 1]) thy
berghofe@28731
   625
          end)
berghofe@21021
   626
        (Abs_inverse_thms ~~ Rep_inverse_thms ~~ Rep_thms ~~ perm_defs ~~
berghofe@21021
   627
           new_type_names ~~ tyvars ~~ perm_closed_thms);
berghofe@17870
   628
berghofe@17870
   629
berghofe@17870
   630
    (** prove that new types are in class cp_<name1>_<name2> **)
berghofe@17870
   631
berghofe@17870
   632
    val _ = warning "prove that new types are in class cp_<name1>_<name2> ...";
berghofe@17870
   633
berghofe@17870
   634
    fun cp_instance (atom1, perm_closed_thms1) (atom2, perm_closed_thms2) thy =
berghofe@17870
   635
      let
berghofe@28731
   636
        val cp_class = cp_class_of thy atom1 atom2;
wenzelm@36428
   637
        val sort = Sign.minimize_sort thy (Sign.certify_sort thy
haftmann@33040
   638
          (pt_class_of thy atom1 :: map (cp_class_of thy atom1) (remove (op =) atom1 dt_atoms) @
berghofe@28736
   639
           (if atom1 = atom2 then [cp_class_of thy atom1 atom1] else
wenzelm@36428
   640
            pt_class_of thy atom2 :: map (cp_class_of thy atom2) (remove (op =) atom2 dt_atoms))));
berghofe@28731
   641
        val cp1' = cp_inst_of thy atom1 atom2 RS cp1
berghofe@21021
   642
      in fold (fn ((((((Abs_inverse, Rep),
berghofe@17870
   643
        perm_def), name), tvs), perm_closed1), perm_closed2) => fn thy =>
berghofe@19275
   644
          AxClass.prove_arity
berghofe@17870
   645
            (Sign.intern_type thy name,
berghofe@28736
   646
              map (inter_sort thy sort o snd) tvs, [cp_class])
haftmann@24218
   647
            (EVERY [Class.intro_classes_tac [],
berghofe@17870
   648
              rewrite_goals_tac [perm_def],
wenzelm@32149
   649
              asm_full_simp_tac (global_simpset_of thy addsimps
berghofe@17870
   650
                ((Rep RS perm_closed1 RS Abs_inverse) ::
berghofe@17870
   651
                 (if atom1 = atom2 then []
berghofe@17870
   652
                  else [Rep RS perm_closed2 RS Abs_inverse]))) 1,
berghofe@18016
   653
              cong_tac 1,
berghofe@17870
   654
              rtac refl 1,
berghofe@17870
   655
              rtac cp1' 1]) thy)
berghofe@21021
   656
        (Abs_inverse_thms ~~ Rep_thms ~~ perm_defs ~~ new_type_names ~~
berghofe@21021
   657
           tyvars ~~ perm_closed_thms1 ~~ perm_closed_thms2) thy
berghofe@17870
   658
      end;
berghofe@17870
   659
berghofe@17870
   660
    val thy7 = fold (fn x => fn thy => thy |>
berghofe@17870
   661
      pt_instance x |>
berghofe@28731
   662
      fold (cp_instance x) (atoms ~~ perm_closed_thmss))
berghofe@28731
   663
        (atoms ~~ perm_closed_thmss) thy6;
berghofe@17870
   664
berghofe@17870
   665
    (**** constructors ****)
berghofe@17870
   666
wenzelm@33338
   667
    fun mk_abs_fun x t =
berghofe@17870
   668
      let
berghofe@17870
   669
        val T = fastype_of x;
berghofe@17870
   670
        val U = fastype_of t
berghofe@17870
   671
      in
berghofe@19494
   672
        Const ("Nominal.abs_fun", T --> U --> T -->
berghofe@19494
   673
          Type ("Nominal.noption", [U])) $ x $ t
berghofe@17870
   674
      end;
berghofe@17870
   675
wenzelm@30190
   676
    val (ty_idxs, _) = List.foldl
berghofe@19494
   677
      (fn ((i, ("Nominal.noption", _, _)), p) => p
berghofe@18016
   678
        | ((i, _), (ty_idxs, j)) => (ty_idxs @ [(i, j)], j + 1)) ([], 0) descr;
berghofe@18016
   679
wenzelm@45896
   680
    fun reindex (Datatype.DtType (s, dts)) = Datatype.DtType (s, map reindex dts)
wenzelm@45896
   681
      | reindex (Datatype.DtRec i) = Datatype.DtRec (the (AList.lookup op = ty_idxs i))
berghofe@18016
   682
      | reindex dt = dt;
berghofe@18016
   683
wenzelm@40627
   684
    fun strip_suffix i s = implode (List.take (raw_explode s, size s - i));  (* FIXME Symbol.explode (?) *)
berghofe@18016
   685
berghofe@18016
   686
    (** strips the "_Rep" in type names *)
wenzelm@21365
   687
    fun strip_nth_name i s =
wenzelm@30364
   688
      let val xs = Long_Name.explode s;
wenzelm@30364
   689
      in Long_Name.implode (Library.nth_map (length xs - i) (strip_suffix 4) xs) end;
berghofe@18016
   690
haftmann@31458
   691
    val (descr'', ndescr) = ListPair.unzip (map_filter
berghofe@19494
   692
      (fn (i, ("Nominal.noption", _, _)) => NONE
berghofe@18107
   693
        | (i, (s, dts, constrs)) =>
berghofe@18107
   694
             let
berghofe@18107
   695
               val SOME index = AList.lookup op = ty_idxs i;
haftmann@31458
   696
               val (constrs2, constrs1) =
haftmann@31458
   697
                 map_split (fn (cname, cargs) =>
haftmann@31458
   698
                   apsnd (pair (strip_nth_name 2 (strip_nth_name 1 cname)))
haftmann@31458
   699
                   (fold_map (fn dt => fn dts =>
berghofe@18107
   700
                     let val (dts', dt') = strip_option dt
haftmann@31458
   701
                     in ((length dts, length dts'), dts @ dts' @ [reindex dt']) end)
haftmann@31458
   702
                       cargs [])) constrs
berghofe@18107
   703
             in SOME ((index, (strip_nth_name 1 s,  map reindex dts, constrs1)),
berghofe@18107
   704
               (index, constrs2))
berghofe@18107
   705
             end) descr);
urbanc@18045
   706
berghofe@19489
   707
    val (descr1, descr2) = chop (length new_type_names) descr'';
berghofe@18016
   708
    val descr' = [descr1, descr2];
berghofe@18016
   709
berghofe@19710
   710
    fun partition_cargs idxs xs = map (fn (i, j) =>
wenzelm@42364
   711
      (List.take (List.drop (xs, i), j), nth xs (i + j))) idxs;
berghofe@19710
   712
berghofe@19833
   713
    val pdescr = map (fn ((i, (s, dts, constrs)), (_, idxss)) => (i, (s, dts,
berghofe@19833
   714
      map (fn ((cname, cargs), idxs) => (cname, partition_cargs idxs cargs))
berghofe@19833
   715
        (constrs ~~ idxss)))) (descr'' ~~ ndescr);
berghofe@19833
   716
wenzelm@45896
   717
    fun nth_dtyp' i = Datatype_Aux.typ_of_dtyp descr'' (Datatype.DtRec i);
berghofe@17870
   718
berghofe@17870
   719
    val rep_names = map (fn s =>
berghofe@17870
   720
      Sign.intern_const thy7 ("Rep_" ^ s)) new_type_names;
berghofe@17870
   721
    val abs_names = map (fn s =>
berghofe@17870
   722
      Sign.intern_const thy7 ("Abs_" ^ s)) new_type_names;
berghofe@17870
   723
wenzelm@45838
   724
    val recTs = Datatype_Aux.get_rec_types descr'';
haftmann@33957
   725
    val newTs' = take (length new_type_names) recTs';
haftmann@33957
   726
    val newTs = take (length new_type_names) recTs;
berghofe@17870
   727
haftmann@28965
   728
    val full_new_type_names = map (Sign.full_bname thy) new_type_names;
berghofe@17870
   729
wenzelm@33244
   730
    fun make_constr_def tname T T' (((cname_rep, _), (cname, cargs)), (cname', mx))
wenzelm@33244
   731
        (thy, defs, eqns) =
berghofe@17870
   732
      let
wenzelm@33338
   733
        fun constr_arg (dts, dt) (j, l_args, r_args) =
berghofe@17870
   734
          let
wenzelm@45838
   735
            val xs =
wenzelm@45838
   736
              map (fn (dt, i) => Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) i)
wenzelm@45838
   737
                (dts ~~ (j upto j + length dts - 1))
wenzelm@45838
   738
            val x = Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts)
berghofe@18261
   739
          in
berghofe@18261
   740
            (j + length dts + 1,
berghofe@18261
   741
             xs @ x :: l_args,
wenzelm@33338
   742
             fold_rev mk_abs_fun xs
berghofe@19833
   743
               (case dt of
wenzelm@45896
   744
                  Datatype.DtRec k => if k < length new_type_names then
wenzelm@45838
   745
                      Const (nth rep_names k, Datatype_Aux.typ_of_dtyp descr'' dt -->
wenzelm@45838
   746
                        Datatype_Aux.typ_of_dtyp descr dt) $ x
berghofe@18261
   747
                    else error "nested recursion not (yet) supported"
wenzelm@33338
   748
                | _ => x) :: r_args)
berghofe@17870
   749
          end
berghofe@17870
   750
wenzelm@33338
   751
        val (_, l_args, r_args) = fold_rev constr_arg cargs (1, [], []);
wenzelm@22578
   752
        val abs_name = Sign.intern_const thy ("Abs_" ^ tname);
wenzelm@22578
   753
        val rep_name = Sign.intern_const thy ("Rep_" ^ tname);
berghofe@17870
   754
        val constrT = map fastype_of l_args ---> T;
berghofe@19833
   755
        val lhs = list_comb (Const (cname, constrT), l_args);
berghofe@19833
   756
        val rhs = list_comb (Const (cname_rep, map fastype_of r_args ---> T'), r_args);
berghofe@17870
   757
        val def = Logic.mk_equals (lhs, Const (abs_name, T' --> T) $ rhs);
berghofe@17870
   758
        val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17870
   759
          (Const (rep_name, T --> T') $ lhs, rhs));
wenzelm@30364
   760
        val def_name = (Long_Name.base_name cname) ^ "_def";
berghofe@18366
   761
        val ([def_thm], thy') = thy |>
wenzelm@45701
   762
          Sign.add_consts_i [(cname', constrT, mx)] |>
wenzelm@39557
   763
          (Global_Theory.add_defs false o map Thm.no_attributes) [(Binding.name def_name, def)]
berghofe@17870
   764
      in (thy', defs @ [def_thm], eqns @ [eqn]) end;
berghofe@17870
   765
wenzelm@33244
   766
    fun dt_constr_defs ((((((_, (_, _, constrs)),
wenzelm@33244
   767
        (_, (_, _, constrs'))), tname), T), T'), constr_syntax) (thy, defs, eqns, dist_lemmas) =
berghofe@17870
   768
      let
berghofe@17870
   769
        val rep_const = cterm_of thy
berghofe@17870
   770
          (Const (Sign.intern_const thy ("Rep_" ^ tname), T --> T'));
wenzelm@33244
   771
        val dist =
wenzelm@35021
   772
          Drule.export_without_context
wenzelm@45909
   773
            (cterm_instantiate [(cterm_of thy distinct_f, rep_const)] Datatype.distinct_lemma);
wenzelm@33244
   774
        val (thy', defs', eqns') = fold (make_constr_def tname T T')
wenzelm@33244
   775
          (constrs ~~ constrs' ~~ constr_syntax) (Sign.add_path tname thy, defs, [])
berghofe@17870
   776
      in
haftmann@32124
   777
        (Sign.parent_path thy', defs', eqns @ [eqns'], dist_lemmas @ [dist])
berghofe@17870
   778
      end;
berghofe@17870
   779
wenzelm@33244
   780
    val (thy8, constr_defs, constr_rep_eqns, dist_lemmas) = fold dt_constr_defs
wenzelm@33244
   781
      (List.take (descr, length new_type_names) ~~
berghofe@19833
   782
        List.take (pdescr, length new_type_names) ~~
wenzelm@33244
   783
        new_type_names ~~ newTs ~~ newTs' ~~ constr_syntax)
wenzelm@33244
   784
      (thy7, [], [], []);
berghofe@17870
   785
wenzelm@35994
   786
    val abs_inject_thms = map (collect_simp o #Abs_inject o snd o fst) typedefs
wenzelm@35994
   787
    val rep_inject_thms = map (#Rep_inject o snd o fst) typedefs
berghofe@17870
   788
berghofe@17870
   789
    (* prove theorem  Rep_i (Constr_j ...) = Constr'_j ...  *)
wenzelm@21365
   790
berghofe@17870
   791
    fun prove_constr_rep_thm eqn =
berghofe@17870
   792
      let
berghofe@17870
   793
        val inj_thms = map (fn r => r RS iffD1) abs_inject_thms;
berghofe@21021
   794
        val rewrites = constr_defs @ map mk_meta_eq Rep_inverse_thms
wenzelm@20046
   795
      in Goal.prove_global thy8 [] [] eqn (fn _ => EVERY
berghofe@17870
   796
        [resolve_tac inj_thms 1,
berghofe@17870
   797
         rewrite_goals_tac rewrites,
berghofe@17870
   798
         rtac refl 3,
berghofe@17870
   799
         resolve_tac rep_intrs 2,
berghofe@21021
   800
         REPEAT (resolve_tac Rep_thms 1)])
berghofe@17870
   801
      end;
berghofe@17870
   802
berghofe@17870
   803
    val constr_rep_thmss = map (map prove_constr_rep_thm) constr_rep_eqns;
berghofe@17870
   804
berghofe@17870
   805
    (* prove theorem  pi \<bullet> Rep_i x = Rep_i (pi \<bullet> x) *)
berghofe@17870
   806
berghofe@17870
   807
    fun prove_perm_rep_perm (atom, perm_closed_thms) = map (fn th =>
berghofe@17870
   808
      let
wenzelm@35845
   809
        val _ $ (_ $ (Rep $ x)) = Logic.unvarify_global (prop_of th);
berghofe@17870
   810
        val Type ("fun", [T, U]) = fastype_of Rep;
berghofe@17870
   811
        val permT = mk_permT (Type (atom, []));
berghofe@17870
   812
        val pi = Free ("pi", permT);
berghofe@17870
   813
      in
berghofe@28731
   814
        Goal.prove_global thy8 [] []
berghofe@28731
   815
          (augment_sort thy8
haftmann@33040
   816
            (pt_class_of thy8 atom :: map (cp_class_of thy8 atom) (remove (op =) atom dt_atoms))
berghofe@28731
   817
            (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@28731
   818
              (Const ("Nominal.perm", permT --> U --> U) $ pi $ (Rep $ x),
berghofe@28731
   819
               Rep $ (Const ("Nominal.perm", permT --> T --> T) $ pi $ x)))))
berghofe@18010
   820
          (fn _ => simp_tac (HOL_basic_ss addsimps (perm_defs @ Abs_inverse_thms @
wenzelm@20046
   821
            perm_closed_thms @ Rep_thms)) 1)
berghofe@17870
   822
      end) Rep_thms;
berghofe@17870
   823
wenzelm@32952
   824
    val perm_rep_perm_thms = maps prove_perm_rep_perm (atoms ~~ perm_closed_thmss);
berghofe@17870
   825
berghofe@17870
   826
    (* prove distinctness theorems *)
berghofe@17870
   827
wenzelm@45822
   828
    val distinct_props = Datatype_Prop.make_distincts descr';
haftmann@27300
   829
    val dist_rewrites = map2 (fn rep_thms => fn dist_lemma =>
haftmann@27300
   830
      dist_lemma :: rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0])
haftmann@27300
   831
        constr_rep_thmss dist_lemmas;
berghofe@17870
   832
wenzelm@45889
   833
    fun prove_distinct_thms _ [] = []
wenzelm@45889
   834
      | prove_distinct_thms (p as (rep_thms, dist_lemma)) (t :: ts) =
berghofe@17870
   835
          let
wenzelm@20046
   836
            val dist_thm = Goal.prove_global thy8 [] [] t (fn _ =>
wenzelm@32149
   837
              simp_tac (global_simpset_of thy8 addsimps (dist_lemma :: rep_thms)) 1)
wenzelm@35021
   838
          in
wenzelm@35021
   839
            dist_thm :: Drule.export_without_context (dist_thm RS not_sym) ::
wenzelm@45889
   840
              prove_distinct_thms p ts
berghofe@17870
   841
          end;
berghofe@17870
   842
haftmann@26969
   843
    val distinct_thms = map2 prove_distinct_thms
haftmann@26969
   844
      (constr_rep_thmss ~~ dist_lemmas) distinct_props;
berghofe@17870
   845
berghofe@17870
   846
    (** prove equations for permutation functions **)
berghofe@17870
   847
berghofe@17870
   848
    val perm_simps' = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) =>
berghofe@19833
   849
      let val T = nth_dtyp' i
wenzelm@32952
   850
      in maps (fn (atom, perm_closed_thms) =>
wenzelm@21365
   851
          map (fn ((cname, dts), constr_rep_thm) =>
berghofe@17870
   852
        let
berghofe@17870
   853
          val cname = Sign.intern_const thy8
wenzelm@30364
   854
            (Long_Name.append tname (Long_Name.base_name cname));
berghofe@17870
   855
          val permT = mk_permT (Type (atom, []));
berghofe@17870
   856
          val pi = Free ("pi", permT);
berghofe@17870
   857
berghofe@17870
   858
          fun perm t =
berghofe@17870
   859
            let val T = fastype_of t
berghofe@19494
   860
            in Const ("Nominal.perm", permT --> T --> T) $ pi $ t end;
berghofe@17870
   861
wenzelm@33338
   862
          fun constr_arg (dts, dt) (j, l_args, r_args) =
berghofe@17870
   863
            let
wenzelm@45838
   864
              val Ts = map (Datatype_Aux.typ_of_dtyp descr'') dts;
wenzelm@45838
   865
              val xs =
wenzelm@45838
   866
                map (fn (T, i) => Datatype_Aux.mk_Free "x" T i)
wenzelm@45838
   867
                  (Ts ~~ (j upto j + length dts - 1));
wenzelm@45838
   868
              val x =
wenzelm@45838
   869
                Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts);
berghofe@18261
   870
            in
berghofe@18261
   871
              (j + length dts + 1,
berghofe@18261
   872
               xs @ x :: l_args,
berghofe@18261
   873
               map perm (xs @ [x]) @ r_args)
berghofe@17870
   874
            end
berghofe@17870
   875
wenzelm@33338
   876
          val (_, l_args, r_args) = fold_rev constr_arg dts (1, [], []);
berghofe@17870
   877
          val c = Const (cname, map fastype_of l_args ---> T)
berghofe@17870
   878
        in
wenzelm@20046
   879
          Goal.prove_global thy8 [] []
berghofe@28731
   880
            (augment_sort thy8
haftmann@33040
   881
              (pt_class_of thy8 atom :: map (cp_class_of thy8 atom) (remove (op =) atom dt_atoms))
berghofe@28731
   882
              (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@28731
   883
                (perm (list_comb (c, l_args)), list_comb (c, r_args)))))
berghofe@18010
   884
            (fn _ => EVERY
wenzelm@32149
   885
              [simp_tac (global_simpset_of thy8 addsimps (constr_rep_thm :: perm_defs)) 1,
berghofe@17870
   886
               simp_tac (HOL_basic_ss addsimps (Rep_thms @ Abs_inverse_thms @
berghofe@17870
   887
                 constr_defs @ perm_closed_thms)) 1,
berghofe@17870
   888
               TRY (simp_tac (HOL_basic_ss addsimps
wenzelm@36945
   889
                 (Thm.symmetric perm_fun_def :: abs_perm)) 1),
berghofe@17870
   890
               TRY (simp_tac (HOL_basic_ss addsimps
berghofe@17870
   891
                 (perm_fun_def :: perm_defs @ Rep_thms @ Abs_inverse_thms @
wenzelm@20046
   892
                    perm_closed_thms)) 1)])
wenzelm@32952
   893
        end) (constrs ~~ constr_rep_thms)) (atoms ~~ perm_closed_thmss)
berghofe@19833
   894
      end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
berghofe@17870
   895
berghofe@17870
   896
    (** prove injectivity of constructors **)
berghofe@17870
   897
berghofe@17870
   898
    val rep_inject_thms' = map (fn th => th RS sym) rep_inject_thms;
wenzelm@39557
   899
    val alpha = Global_Theory.get_thms thy8 "alpha";
wenzelm@39557
   900
    val abs_fresh = Global_Theory.get_thms thy8 "abs_fresh";
berghofe@17870
   901
berghofe@28731
   902
    val pt_cp_sort =
berghofe@28731
   903
      map (pt_class_of thy8) dt_atoms @
haftmann@33040
   904
      maps (fn s => map (cp_class_of thy8 s) (remove (op =) s dt_atoms)) dt_atoms;
berghofe@28731
   905
berghofe@17870
   906
    val inject_thms = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) =>
berghofe@19833
   907
      let val T = nth_dtyp' i
wenzelm@32952
   908
      in map_filter (fn ((cname, dts), constr_rep_thm) =>
berghofe@17870
   909
        if null dts then NONE else SOME
berghofe@17870
   910
        let
berghofe@17870
   911
          val cname = Sign.intern_const thy8
wenzelm@30364
   912
            (Long_Name.append tname (Long_Name.base_name cname));
berghofe@17870
   913
wenzelm@33338
   914
          fun make_inj (dts, dt) (j, args1, args2, eqs) =
berghofe@17870
   915
            let
wenzelm@45838
   916
              val Ts_idx =
wenzelm@45838
   917
                map (Datatype_Aux.typ_of_dtyp descr'') dts ~~ (j upto j + length dts - 1);
wenzelm@45838
   918
              val xs = map (fn (T, i) => Datatype_Aux.mk_Free "x" T i) Ts_idx;
wenzelm@45838
   919
              val ys = map (fn (T, i) => Datatype_Aux.mk_Free "y" T i) Ts_idx;
wenzelm@45838
   920
              val x =
wenzelm@45838
   921
                Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts);
wenzelm@45838
   922
              val y =
wenzelm@45838
   923
                Datatype_Aux.mk_Free "y" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts);
berghofe@18261
   924
            in
berghofe@18261
   925
              (j + length dts + 1,
berghofe@18261
   926
               xs @ (x :: args1), ys @ (y :: args2),
berghofe@18261
   927
               HOLogic.mk_eq
wenzelm@33338
   928
                 (fold_rev mk_abs_fun xs x, fold_rev mk_abs_fun ys y) :: eqs)
berghofe@17870
   929
            end;
berghofe@17870
   930
wenzelm@33338
   931
          val (_, args1, args2, eqs) = fold_rev make_inj dts (1, [], [], []);
berghofe@17870
   932
          val Ts = map fastype_of args1;
berghofe@17870
   933
          val c = Const (cname, Ts ---> T)
berghofe@17870
   934
        in
berghofe@28731
   935
          Goal.prove_global thy8 [] []
berghofe@28731
   936
            (augment_sort thy8 pt_cp_sort
berghofe@28731
   937
              (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@28731
   938
                (HOLogic.mk_eq (list_comb (c, args1), list_comb (c, args2)),
berghofe@28731
   939
                 foldr1 HOLogic.mk_conj eqs))))
berghofe@18010
   940
            (fn _ => EVERY
wenzelm@32149
   941
               [asm_full_simp_tac (global_simpset_of thy8 addsimps (constr_rep_thm ::
berghofe@17870
   942
                  rep_inject_thms')) 1,
berghofe@17870
   943
                TRY (asm_full_simp_tac (HOL_basic_ss addsimps (fresh_def :: supp_def ::
berghofe@17870
   944
                  alpha @ abs_perm @ abs_fresh @ rep_inject_thms @
berghofe@28731
   945
                  perm_rep_perm_thms)) 1)])
berghofe@17870
   946
        end) (constrs ~~ constr_rep_thms)
berghofe@19833
   947
      end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
berghofe@17870
   948
berghofe@17872
   949
    (** equations for support and freshness **)
berghofe@17872
   950
berghofe@17872
   951
    val (supp_thms, fresh_thms) = ListPair.unzip (map ListPair.unzip
berghofe@17872
   952
      (map (fn ((((i, (_, _, constrs)), tname), inject_thms'), perm_thms') =>
berghofe@19833
   953
      let val T = nth_dtyp' i
wenzelm@32952
   954
      in maps (fn (cname, dts) => map (fn atom =>
berghofe@17872
   955
        let
berghofe@17872
   956
          val cname = Sign.intern_const thy8
wenzelm@30364
   957
            (Long_Name.append tname (Long_Name.base_name cname));
berghofe@17872
   958
          val atomT = Type (atom, []);
berghofe@17872
   959
wenzelm@33338
   960
          fun process_constr (dts, dt) (j, args1, args2) =
berghofe@17872
   961
            let
wenzelm@45838
   962
              val Ts_idx =
wenzelm@45838
   963
                map (Datatype_Aux.typ_of_dtyp descr'') dts ~~ (j upto j + length dts - 1);
wenzelm@45838
   964
              val xs = map (fn (T, i) => Datatype_Aux.mk_Free "x" T i) Ts_idx;
wenzelm@45838
   965
              val x =
wenzelm@45838
   966
                Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts);
berghofe@18261
   967
            in
berghofe@18261
   968
              (j + length dts + 1,
wenzelm@33338
   969
               xs @ (x :: args1), fold_rev mk_abs_fun xs x :: args2)
berghofe@17872
   970
            end;
berghofe@17872
   971
wenzelm@33338
   972
          val (_, args1, args2) = fold_rev process_constr dts (1, [], []);
berghofe@17872
   973
          val Ts = map fastype_of args1;
berghofe@17872
   974
          val c = list_comb (Const (cname, Ts ---> T), args1);
berghofe@17872
   975
          fun supp t =
berghofe@19494
   976
            Const ("Nominal.supp", fastype_of t --> HOLogic.mk_setT atomT) $ t;
berghofe@25823
   977
          fun fresh t = fresh_const atomT (fastype_of t) $ Free ("a", atomT) $ t;
wenzelm@20046
   978
          val supp_thm = Goal.prove_global thy8 [] []
berghofe@28731
   979
            (augment_sort thy8 pt_cp_sort
berghofe@17872
   980
              (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17872
   981
                (supp c,
haftmann@30450
   982
                 if null dts then HOLogic.mk_set atomT []
wenzelm@35402
   983
                 else foldr1 (HOLogic.mk_binop @{const_abbrev union}) (map supp args2)))))
berghofe@17872
   984
            (fn _ =>
berghofe@18010
   985
              simp_tac (HOL_basic_ss addsimps (supp_def ::
wenzelm@46161
   986
                 Un_assoc :: @{thm de_Morgan_conj} :: Collect_disj_eq :: finite_Un ::
wenzelm@45654
   987
                 Collect_False_empty :: finite_emptyI :: @{thms simp_thms} @
wenzelm@20046
   988
                 abs_perm @ abs_fresh @ inject_thms' @ perm_thms')) 1)
berghofe@17872
   989
        in
berghofe@17872
   990
          (supp_thm,
berghofe@28731
   991
           Goal.prove_global thy8 [] [] (augment_sort thy8 pt_cp_sort
berghofe@28731
   992
             (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@28731
   993
               (fresh c,
wenzelm@45740
   994
                if null dts then @{term True}
berghofe@28731
   995
                else foldr1 HOLogic.mk_conj (map fresh args2)))))
berghofe@17872
   996
             (fn _ =>
berghofe@24459
   997
               simp_tac (HOL_ss addsimps [Un_iff, empty_iff, fresh_def, supp_thm]) 1))
wenzelm@32952
   998
        end) atoms) constrs
berghofe@19833
   999
      end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ inject_thms ~~ perm_simps')));
berghofe@17872
  1000
berghofe@18107
  1001
    (**** weak induction theorem ****)
berghofe@18016
  1002
wenzelm@33244
  1003
    fun mk_indrule_lemma (((i, _), T), U) (prems, concls) =
berghofe@18016
  1004
      let
wenzelm@45838
  1005
        val Rep_t = Const (nth rep_names i, T --> U) $ Datatype_Aux.mk_Free "x" T i;
berghofe@18016
  1006
wenzelm@42364
  1007
        val Abs_t =  Const (nth abs_names i, U --> T);
berghofe@18016
  1008
wenzelm@45838
  1009
      in
wenzelm@45838
  1010
        (prems @ [HOLogic.imp $
wenzelm@42364
  1011
            (Const (nth rep_set_names'' i, U --> HOLogic.boolT) $ Rep_t) $
wenzelm@45838
  1012
              (Datatype_Aux.mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))],
wenzelm@45838
  1013
         concls @
wenzelm@45838
  1014
           [Datatype_Aux.mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ Datatype_Aux.mk_Free "x" T i])
berghofe@18016
  1015
      end;
berghofe@18016
  1016
berghofe@18016
  1017
    val (indrule_lemma_prems, indrule_lemma_concls) =
wenzelm@33244
  1018
      fold mk_indrule_lemma (descr'' ~~ recTs ~~ recTs') ([], []);
berghofe@18016
  1019
wenzelm@20046
  1020
    val indrule_lemma = Goal.prove_global thy8 [] []
berghofe@18016
  1021
      (Logic.mk_implies
wenzelm@45838
  1022
        (HOLogic.mk_Trueprop (Datatype_Aux.mk_conj indrule_lemma_prems),
wenzelm@45838
  1023
         HOLogic.mk_Trueprop (Datatype_Aux.mk_conj indrule_lemma_concls))) (fn _ => EVERY
berghofe@18016
  1024
           [REPEAT (etac conjE 1),
berghofe@18016
  1025
            REPEAT (EVERY
berghofe@18016
  1026
              [TRY (rtac conjI 1), full_simp_tac (HOL_basic_ss addsimps Rep_inverse_thms) 1,
wenzelm@20046
  1027
               etac mp 1, resolve_tac Rep_thms 1])]);
berghofe@18016
  1028
berghofe@18016
  1029
    val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma)));
berghofe@18016
  1030
    val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else
berghofe@18016
  1031
      map (Free o apfst fst o dest_Var) Ps;
berghofe@18016
  1032
    val indrule_lemma' = cterm_instantiate
berghofe@18016
  1033
      (map (cterm_of thy8) Ps ~~ map (cterm_of thy8) frees) indrule_lemma;
berghofe@18016
  1034
berghofe@19833
  1035
    val Abs_inverse_thms' = map (fn r => r RS subst) Abs_inverse_thms;
berghofe@18016
  1036
wenzelm@45822
  1037
    val dt_induct_prop = Datatype_Prop.make_ind descr';
wenzelm@20046
  1038
    val dt_induct = Goal.prove_global thy8 []
berghofe@18016
  1039
      (Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop)
wenzelm@26711
  1040
      (fn {prems, ...} => EVERY
berghofe@18016
  1041
        [rtac indrule_lemma' 1,
wenzelm@45735
  1042
         (Datatype_Aux.ind_tac rep_induct [] THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1,
berghofe@18016
  1043
         EVERY (map (fn (prem, r) => (EVERY
berghofe@18016
  1044
           [REPEAT (eresolve_tac Abs_inverse_thms' 1),
wenzelm@36945
  1045
            simp_tac (HOL_basic_ss addsimps [Thm.symmetric r]) 1,
berghofe@18016
  1046
            DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)]))
wenzelm@20046
  1047
                (prems ~~ constr_defs))]);
berghofe@18016
  1048
wenzelm@45906
  1049
    val case_names_induct = Datatype.mk_case_names_induct descr'';
berghofe@18016
  1050
berghofe@18066
  1051
    (**** prove that new datatypes have finite support ****)
berghofe@18066
  1052
urbanc@18246
  1053
    val _ = warning "proving finite support for the new datatype";
urbanc@18246
  1054
haftmann@33968
  1055
    val indnames = Datatype_Prop.make_tnames recTs;
berghofe@18066
  1056
wenzelm@39557
  1057
    val abs_supp = Global_Theory.get_thms thy8 "abs_supp";
wenzelm@39557
  1058
    val supp_atm = Global_Theory.get_thms thy8 "supp_atm";
berghofe@18066
  1059
berghofe@18066
  1060
    val finite_supp_thms = map (fn atom =>
berghofe@18066
  1061
      let val atomT = Type (atom, [])
wenzelm@35021
  1062
      in map Drule.export_without_context (List.take
wenzelm@45838
  1063
        (Datatype_Aux.split_conj_thm (Goal.prove_global thy8 [] []
berghofe@28731
  1064
           (augment_sort thy8 (fs_class_of thy8 atom :: pt_cp_sort)
berghofe@28731
  1065
             (HOLogic.mk_Trueprop
berghofe@28731
  1066
               (foldr1 HOLogic.mk_conj (map (fn (s, T) =>
berghofe@28731
  1067
                 Const ("Finite_Set.finite", HOLogic.mk_setT atomT --> HOLogic.boolT) $
berghofe@28731
  1068
                   (Const ("Nominal.supp", T --> HOLogic.mk_setT atomT) $ Free (s, T)))
berghofe@28731
  1069
                   (indnames ~~ recTs)))))
wenzelm@45735
  1070
           (fn _ => Datatype_Aux.ind_tac dt_induct indnames 1 THEN
wenzelm@32149
  1071
            ALLGOALS (asm_full_simp_tac (global_simpset_of thy8 addsimps
urbanc@18067
  1072
              (abs_supp @ supp_atm @
wenzelm@39557
  1073
               Global_Theory.get_thms thy8 ("fs_" ^ Long_Name.base_name atom ^ "1") @
wenzelm@32952
  1074
               flat supp_thms))))),
berghofe@18066
  1075
         length new_type_names))
berghofe@18066
  1076
      end) atoms;
berghofe@18066
  1077
krauss@18759
  1078
    val simp_atts = replicate (length new_type_names) [Simplifier.simp_add];
berghofe@18658
  1079
wenzelm@32960
  1080
        (* Function to add both the simp and eqvt attributes *)
urbanc@22245
  1081
        (* These two attributes are duplicated on all the types in the mutual nominal datatypes *)
urbanc@22245
  1082
urbanc@22245
  1083
    val simp_eqvt_atts = replicate (length new_type_names) [Simplifier.simp_add, NominalThmDecls.eqvt_add];
urbanc@22245
  1084
 
berghofe@18658
  1085
    val (_, thy9) = thy8 |>
wenzelm@24712
  1086
      Sign.add_path big_name |>
wenzelm@39557
  1087
      Global_Theory.add_thms [((Binding.name "induct", dt_induct), [case_names_induct])] ||>>
wenzelm@39557
  1088
      Global_Theory.add_thmss [((Binding.name "inducts", projections dt_induct), [case_names_induct])] ||>
wenzelm@24712
  1089
      Sign.parent_path ||>>
haftmann@33968
  1090
      Datatype_Aux.store_thmss_atts "distinct" new_type_names simp_atts distinct_thms ||>>
haftmann@33968
  1091
      Datatype_Aux.store_thmss "constr_rep" new_type_names constr_rep_thmss ||>>
haftmann@33968
  1092
      Datatype_Aux.store_thmss_atts "perm" new_type_names simp_eqvt_atts perm_simps' ||>>
haftmann@33968
  1093
      Datatype_Aux.store_thmss "inject" new_type_names inject_thms ||>>
haftmann@33968
  1094
      Datatype_Aux.store_thmss "supp" new_type_names supp_thms ||>>
haftmann@33968
  1095
      Datatype_Aux.store_thmss_atts "fresh" new_type_names simp_atts fresh_thms ||>
berghofe@18658
  1096
      fold (fn (atom, ths) => fn thy =>
berghofe@28736
  1097
        let
berghofe@28736
  1098
          val class = fs_class_of thy atom;
wenzelm@36428
  1099
          val sort = Sign.minimize_sort thy (Sign.certify_sort thy (class :: pt_cp_sort));
berghofe@28736
  1100
        in fold (fn Type (s, Ts) => AxClass.prove_arity
berghofe@28736
  1101
          (s, map (inter_sort thy sort o snd o dest_TFree) Ts, [class])
berghofe@28736
  1102
          (Class.intro_classes_tac [] THEN resolve_tac ths 1)) newTs thy
berghofe@18658
  1103
        end) (atoms ~~ finite_supp_thms);
berghofe@18658
  1104
berghofe@18107
  1105
    (**** strong induction theorem ****)
berghofe@18107
  1106
berghofe@18107
  1107
    val pnames = if length descr'' = 1 then ["P"]
berghofe@18107
  1108
      else map (fn i => "P" ^ string_of_int i) (1 upto length descr'');
berghofe@18245
  1109
    val ind_sort = if null dt_atomTs then HOLogic.typeS
wenzelm@36428
  1110
      else Sign.minimize_sort thy9 (Sign.certify_sort thy9 (map (fs_class_of thy9) dt_atoms));
berghofe@18107
  1111
    val fsT = TFree ("'n", ind_sort);
berghofe@18658
  1112
    val fsT' = TFree ("'n", HOLogic.typeS);
berghofe@18107
  1113
berghofe@18658
  1114
    val fresh_fs = map (fn (s, T) => (T, Free (s, fsT' --> HOLogic.mk_setT T)))
haftmann@33968
  1115
      (Datatype_Prop.indexify_names (replicate (length dt_atomTs) "f") ~~ dt_atomTs);
berghofe@18658
  1116
wenzelm@42364
  1117
    fun make_pred fsT i T = Free (nth pnames i, fsT --> T --> HOLogic.boolT);
berghofe@18107
  1118
berghofe@19851
  1119
    fun mk_fresh1 xs [] = []
berghofe@19851
  1120
      | mk_fresh1 xs ((y as (_, T)) :: ys) = map (fn x => HOLogic.mk_Trueprop
berghofe@19851
  1121
            (HOLogic.mk_not (HOLogic.mk_eq (Free y, Free x))))
berghofe@19851
  1122
              (filter (fn (_, U) => T = U) (rev xs)) @
berghofe@19851
  1123
          mk_fresh1 (y :: xs) ys;
berghofe@19851
  1124
berghofe@19851
  1125
    fun mk_fresh2 xss [] = []
wenzelm@32952
  1126
      | mk_fresh2 xss ((p as (ys, _)) :: yss) = maps (fn y as (_, T) =>
berghofe@19851
  1127
            map (fn (_, x as (_, U)) => HOLogic.mk_Trueprop
wenzelm@32952
  1128
              (fresh_const T U $ Free y $ Free x)) (rev xss @ yss)) ys @
berghofe@19851
  1129
          mk_fresh2 (p :: xss) yss;
berghofe@19851
  1130
berghofe@18658
  1131
    fun make_ind_prem fsT f k T ((cname, cargs), idxs) =
berghofe@18107
  1132
      let
wenzelm@45838
  1133
        val recs = filter Datatype_Aux.is_rec_type cargs;
wenzelm@45838
  1134
        val Ts = map (Datatype_Aux.typ_of_dtyp descr'') cargs;
wenzelm@45838
  1135
        val recTs' = map (Datatype_Aux.typ_of_dtyp descr'') recs;
haftmann@33968
  1136
        val tnames = Name.variant_list pnames (Datatype_Prop.make_tnames Ts);
wenzelm@45838
  1137
        val rec_tnames = map fst (filter (Datatype_Aux.is_rec_type o snd) (tnames ~~ cargs));
berghofe@18107
  1138
        val frees = tnames ~~ Ts;
berghofe@19710
  1139
        val frees' = partition_cargs idxs frees;
wenzelm@43324
  1140
        val z = (singleton (Name.variant_list tnames) "z", fsT);
berghofe@18107
  1141
berghofe@18107
  1142
        fun mk_prem ((dt, s), T) =
berghofe@18107
  1143
          let
berghofe@18107
  1144
            val (Us, U) = strip_type T;
wenzelm@45838
  1145
            val l = length Us;
wenzelm@45838
  1146
          in
wenzelm@46218
  1147
            Logic.list_all (z :: map (pair "x") Us,
wenzelm@45838
  1148
              HOLogic.mk_Trueprop
wenzelm@45838
  1149
                (make_pred fsT (Datatype_Aux.body_index dt) U $ Bound l $
wenzelm@45838
  1150
                  Datatype_Aux.app_bnds (Free (s, T)) l))
berghofe@18107
  1151
          end;
berghofe@18107
  1152
berghofe@18107
  1153
        val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs');
berghofe@18107
  1154
        val prems' = map (fn p as (_, T) => HOLogic.mk_Trueprop
wenzelm@32952
  1155
            (f T (Free p) (Free z))) (maps fst frees') @
wenzelm@32952
  1156
          mk_fresh1 [] (maps fst frees') @
berghofe@19710
  1157
          mk_fresh2 [] frees'
berghofe@18107
  1158
wenzelm@46215
  1159
      in
wenzelm@46215
  1160
        fold_rev (Logic.all o Free) (frees @ [z])
wenzelm@46215
  1161
          (Logic.list_implies (prems' @ prems,
wenzelm@46215
  1162
            HOLogic.mk_Trueprop (make_pred fsT k T $ Free z $
wenzelm@46215
  1163
              list_comb (Const (cname, Ts ---> T), map Free frees))))
berghofe@18107
  1164
      end;
berghofe@18107
  1165
wenzelm@32952
  1166
    val ind_prems = maps (fn (((i, (_, _, constrs)), (_, idxss)), T) =>
berghofe@18658
  1167
      map (make_ind_prem fsT (fn T => fn t => fn u =>
berghofe@25823
  1168
        fresh_const T fsT $ t $ u) i T)
wenzelm@32952
  1169
          (constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs);
haftmann@33968
  1170
    val tnames = Datatype_Prop.make_tnames recTs;
wenzelm@20071
  1171
    val zs = Name.variant_list tnames (replicate (length descr'') "z");
haftmann@38795
  1172
    val ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop @{const_name HOL.conj})
berghofe@18658
  1173
      (map (fn ((((i, _), T), tname), z) =>
berghofe@18658
  1174
        make_pred fsT i T $ Free (z, fsT) $ Free (tname, T))
berghofe@18658
  1175
        (descr'' ~~ recTs ~~ tnames ~~ zs)));
berghofe@18107
  1176
    val induct = Logic.list_implies (ind_prems, ind_concl);
berghofe@18107
  1177
berghofe@18658
  1178
    val ind_prems' =
wenzelm@46215
  1179
      map (fn (_, f as Free (_, T)) => Logic.all (Free ("x", fsT'))
wenzelm@46215
  1180
        (HOLogic.mk_Trueprop (Const ("Finite_Set.finite",
huffman@44692
  1181
          Term.range_type T -->
berghofe@26806
  1182
            HOLogic.boolT) $ (f $ Free ("x", fsT'))))) fresh_fs @
wenzelm@32952
  1183
      maps (fn (((i, (_, _, constrs)), (_, idxss)), T) =>
berghofe@18658
  1184
        map (make_ind_prem fsT' (fn T => fn t => fn u => HOLogic.Not $
berghofe@18658
  1185
          HOLogic.mk_mem (t, the (AList.lookup op = fresh_fs T) $ u)) i T)
wenzelm@32952
  1186
            (constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs);
haftmann@38795
  1187
    val ind_concl' = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop @{const_name HOL.conj})
berghofe@18658
  1188
      (map (fn ((((i, _), T), tname), z) =>
berghofe@18658
  1189
        make_pred fsT' i T $ Free (z, fsT') $ Free (tname, T))
berghofe@18658
  1190
        (descr'' ~~ recTs ~~ tnames ~~ zs)));
berghofe@18658
  1191
    val induct' = Logic.list_implies (ind_prems', ind_concl');
berghofe@18658
  1192
berghofe@18658
  1193
    val aux_ind_vars =
haftmann@33968
  1194
      (Datatype_Prop.indexify_names (replicate (length dt_atomTs) "pi") ~~
berghofe@18658
  1195
       map mk_permT dt_atomTs) @ [("z", fsT')];
berghofe@18658
  1196
    val aux_ind_Ts = rev (map snd aux_ind_vars);
haftmann@38795
  1197
    val aux_ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop @{const_name HOL.conj})
berghofe@18658
  1198
      (map (fn (((i, _), T), tname) =>
berghofe@18658
  1199
        HOLogic.list_all (aux_ind_vars, make_pred fsT' i T $ Bound 0 $
berghofe@22311
  1200
          fold_rev (mk_perm aux_ind_Ts) (map Bound (length dt_atomTs downto 1))
berghofe@22311
  1201
            (Free (tname, T))))
berghofe@18658
  1202
        (descr'' ~~ recTs ~~ tnames)));
berghofe@18658
  1203
berghofe@28731
  1204
    val fin_set_supp = map (fn s =>
berghofe@28731
  1205
      at_inst_of thy9 s RS at_fin_set_supp) dt_atoms;
berghofe@28731
  1206
    val fin_set_fresh = map (fn s =>
berghofe@28731
  1207
      at_inst_of thy9 s RS at_fin_set_fresh) dt_atoms;
berghofe@25951
  1208
    val pt1_atoms = map (fn Type (s, _) =>
wenzelm@39557
  1209
      Global_Theory.get_thm thy9 ("pt_" ^ Long_Name.base_name s ^ "1")) dt_atomTs;
berghofe@25951
  1210
    val pt2_atoms = map (fn Type (s, _) =>
wenzelm@39557
  1211
      Global_Theory.get_thm thy9 ("pt_" ^ Long_Name.base_name s ^ "2") RS sym) dt_atomTs;
wenzelm@39557
  1212
    val exists_fresh' = Global_Theory.get_thms thy9 "exists_fresh'";
wenzelm@39557
  1213
    val fs_atoms = Global_Theory.get_thms thy9 "fin_supp";
wenzelm@39557
  1214
    val abs_supp = Global_Theory.get_thms thy9 "abs_supp";
wenzelm@39557
  1215
    val perm_fresh_fresh = Global_Theory.get_thms thy9 "perm_fresh_fresh";
wenzelm@39557
  1216
    val calc_atm = Global_Theory.get_thms thy9 "calc_atm";
wenzelm@39557
  1217
    val fresh_atm = Global_Theory.get_thms thy9 "fresh_atm";
wenzelm@39557
  1218
    val fresh_left = Global_Theory.get_thms thy9 "fresh_left";
wenzelm@39557
  1219
    val perm_swap = Global_Theory.get_thms thy9 "perm_swap";
berghofe@18658
  1220
berghofe@25951
  1221
    fun obtain_fresh_name' ths ts T (freshs1, freshs2, ctxt) =
berghofe@18658
  1222
      let
berghofe@25951
  1223
        val p = foldr1 HOLogic.mk_prod (ts @ freshs1);
berghofe@25951
  1224
        val ex = Goal.prove ctxt [] [] (HOLogic.mk_Trueprop
berghofe@25951
  1225
            (HOLogic.exists_const T $ Abs ("x", T,
berghofe@25951
  1226
              fresh_const T (fastype_of p) $
berghofe@25951
  1227
                Bound 0 $ p)))
berghofe@25951
  1228
          (fn _ => EVERY
berghofe@25951
  1229
            [resolve_tac exists_fresh' 1,
berghofe@25951
  1230
             simp_tac (HOL_ss addsimps (supp_prod :: finite_Un :: fs_atoms @
berghofe@25951
  1231
               fin_set_supp @ ths)) 1]);
wenzelm@32202
  1232
        val (([(_, cx)], ths), ctxt') = Obtain.result
berghofe@25951
  1233
          (fn _ => EVERY
berghofe@25951
  1234
            [etac exE 1,
berghofe@25951
  1235
             full_simp_tac (HOL_ss addsimps (fresh_prod :: fresh_atm)) 1,
berghofe@25951
  1236
             REPEAT (etac conjE 1)])
berghofe@25951
  1237
          [ex] ctxt
berghofe@25951
  1238
      in (freshs1 @ [term_of cx], freshs2 @ ths, ctxt') end;
berghofe@25951
  1239
berghofe@25951
  1240
    fun fresh_fresh_inst thy a b =
berghofe@25951
  1241
      let
berghofe@25951
  1242
        val T = fastype_of a;
berghofe@25951
  1243
        val SOME th = find_first (fn th => case prop_of th of
berghofe@25951
  1244
            _ $ (_ $ (Const (_, Type (_, [U, _])) $ _ $ _)) $ _ => U = T
berghofe@25951
  1245
          | _ => false) perm_fresh_fresh
berghofe@18658
  1246
      in
berghofe@25951
  1247
        Drule.instantiate' []
berghofe@25951
  1248
          [SOME (cterm_of thy a), NONE, SOME (cterm_of thy b)] th
berghofe@18658
  1249
      end;
urbanc@18104
  1250
berghofe@28731
  1251
    val fs_cp_sort =
berghofe@28731
  1252
      map (fs_class_of thy9) dt_atoms @
haftmann@33040
  1253
      maps (fn s => map (cp_class_of thy9 s) (remove (op =) s dt_atoms)) dt_atoms;
berghofe@28731
  1254
berghofe@19710
  1255
    (**********************************************************************
berghofe@19710
  1256
      The subgoals occurring in the proof of induct_aux have the
berghofe@19710
  1257
      following parameters:
berghofe@19710
  1258
berghofe@25951
  1259
        x_1 ... x_k p_1 ... p_m z
berghofe@19710
  1260
berghofe@19710
  1261
      where
berghofe@19710
  1262
berghofe@19710
  1263
        x_i : constructor arguments (introduced by weak induction rule)
berghofe@19710
  1264
        p_i : permutations (one for each atom type in the data type)
berghofe@19710
  1265
        z   : freshness context
berghofe@19710
  1266
    ***********************************************************************)
berghofe@19710
  1267
berghofe@19710
  1268
    val _ = warning "proving strong induction theorem ...";
berghofe@19710
  1269
berghofe@28731
  1270
    val induct_aux = Goal.prove_global thy9 []
berghofe@28731
  1271
        (map (augment_sort thy9 fs_cp_sort) ind_prems')
berghofe@28731
  1272
        (augment_sort thy9 fs_cp_sort ind_concl') (fn {prems, context} =>
berghofe@25951
  1273
      let
berghofe@25951
  1274
        val (prems1, prems2) = chop (length dt_atomTs) prems;
berghofe@25951
  1275
        val ind_ss2 = HOL_ss addsimps
berghofe@25951
  1276
          finite_Diff :: abs_fresh @ abs_supp @ fs_atoms;
berghofe@25951
  1277
        val ind_ss1 = ind_ss2 addsimps fresh_left @ calc_atm @
berghofe@25951
  1278
          fresh_atm @ rev_simps @ app_simps;
berghofe@25951
  1279
        val ind_ss3 = HOL_ss addsimps abs_fun_eq1 ::
berghofe@25951
  1280
          abs_perm @ calc_atm @ perm_swap;
berghofe@25951
  1281
        val ind_ss4 = HOL_basic_ss addsimps fresh_left @ prems1 @
berghofe@25951
  1282
          fin_set_fresh @ calc_atm;
berghofe@25951
  1283
        val ind_ss5 = HOL_basic_ss addsimps pt1_atoms;
berghofe@25951
  1284
        val ind_ss6 = HOL_basic_ss addsimps flat perm_simps';
berghofe@28731
  1285
        val th = Goal.prove context [] []
berghofe@28731
  1286
          (augment_sort thy9 fs_cp_sort aux_ind_concl)
berghofe@25951
  1287
          (fn {context = context1, ...} =>
wenzelm@45735
  1288
             EVERY (Datatype_Aux.ind_tac dt_induct tnames 1 ::
berghofe@25951
  1289
               maps (fn ((_, (_, _, constrs)), (_, constrs')) =>
berghofe@25951
  1290
                 map (fn ((cname, cargs), is) =>
berghofe@25951
  1291
                   REPEAT (rtac allI 1) THEN
berghofe@25951
  1292
                   SUBPROOF (fn {prems = iprems, params, concl,
berghofe@25951
  1293
                       context = context2, ...} =>
berghofe@18658
  1294
                     let
berghofe@25951
  1295
                       val concl' = term_of concl;
berghofe@25951
  1296
                       val _ $ (_ $ _ $ u) = concl';
berghofe@25951
  1297
                       val U = fastype_of u;
berghofe@25951
  1298
                       val (xs, params') =
wenzelm@32202
  1299
                         chop (length cargs) (map (term_of o #2) params);
berghofe@25951
  1300
                       val Ts = map fastype_of xs;
berghofe@25951
  1301
                       val cnstr = Const (cname, Ts ---> U);
berghofe@25951
  1302
                       val (pis, z) = split_last params';
berghofe@25951
  1303
                       val mk_pi = fold_rev (mk_perm []) pis;
berghofe@25951
  1304
                       val xs' = partition_cargs is xs;
berghofe@25951
  1305
                       val xs'' = map (fn (ts, u) => (map mk_pi ts, mk_pi u)) xs';
berghofe@25951
  1306
                       val ts = maps (fn (ts, u) => ts @ [u]) xs'';
berghofe@25951
  1307
                       val (freshs1, freshs2, context3) = fold (fn t =>
berghofe@25951
  1308
                         let val T = fastype_of t
berghofe@25951
  1309
                         in obtain_fresh_name' prems1
berghofe@25951
  1310
                           (the (AList.lookup op = fresh_fs T) $ z :: ts) T
berghofe@25951
  1311
                         end) (maps fst xs') ([], [], context2);
berghofe@25951
  1312
                       val freshs1' = unflat (map fst xs') freshs1;
berghofe@25951
  1313
                       val freshs2' = map (Simplifier.simplify ind_ss4)
berghofe@25951
  1314
                         (mk_not_sym freshs2);
berghofe@25951
  1315
                       val ind_ss1' = ind_ss1 addsimps freshs2';
berghofe@25951
  1316
                       val ind_ss3' = ind_ss3 addsimps freshs2';
berghofe@25951
  1317
                       val rename_eq =
berghofe@25951
  1318
                         if forall (null o fst) xs' then []
berghofe@25951
  1319
                         else [Goal.prove context3 [] []
berghofe@25951
  1320
                           (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@25951
  1321
                             (list_comb (cnstr, ts),
berghofe@25951
  1322
                              list_comb (cnstr, maps (fn ((bs, t), cs) =>
berghofe@25951
  1323
                                cs @ [fold_rev (mk_perm []) (map perm_of_pair
berghofe@25951
  1324
                                  (bs ~~ cs)) t]) (xs'' ~~ freshs1')))))
berghofe@25951
  1325
                           (fn _ => EVERY
berghofe@25951
  1326
                              (simp_tac (HOL_ss addsimps flat inject_thms) 1 ::
berghofe@25951
  1327
                               REPEAT (FIRSTGOAL (rtac conjI)) ::
berghofe@25951
  1328
                               maps (fn ((bs, t), cs) =>
berghofe@25951
  1329
                                 if null bs then []
berghofe@25951
  1330
                                 else rtac sym 1 :: maps (fn (b, c) =>
berghofe@25951
  1331
                                   [rtac trans 1, rtac sym 1,
berghofe@25951
  1332
                                    rtac (fresh_fresh_inst thy9 b c) 1,
berghofe@25951
  1333
                                    simp_tac ind_ss1' 1,
berghofe@25951
  1334
                                    simp_tac ind_ss2 1,
berghofe@25951
  1335
                                    simp_tac ind_ss3' 1]) (bs ~~ cs))
berghofe@25951
  1336
                                 (xs'' ~~ freshs1')))];
berghofe@25951
  1337
                       val th = Goal.prove context3 [] [] concl' (fn _ => EVERY
berghofe@25951
  1338
                         [simp_tac (ind_ss6 addsimps rename_eq) 1,
berghofe@25951
  1339
                          cut_facts_tac iprems 1,
berghofe@25951
  1340
                          (resolve_tac prems THEN_ALL_NEW
berghofe@25951
  1341
                            SUBGOAL (fn (t, i) => case Logic.strip_assums_concl t of
berghofe@25951
  1342
                                _ $ (Const ("Nominal.fresh", _) $ _ $ _) =>
berghofe@25951
  1343
                                  simp_tac ind_ss1' i
haftmann@38558
  1344
                              | _ $ (Const (@{const_name Not}, _) $ _) =>
berghofe@25951
  1345
                                  resolve_tac freshs2' i
berghofe@25951
  1346
                              | _ => asm_simp_tac (HOL_basic_ss addsimps
berghofe@25951
  1347
                                  pt2_atoms addsimprocs [perm_simproc]) i)) 1])
wenzelm@42361
  1348
                       val final = Proof_Context.export context3 context2 [th]
berghofe@18658
  1349
                     in
berghofe@25951
  1350
                       resolve_tac final 1
berghofe@25951
  1351
                     end) context1 1) (constrs ~~ constrs')) (descr'' ~~ ndescr)))
berghofe@25951
  1352
      in
berghofe@25951
  1353
        EVERY
berghofe@25951
  1354
          [cut_facts_tac [th] 1,
wenzelm@27228
  1355
           REPEAT (eresolve_tac [conjE, @{thm allE_Nil}] 1),
berghofe@25951
  1356
           REPEAT (etac allE 1),
berghofe@25951
  1357
           REPEAT (TRY (rtac conjI 1) THEN asm_full_simp_tac ind_ss5 1)]
berghofe@25951
  1358
      end);
berghofe@18658
  1359
berghofe@18658
  1360
    val induct_aux' = Thm.instantiate ([],
berghofe@28731
  1361
      map (fn (s, v as Var (_, T)) =>
berghofe@28731
  1362
        (cterm_of thy9 v, cterm_of thy9 (Free (s, T))))
berghofe@28731
  1363
          (pnames ~~ map head_of (HOLogic.dest_conj
berghofe@28731
  1364
             (HOLogic.dest_Trueprop (concl_of induct_aux)))) @
berghofe@18658
  1365
      map (fn (_, f) =>
wenzelm@35845
  1366
        let val f' = Logic.varify_global f
berghofe@18658
  1367
        in (cterm_of thy9 f',
berghofe@19494
  1368
          cterm_of thy9 (Const ("Nominal.supp", fastype_of f')))
berghofe@18658
  1369
        end) fresh_fs) induct_aux;
berghofe@18658
  1370
berghofe@28731
  1371
    val induct = Goal.prove_global thy9 []
berghofe@28731
  1372
      (map (augment_sort thy9 fs_cp_sort) ind_prems)
berghofe@28731
  1373
      (augment_sort thy9 fs_cp_sort ind_concl)
wenzelm@26711
  1374
      (fn {prems, ...} => EVERY
berghofe@18658
  1375
         [rtac induct_aux' 1,
berghofe@25951
  1376
          REPEAT (resolve_tac fs_atoms 1),
berghofe@18658
  1377
          REPEAT ((resolve_tac prems THEN_ALL_NEW
wenzelm@39159
  1378
            (etac @{thm meta_spec} ORELSE' full_simp_tac (HOL_basic_ss addsimps [fresh_def]))) 1)])
berghofe@18658
  1379
berghofe@18658
  1380
    val (_, thy10) = thy9 |>
wenzelm@24712
  1381
      Sign.add_path big_name |>
wenzelm@39557
  1382
      Global_Theory.add_thms [((Binding.name "strong_induct'", induct_aux), [])] ||>>
wenzelm@39557
  1383
      Global_Theory.add_thms [((Binding.name "strong_induct", induct), [case_names_induct])] ||>>
wenzelm@39557
  1384
      Global_Theory.add_thmss [((Binding.name "strong_inducts", projections induct), [case_names_induct])];
berghofe@18658
  1385
berghofe@19322
  1386
    (**** recursion combinator ****)
berghofe@19251
  1387
berghofe@19322
  1388
    val _ = warning "defining recursion combinator ...";
berghofe@19251
  1389
wenzelm@45741
  1390
    val used = fold Term.add_tfree_namesT recTs [];
berghofe@19251
  1391
wenzelm@45822
  1392
    val (rec_result_Ts', rec_fn_Ts') = Datatype_Prop.make_primrec_Ts descr' used;
berghofe@19985
  1393
wenzelm@21365
  1394
    val rec_sort = if null dt_atomTs then HOLogic.typeS else
wenzelm@36428
  1395
      Sign.minimize_sort thy10 (Sign.certify_sort thy10 pt_cp_sort);
berghofe@19985
  1396
berghofe@19985
  1397
    val rec_result_Ts = map (fn TFree (s, _) => TFree (s, rec_sort)) rec_result_Ts';
berghofe@19985
  1398
    val rec_fn_Ts = map (typ_subst_atomic (rec_result_Ts' ~~ rec_result_Ts)) rec_fn_Ts';
berghofe@19251
  1399
berghofe@21021
  1400
    val rec_set_Ts = map (fn (T1, T2) =>
berghofe@21021
  1401
      rec_fn_Ts @ [T1, T2] ---> HOLogic.boolT) (recTs ~~ rec_result_Ts);
berghofe@19251
  1402
berghofe@19322
  1403
    val big_rec_name = big_name ^ "_rec_set";
berghofe@21021
  1404
    val rec_set_names' =
berghofe@21021
  1405
      if length descr'' = 1 then [big_rec_name] else
berghofe@21021
  1406
        map ((curry (op ^) (big_rec_name ^ "_")) o string_of_int)
berghofe@21021
  1407
          (1 upto (length descr''));
haftmann@28965
  1408
    val rec_set_names =  map (Sign.full_bname thy10) rec_set_names';
berghofe@19251
  1409
wenzelm@45838
  1410
    val rec_fns = map (uncurry (Datatype_Aux.mk_Free "f"))
berghofe@19322
  1411
      (rec_fn_Ts ~~ (1 upto (length rec_fn_Ts)));
berghofe@21021
  1412
    val rec_sets' = map (fn c => list_comb (Free c, rec_fns))
berghofe@21021
  1413
      (rec_set_names' ~~ rec_set_Ts);
berghofe@19322
  1414
    val rec_sets = map (fn c => list_comb (Const c, rec_fns))
berghofe@19322
  1415
      (rec_set_names ~~ rec_set_Ts);
berghofe@19251
  1416
berghofe@19322
  1417
    (* introduction rules for graph of recursion function *)
berghofe@19251
  1418
berghofe@20145
  1419
    val rec_preds = map (fn (a, T) =>
berghofe@20145
  1420
      Free (a, T --> HOLogic.boolT)) (pnames ~~ rec_result_Ts);
berghofe@20145
  1421
berghofe@20267
  1422
    fun mk_fresh3 rs [] = []
wenzelm@32952
  1423
      | mk_fresh3 rs ((p as (ys, z)) :: yss) = maps (fn y as (_, T) =>
wenzelm@32952
  1424
            map_filter (fn ((_, (_, x)), r as (_, U)) => if z = x then NONE
berghofe@20267
  1425
              else SOME (HOLogic.mk_Trueprop
wenzelm@32952
  1426
                (fresh_const T U $ Free y $ Free r))) rs) ys @
berghofe@20267
  1427
          mk_fresh3 rs yss;
berghofe@20267
  1428
berghofe@21088
  1429
    (* FIXME: avoid collisions with other variable names? *)
berghofe@21088
  1430
    val rec_ctxt = Free ("z", fsT');
berghofe@21088
  1431
wenzelm@33244
  1432
    fun make_rec_intr T p rec_set ((cname, cargs), idxs)
wenzelm@33244
  1433
        (rec_intr_ts, rec_prems, rec_prems', rec_eq_prems, l) =
berghofe@19251
  1434
      let
wenzelm@45838
  1435
        val Ts = map (Datatype_Aux.typ_of_dtyp descr'') cargs;
berghofe@19851
  1436
        val frees = map (fn i => "x" ^ string_of_int i) (1 upto length Ts) ~~ Ts;
berghofe@19851
  1437
        val frees' = partition_cargs idxs frees;
wenzelm@32952
  1438
        val binders = maps fst frees';
berghofe@20411
  1439
        val atomTs = distinct op = (maps (map snd o fst) frees');
wenzelm@32952
  1440
        val recs = map_filter
wenzelm@45896
  1441
          (fn ((_, Datatype.DtRec i), p) => SOME (i, p) | _ => NONE)
berghofe@19851
  1442
          (partition_cargs idxs cargs ~~ frees');
berghofe@19851
  1443
        val frees'' = map (fn i => "y" ^ string_of_int i) (1 upto length recs) ~~
wenzelm@42364
  1444
          map (fn (i, _) => nth rec_result_Ts i) recs;
berghofe@20145
  1445
        val prems1 = map (fn ((i, (_, x)), y) => HOLogic.mk_Trueprop
wenzelm@42364
  1446
          (nth rec_sets' i $ Free x $ Free y)) (recs ~~ frees'');
berghofe@20145
  1447
        val prems2 =
berghofe@20145
  1448
          map (fn f => map (fn p as (_, T) => HOLogic.mk_Trueprop
berghofe@25823
  1449
            (fresh_const T (fastype_of f) $ Free p $ f)) binders) rec_fns;
berghofe@21088
  1450
        val prems3 = mk_fresh1 [] binders @ mk_fresh2 [] frees';
berghofe@20145
  1451
        val prems4 = map (fn ((i, _), y) =>
wenzelm@42364
  1452
          HOLogic.mk_Trueprop (nth rec_preds i $ Free y)) (recs ~~ frees'');
berghofe@20267
  1453
        val prems5 = mk_fresh3 (recs ~~ frees'') frees';
berghofe@20411
  1454
        val prems6 = maps (fn aT => map (fn y as (_, T) => HOLogic.mk_Trueprop
berghofe@22274
  1455
          (Const ("Finite_Set.finite", HOLogic.mk_setT aT --> HOLogic.boolT) $
berghofe@22274
  1456
             (Const ("Nominal.supp", T --> HOLogic.mk_setT aT) $ Free y)))
berghofe@20411
  1457
               frees'') atomTs;
berghofe@21088
  1458
        val prems7 = map (fn x as (_, T) => HOLogic.mk_Trueprop
berghofe@25823
  1459
          (fresh_const T fsT' $ Free x $ rec_ctxt)) binders;
wenzelm@42364
  1460
        val result = list_comb (nth rec_fns l, map Free (frees @ frees''));
berghofe@20376
  1461
        val result_freshs = map (fn p as (_, T) =>
berghofe@25823
  1462
          fresh_const T (fastype_of result) $ Free p $ result) binders;
berghofe@20145
  1463
        val P = HOLogic.mk_Trueprop (p $ result)
berghofe@20145
  1464
      in
wenzelm@32952
  1465
        (rec_intr_ts @ [Logic.list_implies (flat prems2 @ prems3 @ prems1,
berghofe@21021
  1466
           HOLogic.mk_Trueprop (rec_set $
berghofe@21021
  1467
             list_comb (Const (cname, Ts ---> T), map Free frees) $ result))],
wenzelm@46215
  1468
         rec_prems @ [fold_rev (Logic.all o Free) (frees @ frees'') (Logic.list_implies (prems4, P))],
wenzelm@46215
  1469
         rec_prems' @ map (fn fr => fold_rev (Logic.all o Free) (frees @ frees'')
wenzelm@46215
  1470
           (Logic.list_implies (nth prems2 l @ prems3 @ prems5 @ prems7 @ prems6 @ [P],
berghofe@21054
  1471
             HOLogic.mk_Trueprop fr))) result_freshs,
wenzelm@32952
  1472
         rec_eq_prems @ [flat prems2 @ prems3],
berghofe@20145
  1473
         l + 1)
berghofe@19251
  1474
      end;
berghofe@19251
  1475
berghofe@20397
  1476
    val (rec_intr_ts, rec_prems, rec_prems', rec_eq_prems, _) =
wenzelm@33244
  1477
      fold (fn ((((d, d'), T), p), rec_set) =>
wenzelm@33244
  1478
        fold (make_rec_intr T p rec_set) (#3 (snd d) ~~ snd d'))
wenzelm@33244
  1479
          (descr'' ~~ ndescr ~~ recTs ~~ rec_preds ~~ rec_sets')
wenzelm@33244
  1480
          ([], [], [], [], 0);
berghofe@19251
  1481
wenzelm@21365
  1482
    val ({intrs = rec_intrs, elims = rec_elims, raw_induct = rec_induct, ...}, thy11) =
wenzelm@33278
  1483
      thy10
wenzelm@33278
  1484
      |> Sign.map_naming Name_Space.conceal
wenzelm@33726
  1485
      |> Inductive.add_inductive_global
wenzelm@33669
  1486
          {quiet_mode = #quiet config, verbose = false, alt_name = Binding.name big_rec_name,
wenzelm@49170
  1487
           coind = false, no_elim = false, no_ind = false, skip_mono = true}
haftmann@28965
  1488
          (map (fn (s, T) => ((Binding.name s, T), NoSyn)) (rec_set_names' ~~ rec_set_Ts))
wenzelm@26128
  1489
          (map dest_Free rec_fns)
wenzelm@33278
  1490
          (map (fn x => (Attrib.empty_binding, x)) rec_intr_ts) []
wenzelm@39557
  1491
      ||> Global_Theory.hide_fact true (Long_Name.append (Sign.full_bname thy10 big_rec_name) "induct")
wenzelm@33278
  1492
      ||> Sign.restore_naming thy10;
berghofe@19251
  1493
berghofe@19985
  1494
    (** equivariance **)
berghofe@19985
  1495
wenzelm@39557
  1496
    val fresh_bij = Global_Theory.get_thms thy11 "fresh_bij";
wenzelm@39557
  1497
    val perm_bij = Global_Theory.get_thms thy11 "perm_bij";
berghofe@19985
  1498
berghofe@19985
  1499
    val (rec_equiv_thms, rec_equiv_thms') = ListPair.unzip (map (fn aT =>
berghofe@19985
  1500
      let
berghofe@19985
  1501
        val permT = mk_permT aT;
berghofe@19985
  1502
        val pi = Free ("pi", permT);
wenzelm@45838
  1503
        val rec_fns_pi = map (mk_perm [] pi o uncurry (Datatype_Aux.mk_Free "f"))
berghofe@19985
  1504
          (rec_fn_Ts ~~ (1 upto (length rec_fn_Ts)));
berghofe@19985
  1505
        val rec_sets_pi = map (fn c => list_comb (Const c, rec_fns_pi))
berghofe@19985
  1506
          (rec_set_names ~~ rec_set_Ts);
berghofe@19985
  1507
        val ps = map (fn ((((T, U), R), R'), i) =>
berghofe@19985
  1508
          let
berghofe@19985
  1509
            val x = Free ("x" ^ string_of_int i, T);
berghofe@19985
  1510
            val y = Free ("y" ^ string_of_int i, U)
berghofe@19985
  1511
          in
berghofe@22311
  1512
            (R $ x $ y, R' $ mk_perm [] pi x $ mk_perm [] pi y)
berghofe@19985
  1513
          end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~ rec_sets_pi ~~ (1 upto length recTs));
wenzelm@45838
  1514
        val ths = map (fn th => Drule.export_without_context (th RS mp)) (Datatype_Aux.split_conj_thm
wenzelm@20046
  1515
          (Goal.prove_global thy11 [] []
berghofe@28731
  1516
            (augment_sort thy1 pt_cp_sort
berghofe@28731
  1517
              (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map HOLogic.mk_imp ps))))
berghofe@19985
  1518
            (fn _ => rtac rec_induct 1 THEN REPEAT
wenzelm@35232
  1519
               (simp_tac (Simplifier.global_context thy11 HOL_basic_ss
berghofe@27450
  1520
                  addsimps flat perm_simps'
berghofe@27450
  1521
                  addsimprocs [NominalPermeq.perm_simproc_app]) 1 THEN
berghofe@19985
  1522
                (resolve_tac rec_intrs THEN_ALL_NEW
berghofe@19985
  1523
                 asm_simp_tac (HOL_ss addsimps (fresh_bij @ perm_bij))) 1))))
wenzelm@20046
  1524
        val ths' = map (fn ((P, Q), th) =>
wenzelm@20046
  1525
          Goal.prove_global thy11 [] []
berghofe@28731
  1526
            (augment_sort thy1 pt_cp_sort
berghofe@28731
  1527
              (Logic.mk_implies (HOLogic.mk_Trueprop Q, HOLogic.mk_Trueprop P)))
berghofe@19985
  1528
            (fn _ => dtac (Thm.instantiate ([],
berghofe@19985
  1529
                 [(cterm_of thy11 (Var (("pi", 0), permT)),
berghofe@19985
  1530
                   cterm_of thy11 (Const ("List.rev", permT --> permT) $ pi))]) th) 1 THEN
wenzelm@20046
  1531
               NominalPermeq.perm_simp_tac HOL_ss 1)) (ps ~~ ths)
berghofe@19985
  1532
      in (ths, ths') end) dt_atomTs);
berghofe@19985
  1533
berghofe@19985
  1534
    (** finite support **)
berghofe@19985
  1535
berghofe@19985
  1536
    val rec_fin_supp_thms = map (fn aT =>
berghofe@19985
  1537
      let
wenzelm@30364
  1538
        val name = Long_Name.base_name (fst (dest_Type aT));
wenzelm@39557
  1539
        val fs_name = Global_Theory.get_thm thy11 ("fs_" ^ name ^ "1");
berghofe@19985
  1540
        val aset = HOLogic.mk_setT aT;
berghofe@22274
  1541
        val finite = Const ("Finite_Set.finite", aset --> HOLogic.boolT);
berghofe@22274
  1542
        val fins = map (fn (f, T) => HOLogic.mk_Trueprop
berghofe@22274
  1543
          (finite $ (Const ("Nominal.supp", T --> aset) $ f)))
berghofe@19985
  1544
            (rec_fns ~~ rec_fn_Ts)
berghofe@19985
  1545
      in
wenzelm@45838
  1546
        map (fn th => Drule.export_without_context (th RS mp)) (Datatype_Aux.split_conj_thm
berghofe@28731
  1547
          (Goal.prove_global thy11 []
berghofe@28731
  1548
            (map (augment_sort thy11 fs_cp_sort) fins)
berghofe@28731
  1549
            (augment_sort thy11 fs_cp_sort
berghofe@28731
  1550
              (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@28731
  1551
                (map (fn (((T, U), R), i) =>
berghofe@28731
  1552
                   let
berghofe@28731
  1553
                     val x = Free ("x" ^ string_of_int i, T);
berghofe@28731
  1554
                     val y = Free ("y" ^ string_of_int i, U)
berghofe@28731
  1555
                   in
berghofe@28731
  1556
                     HOLogic.mk_imp (R $ x $ y,
berghofe@28731
  1557
                       finite $ (Const ("Nominal.supp", U --> aset) $ y))
berghofe@28731
  1558
                   end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~
berghofe@28731
  1559
                     (1 upto length recTs))))))
wenzelm@26711
  1560
            (fn {prems = fins, ...} =>
wenzelm@26711
  1561
              (rtac rec_induct THEN_ALL_NEW cut_facts_tac fins) 1 THEN REPEAT
berghofe@19985
  1562
               (NominalPermeq.finite_guess_tac (HOL_ss addsimps [fs_name]) 1))))
berghofe@19985
  1563
      end) dt_atomTs;
berghofe@19985
  1564
berghofe@20376
  1565
    (** freshness **)
berghofe@20376
  1566
berghofe@20376
  1567
    val finite_premss = map (fn aT =>
berghofe@22274
  1568
      map (fn (f, T) => HOLogic.mk_Trueprop
berghofe@22274
  1569
        (Const ("Finite_Set.finite", HOLogic.mk_setT aT --> HOLogic.boolT) $
berghofe@22274
  1570
           (Const ("Nominal.supp", T --> HOLogic.mk_setT aT) $ f)))
berghofe@20376
  1571
           (rec_fns ~~ rec_fn_Ts)) dt_atomTs;
berghofe@20376
  1572
berghofe@28731
  1573
    val rec_fns' = map (augment_sort thy11 fs_cp_sort) rec_fns;
berghofe@28731
  1574
berghofe@20376
  1575
    val rec_fresh_thms = map (fn ((aT, eqvt_ths), finite_prems) =>
berghofe@20376
  1576
      let
wenzelm@30364
  1577
        val name = Long_Name.base_name (fst (dest_Type aT));
wenzelm@39557
  1578
        val fs_name = Global_Theory.get_thm thy11 ("fs_" ^ name ^ "1");
berghofe@20376
  1579
        val a = Free ("a", aT);
berghofe@20376
  1580
        val freshs = map (fn (f, fT) => HOLogic.mk_Trueprop
berghofe@25823
  1581
          (fresh_const aT fT $ a $ f)) (rec_fns ~~ rec_fn_Ts)
berghofe@20376
  1582
      in
berghofe@20376
  1583
        map (fn (((T, U), R), eqvt_th) =>
berghofe@20376
  1584
          let
berghofe@28731
  1585
            val x = Free ("x", augment_sort_typ thy11 fs_cp_sort T);
berghofe@20376
  1586
            val y = Free ("y", U);
berghofe@20376
  1587
            val y' = Free ("y'", U)
berghofe@20376
  1588
          in
wenzelm@42361
  1589
            Drule.export_without_context (Goal.prove (Proof_Context.init_global thy11) []
berghofe@28731
  1590
              (map (augment_sort thy11 fs_cp_sort)
berghofe@28731
  1591
                (finite_prems @
berghofe@28731
  1592
                   [HOLogic.mk_Trueprop (R $ x $ y),
berghofe@28731
  1593
                    HOLogic.mk_Trueprop (HOLogic.mk_all ("y'", U,
berghofe@28731
  1594
                      HOLogic.mk_imp (R $ x $ y', HOLogic.mk_eq (y', y)))),
berghofe@28731
  1595
                    HOLogic.mk_Trueprop (fresh_const aT T $ a $ x)] @
berghofe@28731
  1596
                 freshs))
berghofe@25823
  1597
              (HOLogic.mk_Trueprop (fresh_const aT U $ a $ y))
berghofe@20376
  1598
              (fn {prems, context} =>
berghofe@20376
  1599
                 let
berghofe@20376
  1600
                   val (finite_prems, rec_prem :: unique_prem ::
berghofe@20376
  1601
                     fresh_prems) = chop (length finite_prems) prems;
berghofe@20376
  1602
                   val unique_prem' = unique_prem RS spec RS mp;
berghofe@20376
  1603
                   val unique = [unique_prem', unique_prem' RS sym] MRS trans;
berghofe@20376
  1604
                   val _ $ (_ $ (_ $ S $ _)) $ _ = prop_of supports_fresh;
berghofe@28731
  1605
                   val tuple = foldr1 HOLogic.mk_prod (x :: rec_fns')
berghofe@20376
  1606
                 in EVERY
berghofe@20376
  1607
                   [rtac (Drule.cterm_instantiate
berghofe@20376
  1608
                      [(cterm_of thy11 S,
berghofe@20376
  1609
                        cterm_of thy11 (Const ("Nominal.supp",
berghofe@20376
  1610
                          fastype_of tuple --> HOLogic.mk_setT aT) $ tuple))]
berghofe@20376
  1611
                      supports_fresh) 1,
berghofe@20376
  1612
                    simp_tac (HOL_basic_ss addsimps
wenzelm@36945
  1613
                      [supports_def, Thm.symmetric fresh_def, fresh_prod]) 1,
berghofe@20376
  1614
                    REPEAT_DETERM (resolve_tac [allI, impI] 1),
berghofe@20376
  1615
                    REPEAT_DETERM (etac conjE 1),
berghofe@20376
  1616
                    rtac unique 1,
wenzelm@32202
  1617
                    SUBPROOF (fn {prems = prems', params = [(_, a), (_, b)], ...} => EVERY
berghofe@20376
  1618
                      [cut_facts_tac [rec_prem] 1,
berghofe@20376
  1619
                       rtac (Thm.instantiate ([],
berghofe@20376
  1620
                         [(cterm_of thy11 (Var (("pi", 0), mk_permT aT)),
berghofe@20376
  1621
                           cterm_of thy11 (perm_of_pair (term_of a, term_of b)))]) eqvt_th) 1,
berghofe@20376
  1622
                       asm_simp_tac (HOL_ss addsimps
berghofe@20376
  1623
                         (prems' @ perm_swap @ perm_fresh_fresh)) 1]) context 1,
berghofe@20376
  1624
                    rtac rec_prem 1,
berghofe@20376
  1625
                    simp_tac (HOL_ss addsimps (fs_name ::
berghofe@20376
  1626
                      supp_prod :: finite_Un :: finite_prems)) 1,
wenzelm@36945
  1627
                    simp_tac (HOL_ss addsimps (Thm.symmetric fresh_def ::
berghofe@20376
  1628
                      fresh_prod :: fresh_prems)) 1]
berghofe@20376
  1629
                 end))
berghofe@20376
  1630
          end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~ eqvt_ths)
berghofe@20376
  1631
      end) (dt_atomTs ~~ rec_equiv_thms' ~~ finite_premss);
berghofe@20376
  1632
berghofe@20376
  1633
    (** uniqueness **)
berghofe@20376
  1634
berghofe@21088
  1635
    val fun_tuple = foldr1 HOLogic.mk_prod (rec_ctxt :: rec_fns);
berghofe@20145
  1636
    val fun_tupleT = fastype_of fun_tuple;
berghofe@20145
  1637
    val rec_unique_frees =
haftmann@33968
  1638
      Datatype_Prop.indexify_names (replicate (length recTs) "x") ~~ recTs;
berghofe@20397
  1639
    val rec_unique_frees'' = map (fn (s, T) => (s ^ "'", T)) rec_unique_frees;
berghofe@20267
  1640
    val rec_unique_frees' =
haftmann@33968
  1641
      Datatype_Prop.indexify_names (replicate (length recTs) "y") ~~ rec_result_Ts;
berghofe@21021
  1642
    val rec_unique_concls = map (fn ((x, U), R) =>
haftmann@38558
  1643
        Const (@{const_name Ex1}, (U --> HOLogic.boolT) --> HOLogic.boolT) $
berghofe@21021
  1644
          Abs ("y", U, R $ Free x $ Bound 0))
berghofe@20145
  1645
      (rec_unique_frees ~~ rec_result_Ts ~~ rec_sets);
berghofe@20376
  1646
berghofe@20145
  1647
    val induct_aux_rec = Drule.cterm_instantiate
berghofe@28731
  1648
      (map (pairself (cterm_of thy11) o apsnd (augment_sort thy11 fs_cp_sort))
wenzelm@35845
  1649
         (map (fn (aT, f) => (Logic.varify_global f, Abs ("z", HOLogic.unitT,
berghofe@20145
  1650
            Const ("Nominal.supp", fun_tupleT --> HOLogic.mk_setT aT) $ fun_tuple)))
berghofe@20145
  1651
              fresh_fs @
berghofe@20145
  1652
          map (fn (((P, T), (x, U)), Q) =>
wenzelm@35845
  1653
           (Var ((P, 0), Logic.varifyT_global (fsT' --> T --> HOLogic.boolT)),
wenzelm@44241
  1654
            Abs ("z", HOLogic.unitT, absfree (x, U) Q)))
berghofe@20145
  1655
              (pnames ~~ recTs ~~ rec_unique_frees ~~ rec_unique_concls) @
wenzelm@35845
  1656
          map (fn (s, T) => (Var ((s, 0), Logic.varifyT_global T), Free (s, T)))
berghofe@20145
  1657
            rec_unique_frees)) induct_aux;
berghofe@20145
  1658
berghofe@20376
  1659
    fun obtain_fresh_name vs ths rec_fin_supp T (freshs1, freshs2, ctxt) =
berghofe@20376
  1660
      let
berghofe@20376
  1661
        val p = foldr1 HOLogic.mk_prod (vs @ freshs1);
berghofe@20376
  1662
        val ex = Goal.prove ctxt [] [] (HOLogic.mk_Trueprop
berghofe@20376
  1663
            (HOLogic.exists_const T $ Abs ("x", T,
berghofe@25823
  1664
              fresh_const T (fastype_of p) $ Bound 0 $ p)))
berghofe@20376
  1665
          (fn _ => EVERY
berghofe@20376
  1666
            [cut_facts_tac ths 1,
berghofe@20376
  1667
             REPEAT_DETERM (dresolve_tac (the (AList.lookup op = rec_fin_supp T)) 1),
urbanc@21377
  1668
             resolve_tac exists_fresh' 1,
berghofe@20376
  1669
             asm_simp_tac (HOL_ss addsimps (supp_prod :: finite_Un :: fs_atoms)) 1]);
wenzelm@32202
  1670
        val (([(_, cx)], ths), ctxt') = Obtain.result
berghofe@20376
  1671
          (fn _ => EVERY
berghofe@20376
  1672
            [etac exE 1,
berghofe@20376
  1673
             full_simp_tac (HOL_ss addsimps (fresh_prod :: fresh_atm)) 1,
berghofe@20376
  1674
             REPEAT (etac conjE 1)])
berghofe@20376
  1675
          [ex] ctxt
berghofe@20376
  1676
      in (freshs1 @ [term_of cx], freshs2 @ ths, ctxt') end;
berghofe@20376
  1677
berghofe@21088
  1678
    val finite_ctxt_prems = map (fn aT =>
berghofe@22274
  1679
      HOLogic.mk_Trueprop
berghofe@22274
  1680
        (Const ("Finite_Set.finite", HOLogic.mk_setT aT --> HOLogic.boolT) $
berghofe@22274
  1681
           (Const ("Nominal.supp", fsT' --> HOLogic.mk_setT aT) $ rec_ctxt))) dt_atomTs;
berghofe@21088
  1682
wenzelm@45838
  1683
    val rec_unique_thms = Datatype_Aux.split_conj_thm (Goal.prove
wenzelm@42361
  1684
      (Proof_Context.init_global thy11) (map fst rec_unique_frees)
berghofe@28731
  1685
      (map (augment_sort thy11 fs_cp_sort)
wenzelm@32952
  1686
        (flat finite_premss @ finite_ctxt_prems @ rec_prems @ rec_prems'))
berghofe@28731
  1687
      (augment_sort thy11 fs_cp_sort
berghofe@28731
  1688
        (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj rec_unique_concls)))
berghofe@20376
  1689
      (fn {prems, context} =>
berghofe@20267
  1690
         let
berghofe@20267
  1691
           val k = length rec_fns;
berghofe@20376
  1692
           val (finite_thss, ths1) = fold_map (fn T => fn xs =>
berghofe@20376
  1693
             apfst (pair T) (chop k xs)) dt_atomTs prems;
berghofe@21088
  1694
           val (finite_ctxt_ths, ths2) = chop (length dt_atomTs) ths1;
berghofe@21088
  1695
           val (P_ind_ths, fcbs) = chop k ths2;
wenzelm@45838
  1696
           val P_ths = map (fn th => th RS mp) (Datatype_Aux.split_conj_thm
berghofe@20376
  1697
             (Goal.prove context
berghofe@20397
  1698
               (map fst (rec_unique_frees'' @ rec_unique_frees')) []
berghofe@28731
  1699
               (augment_sort thy11 fs_cp_sort
berghofe@28731
  1700
                 (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@28731
  1701
                    (map (fn (((x, y), S), P) => HOLogic.mk_imp
berghofe@28731
  1702
                      (S $ Free x $ Free y, P $ (Free y)))
berghofe@28731
  1703
                        (rec_unique_frees'' ~~ rec_unique_frees' ~~
berghofe@28731
  1704
                           rec_sets ~~ rec_preds)))))
berghofe@20267
  1705
               (fn _ =>
berghofe@20267
  1706
                  rtac rec_induct 1 THEN
berghofe@20376
  1707
                  REPEAT ((resolve_tac P_ind_ths THEN_ALL_NEW assume_tac) 1))));
berghofe@20376
  1708
           val rec_fin_supp_thms' = map
berghofe@20376
  1709
             (fn (ths, (T, fin_ths)) => (T, map (curry op MRS fin_ths) ths))
berghofe@20376
  1710
             (rec_fin_supp_thms ~~ finite_thss);
berghofe@20267
  1711
         in EVERY
berghofe@20267
  1712
           ([rtac induct_aux_rec 1] @
berghofe@21088
  1713
            maps (fn ((_, finite_ths), finite_th) =>
berghofe@21088
  1714
              [cut_facts_tac (finite_th :: finite_ths) 1,
berghofe@21088
  1715
               asm_simp_tac (HOL_ss addsimps [supp_prod, finite_Un]) 1])
berghofe@21088
  1716
                (finite_thss ~~ finite_ctxt_ths) @
berghofe@20397
  1717
            maps (fn ((_, idxss), elim) => maps (fn idxs =>
wenzelm@36945
  1718
              [full_simp_tac (HOL_ss addsimps [Thm.symmetric fresh_def, supp_prod, Un_iff]) 1,
berghofe@20397
  1719
               REPEAT_DETERM (eresolve_tac [conjE, ex1E] 1),
berghofe@20397
  1720
               rtac ex1I 1,
berghofe@20397
  1721
               (resolve_tac rec_intrs THEN_ALL_NEW atac) 1,
berghofe@20397
  1722
               rotate_tac ~1 1,
berghofe@20397
  1723
               ((DETERM o etac elim) THEN_ALL_NEW full_simp_tac
wenzelm@32952
  1724
                  (HOL_ss addsimps flat distinct_thms)) 1] @
berghofe@21021
  1725
               (if null idxs then [] else [hyp_subst_tac 1,
berghofe@20397
  1726
                SUBPROOF (fn {asms, concl, prems = prems', params, context = context', ...} =>
berghofe@20376
  1727
                  let
berghofe@21021
  1728
                    val SOME prem = find_first (can (HOLogic.dest_eq o
berghofe@21021
  1729
                      HOLogic.dest_Trueprop o prop_of)) prems';
berghofe@20376
  1730
                    val _ $ (_ $ lhs $ rhs) = prop_of prem;
berghofe@20376
  1731
                    val _ $ (_ $ lhs' $ rhs') = term_of concl;
berghofe@20376
  1732
                    val rT = fastype_of lhs';
berghofe@20376
  1733
                    val (c, cargsl) = strip_comb lhs;
berghofe@20376
  1734
                    val cargsl' = partition_cargs idxs cargsl;
wenzelm@32952
  1735
                    val boundsl = maps fst cargsl';
berghofe@20376
  1736
                    val (_, cargsr) = strip_comb rhs;
berghofe@20376
  1737
                    val cargsr' = partition_cargs idxs cargsr;
wenzelm@32952
  1738
                    val boundsr = maps fst cargsr';
berghofe@20376
  1739
                    val (params1, _ :: params2) =
wenzelm@32202
  1740
                      chop (length params div 2) (map (term_of o #2) params);
berghofe@20376
  1741
                    val params' = params1 @ params2;
berghofe@20376
  1742
                    val rec_prems = filter (fn th => case prop_of th of
berghofe@28731
  1743
                        _ $ p => (case head_of p of
haftmann@36692
  1744
                          Const (s, _) => member (op =) rec_set_names s
berghofe@28731
  1745
                        | _ => false)
berghofe@28731
  1746
                      | _ => false) prems';
berghofe@20376
  1747
                    val fresh_prems = filter (fn th => case prop_of th of
berghofe@20376
  1748
                        _ $ (Const ("Nominal.fresh", _) $ _ $ _) => true
haftmann@38558
  1749
                      | _ $ (Const (@{const_name Not}, _) $ _) => true
berghofe@20376
  1750
                      | _ => false) prems';
berghofe@20376
  1751
                    val Ts = map fastype_of boundsl;
berghofe@20376
  1752
berghofe@20376
  1753
                    val _ = warning "step 1: obtaining fresh names";
berghofe@20376
  1754
                    val (freshs1, freshs2, context'') = fold
berghofe@28731
  1755
                      (obtain_fresh_name (rec_ctxt :: rec_fns' @ params')
wenzelm@32952
  1756
                         (maps snd finite_thss @ finite_ctxt_ths @ rec_prems)
berghofe@20376
  1757
                         rec_fin_supp_thms')
berghofe@20376
  1758
                      Ts ([], [], context');
berghofe@20376
  1759
                    val pi1 = map perm_of_pair (boundsl ~~ freshs1);
berghofe@20376
  1760
                    val rpi1 = rev pi1;
berghofe@20376
  1761
                    val pi2 = map perm_of_pair (boundsr ~~ freshs1);
berghofe@21073
  1762
                    val rpi2 = rev pi2;
berghofe@20376
  1763
berghofe@20376
  1764
                    val fresh_prems' = mk_not_sym fresh_prems;
berghofe@20376
  1765
                    val freshs2' = mk_not_sym freshs2;
berghofe@20376
  1766
berghofe@20376
  1767
                    (** as, bs, cs # K as ts, K bs us **)
berghofe@20376
  1768
                    val _ = warning "step 2: as, bs, cs # K as ts, K bs us";
berghofe@20376
  1769
                    val prove_fresh_ss = HOL_ss addsimps
wenzelm@32952
  1770
                      (finite_Diff :: flat fresh_thms @
berghofe@20376
  1771
                       fs_atoms @ abs_fresh @ abs_supp @ fresh_atm);
berghofe@20376
  1772
                    (* FIXME: avoid asm_full_simp_tac ? *)
berghofe@20376
  1773
                    fun prove_fresh ths y x = Goal.prove context'' [] []
berghofe@25823
  1774
                      (HOLogic.mk_Trueprop (fresh_const
berghofe@25823
  1775
                         (fastype_of x) (fastype_of y) $ x $ y))
berghofe@20376
  1776
                      (fn _ => cut_facts_tac ths 1 THEN asm_full_simp_tac prove_fresh_ss 1);
berghofe@20376
  1777
                    val constr_fresh_thms =
berghofe@20376
  1778
                      map (prove_fresh fresh_prems lhs) boundsl @
berghofe@20376
  1779
                      map (prove_fresh fresh_prems rhs) boundsr @
berghofe@20376
  1780
                      map (prove_fresh freshs2 lhs) freshs1 @
berghofe@20376
  1781
                      map (prove_fresh freshs2 rhs) freshs1;
berghofe@20376
  1782
berghofe@20376
  1783
                    (** pi1 o (K as ts) = pi2 o (K bs us) **)
berghofe@20376
  1784
                    val _ = warning "step 3: pi1 o (K as ts) = pi2 o (K bs us)";
berghofe@20376
  1785
                    val pi1_pi2_eq = Goal.prove context'' [] []
berghofe@20376
  1786
                      (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@22311
  1787
                        (fold_rev (mk_perm []) pi1 lhs, fold_rev (mk_perm []) pi2 rhs)))
berghofe@20376
  1788
                      (fn _ => EVERY
berghofe@20376
  1789
                         [cut_facts_tac constr_fresh_thms 1,
berghofe@20376
  1790
                          asm_simp_tac (HOL_basic_ss addsimps perm_fresh_fresh) 1,
berghofe@20376
  1791
                          rtac prem 1]);
berghofe@20376
  1792
berghofe@20376
  1793
                    (** pi1 o ts = pi2 o us **)
berghofe@20376
  1794
                    val _ = warning "step 4: pi1 o ts = pi2 o us";
berghofe@20376
  1795
                    val pi1_pi2_eqs = map (fn (t, u) =>
berghofe@20376
  1796
                      Goal.prove context'' [] []
berghofe@20376
  1797
                        (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@22311
  1798
                          (fold_rev (mk_perm []) pi1 t, fold_rev (mk_perm []) pi2 u)))
berghofe@20376
  1799
                        (fn _ => EVERY
berghofe@20376
  1800
                           [cut_facts_tac [pi1_pi2_eq] 1,
berghofe@20376
  1801
                            asm_full_simp_tac (HOL_ss addsimps
wenzelm@32952
  1802
                              (calc_atm @ flat perm_simps' @
berghofe@20376
  1803
                               fresh_prems' @ freshs2' @ abs_perm @
wenzelm@32952
  1804
                               alpha @ flat inject_thms)) 1]))
berghofe@20376
  1805
                        (map snd cargsl' ~~ map snd cargsr');
berghofe@20376
  1806
berghofe@20376
  1807
                    (** pi1^-1 o pi2 o us = ts **)
berghofe@20376
  1808
                    val _ = warning "step 5: pi1^-1 o pi2 o us = ts";
berghofe@20376
  1809
                    val rpi1_pi2_eqs = map (fn ((t, u), eq) =>
berghofe@20376
  1810
                      Goal.prove context'' [] []
berghofe@20376
  1811
                        (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@22311
  1812
                          (fold_rev (mk_perm []) (rpi1 @ pi2) u, t)))
berghofe@20376
  1813
                        (fn _ => simp_tac (HOL_ss addsimps
berghofe@20376
  1814
                           ((eq RS sym) :: perm_swap)) 1))
berghofe@20376
  1815
                        (map snd cargsl' ~~ map snd cargsr' ~~ pi1_pi2_eqs);
berghofe@20376
  1816
berghofe@20376
  1817
                    val (rec_prems1, rec_prems2) =
berghofe@20376
  1818
                      chop (length rec_prems div 2) rec_prems;
berghofe@20376
  1819
berghofe@20376
  1820
                    (** (ts, pi1^-1 o pi2 o vs) in rec_set **)
berghofe@20376
  1821
                    val _ = warning "step 6: (ts, pi1^-1 o pi2 o vs) in rec_set";
berghofe@20376
  1822
                    val rec_prems' = map (fn th =>
berghofe@20376
  1823
                      let
berghofe@21021
  1824
                        val _ $ (S $ x $ y) = prop_of th;
berghofe@28731
  1825
                        val Const (s, _) = head_of S;
berghofe@28731
  1826
                        val k = find_index (equal s) rec_set_names;
berghofe@20376
  1827
                        val pi = rpi1 @ pi2;
berghofe@22311
  1828
                        fun mk_pi z = fold_rev (mk_perm []) pi z;
berghofe@20376
  1829
                        fun eqvt_tac p =
berghofe@20376
  1830
                          let
berghofe@20376
  1831
                            val U as Type (_, [Type (_, [T, _])]) = fastype_of p;
berghofe@20376
  1832
                            val l = find_index (equal T) dt_atomTs;
wenzelm@42364
  1833
                            val th = nth (nth rec_equiv_thms' l) k;
berghofe@20376
  1834
                            val th' = Thm.instantiate ([],
berghofe@20376
  1835
                              [(cterm_of thy11 (Var (("pi", 0), U)),
berghofe@20376
  1836
                                cterm_of thy11 p)]) th;
berghofe@20376
  1837
                          in rtac th' 1 end;
berghofe@20376
  1838
                        val th' = Goal.prove context'' [] []
berghofe@21021
  1839
                          (HOLogic.mk_Trueprop (S $ mk_pi x $ mk_pi y))
berghofe@20376
  1840
                          (fn _ => EVERY
berghofe@20376
  1841
                             (map eqvt_tac pi @
berghofe@20376
  1842
                              [simp_tac (HOL_ss addsimps (fresh_prems' @ freshs2' @
berghofe@20376
  1843
                                 perm_swap @ perm_fresh_fresh)) 1,
berghofe@20376
  1844
                               rtac th 1]))
berghofe@20376
  1845
                      in
berghofe@20376
  1846
                        Simplifier.simplify
berghofe@20376
  1847
                          (HOL_basic_ss addsimps rpi1_pi2_eqs) th'
berghofe@20376
  1848
                      end) rec_prems2;
berghofe@20376
  1849
berghofe@20376
  1850
                    val ihs = filter (fn th => case prop_of th of
haftmann@38558
  1851
                      _ $ (Const (@{const_name All}, _) $ _) => true | _ => false) prems';
berghofe@20376
  1852
berghofe@21073
  1853
                    (** pi1 o rs = pi2 o vs , rs = pi1^-1 o pi2 o vs **)
berghofe@21073
  1854
                    val _ = warning "step 7: pi1 o rs = pi2 o vs , rs = pi1^-1 o pi2 o vs";
berghofe@21073
  1855
                    val rec_eqns = map (fn (th, ih) =>
berghofe@20376
  1856
                      let
berghofe@20376
  1857
                        val th' = th RS (ih RS spec RS mp) RS sym;
berghofe@20376
  1858
                        val _ $ (_ $ lhs $ rhs) = prop_of th';
berghofe@20376
  1859
                        fun strip_perm (_ $ _ $ t) = strip_perm t
berghofe@20376
  1860
                          | strip_perm t = t;
berghofe@20376
  1861
                      in
berghofe@21073
  1862
                        Goal.prove context'' [] []
berghofe@20376
  1863
                           (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@22311
  1864
                              (fold_rev (mk_perm []) pi1 lhs,
berghofe@22311
  1865
                               fold_rev (mk_perm []) pi2 (strip_perm rhs))))
berghofe@20376
  1866
                           (fn _ => simp_tac (HOL_basic_ss addsimps
berghofe@21073
  1867
                              (th' :: perm_swap)) 1)
berghofe@21073
  1868
                      end) (rec_prems' ~~ ihs);
berghofe@20376
  1869
berghofe@21073
  1870
                    (** as # rs **)
berghofe@21073
  1871
                    val _ = warning "step 8: as # rs";
wenzelm@32952
  1872
                    val rec_freshs =
wenzelm@32952
  1873
                      maps (fn (rec_prem, ih) =>
berghofe@20376
  1874
                        let
berghofe@21021
  1875
                          val _ $ (S $ x $ (y as Free (_, T))) =
berghofe@20376
  1876
                            prop_of rec_prem;
berghofe@20376
  1877
                          val k = find_index (equal S) rec_sets;
wenzelm@32952
  1878
                          val atoms = flat (map_filter (fn (bs, z) =>
berghofe@21073
  1879
                            if z = x then NONE else SOME bs) cargsl')
berghofe@20376
  1880
                        in
berghofe@21073
  1881
                          map (fn a as Free (_, aT) =>
berghofe@21073
  1882
                            let val l = find_index (equal aT) dt_atomTs;
berghofe@21073
  1883
                            in
berghofe@21073
  1884
                              Goal.prove context'' [] []
berghofe@25823
  1885
                                (HOLogic.mk_Trueprop (fresh_const aT T $ a $ y))
berghofe@20376
  1886
                                (fn _ => EVERY
wenzelm@42364
  1887
                                   (rtac (nth (nth rec_fresh_thms l) k) 1 ::
berghofe@20376
  1888
                                    map (fn th => rtac th 1)
wenzelm@42364
  1889
                                      (snd (nth finite_thss l)) @
berghofe@20376
  1890
                                    [rtac rec_prem 1, rtac ih 1,
berghofe@21073
  1891
                                     REPEAT_DETERM (resolve_tac fresh_prems 1)]))
berghofe@21073
  1892
                            end) atoms
wenzelm@32952
  1893
                        end) (rec_prems1 ~~ ihs);
berghofe@20376
  1894
berghofe@20376
  1895
                    (** as # fK as ts rs , bs # fK bs us vs **)
berghofe@20376
  1896
                    val _ = warning "step 9: as # fK as ts rs , bs # fK bs us vs";
berghofe@21073
  1897
                    fun prove_fresh_result (a as Free (_, aT)) =
berghofe@20376
  1898
                      Goal.prove context'' [] []
berghofe@25823
  1899
                        (HOLogic.mk_Trueprop (fresh_const aT rT $ a $ rhs'))
berghofe@20376
  1900
                        (fn _ => EVERY
berghofe@20376
  1901
                           [resolve_tac fcbs 1,
berghofe@20376
  1902
                            REPEAT_DETERM (resolve_tac
berghofe@21073
  1903
                              (fresh_prems @ rec_freshs) 1),
berghofe@20411
  1904
                            REPEAT_DETERM (resolve_tac (maps snd rec_fin_supp_thms') 1
berghofe@20411
  1905
                              THEN resolve_tac rec_prems 1),
berghofe@20376
  1906
                            resolve_tac P_ind_ths 1,
berghofe@20376
  1907
                            REPEAT_DETERM (resolve_tac (P_ths @ rec_prems) 1)]);
wenzelm@21365
  1908
berghofe@21073
  1909
                    val fresh_results'' = map prove_fresh_result boundsl;
berghofe@21073
  1910
berghofe@21073
  1911
                    fun prove_fresh_result'' ((a as Free (_, aT), b), th) =
berghofe@21073
  1912
                      let val th' = Goal.prove context'' [] []
berghofe@25823
  1913
                        (HOLogic.mk_Trueprop (fresh_const aT rT $
berghofe@22311
  1914
                            fold_rev (mk_perm []) (rpi2 @ pi1) a $
berghofe@22311
  1915
                            fold_rev (mk_perm []) (rpi2 @ pi1) rhs'))
berghofe@21073
  1916
                        (fn _ => simp_tac (HOL_ss addsimps fresh_bij) 1 THEN
berghofe@21073
  1917
                           rtac th 1)
berghofe@21073
  1918
                      in
berghofe@21073
  1919
                        Goal.prove context'' [] []
berghofe@25823
  1920
                          (HOLogic.mk_Trueprop (fresh_const aT rT $ b $ lhs'))
berghofe@21073
  1921
                          (fn _ => EVERY
berghofe@21073
  1922
                             [cut_facts_tac [th'] 1,
wenzelm@35232
  1923
                              full_simp_tac (Simplifier.global_context thy11 HOL_ss
berghofe@25998
  1924
                                addsimps rec_eqns @ pi1_pi2_eqs @ perm_swap
berghofe@25998
  1925
                                addsimprocs [NominalPermeq.perm_simproc_app]) 1,
berghofe@21073
  1926
                              full_simp_tac (HOL_ss addsimps (calc_atm @
berghofe@21073
  1927
                                fresh_prems' @ freshs2' @ perm_fresh_fresh)) 1])
berghofe@21073
  1928
                      end;
berghofe@21073
  1929
berghofe@21073
  1930
                    val fresh_results = fresh_results'' @ map prove_fresh_result''
berghofe@21073
  1931
                      (boundsl ~~ boundsr ~~ fresh_results'');
berghofe@20376
  1932
berghofe@20376
  1933
                    (** cs # fK as ts rs , cs # fK bs us vs **)
berghofe@20376
  1934
                    val _ = warning "step 10: cs # fK as ts rs , cs # fK bs us vs";
berghofe@20376
  1935
                    fun prove_fresh_result' recs t (a as Free (_, aT)) =
berghofe@20376
  1936
                      Goal.prove context'' [] []
berghofe@25823
  1937
                        (HOLogic.mk_Trueprop (fresh_const aT rT $ a $ t))
berghofe@20376
  1938
                        (fn _ => EVERY
berghofe@20376
  1939
                          [cut_facts_tac recs 1,
berghofe@20376
  1940
                           REPEAT_DETERM (dresolve_tac
berghofe@20376
  1941
                             (the (AList.lookup op = rec_fin_supp_thms' aT)) 1),
berghofe@20376
  1942
                           NominalPermeq.fresh_guess_tac
berghofe@20376
  1943
                             (HOL_ss addsimps (freshs2 @
berghofe@20376
  1944
                                fs_atoms @ fresh_atm @
wenzelm@32952
  1945
                                maps snd finite_thss)) 1]);
berghofe@20376
  1946
berghofe@20376
  1947
                    val fresh_results' =
berghofe@20376
  1948
                      map (prove_fresh_result' rec_prems1 rhs') freshs1 @
berghofe@20376
  1949
                      map (prove_fresh_result' rec_prems2 lhs') freshs1;
berghofe@20376
  1950
berghofe@20376
  1951
                    (** pi1 o (fK as ts rs) = pi2 o (fK bs us vs) **)
berghofe@20376
  1952
                    val _ = warning "step 11: pi1 o (fK as ts rs) = pi2 o (fK bs us vs)";
berghofe@20376
  1953
                    val pi1_pi2_result = Goal.prove context'' [] []
berghofe@20376
  1954
                      (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@22311
  1955
                        (fold_rev (mk_perm []) pi1 rhs', fold_rev (mk_perm []) pi2 lhs')))
berghofe@27450
  1956
                      (fn _ => simp_tac (Simplifier.context context'' HOL_ss
berghofe@27450
  1957
                           addsimps pi1_pi2_eqs @ rec_eqns
berghofe@27450
  1958
                           addsimprocs [NominalPermeq.perm_simproc_app]) 1 THEN
berghofe@20376
  1959
                         TRY (simp_tac (HOL_ss addsimps
berghofe@20376
  1960
                           (fresh_prems' @ freshs2' @ calc_atm @ perm_fresh_fresh)) 1));
berghofe@20376
  1961
berghofe@20376
  1962
                    val _ = warning "final result";
berghofe@20376
  1963
                    val final = Goal.prove context'' [] [] (term_of concl)
berghofe@20376
  1964
                      (fn _ => cut_facts_tac [pi1_pi2_result RS sym] 1 THEN
berghofe@20376
  1965
                        full_simp_tac (HOL_basic_ss addsimps perm_fresh_fresh @
berghofe@20376
  1966
                          fresh_results @ fresh_results') 1);
wenzelm@42361
  1967
                    val final' = Proof_Context.export context'' context' [final];
berghofe@20376
  1968
                    val _ = warning "finished!"
berghofe@20376
  1969
                  in
berghofe@20376
  1970
                    resolve_tac final' 1
berghofe@20397
  1971
                  end) context 1])) idxss) (ndescr ~~ rec_elims))
berghofe@20397
  1972
         end));
berghofe@20397
  1973
wenzelm@46161
  1974
    val rec_total_thms = map (fn r => r RS @{thm theI'}) rec_unique_thms;
berghofe@20397
  1975
berghofe@20397
  1976
    (* define primrec combinators *)
berghofe@20397
  1977
wenzelm@45701
  1978
    val big_reccomb_name = space_implode "_" new_type_names ^ "_rec";
haftmann@28965
  1979
    val reccomb_names = map (Sign.full_bname thy11)
berghofe@20397
  1980
      (if length descr'' = 1 then [big_reccomb_name] else
berghofe@20397
  1981
        (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
berghofe@20397
  1982
          (1 upto (length descr''))));
berghofe@20397
  1983
    val reccombs = map (fn ((name, T), T') => list_comb
berghofe@20397
  1984
      (Const (name, rec_fn_Ts @ [T] ---> T'), rec_fns))
berghofe@20397
  1985
        (reccomb_names ~~ recTs ~~ rec_result_Ts);
berghofe@20397
  1986
berghofe@20397
  1987
    val (reccomb_defs, thy12) =
berghofe@20397
  1988
      thy11
wenzelm@24712
  1989
      |> Sign.add_consts_i (map (fn ((name, T), T') =>
wenzelm@30364
  1990
          (Binding.name (Long_Name.base_name name), rec_fn_Ts @ [T] ---> T', NoSyn))
berghofe@20397
  1991
          (reccomb_names ~~ recTs ~~ rec_result_Ts))
wenzelm@39557
  1992
      |> (Global_Theory.add_defs false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') =>
wenzelm@44241
  1993
          (Binding.name (Long_Name.base_name name ^ "_def"), Logic.mk_equals (comb, absfree ("x", T)
wenzelm@44241
  1994
           (Const (@{const_name The}, (T' --> HOLogic.boolT) --> T') $ absfree ("y", T')
wenzelm@44241
  1995
             (set $ Free ("x", T) $ Free ("y", T'))))))
berghofe@20397
  1996
               (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts));
berghofe@20397
  1997
berghofe@20397
  1998
    (* prove characteristic equations for primrec combinators *)
berghofe@20397
  1999
berghofe@20397
  2000
    val rec_thms = map (fn (prems, concl) =>
berghofe@20397
  2001
      let
berghofe@20397
  2002
        val _ $ (_ $ (_ $ x) $ _) = concl;
berghofe@20397
  2003
        val (_, cargs) = strip_comb x;
berghofe@20397
  2004
        val ps = map (fn (x as Free (_, T), i) =>
berghofe@20397
  2005
          (Free ("x" ^ string_of_int i, T), x)) (cargs ~~ (1 upto length cargs));
berghofe@20397
  2006
        val concl' = subst_atomic_types (rec_result_Ts' ~~ rec_result_Ts) concl;
wenzelm@32952
  2007
        val prems' = flat finite_premss @ finite_ctxt_prems @
berghofe@21088
  2008
          rec_prems @ rec_prems' @ map (subst_atomic ps) prems;
berghofe@20397
  2009
        fun solve rules prems = resolve_tac rules THEN_ALL_NEW
berghofe@20397
  2010
          (resolve_tac prems THEN_ALL_NEW atac)
berghofe@20397
  2011
      in
berghofe@28731
  2012
        Goal.prove_global thy12 []
berghofe@28731
  2013
          (map (augment_sort thy12 fs_cp_sort) prems')
berghofe@28731
  2014
          (augment_sort thy12 fs_cp_sort concl')
wenzelm@26711
  2015
          (fn {prems, ...} => EVERY
berghofe@20397
  2016
            [rewrite_goals_tac reccomb_defs,
wenzelm@46161
  2017
             rtac @{thm the1_equality} 1,
berghofe@20397
  2018
             solve rec_unique_thms prems 1,
berghofe@20397
  2019
             resolve_tac rec_intrs 1,
berghofe@20397
  2020
             REPEAT (solve (prems @ rec_total_thms) prems 1)])
berghofe@20397
  2021
      end) (rec_eq_prems ~~
wenzelm@45879
  2022
        Datatype_Prop.make_primrecs reccomb_names descr' thy12);
wenzelm@21365
  2023
wenzelm@45822
  2024
    val dt_infos = map_index (make_dt_info pdescr induct reccomb_names rec_thms)
haftmann@33063
  2025
      (descr1 ~~ distinct_thms ~~ inject_thms);
berghofe@21540
  2026
berghofe@19985
  2027
    (* FIXME: theorems are stored in database for testing only *)
berghofe@20397
  2028
    val (_, thy13) = thy12 |>
wenzelm@39557
  2029
      Global_Theory.add_thmss
wenzelm@32952
  2030
        [((Binding.name "rec_equiv", flat rec_equiv_thms), []),
wenzelm@32952
  2031
         ((Binding.name "rec_equiv'", flat rec_equiv_thms'), []),
wenzelm@32952
  2032
         ((Binding.name "rec_fin_supp", flat rec_fin_supp_thms), []),
wenzelm@32952
  2033
         ((Binding.name "rec_fresh", flat rec_fresh_thms), []),
wenzelm@35021
  2034
         ((Binding.name "rec_unique", map Drule.export_without_context rec_unique_thms), []),
haftmann@29585
  2035
         ((Binding.name "recs", rec_thms), [])] ||>
wenzelm@24712
  2036
      Sign.parent_path ||>
berghofe@21540
  2037
      map_nominal_datatypes (fold Symtab.update dt_infos);
berghofe@19985
  2038
berghofe@17870
  2039
  in
berghofe@20397
  2040
    thy13
berghofe@17870
  2041
  end;
berghofe@17870
  2042
wenzelm@45863
  2043
val nominal_datatype = gen_nominal_datatype Datatype.check_specs;
wenzelm@45863
  2044
val nominal_datatype_cmd = gen_nominal_datatype Datatype.read_specs;
berghofe@17870
  2045
wenzelm@24867
  2046
val _ =
wenzelm@46961
  2047
  Outer_Syntax.command @{command_spec "nominal_datatype"} "define nominal datatypes"
wenzelm@45863
  2048
    (Parse.and_list1 Datatype.spec_cmd >>
wenzelm@45863
  2049
      (Toplevel.theory o nominal_datatype_cmd Datatype.default_config));
berghofe@17870
  2050
berghofe@18261
  2051
end