src/HOL/Nominal/nominal_package.ML
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(*  Title:      HOL/Nominal/nominal_package.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_PACKAGE =
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sig
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  val add_nominal_datatype : bool -> string list -> (string list * bstring * mixfix *
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    (bstring * string list * mixfix) list) list -> theory -> theory
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  type 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 NominalPackage : NOMINAL_PACKAGE =
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struct
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val finite_emptyI = thm "finite.emptyI";
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val finite_Diff = thm "finite_Diff";
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val finite_Un = thm "finite_Un";
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val Un_iff = thm "Un_iff";
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val In0_eq = thm "In0_eq";
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val In1_eq = thm "In1_eq";
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val In0_not_In1 = thm "In0_not_In1";
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val In1_not_In0 = thm "In1_not_In0";
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val Un_assoc = thm "Un_assoc";
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val Collect_disj_eq = thm "Collect_disj_eq";
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val empty_def = thm "empty_def";
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val empty_iff = thm "empty_iff";
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open DatatypeAux;
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open NominalAtoms;
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(** FIXME: DatatypePackage should export this function **)
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local
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fun dt_recs (DtTFree _) = []
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  | dt_recs (DtType (_, dts)) = List.concat (map dt_recs dts)
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  | dt_recs (DtRec i) = [i];
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fun dt_cases (descr: descr) (_, args, constrs) =
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  let
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    fun the_bname i = Long_Name.base_name (#1 (valOf (AList.lookup (op =) descr i)));
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    val bnames = map the_bname (distinct op = (List.concat (map dt_recs args)));
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  in map (fn (c, _) => space_implode "_" (Long_Name.base_name c :: bnames)) constrs end;
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fun induct_cases descr =
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  DatatypeProp.indexify_names (List.concat (map (dt_cases descr) (map #2 descr)));
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fun exhaust_cases descr i = dt_cases descr (valOf (AList.lookup (op =) descr i));
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in
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fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr);
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fun mk_case_names_exhausts descr new =
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  map (RuleCases.case_names o exhaust_cases descr o #1)
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    (List.filter (fn ((_, (name, _, _))) => name mem_string new) descr);
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end;
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(* theory data *)
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type descr = (int * (string * dtyp list * (string * (dtyp list * 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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   sorts : (string * sort) list,
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   rec_names : string list,
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   rec_rewrites : thm list,
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   induction : thm,
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   distinct : thm list,
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   inject : thm list};
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structure NominalDatatypesData = TheoryDataFun
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(
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  type T = nominal_datatype_info Symtab.table;
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  val empty = Symtab.empty;
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  val copy = I;
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  val extend = I;
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  fun merge _ tabs : T = Symtab.merge (K true) tabs;
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);
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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 sorts induct reccomb_names rec_thms
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    (((i, (_, (tname, _, _))), distinct), inject) =
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  (tname,
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   {index = i,
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    descr = descr,
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    sorts = sorts,
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    rec_names = reccomb_names,
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    rec_rewrites = rec_thms,
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    induction = induct,
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    distinct = distinct,
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    inject = inject});
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(*******************************)
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val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma);
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(** simplification procedure for sorting permutations **)
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val dj_cp = thm "dj_cp";
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fun dest_permT (Type ("fun", [Type ("List.list", [Type ("*", [T, _])]),
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      Type ("fun", [_, U])])) = (T, U);
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fun permTs_of (Const ("Nominal.perm", T) $ t $ u) = fst (dest_permT T) :: permTs_of u
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  | permTs_of _ = [];
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fun perm_simproc' thy ss (Const ("Nominal.perm", T) $ t $ (u as Const ("Nominal.perm", U) $ r $ s)) =
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      let
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        val (aT as Type (a, []), S) = dest_permT T;
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        val (bT as Type (b, []), _) = dest_permT U
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      in if aT mem permTs_of u andalso aT <> bT then
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          let
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            val 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 (the_context ()) "perm_simp" ["pi1 \<bullet> (pi2 \<bullet> x)"] perm_simproc';
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val meta_spec = thm "meta_spec";
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fun projections rule =
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  ProjectRule.projections (ProofContext.init (Thm.theory_of_thm rule)) rule
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  |> map (standard #> RuleCases.save rule);
4f4cc426b440 provide projections of induct_weak, induct_unsafe;
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20267
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val supp_prod = thm "supp_prod";
20376
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val fresh_prod = thm "fresh_prod";
53b31f7c1d87 Finished implementation of uniqueness proof for recursion combinator.
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val supports_fresh = thm "supports_fresh";
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1fe9d6384b11 eliminated unnamed infixes;
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val supports_def = thm "Nominal.supports_def";
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53b31f7c1d87 Finished implementation of uniqueness proof for recursion combinator.
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val fresh_def = thm "fresh_def";
53b31f7c1d87 Finished implementation of uniqueness proof for recursion combinator.
berghofe
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val supp_def = thm "supp_def";
53b31f7c1d87 Finished implementation of uniqueness proof for recursion combinator.
berghofe
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val rev_simps = thms "rev.simps";
23029
79ee75dc1e59 constant op @ now named append
haftmann
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val app_simps = thms "append.simps";
25951
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berghofe
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   165
val at_fin_set_supp = thm "at_fin_set_supp";
6ebe26bfed18 Reimplemented proof of strong induction theorem.
berghofe
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val at_fin_set_fresh = thm "at_fin_set_fresh";
6ebe26bfed18 Reimplemented proof of strong induction theorem.
berghofe
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val abs_fun_eq1 = thm "abs_fun_eq1";
20267
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berghofe
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   168
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
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val collect_simp = rewrite_rule [mk_meta_eq mem_Collect_eq];
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
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22311
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berghofe
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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);
ebcd44cb8d61 Curried and exported mk_perm.
berghofe
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    val U = fastype_of1 (Ts, u)
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  in Const ("Nominal.perm", T --> U --> U) $ t $ u end;
ebcd44cb8d61 Curried and exported mk_perm.
berghofe
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   176
22529
902ed60d53a7 Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
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fun perm_of_pair (x, y) =
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  let
902ed60d53a7 Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
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    val T = fastype_of x;
902ed60d53a7 Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
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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) $
902ed60d53a7 Exported perm_of_pair, mk_not_sym, and perm_simproc.
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    HOLogic.mk_prod (x, y) $ Const ("List.list.Nil", pT)
902ed60d53a7 Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
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   183
  end;
902ed60d53a7 Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
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902ed60d53a7 Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
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fun mk_not_sym ths = maps (fn th => case prop_of th of
25951
6ebe26bfed18 Reimplemented proof of strong induction theorem.
berghofe
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   186
    _ $ (Const ("Not", _) $ (Const ("op =", _) $ _ $ _)) => [th, th RS not_sym]
22529
902ed60d53a7 Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
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  | _ => [th]) ths;
902ed60d53a7 Exported perm_of_pair, mk_not_sym, and perm_simproc.
berghofe
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25823
5d75f4b179e2 Added function fresh_const.
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fun fresh_const T U = Const ("Nominal.fresh", T --> U --> HOLogic.boolT);
28373
5e2c526cfaf0 Added fresh_star_const.
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fun fresh_star_const T U =
5e2c526cfaf0 Added fresh_star_const.
berghofe
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   191
  Const ("Nominal.fresh_star", HOLogic.mk_setT T --> U --> HOLogic.boolT);
25823
5d75f4b179e2 Added function fresh_const.
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fun gen_add_nominal_datatype prep_typ err flat_names new_type_names dts thy =
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  let
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    (* this theory is used just for parsing *)
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    val tmp_thy = thy |>
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berghofe
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      Theory.copy |>
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64ed05609568 proper Sign operations instead of Theory aliases;
wenzelm
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      Sign.add_types (map (fn (tvs, tname, mx, _) =>
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76fd85bbf139 more uniform handling of binding in packages;
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        (Binding.name tname, length tvs, mx)) dts);
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    val atoms = atoms_of thy;
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    fun prep_constr ((constrs, sorts), (cname, cargs, mx)) =
22578
b0eb5652f210 removed obsolete sign_of/sign_of_thm;
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      let val (cargs', sorts') = Library.foldl (prep_typ tmp_thy) (([], sorts), cargs)
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      in (constrs @ [(cname, cargs', mx)], sorts') end
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berghofe
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    fun prep_dt_spec ((dts, sorts), (tvs, tname, mx, constrs)) =
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berghofe
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      let val (constrs', sorts') = Library.foldl prep_constr (([], sorts), constrs)
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berghofe
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      in (dts @ [(tvs, tname, mx, constrs')], sorts') end
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c35381811d5c Initial revision.
berghofe
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    val (dts', sorts) = Library.foldl prep_dt_spec (([], []), dts);
28736
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
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   213
    val tyvars = map (map (fn s =>
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
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      (s, the (AList.lookup (op =) sorts s))) o #1) dts';
17870
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   216
    fun inter_sort thy S S' = Type.inter_sort (Sign.tsig_of thy) (S, S');
c60ac7923a06 Added support for parametric datatypes.
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   217
    fun augment_sort_typ thy S =
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berghofe
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      let val S = Sign.certify_sort thy S
c60ac7923a06 Added support for parametric datatypes.
berghofe
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   219
      in map_type_tfree (fn (s, S') => TFree (s,
c60ac7923a06 Added support for parametric datatypes.
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   220
        if member (op = o apsnd fst) sorts s then inter_sort thy S S' else S'))
c60ac7923a06 Added support for parametric datatypes.
berghofe
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   221
      end;
c60ac7923a06 Added support for parametric datatypes.
berghofe
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   222
    fun augment_sort thy S = map_types (augment_sort_typ thy S);
c60ac7923a06 Added support for parametric datatypes.
berghofe
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   223
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   224
    val types_syntax = map (fn (tvs, tname, mx, constrs) => (tname, mx)) dts';
c35381811d5c Initial revision.
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    val constr_syntax = map (fn (tvs, tname, mx, constrs) =>
c35381811d5c Initial revision.
berghofe
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   226
      map (fn (cname, cargs, mx) => (cname, mx)) constrs) dts';
c35381811d5c Initial revision.
berghofe
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   227
c35381811d5c Initial revision.
berghofe
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   228
    val ps = map (fn (_, n, _, _) =>
28965
1de908189869 cleaned up binding module and related code
haftmann
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   229
      (Sign.full_bname tmp_thy n, Sign.full_bname tmp_thy (n ^ "_Rep"))) dts;
17870
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   230
    val rps = map Library.swap ps;
c35381811d5c Initial revision.
berghofe
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   231
21365
4ee8e2702241 InductivePackage.add_inductive_i: canonical argument order;
wenzelm
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   232
    fun replace_types (Type ("Nominal.ABS", [T, U])) =
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
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   233
          Type ("fun", [T, Type ("Nominal.noption", [replace_types U])])
17870
c35381811d5c Initial revision.
berghofe
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      | replace_types (Type (s, Ts)) =
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berghofe
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   235
          Type (getOpt (AList.lookup op = ps s, s), map replace_types Ts)
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berghofe
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      | replace_types T = T;
c35381811d5c Initial revision.
berghofe
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   237
30345
76fd85bbf139 more uniform handling of binding in packages;
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   238
    val dts'' = map (fn (tvs, tname, mx, constrs) => (tvs, Binding.name (tname ^ "_Rep"), NoSyn,
76fd85bbf139 more uniform handling of binding in packages;
wenzelm
parents: 30307
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   239
      map (fn (cname, cargs, mx) => (Binding.name (cname ^ "_Rep"),
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
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   240
        map replace_types cargs, NoSyn)) constrs)) dts';
17870
c35381811d5c Initial revision.
berghofe
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   241
c35381811d5c Initial revision.
berghofe
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   242
    val new_type_names' = map (fn n => n ^ "_Rep") new_type_names;
28965
1de908189869 cleaned up binding module and related code
haftmann
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   243
    val full_new_type_names' = map (Sign.full_bname thy) new_type_names';
17870
c35381811d5c Initial revision.
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   244
18045
6d69a4190eb2 1) have adjusted the swapping of the result type
urbanc
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   245
    val ({induction, ...},thy1) =
27112
661a74bafeb7 polished interface of datatype package
haftmann
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   246
      DatatypePackage.add_datatype err flat_names new_type_names' dts'' thy;
17870
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berghofe
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   247
c35381811d5c Initial revision.
berghofe
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   248
    val SOME {descr, ...} = Symtab.lookup
c35381811d5c Initial revision.
berghofe
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   249
      (DatatypePackage.get_datatypes thy1) (hd full_new_type_names');
28731
c60ac7923a06 Added support for parametric datatypes.
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   250
    fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i);
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
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   251
26651
e630c789ef2b overloading perm: use big_name;
wenzelm
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   252
    val big_name = space_implode "_" new_type_names;
e630c789ef2b overloading perm: use big_name;
wenzelm
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   253
e630c789ef2b overloading perm: use big_name;
wenzelm
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diff changeset
   254
17870
c35381811d5c Initial revision.
berghofe
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    (**** define permutation functions ****)
c35381811d5c Initial revision.
berghofe
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   256
c35381811d5c Initial revision.
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   257
    val permT = mk_permT (TFree ("'x", HOLogic.typeS));
c35381811d5c Initial revision.
berghofe
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   258
    val pi = Free ("pi", permT);
c35381811d5c Initial revision.
berghofe
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   259
    val perm_types = map (fn (i, _) =>
c35381811d5c Initial revision.
berghofe
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   260
      let val T = nth_dtyp i
c35381811d5c Initial revision.
berghofe
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   261
      in permT --> T --> T end) descr;
26680
18ff77116937 Adapted to new primrec package.
berghofe
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   262
    val perm_names' = DatatypeProp.indexify_names (map (fn (i, _) =>
18ff77116937 Adapted to new primrec package.
berghofe
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diff changeset
   263
      "perm_" ^ name_of_typ (nth_dtyp i)) descr);
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
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diff changeset
   264
    val perm_names = replicate (length new_type_names) "Nominal.perm" @
28965
1de908189869 cleaned up binding module and related code
haftmann
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diff changeset
   265
      map (Sign.full_bname thy1) (List.drop (perm_names', length new_type_names));
17870
c35381811d5c Initial revision.
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   266
    val perm_names_types = perm_names ~~ perm_types;
26680
18ff77116937 Adapted to new primrec package.
berghofe
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   267
    val perm_names_types' = perm_names' ~~ perm_types;
17870
c35381811d5c Initial revision.
berghofe
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   268
26680
18ff77116937 Adapted to new primrec package.
berghofe
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   269
    val perm_eqs = maps (fn (i, (_, _, constrs)) =>
17870
c35381811d5c Initial revision.
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      let val T = nth_dtyp i
21365
4ee8e2702241 InductivePackage.add_inductive_i: canonical argument order;
wenzelm
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   271
      in map (fn (cname, dts) =>
17870
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   272
        let
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
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   273
          val Ts = map (typ_of_dtyp descr sorts) dts;
28641
f6e1b2beb766 Names of variables in perm_eqs are now chosen more carefully to avoid
berghofe
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   274
          val names = Name.variant_list ["pi"] (DatatypeProp.make_tnames Ts);
17870
c35381811d5c Initial revision.
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   275
          val args = map Free (names ~~ Ts);
c35381811d5c Initial revision.
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   276
          val c = Const (cname, Ts ---> T);
c35381811d5c Initial revision.
berghofe
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   277
          fun perm_arg (dt, x) =
c35381811d5c Initial revision.
berghofe
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   278
            let val T = type_of x
c35381811d5c Initial revision.
berghofe
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   279
            in if is_rec_type dt then
c35381811d5c Initial revision.
berghofe
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   280
                let val (Us, _) = strip_type T
c35381811d5c Initial revision.
berghofe
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   281
                in list_abs (map (pair "x") Us,
26680
18ff77116937 Adapted to new primrec package.
berghofe
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   282
                  Free (nth perm_names_types' (body_index dt)) $ pi $
17870
c35381811d5c Initial revision.
berghofe
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   283
                    list_comb (x, map (fn (i, U) =>
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
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   284
                      Const ("Nominal.perm", permT --> U --> U) $
17870
c35381811d5c Initial revision.
berghofe
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   285
                        (Const ("List.rev", permT --> permT) $ pi) $
c35381811d5c Initial revision.
berghofe
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   286
                        Bound i) ((length Us - 1 downto 0) ~~ Us)))
c35381811d5c Initial revision.
berghofe
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diff changeset
   287
                end
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   288
              else Const ("Nominal.perm", permT --> T --> T) $ pi $ x
21365
4ee8e2702241 InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents: 21291
diff changeset
   289
            end;
17870
c35381811d5c Initial revision.
berghofe
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diff changeset
   290
        in
28965
1de908189869 cleaned up binding module and related code
haftmann
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diff changeset
   291
          (Attrib.empty_binding, HOLogic.mk_Trueprop (HOLogic.mk_eq
26680
18ff77116937 Adapted to new primrec package.
berghofe
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diff changeset
   292
            (Free (nth perm_names_types' i) $
17870
c35381811d5c Initial revision.
berghofe
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   293
               Free ("pi", mk_permT (TFree ("'x", HOLogic.typeS))) $
c35381811d5c Initial revision.
berghofe
parents:
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   294
               list_comb (c, args),
26680
18ff77116937 Adapted to new primrec package.
berghofe
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   295
             list_comb (c, map perm_arg (dts ~~ args)))))
17870
c35381811d5c Initial revision.
berghofe
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   296
        end) constrs
26680
18ff77116937 Adapted to new primrec package.
berghofe
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   297
      end) descr;
17870
c35381811d5c Initial revision.
berghofe
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diff changeset
   298
26689
105031879f4a Auxiliary permutation functions are no longer declared using add_consts_i,
berghofe
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diff changeset
   299
    val (perm_simps, thy2) =
26680
18ff77116937 Adapted to new primrec package.
berghofe
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diff changeset
   300
      PrimrecPackage.add_primrec_overloaded
26689
105031879f4a Auxiliary permutation functions are no longer declared using add_consts_i,
berghofe
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diff changeset
   301
        (map (fn (s, sT) => (s, sT, false))
105031879f4a Auxiliary permutation functions are no longer declared using add_consts_i,
berghofe
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diff changeset
   302
           (List.take (perm_names' ~~ perm_names_types, length new_type_names)))
28965
1de908189869 cleaned up binding module and related code
haftmann
parents: 28736
diff changeset
   303
        (map (fn s => (Binding.name s, NONE, NoSyn)) perm_names') perm_eqs thy1;
17870
c35381811d5c Initial revision.
berghofe
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   304
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   305
    (**** prove that permutation functions introduced by unfolding are ****)
c35381811d5c Initial revision.
berghofe
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   306
    (**** equivalent to already existing permutation functions         ****)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   307
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   308
    val _ = warning ("length descr: " ^ string_of_int (length descr));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   309
    val _ = warning ("length new_type_names: " ^ string_of_int (length new_type_names));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   310
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   311
    val perm_indnames = DatatypeProp.make_tnames (map body_type perm_types);
26343
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
   312
    val perm_fun_def = PureThy.get_thm thy2 "perm_fun_def";
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   313
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   314
    val unfolded_perm_eq_thms =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   315
      if length descr = length new_type_names then []
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   316
      else map standard (List.drop (split_conj_thm
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   317
        (Goal.prove_global thy2 [] []
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   318
          (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   319
            (map (fn (c as (s, T), x) =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   320
               let val [T1, T2] = binder_types T
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   321
               in HOLogic.mk_eq (Const c $ pi $ Free (x, T2),
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   322
                 Const ("Nominal.perm", T) $ pi $ Free (x, T2))
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   323
               end)
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   324
             (perm_names_types ~~ perm_indnames))))
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   325
          (fn _ => EVERY [indtac induction perm_indnames 1,
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   326
            ALLGOALS (asm_full_simp_tac
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   327
              (simpset_of thy2 addsimps [perm_fun_def]))])),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   328
        length new_type_names));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   329
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   330
    (**** prove [] \<bullet> t = t ****)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   331
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   332
    val _ = warning "perm_empty_thms";
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   333
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   334
    val perm_empty_thms = List.concat (map (fn a =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   335
      let val permT = mk_permT (Type (a, []))
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   336
      in map standard (List.take (split_conj_thm
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   337
        (Goal.prove_global thy2 [] []
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   338
          (augment_sort thy2 [pt_class_of thy2 a]
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   339
            (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   340
              (map (fn ((s, T), x) => HOLogic.mk_eq
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   341
                  (Const (s, permT --> T --> T) $
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   342
                     Const ("List.list.Nil", permT) $ Free (x, T),
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   343
                   Free (x, T)))
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   344
               (perm_names ~~
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   345
                map body_type perm_types ~~ perm_indnames)))))
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   346
          (fn _ => EVERY [indtac induction perm_indnames 1,
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   347
            ALLGOALS (asm_full_simp_tac (simpset_of thy2))])),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   348
        length new_type_names))
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   349
      end)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   350
      atoms);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   351
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   352
    (**** prove (pi1 @ pi2) \<bullet> t = pi1 \<bullet> (pi2 \<bullet> t) ****)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   353
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   354
    val _ = warning "perm_append_thms";
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   355
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   356
    (*FIXME: these should be looked up statically*)
26343
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
   357
    val at_pt_inst = PureThy.get_thm thy2 "at_pt_inst";
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
   358
    val pt2 = PureThy.get_thm thy2 "pt2";
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   359
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   360
    val perm_append_thms = List.concat (map (fn a =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   361
      let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   362
        val permT = mk_permT (Type (a, []));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   363
        val pi1 = Free ("pi1", permT);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   364
        val pi2 = Free ("pi2", permT);
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   365
        val pt_inst = pt_inst_of thy2 a;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   366
        val pt2' = pt_inst RS pt2;
30364
577edc39b501 moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents: 30345
diff changeset
   367
        val pt2_ax = PureThy.get_thm thy2 (Long_Name.map_base_name (fn s => "pt_" ^ s ^ "2") a);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   368
      in List.take (map standard (split_conj_thm
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   369
        (Goal.prove_global thy2 [] []
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   370
           (augment_sort thy2 [pt_class_of thy2 a]
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   371
             (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   372
                (map (fn ((s, T), x) =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   373
                    let val perm = Const (s, permT --> T --> T)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   374
                    in HOLogic.mk_eq
23029
79ee75dc1e59 constant op @ now named append
haftmann
parents: 22846
diff changeset
   375
                      (perm $ (Const ("List.append", permT --> permT --> permT) $
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   376
                         pi1 $ pi2) $ Free (x, T),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   377
                       perm $ pi1 $ (perm $ pi2 $ Free (x, T)))
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   378
                    end)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   379
                  (perm_names ~~
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   380
                   map body_type perm_types ~~ perm_indnames)))))
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   381
           (fn _ => EVERY [indtac induction perm_indnames 1,
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   382
              ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt2', pt2_ax]))]))),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   383
         length new_type_names)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   384
      end) atoms);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   385
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   386
    (**** prove pi1 ~ pi2 ==> pi1 \<bullet> t = pi2 \<bullet> t ****)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   387
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   388
    val _ = warning "perm_eq_thms";
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   389
26343
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
   390
    val pt3 = PureThy.get_thm thy2 "pt3";
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
   391
    val pt3_rev = PureThy.get_thm thy2 "pt3_rev";
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   392
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   393
    val perm_eq_thms = List.concat (map (fn a =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   394
      let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   395
        val permT = mk_permT (Type (a, []));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   396
        val pi1 = Free ("pi1", permT);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   397
        val pi2 = Free ("pi2", permT);
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   398
        val at_inst = at_inst_of thy2 a;
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   399
        val pt_inst = pt_inst_of thy2 a;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   400
        val pt3' = pt_inst RS pt3;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   401
        val pt3_rev' = at_inst RS (pt_inst RS pt3_rev);
30364
577edc39b501 moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents: 30345
diff changeset
   402
        val pt3_ax = PureThy.get_thm thy2 (Long_Name.map_base_name (fn s => "pt_" ^ s ^ "3") a);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   403
      in List.take (map standard (split_conj_thm
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   404
        (Goal.prove_global thy2 [] []
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   405
          (augment_sort thy2 [pt_class_of thy2 a] (Logic.mk_implies
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   406
             (HOLogic.mk_Trueprop (Const ("Nominal.prm_eq",
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   407
                permT --> permT --> HOLogic.boolT) $ pi1 $ pi2),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   408
              HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   409
                (map (fn ((s, T), x) =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   410
                    let val perm = Const (s, permT --> T --> T)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   411
                    in HOLogic.mk_eq
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   412
                      (perm $ pi1 $ Free (x, T),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   413
                       perm $ pi2 $ Free (x, T))
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   414
                    end)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   415
                  (perm_names ~~
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   416
                   map body_type perm_types ~~ perm_indnames))))))
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   417
           (fn _ => EVERY [indtac induction perm_indnames 1,
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   418
              ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt3', pt3_rev', pt3_ax]))]))),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   419
         length new_type_names)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   420
      end) atoms);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   421
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   422
    (**** prove pi1 \<bullet> (pi2 \<bullet> t) = (pi1 \<bullet> pi2) \<bullet> (pi1 \<bullet> t) ****)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   423
26343
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
   424
    val cp1 = PureThy.get_thm thy2 "cp1";
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
   425
    val dj_cp = PureThy.get_thm thy2 "dj_cp";
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
   426
    val pt_perm_compose = PureThy.get_thm thy2 "pt_perm_compose";
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
   427
    val pt_perm_compose_rev = PureThy.get_thm thy2 "pt_perm_compose_rev";
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
   428
    val dj_perm_perm_forget = PureThy.get_thm thy2 "dj_perm_perm_forget";
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   429
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   430
    fun composition_instance name1 name2 thy =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   431
      let
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   432
        val cp_class = cp_class_of thy name1 name2;
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   433
        val pt_class =
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   434
          if name1 = name2 then [pt_class_of thy name1]
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   435
          else [];
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   436
        val permT1 = mk_permT (Type (name1, []));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   437
        val permT2 = mk_permT (Type (name2, []));
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   438
        val Ts = map body_type perm_types;
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   439
        val cp_inst = cp_inst_of thy name1 name2;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   440
        val simps = simpset_of thy addsimps (perm_fun_def ::
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   441
          (if name1 <> name2 then
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   442
             let val dj = dj_thm_of thy name2 name1
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   443
             in [dj RS (cp_inst RS dj_cp), dj RS dj_perm_perm_forget] end
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   444
           else
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   445
             let
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   446
               val at_inst = at_inst_of thy name1;
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   447
               val pt_inst = pt_inst_of thy name1;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   448
             in
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   449
               [cp_inst RS cp1 RS sym,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   450
                at_inst RS (pt_inst RS pt_perm_compose) RS sym,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   451
                at_inst RS (pt_inst RS pt_perm_compose_rev) RS sym]
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   452
            end))
28736
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   453
        val sort = Sign.certify_sort thy (cp_class :: pt_class);
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   454
        val thms = split_conj_thm (Goal.prove_global thy [] []
28736
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   455
          (augment_sort thy sort
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   456
            (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   457
              (map (fn ((s, T), x) =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   458
                  let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   459
                    val pi1 = Free ("pi1", permT1);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   460
                    val pi2 = Free ("pi2", permT2);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   461
                    val perm1 = Const (s, permT1 --> T --> T);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   462
                    val perm2 = Const (s, permT2 --> T --> T);
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   463
                    val perm3 = Const ("Nominal.perm", permT1 --> permT2 --> permT2)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   464
                  in HOLogic.mk_eq
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   465
                    (perm1 $ pi1 $ (perm2 $ pi2 $ Free (x, T)),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   466
                     perm2 $ (perm3 $ pi1 $ pi2) $ (perm1 $ pi1 $ Free (x, T)))
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   467
                  end)
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   468
                (perm_names ~~ Ts ~~ perm_indnames)))))
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   469
          (fn _ => EVERY [indtac induction perm_indnames 1,
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   470
             ALLGOALS (asm_full_simp_tac simps)]))
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   471
      in
28736
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   472
        fold (fn (s, tvs) => fn thy => AxClass.prove_arity
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   473
            (s, map (inter_sort thy sort o snd) tvs, [cp_class])
24218
fbf1646b267c ClassPackage renamed to Class
haftmann
parents: 24110
diff changeset
   474
            (Class.intro_classes_tac [] THEN ALLGOALS (resolve_tac thms)) thy)
28736
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   475
          (full_new_type_names' ~~ tyvars) thy
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   476
      end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   477
18381
246807ef6dfb changed the types in accordance with Florian's changes
urbanc
parents: 18366
diff changeset
   478
    val (perm_thmss,thy3) = thy2 |>
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   479
      fold (fn name1 => fold (composition_instance name1) atoms) atoms |>
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   480
      fold (fn atom => fn thy =>
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   481
        let val pt_name = pt_class_of thy atom
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   482
        in
28736
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   483
          fold (fn (s, tvs) => fn thy => AxClass.prove_arity
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   484
              (s, map (inter_sort thy [pt_name] o snd) tvs, [pt_name])
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   485
              (EVERY
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   486
                [Class.intro_classes_tac [],
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   487
                 resolve_tac perm_empty_thms 1,
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   488
                 resolve_tac perm_append_thms 1,
28736
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   489
                 resolve_tac perm_eq_thms 1, assume_tac 1]) thy)
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   490
            (full_new_type_names' ~~ tyvars) thy
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   491
        end) atoms |>
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   492
      PureThy.add_thmss
29585
c23295521af5 binding replaces bstring
haftmann
parents: 29389
diff changeset
   493
        [((Binding.name (space_implode "_" new_type_names ^ "_unfolded_perm_eq"),
18759
2f55e3e47355 Updated to Isabelle 2006-01-23
krauss
parents: 18707
diff changeset
   494
          unfolded_perm_eq_thms), [Simplifier.simp_add]),
29585
c23295521af5 binding replaces bstring
haftmann
parents: 29389
diff changeset
   495
         ((Binding.name (space_implode "_" new_type_names ^ "_perm_empty"),
18759
2f55e3e47355 Updated to Isabelle 2006-01-23
krauss
parents: 18707
diff changeset
   496
          perm_empty_thms), [Simplifier.simp_add]),
29585
c23295521af5 binding replaces bstring
haftmann
parents: 29389
diff changeset
   497
         ((Binding.name (space_implode "_" new_type_names ^ "_perm_append"),
18759
2f55e3e47355 Updated to Isabelle 2006-01-23
krauss
parents: 18707
diff changeset
   498
          perm_append_thms), [Simplifier.simp_add]),
29585
c23295521af5 binding replaces bstring
haftmann
parents: 29389
diff changeset
   499
         ((Binding.name (space_implode "_" new_type_names ^ "_perm_eq"),
18759
2f55e3e47355 Updated to Isabelle 2006-01-23
krauss
parents: 18707
diff changeset
   500
          perm_eq_thms), [Simplifier.simp_add])];
21365
4ee8e2702241 InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents: 21291
diff changeset
   501
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   502
    (**** Define representing sets ****)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   503
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   504
    val _ = warning "representing sets";
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   505
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   506
    val rep_set_names = DatatypeProp.indexify_names
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   507
      (map (fn (i, _) => name_of_typ (nth_dtyp i) ^ "_set") descr);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   508
    val big_rep_name =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   509
      space_implode "_" (DatatypeProp.indexify_names (List.mapPartial
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   510
        (fn (i, ("Nominal.noption", _, _)) => NONE
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   511
          | (i, _) => SOME (name_of_typ (nth_dtyp i))) descr)) ^ "_set";
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   512
    val _ = warning ("big_rep_name: " ^ big_rep_name);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   513
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   514
    fun strip_option (dtf as DtType ("fun", [dt, DtRec i])) =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   515
          (case AList.lookup op = descr i of
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   516
             SOME ("Nominal.noption", _, [(_, [dt']), _]) =>
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   517
               apfst (cons dt) (strip_option dt')
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   518
           | _ => ([], dtf))
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   519
      | strip_option (DtType ("fun", [dt, DtType ("Nominal.noption", [dt'])])) =
18261
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   520
          apfst (cons dt) (strip_option dt')
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   521
      | strip_option dt = ([], dt);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   522
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   523
    val dt_atomTs = distinct op = (map (typ_of_dtyp descr sorts)
18280
45e139675daf Corrected atom class constraints in strong induction rule.
berghofe
parents: 18261
diff changeset
   524
      (List.concat (map (fn (_, (_, _, cs)) => List.concat
45e139675daf Corrected atom class constraints in strong induction rule.
berghofe
parents: 18261
diff changeset
   525
        (map (List.concat o map (fst o strip_option) o snd) cs)) descr)));
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   526
    val dt_atoms = map (fst o dest_Type) dt_atomTs;
18280
45e139675daf Corrected atom class constraints in strong induction rule.
berghofe
parents: 18261
diff changeset
   527
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   528
    fun make_intr s T (cname, cargs) =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   529
      let
21365
4ee8e2702241 InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents: 21291
diff changeset
   530
        fun mk_prem (dt, (j, j', prems, ts)) =
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   531
          let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   532
            val (dts, dt') = strip_option dt;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   533
            val (dts', dt'') = strip_dtyp dt';
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   534
            val Ts = map (typ_of_dtyp descr sorts) dts;
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   535
            val Us = map (typ_of_dtyp descr sorts) dts';
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   536
            val T = typ_of_dtyp descr sorts dt'';
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   537
            val free = mk_Free "x" (Us ---> T) j;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   538
            val free' = app_bnds free (length Us);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   539
            fun mk_abs_fun (T, (i, t)) =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   540
              let val U = fastype_of t
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   541
              in (i + 1, Const ("Nominal.abs_fun", [T, U, T] --->
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   542
                Type ("Nominal.noption", [U])) $ mk_Free "y" T i $ t)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   543
              end
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   544
          in (j + 1, j' + length Ts,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   545
            case dt'' of
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   546
                DtRec k => list_all (map (pair "x") Us,
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   547
                  HOLogic.mk_Trueprop (Free (List.nth (rep_set_names, k),
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   548
                    T --> HOLogic.boolT) $ free')) :: prems
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   549
              | _ => prems,
30190
479806475f3c use long names for old-style fold combinators;
wenzelm
parents: 29585
diff changeset
   550
            snd (List.foldr mk_abs_fun (j', free) Ts) :: ts)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   551
          end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   552
30190
479806475f3c use long names for old-style fold combinators;
wenzelm
parents: 29585
diff changeset
   553
        val (_, _, prems, ts) = List.foldr mk_prem (1, 1, [], []) cargs;
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   554
        val concl = HOLogic.mk_Trueprop (Free (s, T --> HOLogic.boolT) $
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   555
          list_comb (Const (cname, map fastype_of ts ---> T), ts))
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   556
      in Logic.list_implies (prems, concl)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   557
      end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   558
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   559
    val (intr_ts, (rep_set_names', recTs')) =
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   560
      apfst List.concat (apsnd ListPair.unzip (ListPair.unzip (List.mapPartial
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   561
        (fn ((_, ("Nominal.noption", _, _)), _) => NONE
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   562
          | ((i, (_, _, constrs)), rep_set_name) =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   563
              let val T = nth_dtyp i
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   564
              in SOME (map (make_intr rep_set_name T) constrs,
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   565
                (rep_set_name, T))
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   566
              end)
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   567
                (descr ~~ rep_set_names))));
28965
1de908189869 cleaned up binding module and related code
haftmann
parents: 28736
diff changeset
   568
    val rep_set_names'' = map (Sign.full_bname thy3) rep_set_names';
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   569
21365
4ee8e2702241 InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents: 21291
diff changeset
   570
    val ({raw_induct = rep_induct, intrs = rep_intrs, ...}, thy4) =
26475
3cc1e48d0ce1 eliminated quiet_mode ref of some packages (avoid CRITICAL setmp!);
wenzelm
parents: 26359
diff changeset
   571
        InductivePackage.add_inductive_global (serial_string ())
3cc1e48d0ce1 eliminated quiet_mode ref of some packages (avoid CRITICAL setmp!);
wenzelm
parents: 26359
diff changeset
   572
          {quiet_mode = false, verbose = false, kind = Thm.internalK,
28965
1de908189869 cleaned up binding module and related code
haftmann
parents: 28736
diff changeset
   573
           alt_name = Binding.name big_rep_name, coind = false, no_elim = true, no_ind = false,
29389
0a49f940d729 inductive: added fork_mono flag;
wenzelm
parents: 29270
diff changeset
   574
           skip_mono = true, fork_mono = false}
28965
1de908189869 cleaned up binding module and related code
haftmann
parents: 28736
diff changeset
   575
          (map (fn (s, T) => ((Binding.name s, T --> HOLogic.boolT), NoSyn))
26128
fe2d24c26e0c inductive package: simplified group handling;
wenzelm
parents: 26067
diff changeset
   576
             (rep_set_names' ~~ recTs'))
28965
1de908189869 cleaned up binding module and related code
haftmann
parents: 28736
diff changeset
   577
          [] (map (fn x => (Attrib.empty_binding, x)) intr_ts) [] thy3;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   578
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   579
    (**** Prove that representing set is closed under permutation ****)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   580
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   581
    val _ = warning "proving closure under permutation...";
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   582
26343
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
   583
    val abs_perm = PureThy.get_thms thy4 "abs_perm";
25951
6ebe26bfed18 Reimplemented proof of strong induction theorem.
berghofe
parents: 25823
diff changeset
   584
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   585
    val perm_indnames' = List.mapPartial
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   586
      (fn (x, (_, ("Nominal.noption", _, _))) => NONE | (x, _) => SOME x)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   587
      (perm_indnames ~~ descr);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   588
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   589
    fun mk_perm_closed name = map (fn th => standard (th RS mp))
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   590
      (List.take (split_conj_thm (Goal.prove_global thy4 [] []
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   591
        (augment_sort thy4
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   592
          (pt_class_of thy4 name :: map (cp_class_of thy4 name) (dt_atoms \ name))
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   593
          (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   594
            (fn ((s, T), x) =>
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   595
               let
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   596
                 val S = Const (s, T --> HOLogic.boolT);
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   597
                 val permT = mk_permT (Type (name, []))
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   598
               in HOLogic.mk_imp (S $ Free (x, T),
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   599
                 S $ (Const ("Nominal.perm", permT --> T --> T) $
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   600
                   Free ("pi", permT) $ Free (x, T)))
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   601
               end) (rep_set_names'' ~~ recTs' ~~ perm_indnames')))))
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   602
        (fn _ => EVERY
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   603
           [indtac rep_induct [] 1,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   604
            ALLGOALS (simp_tac (simpset_of thy4 addsimps
25951
6ebe26bfed18 Reimplemented proof of strong induction theorem.
berghofe
parents: 25823
diff changeset
   605
              (symmetric perm_fun_def :: abs_perm))),
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   606
            ALLGOALS (resolve_tac rep_intrs THEN_ALL_NEW assume_tac)])),
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   607
        length new_type_names));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   608
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   609
    val perm_closed_thmss = map mk_perm_closed atoms;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   610
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   611
    (**** typedef ****)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   612
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   613
    val _ = warning "defining type...";
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   614
18366
78b4f225b640 Adapted to new type of PureThy.add_defs_i.
berghofe
parents: 18350
diff changeset
   615
    val (typedefs, thy6) =
26651
e630c789ef2b overloading perm: use big_name;
wenzelm
parents: 26646
diff changeset
   616
      thy4
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   617
      |> fold_map (fn ((((name, mx), tvs), (cname, U)), name') => fn thy =>
30345
76fd85bbf139 more uniform handling of binding in packages;
wenzelm
parents: 30307
diff changeset
   618
          TypedefPackage.add_typedef false (SOME (Binding.name name'))
76fd85bbf139 more uniform handling of binding in packages;
wenzelm
parents: 30307
diff changeset
   619
            (Binding.name name, map fst tvs, mx)
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   620
            (Const ("Collect", (U --> HOLogic.boolT) --> HOLogic.mk_setT U) $
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   621
               Const (cname, U --> HOLogic.boolT)) NONE
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   622
            (rtac exI 1 THEN rtac CollectI 1 THEN
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   623
              QUIET_BREADTH_FIRST (has_fewer_prems 1)
26475
3cc1e48d0ce1 eliminated quiet_mode ref of some packages (avoid CRITICAL setmp!);
wenzelm
parents: 26359
diff changeset
   624
              (resolve_tac rep_intrs 1)) thy |> (fn ((_, r), thy) =>
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   625
        let
28736
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   626
          val permT = mk_permT
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   627
            (TFree (Name.variant (map fst tvs) "'a", HOLogic.typeS));
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   628
          val pi = Free ("pi", permT);
28736
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   629
          val T = Type (Sign.intern_type thy name, map TFree tvs);
18366
78b4f225b640 Adapted to new type of PureThy.add_defs_i.
berghofe
parents: 18350
diff changeset
   630
        in apfst (pair r o hd)
29585
c23295521af5 binding replaces bstring
haftmann
parents: 29389
diff changeset
   631
          (PureThy.add_defs_unchecked true [((Binding.name ("prm_" ^ name ^ "_def"), Logic.mk_equals
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   632
            (Const ("Nominal.perm", permT --> T --> T) $ pi $ Free ("x", T),
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   633
             Const (Sign.intern_const thy ("Abs_" ^ name), U --> T) $
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   634
               (Const ("Nominal.perm", permT --> U --> U) $ pi $
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   635
                 (Const (Sign.intern_const thy ("Rep_" ^ name), T --> U) $
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   636
                   Free ("x", T))))), [])] thy)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   637
        end))
18366
78b4f225b640 Adapted to new type of PureThy.add_defs_i.
berghofe
parents: 18350
diff changeset
   638
          (types_syntax ~~ tyvars ~~
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   639
            List.take (rep_set_names'' ~~ recTs', length new_type_names) ~~
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   640
            new_type_names);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   641
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   642
    val perm_defs = map snd typedefs;
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   643
    val Abs_inverse_thms = map (collect_simp o #Abs_inverse o fst) typedefs;
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   644
    val Rep_inverse_thms = map (#Rep_inverse o fst) typedefs;
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   645
    val Rep_thms = map (collect_simp o #Rep o fst) typedefs;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   646
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   647
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   648
    (** prove that new types are in class pt_<name> **)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   649
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   650
    val _ = warning "prove that new types are in class pt_<name> ...";
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   651
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   652
    fun pt_instance (atom, perm_closed_thms) =
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   653
      fold (fn ((((((Abs_inverse, Rep_inverse), Rep),
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   654
        perm_def), name), tvs), perm_closed) => fn thy =>
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   655
          let
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   656
            val pt_class = pt_class_of thy atom;
28736
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   657
            val sort = Sign.certify_sort thy
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   658
              (pt_class :: map (cp_class_of thy atom) (dt_atoms \ atom))
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   659
          in AxClass.prove_arity
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   660
            (Sign.intern_type thy name,
28736
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   661
              map (inter_sort thy sort o snd) tvs, [pt_class])
24218
fbf1646b267c ClassPackage renamed to Class
haftmann
parents: 24110
diff changeset
   662
            (EVERY [Class.intro_classes_tac [],
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   663
              rewrite_goals_tac [perm_def],
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   664
              asm_full_simp_tac (simpset_of thy addsimps [Rep_inverse]) 1,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   665
              asm_full_simp_tac (simpset_of thy addsimps
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   666
                [Rep RS perm_closed RS Abs_inverse]) 1,
26343
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
   667
              asm_full_simp_tac (HOL_basic_ss addsimps [PureThy.get_thm thy
30364
577edc39b501 moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents: 30345
diff changeset
   668
                ("pt_" ^ Long_Name.base_name atom ^ "3")]) 1]) thy
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   669
          end)
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   670
        (Abs_inverse_thms ~~ Rep_inverse_thms ~~ Rep_thms ~~ perm_defs ~~
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   671
           new_type_names ~~ tyvars ~~ perm_closed_thms);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   672
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   673
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   674
    (** prove that new types are in class cp_<name1>_<name2> **)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   675
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   676
    val _ = warning "prove that new types are in class cp_<name1>_<name2> ...";
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   677
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   678
    fun cp_instance (atom1, perm_closed_thms1) (atom2, perm_closed_thms2) thy =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   679
      let
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   680
        val cp_class = cp_class_of thy atom1 atom2;
28736
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   681
        val sort = Sign.certify_sort thy
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   682
          (pt_class_of thy atom1 :: map (cp_class_of thy atom1) (dt_atoms \ atom1) @
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   683
           (if atom1 = atom2 then [cp_class_of thy atom1 atom1] else
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   684
            pt_class_of thy atom2 :: map (cp_class_of thy atom2) (dt_atoms \ atom2)));
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   685
        val cp1' = cp_inst_of thy atom1 atom2 RS cp1
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   686
      in fold (fn ((((((Abs_inverse, Rep),
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   687
        perm_def), name), tvs), perm_closed1), perm_closed2) => fn thy =>
19275
3d10de7a8ca7 add_inst_arity_i renamed to prove_arity.
berghofe
parents: 19251
diff changeset
   688
          AxClass.prove_arity
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   689
            (Sign.intern_type thy name,
28736
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
   690
              map (inter_sort thy sort o snd) tvs, [cp_class])
24218
fbf1646b267c ClassPackage renamed to Class
haftmann
parents: 24110
diff changeset
   691
            (EVERY [Class.intro_classes_tac [],
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   692
              rewrite_goals_tac [perm_def],
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   693
              asm_full_simp_tac (simpset_of thy addsimps
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   694
                ((Rep RS perm_closed1 RS Abs_inverse) ::
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   695
                 (if atom1 = atom2 then []
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   696
                  else [Rep RS perm_closed2 RS Abs_inverse]))) 1,
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   697
              cong_tac 1,
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   698
              rtac refl 1,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   699
              rtac cp1' 1]) thy)
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   700
        (Abs_inverse_thms ~~ Rep_thms ~~ perm_defs ~~ new_type_names ~~
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   701
           tyvars ~~ perm_closed_thms1 ~~ perm_closed_thms2) thy
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   702
      end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   703
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   704
    val thy7 = fold (fn x => fn thy => thy |>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   705
      pt_instance x |>
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   706
      fold (cp_instance x) (atoms ~~ perm_closed_thmss))
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   707
        (atoms ~~ perm_closed_thmss) thy6;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   708
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   709
    (**** constructors ****)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   710
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   711
    fun mk_abs_fun (x, t) =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   712
      let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   713
        val T = fastype_of x;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   714
        val U = fastype_of t
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   715
      in
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   716
        Const ("Nominal.abs_fun", T --> U --> T -->
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   717
          Type ("Nominal.noption", [U])) $ x $ t
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   718
      end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   719
30190
479806475f3c use long names for old-style fold combinators;
wenzelm
parents: 29585
diff changeset
   720
    val (ty_idxs, _) = List.foldl
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   721
      (fn ((i, ("Nominal.noption", _, _)), p) => p
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   722
        | ((i, _), (ty_idxs, j)) => (ty_idxs @ [(i, j)], j + 1)) ([], 0) descr;
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   723
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   724
    fun reindex (DtType (s, dts)) = DtType (s, map reindex dts)
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   725
      | reindex (DtRec i) = DtRec (the (AList.lookup op = ty_idxs i))
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   726
      | reindex dt = dt;
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   727
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   728
    fun strip_suffix i s = implode (List.take (explode s, size s - i));
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   729
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   730
    (** strips the "_Rep" in type names *)
21365
4ee8e2702241 InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents: 21291
diff changeset
   731
    fun strip_nth_name i s =
30364
577edc39b501 moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents: 30345
diff changeset
   732
      let val xs = Long_Name.explode s;
577edc39b501 moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents: 30345
diff changeset
   733
      in Long_Name.implode (Library.nth_map (length xs - i) (strip_suffix 4) xs) end;
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   734
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   735
    val (descr'', ndescr) = ListPair.unzip (List.mapPartial
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   736
      (fn (i, ("Nominal.noption", _, _)) => NONE
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   737
        | (i, (s, dts, constrs)) =>
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   738
             let
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   739
               val SOME index = AList.lookup op = ty_idxs i;
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   740
               val (constrs1, constrs2) = ListPair.unzip
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   741
                 (map (fn (cname, cargs) => apfst (pair (strip_nth_name 2 (strip_nth_name 1 cname)))
30190
479806475f3c use long names for old-style fold combinators;
wenzelm
parents: 29585
diff changeset
   742
                   (Library.foldl_map (fn (dts, dt) =>
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   743
                     let val (dts', dt') = strip_option dt
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   744
                     in (dts @ dts' @ [reindex dt'], (length dts, length dts')) end)
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   745
                       ([], cargs))) constrs)
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   746
             in SOME ((index, (strip_nth_name 1 s,  map reindex dts, constrs1)),
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   747
               (index, constrs2))
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   748
             end) descr);
18045
6d69a4190eb2 1) have adjusted the swapping of the result type
urbanc
parents: 18017
diff changeset
   749
19489
4441b637871b SplitAt -> chop
berghofe
parents: 19403
diff changeset
   750
    val (descr1, descr2) = chop (length new_type_names) descr'';
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   751
    val descr' = [descr1, descr2];
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   752
19710
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
   753
    fun partition_cargs idxs xs = map (fn (i, j) =>
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
   754
      (List.take (List.drop (xs, i), j), List.nth (xs, i + j))) idxs;
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
   755
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   756
    val pdescr = map (fn ((i, (s, dts, constrs)), (_, idxss)) => (i, (s, dts,
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   757
      map (fn ((cname, cargs), idxs) => (cname, partition_cargs idxs cargs))
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   758
        (constrs ~~ idxss)))) (descr'' ~~ ndescr);
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   759
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   760
    fun nth_dtyp' i = typ_of_dtyp descr'' sorts (DtRec i);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   761
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   762
    val rep_names = map (fn s =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   763
      Sign.intern_const thy7 ("Rep_" ^ s)) new_type_names;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   764
    val abs_names = map (fn s =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   765
      Sign.intern_const thy7 ("Abs_" ^ s)) new_type_names;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   766
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   767
    val recTs = get_rec_types descr'' sorts;
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   768
    val newTs' = Library.take (length new_type_names, recTs');
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   769
    val newTs = Library.take (length new_type_names, recTs);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   770
28965
1de908189869 cleaned up binding module and related code
haftmann
parents: 28736
diff changeset
   771
    val full_new_type_names = map (Sign.full_bname thy) new_type_names;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   772
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   773
    fun make_constr_def tname T T' ((thy, defs, eqns),
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   774
        (((cname_rep, _), (cname, cargs)), (cname', mx))) =
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   775
      let
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   776
        fun constr_arg ((dts, dt), (j, l_args, r_args)) =
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   777
          let
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   778
            val xs = map (fn (dt, i) => mk_Free "x" (typ_of_dtyp descr'' sorts dt) i)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   779
              (dts ~~ (j upto j + length dts - 1))
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   780
            val x = mk_Free "x" (typ_of_dtyp descr'' sorts dt) (j + length dts)
18261
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   781
          in
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   782
            (j + length dts + 1,
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   783
             xs @ x :: l_args,
30190
479806475f3c use long names for old-style fold combinators;
wenzelm
parents: 29585
diff changeset
   784
             List.foldr mk_abs_fun
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   785
               (case dt of
18261
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   786
                  DtRec k => if k < length new_type_names then
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   787
                      Const (List.nth (rep_names, k), typ_of_dtyp descr'' sorts dt -->
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   788
                        typ_of_dtyp descr sorts dt) $ x
18261
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   789
                    else error "nested recursion not (yet) supported"
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   790
                | _ => x) xs :: r_args)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   791
          end
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   792
30190
479806475f3c use long names for old-style fold combinators;
wenzelm
parents: 29585
diff changeset
   793
        val (_, l_args, r_args) = List.foldr constr_arg (1, [], []) cargs;
22578
b0eb5652f210 removed obsolete sign_of/sign_of_thm;
wenzelm
parents: 22543
diff changeset
   794
        val abs_name = Sign.intern_const thy ("Abs_" ^ tname);
b0eb5652f210 removed obsolete sign_of/sign_of_thm;
wenzelm
parents: 22543
diff changeset
   795
        val rep_name = Sign.intern_const thy ("Rep_" ^ tname);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   796
        val constrT = map fastype_of l_args ---> T;
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   797
        val lhs = list_comb (Const (cname, constrT), l_args);
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   798
        val rhs = list_comb (Const (cname_rep, map fastype_of r_args ---> T'), r_args);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   799
        val def = Logic.mk_equals (lhs, Const (abs_name, T' --> T) $ rhs);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   800
        val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   801
          (Const (rep_name, T --> T') $ lhs, rhs));
30364
577edc39b501 moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents: 30345
diff changeset
   802
        val def_name = (Long_Name.base_name cname) ^ "_def";
18366
78b4f225b640 Adapted to new type of PureThy.add_defs_i.
berghofe
parents: 18350
diff changeset
   803
        val ([def_thm], thy') = thy |>
30345
76fd85bbf139 more uniform handling of binding in packages;
wenzelm
parents: 30307
diff changeset
   804
          Sign.add_consts_i [(Binding.name cname', constrT, mx)] |>
29585
c23295521af5 binding replaces bstring
haftmann
parents: 29389
diff changeset
   805
          (PureThy.add_defs false o map Thm.no_attributes) [(Binding.name def_name, def)]
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   806
      in (thy', defs @ [def_thm], eqns @ [eqn]) end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   807
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   808
    fun dt_constr_defs ((thy, defs, eqns, dist_lemmas), ((((((_, (_, _, constrs)),
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   809
        (_, (_, _, constrs'))), tname), T), T'), constr_syntax)) =
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   810
      let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   811
        val rep_const = cterm_of thy
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   812
          (Const (Sign.intern_const thy ("Rep_" ^ tname), T --> T'));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   813
        val dist = standard (cterm_instantiate [(cterm_of thy distinct_f, rep_const)] distinct_lemma);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   814
        val (thy', defs', eqns') = Library.foldl (make_constr_def tname T T')
24712
64ed05609568 proper Sign operations instead of Theory aliases;
wenzelm
parents: 24459
diff changeset
   815
          ((Sign.add_path tname thy, defs, []), constrs ~~ constrs' ~~ constr_syntax)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   816
      in
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   817
        (parent_path flat_names thy', defs', eqns @ [eqns'], dist_lemmas @ [dist])
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   818
      end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   819
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   820
    val (thy8, constr_defs, constr_rep_eqns, dist_lemmas) = Library.foldl dt_constr_defs
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   821
      ((thy7, [], [], []), List.take (descr, length new_type_names) ~~
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   822
        List.take (pdescr, length new_type_names) ~~
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   823
        new_type_names ~~ newTs ~~ newTs' ~~ constr_syntax);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   824
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   825
    val abs_inject_thms = map (collect_simp o #Abs_inject o fst) typedefs
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   826
    val rep_inject_thms = map (#Rep_inject o fst) typedefs
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   827
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   828
    (* prove theorem  Rep_i (Constr_j ...) = Constr'_j ...  *)
21365
4ee8e2702241 InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents: 21291
diff changeset
   829
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   830
    fun prove_constr_rep_thm eqn =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   831
      let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   832
        val inj_thms = map (fn r => r RS iffD1) abs_inject_thms;
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   833
        val rewrites = constr_defs @ map mk_meta_eq Rep_inverse_thms
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   834
      in Goal.prove_global thy8 [] [] eqn (fn _ => EVERY
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   835
        [resolve_tac inj_thms 1,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   836
         rewrite_goals_tac rewrites,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   837
         rtac refl 3,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   838
         resolve_tac rep_intrs 2,
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   839
         REPEAT (resolve_tac Rep_thms 1)])
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   840
      end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   841
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   842
    val constr_rep_thmss = map (map prove_constr_rep_thm) constr_rep_eqns;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   843
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   844
    (* prove theorem  pi \<bullet> Rep_i x = Rep_i (pi \<bullet> x) *)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   845
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   846
    fun prove_perm_rep_perm (atom, perm_closed_thms) = map (fn th =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   847
      let
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
   848
        val _ $ (_ $ (Rep $ x)) = Logic.unvarify (prop_of th);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   849
        val Type ("fun", [T, U]) = fastype_of Rep;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   850
        val permT = mk_permT (Type (atom, []));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   851
        val pi = Free ("pi", permT);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   852
      in
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   853
        Goal.prove_global thy8 [] []
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   854
          (augment_sort thy8
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   855
            (pt_class_of thy8 atom :: map (cp_class_of thy8 atom) (dt_atoms \ atom))
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   856
            (HOLogic.mk_Trueprop (HOLogic.mk_eq
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   857
              (Const ("Nominal.perm", permT --> U --> U) $ pi $ (Rep $ x),
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   858
               Rep $ (Const ("Nominal.perm", permT --> T --> T) $ pi $ x)))))
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   859
          (fn _ => simp_tac (HOL_basic_ss addsimps (perm_defs @ Abs_inverse_thms @
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   860
            perm_closed_thms @ Rep_thms)) 1)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   861
      end) Rep_thms;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   862
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   863
    val perm_rep_perm_thms = List.concat (map prove_perm_rep_perm
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   864
      (atoms ~~ perm_closed_thmss));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   865
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   866
    (* prove distinctness theorems *)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   867
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   868
    val distinct_props = DatatypeProp.make_distincts descr' sorts;
27300
4cb3101d2bf7 DatatypeProp.make_distincts: only one half of each symmetric pair is constructed
haftmann
parents: 27275
diff changeset
   869
    val dist_rewrites = map2 (fn rep_thms => fn dist_lemma =>
4cb3101d2bf7 DatatypeProp.make_distincts: only one half of each symmetric pair is constructed
haftmann
parents: 27275
diff changeset
   870
      dist_lemma :: rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0])
4cb3101d2bf7 DatatypeProp.make_distincts: only one half of each symmetric pair is constructed
haftmann
parents: 27275
diff changeset
   871
        constr_rep_thmss dist_lemmas;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   872
26969
cf3f998d0631 moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents: 26966
diff changeset
   873
    fun prove_distinct_thms _ (_, []) = []
cf3f998d0631 moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents: 26966
diff changeset
   874
      | prove_distinct_thms (p as (rep_thms, dist_lemma)) (k, t :: ts) =
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   875
          let
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   876
            val dist_thm = Goal.prove_global thy8 [] [] t (fn _ =>
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   877
              simp_tac (simpset_of thy8 addsimps (dist_lemma :: rep_thms)) 1)
27300
4cb3101d2bf7 DatatypeProp.make_distincts: only one half of each symmetric pair is constructed
haftmann
parents: 27275
diff changeset
   878
          in dist_thm :: standard (dist_thm RS not_sym) ::
4cb3101d2bf7 DatatypeProp.make_distincts: only one half of each symmetric pair is constructed
haftmann
parents: 27275
diff changeset
   879
            prove_distinct_thms p (k, ts)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   880
          end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   881
26969
cf3f998d0631 moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents: 26966
diff changeset
   882
    val distinct_thms = map2 prove_distinct_thms
cf3f998d0631 moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents: 26966
diff changeset
   883
      (constr_rep_thmss ~~ dist_lemmas) distinct_props;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   884
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   885
    (** prove equations for permutation functions **)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   886
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   887
    val perm_simps' = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) =>
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   888
      let val T = nth_dtyp' i
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   889
      in List.concat (map (fn (atom, perm_closed_thms) =>
21365
4ee8e2702241 InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents: 21291
diff changeset
   890
          map (fn ((cname, dts), constr_rep_thm) =>
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   891
        let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   892
          val cname = Sign.intern_const thy8
30364
577edc39b501 moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents: 30345
diff changeset
   893
            (Long_Name.append tname (Long_Name.base_name cname));
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   894
          val permT = mk_permT (Type (atom, []));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   895
          val pi = Free ("pi", permT);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   896
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   897
          fun perm t =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   898
            let val T = fastype_of t
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   899
            in Const ("Nominal.perm", permT --> T --> T) $ pi $ t end;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   900
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   901
          fun constr_arg ((dts, dt), (j, l_args, r_args)) =
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   902
            let
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   903
              val Ts = map (typ_of_dtyp descr'' sorts) dts;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   904
              val xs = map (fn (T, i) => mk_Free "x" T i)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   905
                (Ts ~~ (j upto j + length dts - 1))
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   906
              val x = mk_Free "x" (typ_of_dtyp descr'' sorts dt) (j + length dts)
18261
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   907
            in
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   908
              (j + length dts + 1,
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   909
               xs @ x :: l_args,
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   910
               map perm (xs @ [x]) @ r_args)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   911
            end
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   912
30190
479806475f3c use long names for old-style fold combinators;
wenzelm
parents: 29585
diff changeset
   913
          val (_, l_args, r_args) = List.foldr constr_arg (1, [], []) dts;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   914
          val c = Const (cname, map fastype_of l_args ---> T)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   915
        in
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   916
          Goal.prove_global thy8 [] []
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   917
            (augment_sort thy8
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   918
              (pt_class_of thy8 atom :: map (cp_class_of thy8 atom) (dt_atoms \ atom))
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   919
              (HOLogic.mk_Trueprop (HOLogic.mk_eq
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   920
                (perm (list_comb (c, l_args)), list_comb (c, r_args)))))
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   921
            (fn _ => EVERY
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   922
              [simp_tac (simpset_of thy8 addsimps (constr_rep_thm :: perm_defs)) 1,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   923
               simp_tac (HOL_basic_ss addsimps (Rep_thms @ Abs_inverse_thms @
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   924
                 constr_defs @ perm_closed_thms)) 1,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   925
               TRY (simp_tac (HOL_basic_ss addsimps
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   926
                 (symmetric perm_fun_def :: abs_perm)) 1),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   927
               TRY (simp_tac (HOL_basic_ss addsimps
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   928
                 (perm_fun_def :: perm_defs @ Rep_thms @ Abs_inverse_thms @
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   929
                    perm_closed_thms)) 1)])
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   930
        end) (constrs ~~ constr_rep_thms)) (atoms ~~ perm_closed_thmss))
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   931
      end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   932
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   933
    (** prove injectivity of constructors **)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   934
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   935
    val rep_inject_thms' = map (fn th => th RS sym) rep_inject_thms;
26343
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
   936
    val alpha = PureThy.get_thms thy8 "alpha";
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
   937
    val abs_fresh = PureThy.get_thms thy8 "abs_fresh";
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   938
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   939
    val pt_cp_sort =
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   940
      map (pt_class_of thy8) dt_atoms @
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   941
      maps (fn s => map (cp_class_of thy8 s) (dt_atoms \ s)) dt_atoms;
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   942
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   943
    val inject_thms = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) =>
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   944
      let val T = nth_dtyp' i
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   945
      in List.mapPartial (fn ((cname, dts), constr_rep_thm) =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   946
        if null dts then NONE else SOME
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   947
        let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   948
          val cname = Sign.intern_const thy8
30364
577edc39b501 moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents: 30345
diff changeset
   949
            (Long_Name.append tname (Long_Name.base_name cname));
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   950
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   951
          fun make_inj ((dts, dt), (j, args1, args2, eqs)) =
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   952
            let
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   953
              val Ts_idx = map (typ_of_dtyp descr'' sorts) dts ~~ (j upto j + length dts - 1);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   954
              val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   955
              val ys = map (fn (T, i) => mk_Free "y" T i) Ts_idx;
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   956
              val x = mk_Free "x" (typ_of_dtyp descr'' sorts dt) (j + length dts);
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   957
              val y = mk_Free "y" (typ_of_dtyp descr'' sorts dt) (j + length dts)
18261
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   958
            in
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   959
              (j + length dts + 1,
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   960
               xs @ (x :: args1), ys @ (y :: args2),
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   961
               HOLogic.mk_eq
30190
479806475f3c use long names for old-style fold combinators;
wenzelm
parents: 29585
diff changeset
   962
                 (List.foldr mk_abs_fun x xs, List.foldr mk_abs_fun y ys) :: eqs)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   963
            end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   964
30190
479806475f3c use long names for old-style fold combinators;
wenzelm
parents: 29585
diff changeset
   965
          val (_, args1, args2, eqs) = List.foldr make_inj (1, [], [], []) dts;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   966
          val Ts = map fastype_of args1;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   967
          val c = Const (cname, Ts ---> T)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   968
        in
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   969
          Goal.prove_global thy8 [] []
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   970
            (augment_sort thy8 pt_cp_sort
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   971
              (HOLogic.mk_Trueprop (HOLogic.mk_eq
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   972
                (HOLogic.mk_eq (list_comb (c, args1), list_comb (c, args2)),
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   973
                 foldr1 HOLogic.mk_conj eqs))))
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   974
            (fn _ => EVERY
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   975
               [asm_full_simp_tac (simpset_of thy8 addsimps (constr_rep_thm ::
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   976
                  rep_inject_thms')) 1,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   977
                TRY (asm_full_simp_tac (HOL_basic_ss addsimps (fresh_def :: supp_def ::
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   978
                  alpha @ abs_perm @ abs_fresh @ rep_inject_thms @
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   979
                  perm_rep_perm_thms)) 1)])
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   980
        end) (constrs ~~ constr_rep_thms)
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   981
      end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   982
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   983
    (** equations for support and freshness **)
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   984
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   985
    val (supp_thms, fresh_thms) = ListPair.unzip (map ListPair.unzip
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   986
      (map (fn ((((i, (_, _, constrs)), tname), inject_thms'), perm_thms') =>
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   987
      let val T = nth_dtyp' i
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   988
      in List.concat (map (fn (cname, dts) => map (fn atom =>
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   989
        let
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   990
          val cname = Sign.intern_const thy8
30364
577edc39b501 moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents: 30345
diff changeset
   991
            (Long_Name.append tname (Long_Name.base_name cname));
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   992
          val atomT = Type (atom, []);
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   993
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   994
          fun process_constr ((dts, dt), (j, args1, args2)) =
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   995
            let
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   996
              val Ts_idx = map (typ_of_dtyp descr'' sorts) dts ~~ (j upto j + length dts - 1);
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   997
              val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
   998
              val x = mk_Free "x" (typ_of_dtyp descr'' sorts dt) (j + length dts)
18261
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   999
            in
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
  1000
              (j + length dts + 1,
30190
479806475f3c use long names for old-style fold combinators;
wenzelm
parents: 29585
diff changeset
  1001
               xs @ (x :: args1), List.foldr mk_abs_fun x xs :: args2)
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
  1002
            end;
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
  1003
30190
479806475f3c use long names for old-style fold combinators;
wenzelm
parents: 29585
diff changeset
  1004
          val (_, args1, args2) = List.foldr process_constr (1, [], []) dts;
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
  1005
          val Ts = map fastype_of args1;
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
  1006
          val c = list_comb (Const (cname, Ts ---> T), args1);
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
  1007
          fun supp t =
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
  1008
            Const ("Nominal.supp", fastype_of t --> HOLogic.mk_setT atomT) $ t;
25823
5d75f4b179e2 Added function fresh_const.
berghofe
parents: 25674
diff changeset
  1009
          fun fresh t = fresh_const atomT (fastype_of t) $ Free ("a", atomT) $ t;
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
  1010
          val supp_thm = Goal.prove_global thy8 [] []
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1011
            (augment_sort thy8 pt_cp_sort
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
  1012
              (HOLogic.mk_Trueprop (HOLogic.mk_eq
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
  1013
                (supp c,
30304
d8e4cd2ac2a1 set operations Int, Un, INTER, UNION, Inter, Union, empty, UNIV are now proper qualified constants with authentic syntax
haftmann
parents: 29585
diff changeset
  1014
                 if null dts then Const (@{const_name Set.empty}, HOLogic.mk_setT atomT)
d8e4cd2ac2a1 set operations Int, Un, INTER, UNION, Inter, Union, empty, UNIV are now proper qualified constants with authentic syntax
haftmann
parents: 29585
diff changeset
  1015
                 else foldr1 (HOLogic.mk_binop @{const_name Un}) (map supp args2)))))
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
  1016
            (fn _ =>
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
  1017
              simp_tac (HOL_basic_ss addsimps (supp_def ::
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
  1018
                 Un_assoc :: de_Morgan_conj :: Collect_disj_eq :: finite_Un ::
22274
ce1459004c8d Adapted to changes in Finite_Set theory.
berghofe
parents: 22245
diff changeset
  1019
                 symmetric empty_def :: finite_emptyI :: simp_thms @
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
  1020
                 abs_perm @ abs_fresh @ inject_thms' @ perm_thms')) 1)
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
  1021
        in
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
  1022
          (supp_thm,
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1023
           Goal.prove_global thy8 [] [] (augment_sort thy8 pt_cp_sort
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1024
             (HOLogic.mk_Trueprop (HOLogic.mk_eq
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1025
               (fresh c,
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1026
                if null dts then HOLogic.true_const
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1027
                else foldr1 HOLogic.mk_conj (map fresh args2)))))
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
  1028
             (fn _ =>
24459
fd114392bca9 Got rid of large simpset in proof of characteristic equations
berghofe
parents: 24218
diff changeset
  1029
               simp_tac (HOL_ss addsimps [Un_iff, empty_iff, fresh_def, supp_thm]) 1))
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
  1030
        end) atoms) constrs)
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
  1031
      end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ inject_thms ~~ perm_simps')));
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
  1032
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1033
    (**** weak induction theorem ****)
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1034
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1035
    fun mk_indrule_lemma ((prems, concls), (((i, _), T), U)) =
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1036
      let
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1037
        val Rep_t = Const (List.nth (rep_names, i), T --> U) $
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1038
          mk_Free "x" T i;
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1039
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1040
        val Abs_t =  Const (List.nth (abs_names, i), U --> T)
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1041
21021
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
  1042
      in (prems @ [HOLogic.imp $
6f19e5eb3a44 Adapted to new inductive definition package.
berghofe
parents: 20548
diff changeset
  1043
            (Const (List.nth (rep_set_names'', i), U --> HOLogic.boolT) $ Rep_t) $
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1044
              (mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))],
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1045
          concls @ [mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ mk_Free "x" T i])
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1046
      end;
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1047
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1048
    val (indrule_lemma_prems, indrule_lemma_concls) =
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1049
      Library.foldl mk_indrule_lemma (([], []), (descr'' ~~ recTs ~~ recTs'));
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1050
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
  1051
    val indrule_lemma = Goal.prove_global thy8 [] []
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1052
      (Logic.mk_implies
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1053
        (HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems),
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1054
         HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls))) (fn _ => EVERY
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1055
           [REPEAT (etac conjE 1),
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1056
            REPEAT (EVERY
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1057
              [TRY (rtac conjI 1), full_simp_tac (HOL_basic_ss addsimps Rep_inverse_thms) 1,
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
  1058
               etac mp 1, resolve_tac Rep_thms 1])]);
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1059
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1060
    val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma)));
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1061
    val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1062
      map (Free o apfst fst o dest_Var) Ps;
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1063
    val indrule_lemma' = cterm_instantiate
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1064
      (map (cterm_of thy8) Ps ~~ map (cterm_of thy8) frees) indrule_lemma;
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1065
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
  1066
    val Abs_inverse_thms' = map (fn r => r RS subst) Abs_inverse_thms;
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1067
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1068
    val dt_induct_prop = DatatypeProp.make_ind descr' sorts;
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
  1069
    val dt_induct = Goal.prove_global thy8 []
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1070
      (Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop)
26711
3a478bfa1650 prove_global: pass context;
wenzelm
parents: 26689
diff changeset
  1071
      (fn {prems, ...} => EVERY
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1072
        [rtac indrule_lemma' 1,
25674
b04508c59b9d Deleted copy of indtac.
berghofe
parents: 25557
diff changeset
  1073
         (indtac rep_induct [] THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1,
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1074
         EVERY (map (fn (prem, r) => (EVERY
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1075
           [REPEAT (eresolve_tac Abs_inverse_thms' 1),
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1076
            simp_tac (HOL_basic_ss addsimps [symmetric r]) 1,
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1077
            DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)]))
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
  1078
                (prems ~~ constr_defs))]);
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1079
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1080
    val case_names_induct = mk_case_names_induct descr'';
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1081
18066
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1082
    (**** prove that new datatypes have finite support ****)
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1083
18246
676d2e625d98 added fsub.thy (poplmark challenge) to the examples
urbanc
parents: 18245
diff changeset
  1084
    val _ = warning "proving finite support for the new datatype";
676d2e625d98 added fsub.thy (poplmark challenge) to the examples
urbanc
parents: 18245
diff changeset
  1085
18066
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1086
    val indnames = DatatypeProp.make_tnames recTs;
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1087
26343
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
  1088
    val abs_supp = PureThy.get_thms thy8 "abs_supp";
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
  1089
    val supp_atm = PureThy.get_thms thy8 "supp_atm";
18066
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1090
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1091
    val finite_supp_thms = map (fn atom =>
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1092
      let val atomT = Type (atom, [])
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1093
      in map standard (List.take
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1094
        (split_conj_thm (Goal.prove_global thy8 [] []
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1095
           (augment_sort thy8 (fs_class_of thy8 atom :: pt_cp_sort)
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1096
             (HOLogic.mk_Trueprop
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1097
               (foldr1 HOLogic.mk_conj (map (fn (s, T) =>
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1098
                 Const ("Finite_Set.finite", HOLogic.mk_setT atomT --> HOLogic.boolT) $
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1099
                   (Const ("Nominal.supp", T --> HOLogic.mk_setT atomT) $ Free (s, T)))
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1100
                   (indnames ~~ recTs)))))
18066
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1101
           (fn _ => indtac dt_induct indnames 1 THEN
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1102
            ALLGOALS (asm_full_simp_tac (simpset_of thy8 addsimps
18067
8b9848d150ba - completed the list of thms for supp_atm
urbanc
parents: 18066
diff changeset
  1103
              (abs_supp @ supp_atm @
30364
577edc39b501 moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents: 30345
diff changeset
  1104
               PureThy.get_thms thy8 ("fs_" ^ Long_Name.base_name atom ^ "1") @
18066
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1105
               List.concat supp_thms))))),
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1106
         length new_type_names))
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1107
      end) atoms;
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1108
18759
2f55e3e47355 Updated to Isabelle 2006-01-23
krauss
parents: 18707
diff changeset
  1109
    val simp_atts = replicate (length new_type_names) [Simplifier.simp_add];
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1110
22245
1b8f4ef50c48 moved the infrastructure from the nominal_tags file to nominal_thmdecls
urbanc
parents: 22231
diff changeset
  1111
	(* Function to add both the simp and eqvt attributes *)
1b8f4ef50c48 moved the infrastructure from the nominal_tags file to nominal_thmdecls
urbanc
parents: 22231
diff changeset
  1112
        (* These two attributes are duplicated on all the types in the mutual nominal datatypes *)
1b8f4ef50c48 moved the infrastructure from the nominal_tags file to nominal_thmdecls
urbanc
parents: 22231
diff changeset
  1113
1b8f4ef50c48 moved the infrastructure from the nominal_tags file to nominal_thmdecls
urbanc
parents: 22231
diff changeset
  1114
    val simp_eqvt_atts = replicate (length new_type_names) [Simplifier.simp_add, NominalThmDecls.eqvt_add];
1b8f4ef50c48 moved the infrastructure from the nominal_tags file to nominal_thmdecls
urbanc
parents: 22231
diff changeset
  1115
 
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1116
    val (_, thy9) = thy8 |>
24712
64ed05609568 proper Sign operations instead of Theory aliases;
wenzelm
parents: 24459
diff changeset
  1117
      Sign.add_path big_name |>
29585
c23295521af5 binding replaces bstring
haftmann
parents: 29389
diff changeset
  1118
      PureThy.add_thms [((Binding.name "induct", dt_induct), [case_names_induct])] ||>>
c23295521af5 binding replaces bstring
haftmann
parents: 29389
diff changeset
  1119
      PureThy.add_thmss [((Binding.name "inducts", projections dt_induct), [case_names_induct])] ||>
24712
64ed05609568 proper Sign operations instead of Theory aliases;
wenzelm
parents: 24459
diff changeset
  1120
      Sign.parent_path ||>>
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1121
      DatatypeAux.store_thmss_atts "distinct" new_type_names simp_atts distinct_thms ||>>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1122
      DatatypeAux.store_thmss "constr_rep" new_type_names constr_rep_thmss ||>>
22231
f76f187c91f9 added an infrastructure that allows the user to declare lemmas to be equivariance lemmas; the intention is to use these lemmas in automated tools but also can be employed by the user
urbanc
parents: 21858
diff changeset
  1123
      DatatypeAux.store_thmss_atts "perm" new_type_names simp_eqvt_atts perm_simps' ||>>
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1124
      DatatypeAux.store_thmss "inject" new_type_names inject_thms ||>>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1125
      DatatypeAux.store_thmss "supp" new_type_names supp_thms ||>>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1126
      DatatypeAux.store_thmss_atts "fresh" new_type_names simp_atts fresh_thms ||>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1127
      fold (fn (atom, ths) => fn thy =>
28736
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
  1128
        let
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
  1129
          val class = fs_class_of thy atom;
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
  1130
          val sort = Sign.certify_sort thy (class :: pt_cp_sort)
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
  1131
        in fold (fn Type (s, Ts) => AxClass.prove_arity
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
  1132
          (s, map (inter_sort thy sort o snd o dest_TFree) Ts, [class])
b1fd60fee652 Some modifications in code for proving arities to make it work for datatype
berghofe
parents: 28731
diff changeset
  1133
          (Class.intro_classes_tac [] THEN resolve_tac ths 1)) newTs thy
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1134
        end) (atoms ~~ finite_supp_thms);
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1135
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1136
    (**** strong induction theorem ****)
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1137
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1138
    val pnames = if length descr'' = 1 then ["P"]
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1139
      else map (fn i => "P" ^ string_of_int i) (1 upto length descr'');
18245
65e60434b3c2 Fixed problem with strong induction theorem for datatypes containing
berghofe
parents: 18142
diff changeset
  1140
    val ind_sort = if null dt_atomTs then HOLogic.typeS
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1141
      else Sign.certify_sort thy9 (map (fs_class_of thy9) dt_atoms);
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1142
    val fsT = TFree ("'n", ind_sort);
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1143
    val fsT' = TFree ("'n", HOLogic.typeS);
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1144
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1145
    val fresh_fs = map (fn (s, T) => (T, Free (s, fsT' --> HOLogic.mk_setT T)))
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1146
      (DatatypeProp.indexify_names (replicate (length dt_atomTs) "f") ~~ dt_atomTs);
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1147
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1148
    fun make_pred fsT i T =
18302
577e5d19b33c Changed order of predicate arguments and quantifiers in strong induction rule.
berghofe
parents: 18280
diff changeset
  1149
      Free (List.nth (pnames, i), fsT --> T --> HOLogic.boolT);
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1150
19851
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1151
    fun mk_fresh1 xs [] = []
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1152
      | mk_fresh1 xs ((y as (_, T)) :: ys) = map (fn x => HOLogic.mk_Trueprop
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1153
            (HOLogic.mk_not (HOLogic.mk_eq (Free y, Free x))))
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1154
              (filter (fn (_, U) => T = U) (rev xs)) @
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1155
          mk_fresh1 (y :: xs) ys;
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1156
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1157
    fun mk_fresh2 xss [] = []
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1158
      | mk_fresh2 xss ((p as (ys, _)) :: yss) = List.concat (map (fn y as (_, T) =>
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1159
            map (fn (_, x as (_, U)) => HOLogic.mk_Trueprop
25823
5d75f4b179e2 Added function fresh_const.
berghofe
parents: 25674
diff changeset
  1160
              (fresh_const T U $ Free y $ Free x)) (rev xss @ yss)) ys) @
19851
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1161
          mk_fresh2 (p :: xss) yss;
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1162
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1163
    fun make_ind_prem fsT f k T ((cname, cargs), idxs) =
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1164
      let
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1165
        val recs = List.filter is_rec_type cargs;
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1166
        val Ts = map (typ_of_dtyp descr'' sorts) cargs;
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1167
        val recTs' = map (typ_of_dtyp descr'' sorts) recs;
20071
8f3e1ddb50e6 replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents: 20046
diff changeset
  1168
        val tnames = Name.variant_list pnames (DatatypeProp.make_tnames Ts);
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1169
        val rec_tnames = map fst (List.filter (is_rec_type o snd) (tnames ~~ cargs));
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1170
        val frees = tnames ~~ Ts;
19710
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1171
        val frees' = partition_cargs idxs frees;
20071
8f3e1ddb50e6 replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents: 20046
diff changeset
  1172
        val z = (Name.variant tnames "z", fsT);
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1173
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1174
        fun mk_prem ((dt, s), T) =
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1175
          let
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1176
            val (Us, U) = strip_type T;
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1177
            val l = length Us
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1178
          in list_all (z :: map (pair "x") Us, HOLogic.mk_Trueprop
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1179
            (make_pred fsT (body_index dt) U $ Bound l $ app_bnds (Free (s, T)) l))
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1180
          end;
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1181
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1182
        val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs');
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1183
        val prems' = map (fn p as (_, T) => HOLogic.mk_Trueprop
19710
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1184
            (f T (Free p) (Free z))) (List.concat (map fst frees')) @
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1185
          mk_fresh1 [] (List.concat (map fst frees')) @
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1186
          mk_fresh2 [] frees'
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1187
18302
577e5d19b33c Changed order of predicate arguments and quantifiers in strong induction rule.
berghofe
parents: 18280
diff changeset
  1188
      in list_all_free (frees @ [z], Logic.list_implies (prems' @ prems,
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1189
        HOLogic.mk_Trueprop (make_pred fsT k T $ Free z $
18302
577e5d19b33c Changed order of predicate arguments and quantifiers in strong induction rule.
berghofe
parents: 18280
diff changeset
  1190
          list_comb (Const (cname, Ts ---> T), map Free frees))))
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1191
      end;
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1192
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1193
    val ind_prems = List.concat (map (fn (((i, (_, _, constrs)), (_, idxss)), T) =>
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1194
      map (make_ind_prem fsT (fn T => fn t => fn u =>
25823
5d75f4b179e2 Added function fresh_const.
berghofe
parents: 25674
diff changeset
  1195
        fresh_const T fsT $ t $ u) i T)
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1196
          (constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs));
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1197
    val tnames = DatatypeProp.make_tnames recTs;
20071
8f3e1ddb50e6 replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents: 20046
diff changeset
  1198
    val zs = Name.variant_list tnames (replicate (length descr'') "z");
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1199
    val ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1200
      (map (fn ((((i, _), T), tname), z) =>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1201
        make_pred fsT i T $ Free (z, fsT) $ Free (tname, T))
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1202
        (descr'' ~~ recTs ~~ tnames ~~ zs)));
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1203
    val induct = Logic.list_implies (ind_prems, ind_concl);
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1204
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1205
    val ind_prems' =
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1206
      map (fn (_, f as Free (_, T)) => list_all_free ([("x", fsT')],
26806
40b411ec05aa Adapted to encoding of sets as predicates
berghofe
parents: 26711
diff changeset
  1207
        HOLogic.mk_Trueprop (Const ("Finite_Set.finite",
40b411ec05aa Adapted to encoding of sets as predicates
berghofe
parents: 26711
diff changeset
  1208
          (snd (split_last (binder_types T)) --> HOLogic.boolT) -->
40b411ec05aa Adapted to encoding of sets as predicates
berghofe
parents: 26711
diff changeset
  1209
            HOLogic.boolT) $ (f $ Free ("x", fsT'))))) fresh_fs @
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1210
      List.concat (map (fn (((i, (_, _, constrs)), (_, idxss)), T) =>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1211
        map (make_ind_prem fsT' (fn T => fn t => fn u => HOLogic.Not $
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1212
          HOLogic.mk_mem (t, the (AList.lookup op = fresh_fs T) $ u)) i T)
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1213
            (constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs));
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1214
    val ind_concl' = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1215
      (map (fn ((((i, _), T), tname), z) =>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1216
        make_pred fsT' i T $ Free (z, fsT') $ Free (tname, T))
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1217
        (descr'' ~~ recTs ~~ tnames ~~ zs)));
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1218
    val induct' = Logic.list_implies (ind_prems', ind_concl');
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1219
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1220
    val aux_ind_vars =
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1221
      (DatatypeProp.indexify_names (replicate (length dt_atomTs) "pi") ~~
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1222
       map mk_permT dt_atomTs) @ [("z", fsT')];
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1223
    val aux_ind_Ts = rev (map snd aux_ind_vars);
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1224
    val aux_ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1225
      (map (fn (((i, _), T), tname) =>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1226
        HOLogic.list_all (aux_ind_vars, make_pred fsT' i T $ Bound 0 $
22311
ebcd44cb8d61 Curried and exported mk_perm.
berghofe
parents: 22274
diff changeset
  1227
          fold_rev (mk_perm aux_ind_Ts) (map Bound (length dt_atomTs downto 1))
ebcd44cb8d61 Curried and exported mk_perm.
berghofe
parents: 22274
diff changeset
  1228
            (Free (tname, T))))
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1229
        (descr'' ~~ recTs ~~ tnames)));
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1230
28731
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1231
    val fin_set_supp = map (fn s =>
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1232
      at_inst_of thy9 s RS at_fin_set_supp) dt_atoms;
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1233
    val fin_set_fresh = map (fn s =>
c60ac7923a06 Added support for parametric datatypes.
berghofe
parents: 28662
diff changeset
  1234
      at_inst_of thy9 s RS at_fin_set_fresh) dt_atoms;
25951
6ebe26bfed18 Reimplemented proof of strong induction theorem.
berghofe
parents: 25823
diff changeset
  1235
    val pt1_atoms = map (fn Type (s, _) =>
30364
577edc39b501 moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents: 30345
diff changeset
  1236
      PureThy.get_thm thy9 ("pt_" ^ Long_Name.base_name s ^ "1")) dt_atomTs;
25951
6ebe26bfed18 Reimplemented proof of strong induction theorem.
berghofe
parents: 25823
diff changeset
  1237
    val pt2_atoms = map (fn Type (s, _) =>
30364
577edc39b501 moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents: 30345
diff changeset
  1238
      PureThy.get_thm thy9 ("pt_" ^ Long_Name.base_name s ^ "2") RS sym) dt_atomTs;
26343
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
  1239
    val exists_fresh' = PureThy.get_thms thy9 "exists_fresh'";
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
  1240
    val fs_atoms = PureThy.get_thms thy9 "fin_supp";
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
  1241
    val abs_supp = PureThy.get_thms thy9 "abs_supp";
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
  1242
    val perm_fresh_fresh = PureThy.get_thms thy9 "perm_fresh_fresh";
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
  1243
    val calc_atm = PureThy.get_thms thy9 "calc_atm";
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
  1244
    val fresh_atm = PureThy.get_thms thy9 "fresh_atm";
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
  1245
    val fresh_left = PureThy.get_thms thy9 "fresh_left";
0dd2eab7b296 simplified get_thm(s): back to plain name argument;
wenzelm
parents: 26337
diff changeset
  1246
    val perm_swap = PureThy.get_thms thy9 "perm_swap";
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1247
25951
6ebe26bfed18 Reimplemented proof of strong induction theorem.
berghofe
parents: 25823
diff changeset
  1248
    fun obtain_fresh_name' ths ts T (freshs1, freshs2, ctxt) =
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1249
      let
25951
6ebe26bfed18 Reimplemented proof of strong induction theorem.
berghofe
parents: 25823
diff changeset
  1250
        val p = foldr1 HOLogic.mk_prod (ts @ freshs1);
6ebe26bfed18 Reimplemented proof of strong induction theorem.
berghofe
parents: 25823
diff changeset
  1251
        val ex = Goal.prove ctxt [] [] (HOLogic.mk_Trueprop
6ebe26bfed18 Reimplemented proof of strong induction theorem.
berghofe
parents: 25823
diff changeset
  1252
            (HOLogic.exists_const T $ Abs ("x", T,
6ebe26bfed18 Reimplemented proof of strong induction theorem.
berghofe
parents: 25823
diff changeset
  1253
              fresh_const T (fastype_of p) $
6ebe26bfed18 Reimplemented proof of strong induction theorem.
berghofe
parents: 25823
diff