src/HOL/Nominal/nominal_package.ML
author berghofe
Fri, 18 Aug 2006 17:03:23 +0200
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parent 20376 53b31f7c1d87
child 20411 dd8a1cda2eaf
permissions -rw-r--r--
- Fixed bug that caused uniqueness proof for recursion combinator to fail for mutually recursive datatypes - Implemented proofs of characteristic equations for recursion combinator.
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(*  Title:      HOL/Nominal/nominal_package.ML
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    ID:         $Id$
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    Author:     Stefan Berghofer and Christian Urban, TU Muenchen
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Nominal datatype package for Isabelle/HOL.
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*)
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signature NOMINAL_PACKAGE =
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sig
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  val add_nominal_datatype : bool -> string list -> (string list * bstring * mixfix *
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    (bstring * string list * mixfix) list) list -> theory -> theory
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end
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structure NominalPackage : NOMINAL_PACKAGE =
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struct
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open DatatypeAux;
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open NominalAtoms;
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(** FIXME: DatatypePackage should export this function **)
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local
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fun dt_recs (DtTFree _) = []
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  | dt_recs (DtType (_, dts)) = List.concat (map dt_recs dts)
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  | dt_recs (DtRec i) = [i];
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fun dt_cases (descr: descr) (_, args, constrs) =
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  let
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    fun the_bname i = Sign.base_name (#1 (valOf (AList.lookup (op =) descr i)));
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    val bnames = map the_bname (distinct op = (List.concat (map dt_recs args)));
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  in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end;
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fun induct_cases descr =
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  DatatypeProp.indexify_names (List.concat (map (dt_cases descr) (map #2 descr)));
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fun exhaust_cases descr i = dt_cases descr (valOf (AList.lookup (op =) descr i));
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in
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fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr);
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fun mk_case_names_exhausts descr new =
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  map (RuleCases.case_names o exhaust_cases descr o #1)
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    (List.filter (fn ((_, (name, _, _))) => name mem_string new) descr);
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end;
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(*******************************)
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val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma);
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fun read_typ sign ((Ts, sorts), str) =
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  let
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    val T = Type.no_tvars (Sign.read_typ (sign, (AList.lookup op =)
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      (map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg
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  in (Ts @ [T], add_typ_tfrees (T, sorts)) end;
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(** taken from HOL/Tools/datatype_aux.ML **)
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fun indtac indrule indnames i st =
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  let
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    val ts = HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule));
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    val ts' = HOLogic.dest_conj (HOLogic.dest_Trueprop
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      (Logic.strip_imp_concl (List.nth (prems_of st, i - 1))));
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    val getP = if can HOLogic.dest_imp (hd ts) then
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      (apfst SOME) o HOLogic.dest_imp else pair NONE;
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    fun abstr (t1, t2) = (case t1 of
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        NONE => (case filter (fn Free (s, _) => s mem indnames | _ => false)
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              (term_frees t2) of
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            [Free (s, T)] => absfree (s, T, t2)
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          | _ => sys_error "indtac")
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      | SOME (_ $ t' $ _) => Abs ("x", fastype_of t', abstract_over (t', t2)))
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    val cert = cterm_of (Thm.sign_of_thm st);
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    val Ps = map (cert o head_of o snd o getP) ts;
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    val indrule' = cterm_instantiate (Ps ~~
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      (map (cert o abstr o getP) ts')) indrule
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  in
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    rtac indrule' i st
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  end;
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fun mk_subgoal i f st =
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  let
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    val cg = List.nth (cprems_of st, i - 1);
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    val g = term_of cg;
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    val revcut_rl' = Thm.lift_rule cg revcut_rl;
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    val v = head_of (Logic.strip_assums_concl (hd (prems_of revcut_rl')));
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    val ps = Logic.strip_params g;
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    val cert = cterm_of (sign_of_thm st);
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  in
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    compose_tac (false,
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      Thm.instantiate ([], [(cert v, cert (list_abs (ps,
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        f (rev ps) (Logic.strip_assums_hyp g) (Logic.strip_assums_concl g))))])
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      revcut_rl', 2) i st
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  end;
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(** simplification procedure for sorting permutations **)
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val dj_cp = thm "dj_cp";
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fun dest_permT (Type ("fun", [Type ("List.list", [Type ("*", [T, _])]),
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      Type ("fun", [_, U])])) = (T, U);
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fun permTs_of (Const ("Nominal.perm", T) $ t $ u) = fst (dest_permT T) :: permTs_of u
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  | permTs_of _ = [];
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fun perm_simproc' thy ss (Const ("Nominal.perm", T) $ t $ (u as Const ("Nominal.perm", U) $ r $ s)) =
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      let
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        val (aT as Type (a, []), S) = dest_permT T;
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        val (bT as Type (b, []), _) = dest_permT U
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      in if aT mem permTs_of u andalso aT <> bT then
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          let
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            val a' = Sign.base_name a;
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            val b' = Sign.base_name b;
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            val cp = PureThy.get_thm thy (Name ("cp_" ^ a' ^ "_" ^ b' ^ "_inst"));
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            val dj = PureThy.get_thm thy (Name ("dj_" ^ b' ^ "_" ^ a'));
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            val dj_cp' = [cp, dj] MRS dj_cp;
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            val cert = SOME o cterm_of thy
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          in
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            SOME (mk_meta_eq (Drule.instantiate' [SOME (ctyp_of thy S)]
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              [cert t, cert r, cert s] dj_cp'))
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          end
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        else NONE
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      end
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  | perm_simproc' thy ss _ = NONE;
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val perm_simproc =
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  Simplifier.simproc (the_context ()) "perm_simp" ["pi1 \\<bullet> (pi2 \\<bullet> x)"] perm_simproc';
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val allE_Nil = read_instantiate_sg (the_context()) [("x", "[]")] allE;
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val meta_spec = thm "meta_spec";
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fun projections rule =
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  ProjectRule.projections (ProofContext.init (Thm.theory_of_thm rule)) rule
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  |> map (standard #> RuleCases.save rule);
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val supp_prod = thm "supp_prod";
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val fresh_prod = thm "fresh_prod";
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val supports_fresh = thm "supports_fresh";
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val supports_def = thm "Nominal.op supports_def";
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val fresh_def = thm "fresh_def";
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val supp_def = thm "supp_def";
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val rev_simps = thms "rev.simps";
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val app_simps = thms "op @.simps";
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fun gen_add_nominal_datatype prep_typ err flat_names new_type_names dts thy =
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  let
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    (* this theory is used just for parsing *)
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    val tmp_thy = thy |>
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      Theory.copy |>
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      Theory.add_types (map (fn (tvs, tname, mx, _) =>
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        (tname, length tvs, mx)) dts);
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    val sign = Theory.sign_of tmp_thy;
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    val atoms = atoms_of thy;
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    val classes = map (NameSpace.map_base (fn s => "pt_" ^ s)) atoms;
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    val cp_classes = List.concat (map (fn atom1 => map (fn atom2 =>
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      Sign.intern_class thy ("cp_" ^ Sign.base_name atom1 ^ "_" ^
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        Sign.base_name atom2)) atoms) atoms);
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    fun augment_sort S = S union classes;
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    val augment_sort_typ = map_type_tfree (fn (s, S) => TFree (s, augment_sort S));
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    fun prep_constr ((constrs, sorts), (cname, cargs, mx)) =
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      let val (cargs', sorts') = Library.foldl (prep_typ sign) (([], sorts), cargs)
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      in (constrs @ [(cname, cargs', mx)], sorts') end
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    fun prep_dt_spec ((dts, sorts), (tvs, tname, mx, constrs)) =
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      let val (constrs', sorts') = Library.foldl prep_constr (([], sorts), constrs)
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      in (dts @ [(tvs, tname, mx, constrs')], sorts') end
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    val (dts', sorts) = Library.foldl prep_dt_spec (([], []), dts);
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    val sorts' = map (apsnd augment_sort) sorts;
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    val tyvars = map #1 dts';
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    val types_syntax = map (fn (tvs, tname, mx, constrs) => (tname, mx)) dts';
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    val constr_syntax = map (fn (tvs, tname, mx, constrs) =>
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      map (fn (cname, cargs, mx) => (cname, mx)) constrs) dts';
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    val ps = map (fn (_, n, _, _) =>
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      (Sign.full_name sign n, Sign.full_name sign (n ^ "_Rep"))) dts;
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    val rps = map Library.swap ps;
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    fun replace_types (Type ("Nominal.ABS", [T, U])) = 
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          Type ("fun", [T, Type ("Nominal.noption", [replace_types U])])
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      | replace_types (Type (s, Ts)) =
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          Type (getOpt (AList.lookup op = ps s, s), map replace_types Ts)
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      | replace_types T = T;
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    val dts'' = map (fn (tvs, tname, mx, constrs) => (tvs, tname ^ "_Rep", NoSyn,
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
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      map (fn (cname, cargs, mx) => (cname ^ "_Rep",
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        map (augment_sort_typ o replace_types) cargs, NoSyn)) constrs)) dts';
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    val new_type_names' = map (fn n => n ^ "_Rep") new_type_names;
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    val full_new_type_names' = map (Sign.full_name (sign_of thy)) new_type_names';
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6d69a4190eb2 1) have adjusted the swapping of the result type
urbanc
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    val ({induction, ...},thy1) =
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      DatatypePackage.add_datatype_i err flat_names new_type_names' dts'' thy;
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    val SOME {descr, ...} = Symtab.lookup
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      (DatatypePackage.get_datatypes thy1) (hd full_new_type_names');
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ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
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    fun nth_dtyp i = typ_of_dtyp descr sorts' (DtRec i);
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
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    (**** define permutation functions ****)
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    val permT = mk_permT (TFree ("'x", HOLogic.typeS));
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    val pi = Free ("pi", permT);
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    val perm_types = map (fn (i, _) =>
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      let val T = nth_dtyp i
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      in permT --> T --> T end) descr;
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2e909d5309f4 Renamed "nominal" theory to "Nominal".
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    val perm_names = replicate (length new_type_names) "Nominal.perm" @
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      DatatypeProp.indexify_names (map (fn i => Sign.full_name (sign_of thy1)
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        ("perm_" ^ name_of_typ (nth_dtyp i)))
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          (length new_type_names upto length descr - 1));
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    val perm_names_types = perm_names ~~ perm_types;
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    val perm_eqs = List.concat (map (fn (i, (_, _, constrs)) =>
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      let val T = nth_dtyp i
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      in map (fn (cname, dts) => 
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        let
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ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
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          val Ts = map (typ_of_dtyp descr sorts') dts;
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          val names = DatatypeProp.make_tnames Ts;
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          val args = map Free (names ~~ Ts);
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          val c = Const (cname, Ts ---> T);
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          fun perm_arg (dt, x) =
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            let val T = type_of x
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            in if is_rec_type dt then
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                let val (Us, _) = strip_type T
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                in list_abs (map (pair "x") Us,
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                  Const (List.nth (perm_names_types, body_index dt)) $ pi $
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                    list_comb (x, map (fn (i, U) =>
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2e909d5309f4 Renamed "nominal" theory to "Nominal".
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                      Const ("Nominal.perm", permT --> U --> U) $
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                        (Const ("List.rev", permT --> permT) $ pi) $
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                        Bound i) ((length Us - 1 downto 0) ~~ Us)))
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   238
                end
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
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              else Const ("Nominal.perm", permT --> T --> T) $ pi $ x
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            end;  
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        in
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          (("", HOLogic.mk_Trueprop (HOLogic.mk_eq
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            (Const (List.nth (perm_names_types, i)) $
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               Free ("pi", mk_permT (TFree ("'x", HOLogic.typeS))) $
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               list_comb (c, args),
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   246
             list_comb (c, map perm_arg (dts ~~ args))))), [])
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   247
        end) constrs
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   248
      end) descr);
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   249
20179
a2f3f523c84b adaption to argument change in primrec_package
haftmann
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   250
    val (perm_simps, thy2) = thy1 |>
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      Theory.add_consts_i (map (fn (s, T) => (Sign.base_name s, T, NoSyn))
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        (List.drop (perm_names_types, length new_type_names))) |>
19635
f7aa7d174343 unchecked definitions;
wenzelm
parents: 19494
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      PrimrecPackage.add_primrec_unchecked_i "" perm_eqs;
17870
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    (**** prove that permutation functions introduced by unfolding are ****)
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    (**** equivalent to already existing permutation functions         ****)
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   257
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   258
    val _ = warning ("length descr: " ^ string_of_int (length descr));
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   259
    val _ = warning ("length new_type_names: " ^ string_of_int (length new_type_names));
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   260
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   261
    val perm_indnames = DatatypeProp.make_tnames (map body_type perm_types);
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   262
    val perm_fun_def = PureThy.get_thm thy2 (Name "perm_fun_def");
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   263
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   264
    val unfolded_perm_eq_thms =
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   265
      if length descr = length new_type_names then []
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   266
      else map standard (List.drop (split_conj_thm
20046
9c8909fc5865 Goal.prove_global;
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        (Goal.prove_global thy2 [] []
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          (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
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            (map (fn (c as (s, T), x) =>
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   270
               let val [T1, T2] = binder_types T
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   271
               in HOLogic.mk_eq (Const c $ pi $ Free (x, T2),
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
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   272
                 Const ("Nominal.perm", T) $ pi $ Free (x, T2))
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   273
               end)
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
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             (perm_names_types ~~ perm_indnames))))
c885c93a9324 Removed legacy prove_goalw_cterm command.
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          (fn _ => EVERY [indtac induction perm_indnames 1,
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            ALLGOALS (asm_full_simp_tac
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              (simpset_of thy2 addsimps [perm_fun_def]))])),
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   278
        length new_type_names));
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berghofe
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   279
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    (**** prove [] \<bullet> t = t ****)
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   281
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    val _ = warning "perm_empty_thms";
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berghofe
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   283
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   284
    val perm_empty_thms = List.concat (map (fn a =>
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berghofe
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   285
      let val permT = mk_permT (Type (a, []))
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berghofe
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   286
      in map standard (List.take (split_conj_thm
20046
9c8909fc5865 Goal.prove_global;
wenzelm
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   287
        (Goal.prove_global thy2 [] []
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berghofe
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   288
          (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
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   289
            (map (fn ((s, T), x) => HOLogic.mk_eq
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   290
                (Const (s, permT --> T --> T) $
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   291
                   Const ("List.list.Nil", permT) $ Free (x, T),
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berghofe
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   292
                 Free (x, T)))
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   293
             (perm_names ~~
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
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   294
              map body_type perm_types ~~ perm_indnames))))
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
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   295
          (fn _ => EVERY [indtac induction perm_indnames 1,
17870
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   296
            ALLGOALS (asm_full_simp_tac (simpset_of thy2))])),
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   297
        length new_type_names))
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   298
      end)
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   299
      atoms);
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   300
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berghofe
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   301
    (**** prove (pi1 @ pi2) \<bullet> t = pi1 \<bullet> (pi2 \<bullet> t) ****)
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berghofe
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   302
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   303
    val _ = warning "perm_append_thms";
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   304
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berghofe
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   305
    (*FIXME: these should be looked up statically*)
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   306
    val at_pt_inst = PureThy.get_thm thy2 (Name "at_pt_inst");
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berghofe
parents:
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   307
    val pt2 = PureThy.get_thm thy2 (Name "pt2");
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berghofe
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   308
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berghofe
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   309
    val perm_append_thms = List.concat (map (fn a =>
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   310
      let
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   311
        val permT = mk_permT (Type (a, []));
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berghofe
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   312
        val pi1 = Free ("pi1", permT);
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berghofe
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   313
        val pi2 = Free ("pi2", permT);
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berghofe
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   314
        val pt_inst = PureThy.get_thm thy2 (Name ("pt_" ^ Sign.base_name a ^ "_inst"));
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berghofe
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   315
        val pt2' = pt_inst RS pt2;
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berghofe
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   316
        val pt2_ax = PureThy.get_thm thy2
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berghofe
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   317
          (Name (NameSpace.map_base (fn s => "pt_" ^ s ^ "2") a));
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berghofe
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   318
      in List.take (map standard (split_conj_thm
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   319
        (Goal.prove_global thy2 [] []
17870
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berghofe
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   320
             (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
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berghofe
parents:
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   321
                (map (fn ((s, T), x) =>
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berghofe
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   322
                    let val perm = Const (s, permT --> T --> T)
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berghofe
parents:
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   323
                    in HOLogic.mk_eq
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   324
                      (perm $ (Const ("List.op @", permT --> permT --> permT) $
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   325
                         pi1 $ pi2) $ Free (x, T),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   326
                       perm $ pi1 $ (perm $ pi2 $ Free (x, T)))
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   327
                    end)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   328
                  (perm_names ~~
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   329
                   map body_type perm_types ~~ perm_indnames))))
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   330
           (fn _ => EVERY [indtac induction perm_indnames 1,
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   331
              ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt2', pt2_ax]))]))),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   332
         length new_type_names)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   333
      end) atoms);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   334
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   335
    (**** prove pi1 ~ pi2 ==> pi1 \<bullet> t = pi2 \<bullet> t ****)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   336
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   337
    val _ = warning "perm_eq_thms";
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   338
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   339
    val pt3 = PureThy.get_thm thy2 (Name "pt3");
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   340
    val pt3_rev = PureThy.get_thm thy2 (Name "pt3_rev");
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   341
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   342
    val perm_eq_thms = List.concat (map (fn a =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   343
      let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   344
        val permT = mk_permT (Type (a, []));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   345
        val pi1 = Free ("pi1", permT);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   346
        val pi2 = Free ("pi2", permT);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   347
        (*FIXME: not robust - better access these theorems using NominalData?*)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   348
        val at_inst = PureThy.get_thm thy2 (Name ("at_" ^ Sign.base_name a ^ "_inst"));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   349
        val pt_inst = PureThy.get_thm thy2 (Name ("pt_" ^ Sign.base_name a ^ "_inst"));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   350
        val pt3' = pt_inst RS pt3;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   351
        val pt3_rev' = at_inst RS (pt_inst RS pt3_rev);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   352
        val pt3_ax = PureThy.get_thm thy2
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   353
          (Name (NameSpace.map_base (fn s => "pt_" ^ s ^ "3") a));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   354
      in List.take (map standard (split_conj_thm
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   355
        (Goal.prove_global thy2 [] [] (Logic.mk_implies
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   356
             (HOLogic.mk_Trueprop (Const ("Nominal.prm_eq",
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   357
                permT --> permT --> HOLogic.boolT) $ pi1 $ pi2),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   358
              HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   359
                (map (fn ((s, T), x) =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   360
                    let val perm = Const (s, permT --> T --> T)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   361
                    in HOLogic.mk_eq
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   362
                      (perm $ pi1 $ Free (x, T),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   363
                       perm $ pi2 $ Free (x, T))
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   364
                    end)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   365
                  (perm_names ~~
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   366
                   map body_type perm_types ~~ perm_indnames)))))
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   367
           (fn _ => EVERY [indtac induction perm_indnames 1,
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   368
              ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt3', pt3_rev', pt3_ax]))]))),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   369
         length new_type_names)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   370
      end) atoms);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   371
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   372
    (**** prove pi1 \<bullet> (pi2 \<bullet> t) = (pi1 \<bullet> pi2) \<bullet> (pi1 \<bullet> t) ****)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   373
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   374
    val cp1 = PureThy.get_thm thy2 (Name "cp1");
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   375
    val dj_cp = PureThy.get_thm thy2 (Name "dj_cp");
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   376
    val pt_perm_compose = PureThy.get_thm thy2 (Name "pt_perm_compose");
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   377
    val pt_perm_compose_rev = PureThy.get_thm thy2 (Name "pt_perm_compose_rev");
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   378
    val dj_perm_perm_forget = PureThy.get_thm thy2 (Name "dj_perm_perm_forget");
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   379
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   380
    fun composition_instance name1 name2 thy =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   381
      let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   382
        val name1' = Sign.base_name name1;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   383
        val name2' = Sign.base_name name2;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   384
        val cp_class = Sign.intern_class thy ("cp_" ^ name1' ^ "_" ^ name2');
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   385
        val permT1 = mk_permT (Type (name1, []));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   386
        val permT2 = mk_permT (Type (name2, []));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   387
        val augment = map_type_tfree
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   388
          (fn (x, S) => TFree (x, cp_class :: S));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   389
        val Ts = map (augment o body_type) perm_types;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   390
        val cp_inst = PureThy.get_thm thy
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   391
          (Name ("cp_" ^ name1' ^ "_" ^ name2' ^ "_inst"));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   392
        val simps = simpset_of thy addsimps (perm_fun_def ::
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   393
          (if name1 <> name2 then
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   394
             let val dj = PureThy.get_thm thy (Name ("dj_" ^ name2' ^ "_" ^ name1'))
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   395
             in [dj RS (cp_inst RS dj_cp), dj RS dj_perm_perm_forget] end
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   396
           else
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   397
             let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   398
               val at_inst = PureThy.get_thm thy (Name ("at_" ^ name1' ^ "_inst"));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   399
               val pt_inst = PureThy.get_thm thy (Name ("pt_" ^ name1' ^ "_inst"))
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   400
             in
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   401
               [cp_inst RS cp1 RS sym,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   402
                at_inst RS (pt_inst RS pt_perm_compose) RS sym,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   403
                at_inst RS (pt_inst RS pt_perm_compose_rev) RS sym]
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   404
            end))
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   405
        val thms = split_conj_thm (Goal.prove_global thy [] []
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   406
            (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   407
              (map (fn ((s, T), x) =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   408
                  let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   409
                    val pi1 = Free ("pi1", permT1);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   410
                    val pi2 = Free ("pi2", permT2);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   411
                    val perm1 = Const (s, permT1 --> T --> T);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   412
                    val perm2 = Const (s, permT2 --> T --> T);
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   413
                    val perm3 = Const ("Nominal.perm", permT1 --> permT2 --> permT2)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   414
                  in HOLogic.mk_eq
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   415
                    (perm1 $ pi1 $ (perm2 $ pi2 $ Free (x, T)),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   416
                     perm2 $ (perm3 $ pi1 $ pi2) $ (perm1 $ pi1 $ Free (x, T)))
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   417
                  end)
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   418
                (perm_names ~~ Ts ~~ perm_indnames))))
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   419
          (fn _ => EVERY [indtac induction perm_indnames 1,
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   420
             ALLGOALS (asm_full_simp_tac simps)]))
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   421
      in
19275
3d10de7a8ca7 add_inst_arity_i renamed to prove_arity.
berghofe
parents: 19251
diff changeset
   422
        foldl (fn ((s, tvs), thy) => AxClass.prove_arity
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   423
            (s, replicate (length tvs) (cp_class :: classes), [cp_class])
19133
7e84a1a3741c Adapted to Florian's recent changes to the AxClass package.
berghofe
parents: 18759
diff changeset
   424
            (ClassPackage.intro_classes_tac [] THEN ALLGOALS (resolve_tac thms)) thy)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   425
          thy (full_new_type_names' ~~ tyvars)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   426
      end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   427
18381
246807ef6dfb changed the types in accordance with Florian's changes
urbanc
parents: 18366
diff changeset
   428
    val (perm_thmss,thy3) = thy2 |>
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   429
      fold (fn name1 => fold (composition_instance name1) atoms) atoms |>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   430
      curry (Library.foldr (fn ((i, (tyname, args, _)), thy) =>
19275
3d10de7a8ca7 add_inst_arity_i renamed to prove_arity.
berghofe
parents: 19251
diff changeset
   431
        AxClass.prove_arity (tyname, replicate (length args) classes, classes)
19133
7e84a1a3741c Adapted to Florian's recent changes to the AxClass package.
berghofe
parents: 18759
diff changeset
   432
        (ClassPackage.intro_classes_tac [] THEN REPEAT (EVERY
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   433
           [resolve_tac perm_empty_thms 1,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   434
            resolve_tac perm_append_thms 1,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   435
            resolve_tac perm_eq_thms 1, assume_tac 1])) thy))
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   436
        (List.take (descr, length new_type_names)) |>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   437
      PureThy.add_thmss
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   438
        [((space_implode "_" new_type_names ^ "_unfolded_perm_eq",
18759
2f55e3e47355 Updated to Isabelle 2006-01-23
krauss
parents: 18707
diff changeset
   439
          unfolded_perm_eq_thms), [Simplifier.simp_add]),
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   440
         ((space_implode "_" new_type_names ^ "_perm_empty",
18759
2f55e3e47355 Updated to Isabelle 2006-01-23
krauss
parents: 18707
diff changeset
   441
          perm_empty_thms), [Simplifier.simp_add]),
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   442
         ((space_implode "_" new_type_names ^ "_perm_append",
18759
2f55e3e47355 Updated to Isabelle 2006-01-23
krauss
parents: 18707
diff changeset
   443
          perm_append_thms), [Simplifier.simp_add]),
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   444
         ((space_implode "_" new_type_names ^ "_perm_eq",
18759
2f55e3e47355 Updated to Isabelle 2006-01-23
krauss
parents: 18707
diff changeset
   445
          perm_eq_thms), [Simplifier.simp_add])];
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   446
  
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   447
    (**** Define representing sets ****)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   448
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   449
    val _ = warning "representing sets";
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   450
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   451
    val rep_set_names = map (Sign.full_name thy3) (DatatypeProp.indexify_names
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   452
      (map (fn (i, _) => name_of_typ (nth_dtyp i) ^ "_set") descr));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   453
    val big_rep_name =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   454
      space_implode "_" (DatatypeProp.indexify_names (List.mapPartial
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   455
        (fn (i, ("Nominal.noption", _, _)) => NONE
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   456
          | (i, _) => SOME (name_of_typ (nth_dtyp i))) descr)) ^ "_set";
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   457
    val _ = warning ("big_rep_name: " ^ big_rep_name);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   458
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   459
    fun strip_option (dtf as DtType ("fun", [dt, DtRec i])) =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   460
          (case AList.lookup op = descr i of
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   461
             SOME ("Nominal.noption", _, [(_, [dt']), _]) =>
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   462
               apfst (cons dt) (strip_option dt')
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   463
           | _ => ([], dtf))
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   464
      | strip_option (DtType ("fun", [dt, DtType ("Nominal.noption", [dt'])])) =
18261
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   465
          apfst (cons dt) (strip_option dt')
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   466
      | strip_option dt = ([], dt);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   467
19133
7e84a1a3741c Adapted to Florian's recent changes to the AxClass package.
berghofe
parents: 18759
diff changeset
   468
    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
   469
      (List.concat (map (fn (_, (_, _, cs)) => List.concat
45e139675daf Corrected atom class constraints in strong induction rule.
berghofe
parents: 18261
diff changeset
   470
        (map (List.concat o map (fst o strip_option) o snd) cs)) descr)));
45e139675daf Corrected atom class constraints in strong induction rule.
berghofe
parents: 18261
diff changeset
   471
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   472
    fun make_intr s T (cname, cargs) =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   473
      let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   474
        fun mk_prem (dt, (j, j', prems, ts)) = 
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   475
          let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   476
            val (dts, dt') = strip_option dt;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   477
            val (dts', dt'') = strip_dtyp dt';
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   478
            val Ts = map (typ_of_dtyp descr sorts') dts;
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   479
            val Us = map (typ_of_dtyp descr sorts') dts';
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   480
            val T = typ_of_dtyp descr sorts' dt'';
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   481
            val free = mk_Free "x" (Us ---> T) j;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   482
            val free' = app_bnds free (length Us);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   483
            fun mk_abs_fun (T, (i, t)) =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   484
              let val U = fastype_of t
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   485
              in (i + 1, Const ("Nominal.abs_fun", [T, U, T] --->
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   486
                Type ("Nominal.noption", [U])) $ mk_Free "y" T i $ t)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   487
              end
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   488
          in (j + 1, j' + length Ts,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   489
            case dt'' of
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   490
                DtRec k => list_all (map (pair "x") Us,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   491
                  HOLogic.mk_Trueprop (HOLogic.mk_mem (free',
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   492
                    Const (List.nth (rep_set_names, k),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   493
                      HOLogic.mk_setT T)))) :: prems
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   494
              | _ => prems,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   495
            snd (foldr mk_abs_fun (j', free) Ts) :: ts)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   496
          end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   497
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   498
        val (_, _, prems, ts) = foldr mk_prem (1, 1, [], []) cargs;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   499
        val concl = HOLogic.mk_Trueprop (HOLogic.mk_mem
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   500
          (list_comb (Const (cname, map fastype_of ts ---> T), ts),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   501
           Const (s, HOLogic.mk_setT T)))
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   502
      in Logic.list_implies (prems, concl)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   503
      end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   504
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   505
    val (intr_ts, ind_consts) =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   506
      apfst List.concat (ListPair.unzip (List.mapPartial
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   507
        (fn ((_, ("Nominal.noption", _, _)), _) => NONE
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   508
          | ((i, (_, _, constrs)), rep_set_name) =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   509
              let val T = nth_dtyp i
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   510
              in SOME (map (make_intr rep_set_name T) constrs,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   511
                Const (rep_set_name, HOLogic.mk_setT T))
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   512
              end)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   513
                (descr ~~ rep_set_names)));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   514
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   515
    val (thy4, {raw_induct = rep_induct, intrs = rep_intrs, ...}) =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   516
      setmp InductivePackage.quiet_mode false
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   517
        (InductivePackage.add_inductive_i false true big_rep_name false true false
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   518
           ind_consts (map (fn x => (("", x), [])) intr_ts) []) thy3;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   519
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   520
    (**** Prove that representing set is closed under permutation ****)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   521
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   522
    val _ = warning "proving closure under permutation...";
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   523
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   524
    val perm_indnames' = List.mapPartial
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   525
      (fn (x, (_, ("Nominal.noption", _, _))) => NONE | (x, _) => SOME x)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   526
      (perm_indnames ~~ descr);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   527
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   528
    fun mk_perm_closed name = map (fn th => standard (th RS mp))
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   529
      (List.take (split_conj_thm (Goal.prove_global thy4 [] []
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   530
        (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   531
           (fn (S, x) =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   532
              let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   533
                val S = map_term_types (map_type_tfree
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   534
                  (fn (s, cs) => TFree (s, cs union cp_classes))) S;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   535
                val T = HOLogic.dest_setT (fastype_of S);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   536
                val permT = mk_permT (Type (name, []))
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   537
              in HOLogic.mk_imp (HOLogic.mk_mem (Free (x, T), S),
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   538
                HOLogic.mk_mem (Const ("Nominal.perm", permT --> T --> T) $
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   539
                  Free ("pi", permT) $ Free (x, T), S))
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   540
              end) (ind_consts ~~ perm_indnames'))))
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   541
        (fn _ => EVERY (* CU: added perm_fun_def in the final tactic in order to deal with funs *)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   542
           [indtac rep_induct [] 1,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   543
            ALLGOALS (simp_tac (simpset_of thy4 addsimps
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   544
              (symmetric perm_fun_def :: PureThy.get_thms thy4 (Name ("abs_perm"))))),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   545
            ALLGOALS (resolve_tac rep_intrs 
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   546
               THEN_ALL_NEW (asm_full_simp_tac (simpset_of thy4 addsimps [perm_fun_def])))])),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   547
        length new_type_names));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   548
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   549
    (* FIXME: theorems are stored in database for testing only *)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   550
    val perm_closed_thmss = map mk_perm_closed atoms;
18381
246807ef6dfb changed the types in accordance with Florian's changes
urbanc
parents: 18366
diff changeset
   551
    val (_,thy5) = PureThy.add_thmss [(("perm_closed", List.concat perm_closed_thmss), [])] thy4;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   552
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   553
    (**** typedef ****)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   554
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   555
    val _ = warning "defining type...";
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   556
18366
78b4f225b640 Adapted to new type of PureThy.add_defs_i.
berghofe
parents: 18350
diff changeset
   557
    val (typedefs, thy6) =
78b4f225b640 Adapted to new type of PureThy.add_defs_i.
berghofe
parents: 18350
diff changeset
   558
      fold_map (fn ((((name, mx), tvs), c), name') => fn thy =>
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   559
        setmp TypedefPackage.quiet_mode true
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   560
          (TypedefPackage.add_typedef_i false (SOME name') (name, tvs, mx) c NONE
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   561
            (rtac exI 1 THEN
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   562
              QUIET_BREADTH_FIRST (has_fewer_prems 1)
19403
5c15cd397a82 Adapted to changed type of add_typedef_i.
berghofe
parents: 19322
diff changeset
   563
              (resolve_tac rep_intrs 1))) thy |> (fn (r, thy) =>
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   564
        let
20071
8f3e1ddb50e6 replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents: 20046
diff changeset
   565
          val permT = mk_permT (TFree (Name.variant tvs "'a", HOLogic.typeS));
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   566
          val pi = Free ("pi", permT);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   567
          val tvs' = map (fn s => TFree (s, the (AList.lookup op = sorts' s))) tvs;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   568
          val T = Type (Sign.intern_type thy name, tvs');
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   569
          val Const (_, Type (_, [U])) = c
18366
78b4f225b640 Adapted to new type of PureThy.add_defs_i.
berghofe
parents: 18350
diff changeset
   570
        in apfst (pair r o hd)
19635
f7aa7d174343 unchecked definitions;
wenzelm
parents: 19494
diff changeset
   571
          (PureThy.add_defs_unchecked_i true [(("prm_" ^ name ^ "_def", Logic.mk_equals
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   572
            (Const ("Nominal.perm", permT --> T --> T) $ pi $ Free ("x", T),
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   573
             Const (Sign.intern_const thy ("Abs_" ^ name), U --> T) $
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   574
               (Const ("Nominal.perm", permT --> U --> U) $ pi $
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   575
                 (Const (Sign.intern_const thy ("Rep_" ^ name), T --> U) $
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   576
                   Free ("x", T))))), [])] thy)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   577
        end))
18366
78b4f225b640 Adapted to new type of PureThy.add_defs_i.
berghofe
parents: 18350
diff changeset
   578
          (types_syntax ~~ tyvars ~~
78b4f225b640 Adapted to new type of PureThy.add_defs_i.
berghofe
parents: 18350
diff changeset
   579
            (List.take (ind_consts, length new_type_names)) ~~ new_type_names) thy5;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   580
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   581
    val perm_defs = map snd typedefs;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   582
    val Abs_inverse_thms = map (#Abs_inverse o fst) typedefs;
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   583
    val Rep_inverse_thms = map (#Rep_inverse o fst) typedefs;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   584
    val Rep_thms = map (#Rep o fst) typedefs;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   585
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   586
    val big_name = space_implode "_" new_type_names;
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   587
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   588
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   589
    (** prove that new types are in class pt_<name> **)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   590
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   591
    val _ = warning "prove that new types are in class pt_<name> ...";
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   592
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   593
    fun pt_instance ((class, atom), perm_closed_thms) =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   594
      fold (fn (((({Abs_inverse, Rep_inverse, Rep, ...},
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   595
        perm_def), name), tvs), perm_closed) => fn thy =>
19275
3d10de7a8ca7 add_inst_arity_i renamed to prove_arity.
berghofe
parents: 19251
diff changeset
   596
          AxClass.prove_arity
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   597
            (Sign.intern_type thy name,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   598
              replicate (length tvs) (classes @ cp_classes), [class])
19133
7e84a1a3741c Adapted to Florian's recent changes to the AxClass package.
berghofe
parents: 18759
diff changeset
   599
            (EVERY [ClassPackage.intro_classes_tac [],
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   600
              rewrite_goals_tac [perm_def],
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   601
              asm_full_simp_tac (simpset_of thy addsimps [Rep_inverse]) 1,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   602
              asm_full_simp_tac (simpset_of thy addsimps
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   603
                [Rep RS perm_closed RS Abs_inverse]) 1,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   604
              asm_full_simp_tac (HOL_basic_ss addsimps [PureThy.get_thm thy
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   605
                (Name ("pt_" ^ Sign.base_name atom ^ "3"))]) 1]) thy)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   606
        (typedefs ~~ new_type_names ~~ tyvars ~~ perm_closed_thms);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   607
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   608
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   609
    (** prove that new types are in class cp_<name1>_<name2> **)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   610
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   611
    val _ = warning "prove that new types are in class cp_<name1>_<name2> ...";
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   612
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   613
    fun cp_instance (atom1, perm_closed_thms1) (atom2, perm_closed_thms2) thy =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   614
      let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   615
        val name = "cp_" ^ Sign.base_name atom1 ^ "_" ^ Sign.base_name atom2;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   616
        val class = Sign.intern_class thy name;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   617
        val cp1' = PureThy.get_thm thy (Name (name ^ "_inst")) RS cp1
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   618
      in fold (fn ((((({Abs_inverse, Rep_inverse, Rep, ...},
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   619
        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
   620
          AxClass.prove_arity
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   621
            (Sign.intern_type thy name,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   622
              replicate (length tvs) (classes @ cp_classes), [class])
19133
7e84a1a3741c Adapted to Florian's recent changes to the AxClass package.
berghofe
parents: 18759
diff changeset
   623
            (EVERY [ClassPackage.intro_classes_tac [],
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   624
              rewrite_goals_tac [perm_def],
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   625
              asm_full_simp_tac (simpset_of thy addsimps
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   626
                ((Rep RS perm_closed1 RS Abs_inverse) ::
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   627
                 (if atom1 = atom2 then []
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   628
                  else [Rep RS perm_closed2 RS Abs_inverse]))) 1,
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   629
              cong_tac 1,
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   630
              rtac refl 1,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   631
              rtac cp1' 1]) thy)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   632
        (typedefs ~~ new_type_names ~~ tyvars ~~ perm_closed_thms1 ~~
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   633
          perm_closed_thms2) thy
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   634
      end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   635
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   636
    val thy7 = fold (fn x => fn thy => thy |>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   637
      pt_instance x |>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   638
      fold (cp_instance (apfst snd x)) (atoms ~~ perm_closed_thmss))
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   639
        (classes ~~ atoms ~~ perm_closed_thmss) thy6;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   640
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   641
    (**** constructors ****)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   642
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   643
    fun mk_abs_fun (x, t) =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   644
      let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   645
        val T = fastype_of x;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   646
        val U = fastype_of t
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   647
      in
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   648
        Const ("Nominal.abs_fun", T --> U --> T -->
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   649
          Type ("Nominal.noption", [U])) $ x $ t
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   650
      end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   651
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   652
    val (ty_idxs, _) = foldl
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   653
      (fn ((i, ("Nominal.noption", _, _)), p) => p
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   654
        | ((i, _), (ty_idxs, j)) => (ty_idxs @ [(i, j)], j + 1)) ([], 0) descr;
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   655
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   656
    fun reindex (DtType (s, dts)) = DtType (s, map reindex dts)
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   657
      | reindex (DtRec i) = DtRec (the (AList.lookup op = ty_idxs i))
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   658
      | reindex dt = dt;
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   659
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   660
    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
   661
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   662
    (** strips the "_Rep" in type names *)
18045
6d69a4190eb2 1) have adjusted the swapping of the result type
urbanc
parents: 18017
diff changeset
   663
    fun strip_nth_name i s = 
6d69a4190eb2 1) have adjusted the swapping of the result type
urbanc
parents: 18017
diff changeset
   664
      let val xs = NameSpace.unpack s; 
6d69a4190eb2 1) have adjusted the swapping of the result type
urbanc
parents: 18017
diff changeset
   665
      in NameSpace.pack (Library.nth_map (length xs - i) (strip_suffix 4) xs) end;
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   666
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   667
    val (descr'', ndescr) = ListPair.unzip (List.mapPartial
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   668
      (fn (i, ("Nominal.noption", _, _)) => NONE
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   669
        | (i, (s, dts, constrs)) =>
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   670
             let
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   671
               val SOME index = AList.lookup op = ty_idxs i;
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   672
               val (constrs1, constrs2) = ListPair.unzip
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   673
                 (map (fn (cname, cargs) => apfst (pair (strip_nth_name 2 (strip_nth_name 1 cname)))
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   674
                   (foldl_map (fn (dts, dt) =>
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   675
                     let val (dts', dt') = strip_option dt
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   676
                     in (dts @ dts' @ [reindex dt'], (length dts, length dts')) end)
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   677
                       ([], cargs))) constrs)
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   678
             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
   679
               (index, constrs2))
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   680
             end) descr);
18045
6d69a4190eb2 1) have adjusted the swapping of the result type
urbanc
parents: 18017
diff changeset
   681
19489
4441b637871b SplitAt -> chop
berghofe
parents: 19403
diff changeset
   682
    val (descr1, descr2) = chop (length new_type_names) descr'';
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   683
    val descr' = [descr1, descr2];
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   684
19710
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
   685
    fun partition_cargs idxs xs = map (fn (i, j) =>
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
   686
      (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
   687
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   688
    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
   689
      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
   690
        (constrs ~~ idxss)))) (descr'' ~~ ndescr);
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   691
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   692
    fun nth_dtyp' i = typ_of_dtyp descr'' sorts' (DtRec i);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   693
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   694
    val rep_names = map (fn s =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   695
      Sign.intern_const thy7 ("Rep_" ^ s)) new_type_names;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   696
    val abs_names = map (fn s =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   697
      Sign.intern_const thy7 ("Abs_" ^ s)) new_type_names;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   698
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   699
    val recTs' = List.mapPartial
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   700
      (fn ((_, ("Nominal.noption", _, _)), T) => NONE
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   701
        | (_, T) => SOME T) (descr ~~ get_rec_types descr sorts');
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   702
    val recTs = get_rec_types descr'' sorts';
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   703
    val newTs' = Library.take (length new_type_names, recTs');
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   704
    val newTs = Library.take (length new_type_names, recTs);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   705
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   706
    val full_new_type_names = map (Sign.full_name (sign_of thy)) new_type_names;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   707
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   708
    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
   709
        (((cname_rep, _), (cname, cargs)), (cname', mx))) =
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   710
      let
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   711
        fun constr_arg ((dts, dt), (j, l_args, r_args)) =
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   712
          let
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   713
            val xs = map (fn (dt, i) => mk_Free "x" (typ_of_dtyp descr'' sorts' dt) i)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   714
              (dts ~~ (j upto j + length dts - 1))
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   715
            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
   716
          in
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   717
            (j + length dts + 1,
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   718
             xs @ x :: l_args,
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   719
             foldr mk_abs_fun
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   720
               (case dt of
18261
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   721
                  DtRec k => if k < length new_type_names then
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   722
                      Const (List.nth (rep_names, k), typ_of_dtyp descr'' sorts' dt -->
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   723
                        typ_of_dtyp descr sorts' dt) $ x
18261
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   724
                    else error "nested recursion not (yet) supported"
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   725
                | _ => x) xs :: r_args)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   726
          end
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   727
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   728
        val (_, l_args, r_args) = foldr constr_arg (1, [], []) cargs;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   729
        val abs_name = Sign.intern_const (Theory.sign_of thy) ("Abs_" ^ tname);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   730
        val rep_name = Sign.intern_const (Theory.sign_of thy) ("Rep_" ^ tname);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   731
        val constrT = map fastype_of l_args ---> T;
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   732
        val lhs = list_comb (Const (cname, constrT), l_args);
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   733
        val rhs = list_comb (Const (cname_rep, map fastype_of r_args ---> T'), r_args);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   734
        val def = Logic.mk_equals (lhs, Const (abs_name, T' --> T) $ rhs);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   735
        val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   736
          (Const (rep_name, T --> T') $ lhs, rhs));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   737
        val def_name = (Sign.base_name cname) ^ "_def";
18366
78b4f225b640 Adapted to new type of PureThy.add_defs_i.
berghofe
parents: 18350
diff changeset
   738
        val ([def_thm], thy') = thy |>
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   739
          Theory.add_consts_i [(cname', constrT, mx)] |>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   740
          (PureThy.add_defs_i false o map Thm.no_attributes) [(def_name, def)]
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   741
      in (thy', defs @ [def_thm], eqns @ [eqn]) end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   742
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   743
    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
   744
        (_, (_, _, constrs'))), tname), T), T'), constr_syntax)) =
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   745
      let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   746
        val rep_const = cterm_of thy
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   747
          (Const (Sign.intern_const thy ("Rep_" ^ tname), T --> T'));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   748
        val dist = standard (cterm_instantiate [(cterm_of thy distinct_f, rep_const)] distinct_lemma);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   749
        val (thy', defs', eqns') = Library.foldl (make_constr_def tname T T')
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   750
          ((Theory.add_path tname thy, defs, []), constrs ~~ constrs' ~~ constr_syntax)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   751
      in
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   752
        (parent_path flat_names thy', defs', eqns @ [eqns'], dist_lemmas @ [dist])
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   753
      end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   754
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   755
    val (thy8, constr_defs, constr_rep_eqns, dist_lemmas) = Library.foldl dt_constr_defs
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   756
      ((thy7, [], [], []), List.take (descr, length new_type_names) ~~
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   757
        List.take (pdescr, length new_type_names) ~~
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   758
        new_type_names ~~ newTs ~~ newTs' ~~ constr_syntax);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   759
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   760
    val abs_inject_thms = map (fn tname =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   761
      PureThy.get_thm thy8 (Name ("Abs_" ^ tname ^ "_inject"))) new_type_names;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   762
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   763
    val rep_inject_thms = map (fn tname =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   764
      PureThy.get_thm thy8 (Name ("Rep_" ^ tname ^ "_inject"))) new_type_names;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   765
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   766
    val rep_thms = map (fn tname =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   767
      PureThy.get_thm thy8 (Name ("Rep_" ^ tname))) new_type_names;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   768
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   769
    val rep_inverse_thms = map (fn tname =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   770
      PureThy.get_thm thy8 (Name ("Rep_" ^ tname ^ "_inverse"))) new_type_names;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   771
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   772
    (* prove theorem  Rep_i (Constr_j ...) = Constr'_j ...  *)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   773
    
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   774
    fun prove_constr_rep_thm eqn =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   775
      let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   776
        val inj_thms = map (fn r => r RS iffD1) abs_inject_thms;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   777
        val rewrites = constr_defs @ map mk_meta_eq rep_inverse_thms
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   778
      in Goal.prove_global thy8 [] [] eqn (fn _ => EVERY
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   779
        [resolve_tac inj_thms 1,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   780
         rewrite_goals_tac rewrites,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   781
         rtac refl 3,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   782
         resolve_tac rep_intrs 2,
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   783
         REPEAT (resolve_tac rep_thms 1)])
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   784
      end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   785
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   786
    val constr_rep_thmss = map (map prove_constr_rep_thm) constr_rep_eqns;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   787
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   788
    (* prove theorem  pi \<bullet> Rep_i x = Rep_i (pi \<bullet> x) *)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   789
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   790
    fun prove_perm_rep_perm (atom, perm_closed_thms) = map (fn th =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   791
      let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   792
        val _ $ (_ $ (Rep $ x) $ _) = Logic.unvarify (prop_of th);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   793
        val Type ("fun", [T, U]) = fastype_of Rep;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   794
        val permT = mk_permT (Type (atom, []));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   795
        val pi = Free ("pi", permT);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   796
      in
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   797
        Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   798
            (Const ("Nominal.perm", permT --> U --> U) $ pi $ (Rep $ x),
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   799
             Rep $ (Const ("Nominal.perm", permT --> T --> T) $ pi $ x))))
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   800
          (fn _ => simp_tac (HOL_basic_ss addsimps (perm_defs @ Abs_inverse_thms @
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   801
            perm_closed_thms @ Rep_thms)) 1)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   802
      end) Rep_thms;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   803
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   804
    val perm_rep_perm_thms = List.concat (map prove_perm_rep_perm
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   805
      (atoms ~~ perm_closed_thmss));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   806
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   807
    (* prove distinctness theorems *)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   808
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   809
    val distinct_props = setmp DatatypeProp.dtK 1000
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   810
      (DatatypeProp.make_distincts new_type_names descr' sorts') thy8;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   811
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   812
    val dist_rewrites = map (fn (rep_thms, dist_lemma) =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   813
      dist_lemma::(rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0]))
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   814
        (constr_rep_thmss ~~ dist_lemmas);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   815
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   816
    fun prove_distinct_thms (_, []) = []
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   817
      | prove_distinct_thms (p as (rep_thms, dist_lemma), t::ts) =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   818
          let
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   819
            val dist_thm = Goal.prove_global thy8 [] [] t (fn _ =>
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   820
              simp_tac (simpset_of thy8 addsimps (dist_lemma :: rep_thms)) 1)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   821
          in dist_thm::(standard (dist_thm RS not_sym))::
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   822
            (prove_distinct_thms (p, ts))
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   823
          end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   824
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   825
    val distinct_thms = map prove_distinct_thms
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   826
      (constr_rep_thmss ~~ dist_lemmas ~~ distinct_props);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   827
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   828
    (** prove equations for permutation functions **)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   829
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   830
    val abs_perm = PureThy.get_thms thy8 (Name "abs_perm"); (* FIXME *)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   831
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   832
    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
   833
      let val T = nth_dtyp' i
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   834
      in List.concat (map (fn (atom, perm_closed_thms) =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   835
          map (fn ((cname, dts), constr_rep_thm) => 
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   836
        let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   837
          val cname = Sign.intern_const thy8
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   838
            (NameSpace.append tname (Sign.base_name cname));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   839
          val permT = mk_permT (Type (atom, []));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   840
          val pi = Free ("pi", permT);
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   841
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   842
          fun perm t =
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   843
            let val T = fastype_of t
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   844
            in Const ("Nominal.perm", permT --> T --> T) $ pi $ t end;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   845
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   846
          fun constr_arg ((dts, dt), (j, l_args, r_args)) =
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   847
            let
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   848
              val Ts = map (typ_of_dtyp descr'' sorts') dts;
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   849
              val xs = map (fn (T, i) => mk_Free "x" T i)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   850
                (Ts ~~ (j upto j + length dts - 1))
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   851
              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
   852
            in
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   853
              (j + length dts + 1,
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   854
               xs @ x :: l_args,
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   855
               map perm (xs @ [x]) @ r_args)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   856
            end
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   857
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   858
          val (_, l_args, r_args) = foldr constr_arg (1, [], []) dts;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   859
          val c = Const (cname, map fastype_of l_args ---> T)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   860
        in
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   861
          Goal.prove_global thy8 [] []
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   862
            (HOLogic.mk_Trueprop (HOLogic.mk_eq
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   863
              (perm (list_comb (c, l_args)), list_comb (c, r_args))))
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   864
            (fn _ => EVERY
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   865
              [simp_tac (simpset_of thy8 addsimps (constr_rep_thm :: perm_defs)) 1,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   866
               simp_tac (HOL_basic_ss addsimps (Rep_thms @ Abs_inverse_thms @
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   867
                 constr_defs @ perm_closed_thms)) 1,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   868
               TRY (simp_tac (HOL_basic_ss addsimps
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   869
                 (symmetric perm_fun_def :: abs_perm)) 1),
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   870
               TRY (simp_tac (HOL_basic_ss addsimps
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   871
                 (perm_fun_def :: perm_defs @ Rep_thms @ Abs_inverse_thms @
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   872
                    perm_closed_thms)) 1)])
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   873
        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
   874
      end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   875
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   876
    (** prove injectivity of constructors **)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   877
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   878
    val rep_inject_thms' = map (fn th => th RS sym) rep_inject_thms;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   879
    val alpha = PureThy.get_thms thy8 (Name "alpha");
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   880
    val abs_fresh = PureThy.get_thms thy8 (Name "abs_fresh");
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   881
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   882
    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
   883
      let val T = nth_dtyp' i
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   884
      in List.mapPartial (fn ((cname, dts), constr_rep_thm) =>
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   885
        if null dts then NONE else SOME
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   886
        let
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   887
          val cname = Sign.intern_const thy8
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   888
            (NameSpace.append tname (Sign.base_name cname));
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   889
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   890
          fun make_inj ((dts, dt), (j, args1, args2, eqs)) =
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   891
            let
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   892
              val Ts_idx = map (typ_of_dtyp descr'' sorts') dts ~~ (j upto j + length dts - 1);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   893
              val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   894
              val ys = map (fn (T, i) => mk_Free "y" T i) Ts_idx;
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   895
              val x = mk_Free "x" (typ_of_dtyp descr'' sorts' dt) (j + length dts);
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   896
              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
   897
            in
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   898
              (j + length dts + 1,
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   899
               xs @ (x :: args1), ys @ (y :: args2),
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   900
               HOLogic.mk_eq
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   901
                 (foldr mk_abs_fun x xs, foldr mk_abs_fun y ys) :: eqs)
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   902
            end;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   903
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   904
          val (_, args1, args2, eqs) = foldr make_inj (1, [], [], []) dts;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   905
          val Ts = map fastype_of args1;
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   906
          val c = Const (cname, Ts ---> T)
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   907
        in
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   908
          Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   909
              (HOLogic.mk_eq (list_comb (c, args1), list_comb (c, args2)),
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   910
               foldr1 HOLogic.mk_conj eqs)))
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   911
            (fn _ => EVERY
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   912
               [asm_full_simp_tac (simpset_of thy8 addsimps (constr_rep_thm ::
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   913
                  rep_inject_thms')) 1,
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   914
                TRY (asm_full_simp_tac (HOL_basic_ss addsimps (fresh_def :: supp_def ::
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   915
                  alpha @ abs_perm @ abs_fresh @ rep_inject_thms @
17874
8be65cf94d2e Improved proof of injectivity theorems to make it work on
berghofe
parents: 17873
diff changeset
   916
                  perm_rep_perm_thms)) 1),
8be65cf94d2e Improved proof of injectivity theorems to make it work on
berghofe
parents: 17873
diff changeset
   917
                TRY (asm_full_simp_tac (HOL_basic_ss addsimps (perm_fun_def ::
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   918
                  expand_fun_eq :: rep_inject_thms @ perm_rep_perm_thms)) 1)])
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   919
        end) (constrs ~~ constr_rep_thms)
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   920
      end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
17870
c35381811d5c Initial revision.
berghofe
parents:
diff changeset
   921
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   922
    (** equations for support and freshness **)
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   923
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   924
    val (supp_thms, fresh_thms) = ListPair.unzip (map ListPair.unzip
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   925
      (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
   926
      let val T = nth_dtyp' i
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   927
      in List.concat (map (fn (cname, dts) => map (fn atom =>
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   928
        let
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   929
          val cname = Sign.intern_const thy8
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   930
            (NameSpace.append tname (Sign.base_name cname));
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   931
          val atomT = Type (atom, []);
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   932
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   933
          fun process_constr ((dts, dt), (j, args1, args2)) =
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   934
            let
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   935
              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
   936
              val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   937
              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
   938
            in
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   939
              (j + length dts + 1,
1318955d57ac Corrected treatment of non-recursive abstraction types.
berghofe
parents: 18246
diff changeset
   940
               xs @ (x :: args1), foldr mk_abs_fun x xs :: args2)
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   941
            end;
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   942
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   943
          val (_, args1, args2) = foldr process_constr (1, [], []) dts;
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   944
          val Ts = map fastype_of args1;
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   945
          val c = list_comb (Const (cname, Ts ---> T), args1);
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   946
          fun supp t =
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   947
            Const ("Nominal.supp", fastype_of t --> HOLogic.mk_setT atomT) $ t;
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   948
          fun fresh t =
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
   949
            Const ("Nominal.fresh", atomT --> fastype_of t --> HOLogic.boolT) $
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   950
              Free ("a", atomT) $ t;
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   951
          val supp_thm = Goal.prove_global thy8 [] []
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   952
              (HOLogic.mk_Trueprop (HOLogic.mk_eq
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   953
                (supp c,
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   954
                 if null dts then Const ("{}", HOLogic.mk_setT atomT)
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   955
                 else foldr1 (HOLogic.mk_binop "op Un") (map supp args2))))
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   956
            (fn _ =>
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   957
              simp_tac (HOL_basic_ss addsimps (supp_def ::
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   958
                 Un_assoc :: de_Morgan_conj :: Collect_disj_eq :: finite_Un ::
17874
8be65cf94d2e Improved proof of injectivity theorems to make it work on
berghofe
parents: 17873
diff changeset
   959
                 symmetric empty_def :: Finites.emptyI :: simp_thms @
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   960
                 abs_perm @ abs_fresh @ inject_thms' @ perm_thms')) 1)
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   961
        in
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   962
          (supp_thm,
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   963
           Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   964
              (fresh c,
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   965
               if null dts then HOLogic.true_const
18010
c885c93a9324 Removed legacy prove_goalw_cterm command.
berghofe
parents: 17874
diff changeset
   966
               else foldr1 HOLogic.mk_conj (map fresh args2))))
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   967
             (fn _ =>
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   968
               simp_tac (simpset_of thy8 addsimps [fresh_def, supp_thm]) 1))
17872
f08fc98a164a Implemented proofs for support and freshness theorems.
berghofe
parents: 17870
diff changeset
   969
        end) atoms) constrs)
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
   970
      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
   971
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   972
    (**** weak induction theorem ****)
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   973
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   974
    fun mk_indrule_lemma ((prems, concls), (((i, _), T), U)) =
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   975
      let
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   976
        val Rep_t = Const (List.nth (rep_names, i), T --> U) $
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   977
          mk_Free "x" T i;
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   978
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   979
        val Abs_t =  Const (List.nth (abs_names, i), U --> T)
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   980
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   981
      in (prems @ [HOLogic.imp $ HOLogic.mk_mem (Rep_t,
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   982
            Const (List.nth (rep_set_names, i), HOLogic.mk_setT U)) $
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   983
              (mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))],
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   984
          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
   985
      end;
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   986
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   987
    val (indrule_lemma_prems, indrule_lemma_concls) =
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
   988
      Library.foldl mk_indrule_lemma (([], []), (descr'' ~~ recTs ~~ recTs'));
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   989
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
   990
    val indrule_lemma = Goal.prove_global thy8 [] []
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   991
      (Logic.mk_implies
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   992
        (HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems),
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   993
         HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls))) (fn _ => EVERY
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   994
           [REPEAT (etac conjE 1),
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   995
            REPEAT (EVERY
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   996
              [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
   997
               etac mp 1, resolve_tac Rep_thms 1])]);
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   998
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
   999
    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
  1000
    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
  1001
      map (Free o apfst fst o dest_Var) Ps;
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1002
    val indrule_lemma' = cterm_instantiate
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1003
      (map (cterm_of thy8) Ps ~~ map (cterm_of thy8) frees) indrule_lemma;
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1004
19833
3a3f591c838d - Changed naming scheme: names of "internal" constructors now have
berghofe
parents: 19710
diff changeset
  1005
    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
  1006
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1007
    val dt_induct_prop = DatatypeProp.make_ind descr' sorts';
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
  1008
    val dt_induct = Goal.prove_global thy8 []
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1009
      (Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop)
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1010
      (fn prems => EVERY
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1011
        [rtac indrule_lemma' 1,
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1012
         (DatatypeAux.indtac rep_induct THEN_ALL_NEW ObjectLogic.atomize_tac) 1,
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1013
         EVERY (map (fn (prem, r) => (EVERY
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1014
           [REPEAT (eresolve_tac Abs_inverse_thms' 1),
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1015
            simp_tac (HOL_basic_ss addsimps [symmetric r]) 1,
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1016
            DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)]))
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
  1017
                (prems ~~ constr_defs))]);
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1018
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1019
    val case_names_induct = mk_case_names_induct descr'';
18016
8f3a80033ba4 Implemented proof of weak induction theorem.
berghofe
parents: 18010
diff changeset
  1020
18066
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1021
    (**** prove that new datatypes have finite support ****)
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1022
18246
676d2e625d98 added fsub.thy (poplmark challenge) to the examples
urbanc
parents: 18245
diff changeset
  1023
    val _ = warning "proving finite support for the new datatype";
676d2e625d98 added fsub.thy (poplmark challenge) to the examples
urbanc
parents: 18245
diff changeset
  1024
18066
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1025
    val indnames = DatatypeProp.make_tnames recTs;
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1026
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1027
    val abs_supp = PureThy.get_thms thy8 (Name "abs_supp");
18067
8b9848d150ba - completed the list of thms for supp_atm
urbanc
parents: 18066
diff changeset
  1028
    val supp_atm = PureThy.get_thms thy8 (Name "supp_atm");
18066
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1029
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1030
    val finite_supp_thms = map (fn atom =>
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1031
      let val atomT = Type (atom, [])
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1032
      in map standard (List.take
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
  1033
        (split_conj_thm (Goal.prove_global thy8 [] [] (HOLogic.mk_Trueprop
18066
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1034
           (foldr1 HOLogic.mk_conj (map (fn (s, T) => HOLogic.mk_mem
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
  1035
             (Const ("Nominal.supp", T --> HOLogic.mk_setT atomT) $ Free (s, T),
18066
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1036
              Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT atomT))))
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1037
               (indnames ~~ recTs))))
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1038
           (fn _ => indtac dt_induct indnames 1 THEN
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1039
            ALLGOALS (asm_full_simp_tac (simpset_of thy8 addsimps
18067
8b9848d150ba - completed the list of thms for supp_atm
urbanc
parents: 18066
diff changeset
  1040
              (abs_supp @ supp_atm @
18066
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1041
               PureThy.get_thms thy8 (Name ("fs_" ^ Sign.base_name atom ^ "1")) @
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1042
               List.concat supp_thms))))),
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1043
         length new_type_names))
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1044
      end) atoms;
d1e47ee13070 Added code for proving that new datatype has finite support.
berghofe
parents: 18054
diff changeset
  1045
18759
2f55e3e47355 Updated to Isabelle 2006-01-23
krauss
parents: 18707
diff changeset
  1046
    val simp_atts = replicate (length new_type_names) [Simplifier.simp_add];
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1047
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1048
    val (_, thy9) = thy8 |>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1049
      Theory.add_path big_name |>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1050
      PureThy.add_thms [(("induct_weak", dt_induct), [case_names_induct])] ||>>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1051
      PureThy.add_thmss [(("inducts_weak", projections dt_induct), [case_names_induct])] ||>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1052
      Theory.parent_path ||>>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1053
      DatatypeAux.store_thmss_atts "distinct" new_type_names simp_atts distinct_thms ||>>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1054
      DatatypeAux.store_thmss "constr_rep" new_type_names constr_rep_thmss ||>>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1055
      DatatypeAux.store_thmss_atts "perm" new_type_names simp_atts perm_simps' ||>>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1056
      DatatypeAux.store_thmss "inject" new_type_names inject_thms ||>>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1057
      DatatypeAux.store_thmss "supp" new_type_names supp_thms ||>>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1058
      DatatypeAux.store_thmss_atts "fresh" new_type_names simp_atts fresh_thms ||>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1059
      fold (fn (atom, ths) => fn thy =>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1060
        let val class = Sign.intern_class thy ("fs_" ^ Sign.base_name atom)
19275
3d10de7a8ca7 add_inst_arity_i renamed to prove_arity.
berghofe
parents: 19251
diff changeset
  1061
        in fold (fn T => AxClass.prove_arity
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1062
            (fst (dest_Type T),
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1063
              replicate (length sorts) [class], [class])
19133
7e84a1a3741c Adapted to Florian's recent changes to the AxClass package.
berghofe
parents: 18759
diff changeset
  1064
            (ClassPackage.intro_classes_tac [] THEN resolve_tac ths 1)) newTs thy
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1065
        end) (atoms ~~ finite_supp_thms);
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1066
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1067
    (**** strong induction theorem ****)
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1068
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1069
    val pnames = if length descr'' = 1 then ["P"]
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1070
      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
  1071
    val ind_sort = if null dt_atomTs then HOLogic.typeS
19649
c887656778bc Sign.certify_sort;
wenzelm
parents: 19635
diff changeset
  1072
      else Sign.certify_sort thy9 (map (fn T => Sign.intern_class thy9 ("fs_" ^
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1073
        Sign.base_name (fst (dest_Type T)))) dt_atomTs);
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1074
    val fsT = TFree ("'n", ind_sort);
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1075
    val fsT' = TFree ("'n", HOLogic.typeS);
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1076
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1077
    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
  1078
      (DatatypeProp.indexify_names (replicate (length dt_atomTs) "f") ~~ dt_atomTs);
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1079
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1080
    fun make_pred fsT i T =
18302
577e5d19b33c Changed order of predicate arguments and quantifiers in strong induction rule.
berghofe
parents: 18280
diff changeset
  1081
      Free (List.nth (pnames, i), fsT --> T --> HOLogic.boolT);
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1082
19851
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1083
    fun mk_fresh1 xs [] = []
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1084
      | 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
  1085
            (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
  1086
              (filter (fn (_, U) => T = U) (rev xs)) @
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1087
          mk_fresh1 (y :: xs) ys;
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1088
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1089
    fun mk_fresh2 xss [] = []
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1090
      | 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
  1091
            map (fn (_, x as (_, U)) => HOLogic.mk_Trueprop
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1092
              (Const ("Nominal.fresh", T --> U --> HOLogic.boolT) $ Free y $ Free x))
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1093
                (rev xss @ yss)) ys) @
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1094
          mk_fresh2 (p :: xss) yss;
10162c01bd78 Completely rewrote code for defining graph of recursion combinator.
berghofe
parents: 19833
diff changeset
  1095
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1096
    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
  1097
      let
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1098
        val recs = List.filter is_rec_type cargs;
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1099
        val Ts = map (typ_of_dtyp descr'' sorts') cargs;
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1100
        val recTs' = map (typ_of_dtyp descr'' sorts') recs;
20071
8f3e1ddb50e6 replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents: 20046
diff changeset
  1101
        val tnames = Name.variant_list pnames (DatatypeProp.make_tnames Ts);
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1102
        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
  1103
        val frees = tnames ~~ Ts;
19710
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1104
        val frees' = partition_cargs idxs frees;
20071
8f3e1ddb50e6 replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents: 20046
diff changeset
  1105
        val z = (Name.variant tnames "z", fsT);
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1106
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1107
        fun mk_prem ((dt, s), T) =
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1108
          let
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1109
            val (Us, U) = strip_type T;
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1110
            val l = length Us
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1111
          in list_all (z :: map (pair "x") Us, HOLogic.mk_Trueprop
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1112
            (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
  1113
          end;
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1114
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1115
        val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs');
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1116
        val prems' = map (fn p as (_, T) => HOLogic.mk_Trueprop
19710
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1117
            (f T (Free p) (Free z))) (List.concat (map fst frees')) @
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1118
          mk_fresh1 [] (List.concat (map fst frees')) @
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1119
          mk_fresh2 [] frees'
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1120
18302
577e5d19b33c Changed order of predicate arguments and quantifiers in strong induction rule.
berghofe
parents: 18280
diff changeset
  1121
      in list_all_free (frees @ [z], Logic.list_implies (prems' @ prems,
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1122
        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
  1123
          list_comb (Const (cname, Ts ---> T), map Free frees))))
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1124
      end;
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1125
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1126
    val ind_prems = List.concat (map (fn (((i, (_, _, constrs)), (_, idxss)), T) =>
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1127
      map (make_ind_prem fsT (fn T => fn t => fn u =>
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
  1128
        Const ("Nominal.fresh", T --> fsT --> HOLogic.boolT) $ t $ u) i T)
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1129
          (constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs));
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1130
    val tnames = DatatypeProp.make_tnames recTs;
20071
8f3e1ddb50e6 replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents: 20046
diff changeset
  1131
    val zs = Name.variant_list tnames (replicate (length descr'') "z");
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1132
    val ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1133
      (map (fn ((((i, _), T), tname), z) =>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1134
        make_pred fsT i T $ Free (z, fsT) $ Free (tname, T))
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1135
        (descr'' ~~ recTs ~~ tnames ~~ zs)));
18107
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1136
    val induct = Logic.list_implies (ind_prems, ind_concl);
ee6b4d3af498 Added strong induction theorem (currently only axiomatized!).
berghofe
parents: 18104
diff changeset
  1137
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1138
    val ind_prems' =
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1139
      map (fn (_, f as Free (_, T)) => list_all_free ([("x", fsT')],
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1140
        HOLogic.mk_Trueprop (HOLogic.mk_mem (f $ Free ("x", fsT'),
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1141
          Const ("Finite_Set.Finites", HOLogic.mk_setT (body_type T)))))) fresh_fs @
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1142
      List.concat (map (fn (((i, (_, _, constrs)), (_, idxss)), T) =>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1143
        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
  1144
          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
  1145
            (constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs));
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1146
    val ind_concl' = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1147
      (map (fn ((((i, _), T), tname), z) =>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1148
        make_pred fsT' i T $ Free (z, fsT') $ Free (tname, T))
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1149
        (descr'' ~~ recTs ~~ tnames ~~ zs)));
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1150
    val induct' = Logic.list_implies (ind_prems', ind_concl');
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1151
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1152
    fun mk_perm Ts (t, u) =
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1153
      let
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1154
        val T = fastype_of1 (Ts, t);
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1155
        val U = fastype_of1 (Ts, u)
19494
2e909d5309f4 Renamed "nominal" theory to "Nominal".
berghofe
parents: 19489
diff changeset
  1156
      in Const ("Nominal.perm", T --> U --> U) $ t $ u end;
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1157
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1158
    val aux_ind_vars =
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1159
      (DatatypeProp.indexify_names (replicate (length dt_atomTs) "pi") ~~
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1160
       map mk_permT dt_atomTs) @ [("z", fsT')];
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1161
    val aux_ind_Ts = rev (map snd aux_ind_vars);
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1162
    val aux_ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1163
      (map (fn (((i, _), T), tname) =>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1164
        HOLogic.list_all (aux_ind_vars, make_pred fsT' i T $ Bound 0 $
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1165
          foldr (mk_perm aux_ind_Ts) (Free (tname, T))
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1166
            (map Bound (length dt_atomTs downto 1))))
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1167
        (descr'' ~~ recTs ~~ tnames)));
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1168
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1169
    fun mk_ind_perm i k p l vs j =
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1170
      let
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1171
        val n = length vs;
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1172
        val Ts = map snd vs;
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1173
        val T = List.nth (Ts, i - j);
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1174
        val pT = NominalAtoms.mk_permT T
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1175
      in
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1176
        Const ("List.list.Cons", HOLogic.mk_prodT (T, T) --> pT --> pT) $
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1177
          (HOLogic.pair_const T T $ Bound (l - j) $ foldr (mk_perm Ts)
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1178
            (Bound (i - j))
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1179
            (map (mk_ind_perm i k p l vs) (j - 1 downto 0) @
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1180
             map Bound (n - k - 1 downto n - k - p))) $
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1181
          Const ("List.list.Nil", pT)
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1182
      end;
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1183
19710
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1184
    fun mk_fresh i i' j k p l is vs _ _ =
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1185
      let
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1186
        val n = length vs;
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1187
        val Ts = map snd vs;
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1188
        val T = List.nth (Ts, n - i - 1 - j);
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1189
        val f = the (AList.lookup op = fresh_fs T);
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1190
        val U = List.nth (Ts, n - i' - 1);
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1191
        val S = HOLogic.mk_setT T;
19710
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1192
        val prms' = map Bound (n - k downto n - k - p + 1);
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1193
        val prms = map (mk_ind_perm (n - i) k p (n - l) (("a", T) :: vs))
19710
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1194
            (j - 1 downto 0) @ prms';
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1195
        val bs = rev (List.mapPartial
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1196
          (fn ((_, T'), i) => if T = T' then SOME (Bound i) else NONE)
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1197
          (List.take (vs, n - k - p - 1) ~~ (1 upto n - k - p - 1)));
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1198
        val ts = map (fn i =>
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1199
          Const ("Nominal.supp", List.nth (Ts, n - i - 1) --> S) $
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1200
            foldr (mk_perm (T :: Ts)) (Bound (n - i)) prms') is
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1201
      in
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1202
        HOLogic.mk_Trueprop (Const ("Ex", (T --> HOLogic.boolT) --> HOLogic.boolT) $
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1203
          Abs ("a", T, HOLogic.Not $
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1204
            (Const ("op :", T --> S --> HOLogic.boolT) $ Bound 0 $
19710
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1205
              (foldr (fn (t, u) => Const ("insert", T --> S --> S) $ t $ u)
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1206
                (foldl (fn (t, u) => Const ("op Un", S --> S --> S) $ u $ t)
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1207
                  (f $ Bound (n - k - p))
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1208
                  (Const ("Nominal.supp", U --> S) $
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1209
                     foldr (mk_perm (T :: Ts)) (Bound (n - i')) prms :: ts))
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1210
                (foldr (mk_perm (T :: Ts)) (Bound (n - i - j)) prms :: bs)))))
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1211
      end;
18104
dbe58b104cb9 added thms perm, distinct and fresh to the simplifier.
urbanc
parents: 18068
diff changeset
  1212
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1213
    fun mk_fresh_constr is p vs _ concl =
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1214
      let
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1215
        val n = length vs;
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1216
        val Ts = map snd vs;
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1217
        val _ $ (_ $ _ $ t) = concl;
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1218
        val c = head_of t;
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1219
        val T = body_type (fastype_of c);
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1220
        val k = foldr op + 0 (map (fn (_, i) => i + 1) is);
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1221
        val ps = map Bound (n - k - 1 downto n - k - p);
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1222
        val (_, _, ts, us) = foldl (fn ((_, i), (m, n, ts, us)) =>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1223
          (m - i - 1, n - i,
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1224
           ts @ map Bound (n downto n - i + 1) @
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1225
             [foldr (mk_perm Ts) (Bound (m - i))
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1226
                (map (mk_ind_perm m k p n vs) (i - 1 downto 0) @ ps)],
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1227
           us @ map (fn j => foldr (mk_perm Ts) (Bound j) ps) (m downto m - i)))
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1228
          (n - 1, n - k - p - 2, [], []) is
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1229
      in
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1230
        HOLogic.mk_Trueprop (HOLogic.eq_const T $ list_comb (c, ts) $ list_comb (c, us))
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1231
      end;
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1232
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1233
    val abs_fun_finite_supp = PureThy.get_thm thy9 (Name "abs_fun_finite_supp");
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1234
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1235
    val at_finite_select = PureThy.get_thm thy9 (Name "at_finite_select");
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1236
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1237
    val induct_aux_lemmas = List.concat (map (fn Type (s, _) =>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1238
      [PureThy.get_thm thy9 (Name ("pt_" ^ Sign.base_name s ^ "_inst")),
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1239
       PureThy.get_thm thy9 (Name ("fs_" ^ Sign.base_name s ^ "1")),
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1240
       PureThy.get_thm thy9 (Name ("at_" ^ Sign.base_name s ^ "_inst"))]) dt_atomTs);
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1241
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1242
    val induct_aux_lemmas' = map (fn Type (s, _) =>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1243
      PureThy.get_thm thy9 (Name ("pt_" ^ Sign.base_name s ^ "2")) RS sym) dt_atomTs;
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1244
19710
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1245
    val fresh_aux = PureThy.get_thms thy9 (Name "fresh_aux");
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1246
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1247
    (**********************************************************************
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1248
      The subgoals occurring in the proof of induct_aux have the
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1249
      following parameters:
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1250
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1251
        x_1 ... x_k p_1 ... p_m z b_1 ... b_n
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1252
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1253
      where
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1254
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1255
        x_i : constructor arguments (introduced by weak induction rule)
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1256
        p_i : permutations (one for each atom type in the data type)
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1257
        z   : freshness context
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1258
        b_i : newly introduced names for binders (sufficiently fresh)
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1259
    ***********************************************************************)
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1260
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1261
    val _ = warning "proving strong induction theorem ...";
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1262
20046
9c8909fc5865 Goal.prove_global;
wenzelm
parents: 19985
diff changeset
  1263
    val induct_aux = Goal.prove_global thy9 [] ind_prems' ind_concl'
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1264
      (fn prems => EVERY
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1265
        ([mk_subgoal 1 (K (K (K aux_ind_concl))),
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1266
          indtac dt_induct tnames 1] @
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1267
         List.concat (map (fn ((_, (_, _, constrs)), (_, constrs')) =>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1268
           List.concat (map (fn ((cname, cargs), is) =>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1269
             [simp_tac (HOL_basic_ss addsimps List.concat perm_simps') 1,
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1270
              REPEAT (rtac allI 1)] @
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1271
             List.concat (map
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1272
               (fn ((_, 0), _) => []
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1273
                 | ((i, j), k) => List.concat (map (fn j' =>
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1274
                     let
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1275
                       val DtType (tname, _) = List.nth (cargs, i + j');
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1276
                       val atom = Sign.base_name tname
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1277
                     in
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1278
                       [mk_subgoal 1 (mk_fresh i (i + j) j'
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1279
                          (length cargs) (length dt_atomTs)
19710
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1280
                          (length cargs + length dt_atomTs + 1 + i - k)
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1281
                          (List.mapPartial (fn (i', j) =>
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1282
                             if i = i' then NONE else SOME (i' + j)) is)),
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1283
                        rtac at_finite_select 1,
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1284
                        rtac (PureThy.get_thm thy9 (Name ("at_" ^ atom ^ "_inst"))) 1,
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1285
                        asm_full_simp_tac (simpset_of thy9 addsimps
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1286
                          [PureThy.get_thm thy9 (Name ("fs_" ^ atom ^ "1"))]) 1,
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1287
                        resolve_tac prems 1,
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1288
                        etac exE 1,
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1289
                        asm_full_simp_tac (simpset_of thy9 addsimps
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1290
                          [symmetric fresh_def]) 1]
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1291
                     end) (0 upto j - 1))) (is ~~ (0 upto length is - 1))) @
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1292
             (if exists (not o equal 0 o snd) is then
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1293
                [mk_subgoal 1 (mk_fresh_constr is (length dt_atomTs)),
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1294
                 asm_full_simp_tac (simpset_of thy9 addsimps
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1295
                   (List.concat inject_thms @
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1296
                    alpha @ abs_perm @ abs_fresh @ [abs_fun_finite_supp] @
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1297
                    induct_aux_lemmas)) 1,
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1298
                 dtac sym 1,
19710
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1299
                 asm_full_simp_tac (simpset_of thy9) 1,
18658
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1300
                 REPEAT (etac conjE 1)]
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1301
              else
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1302
                []) @
317a6f0ef8b9 Implemented proof of (strong) induction rule.
berghofe
parents: 18582
diff changeset
  1303
             [(resolve_tac prems THEN_ALL_NEW
19710
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1304
                (atac ORELSE'
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1305
                  SUBGOAL (fn (t, i) => case Logic.strip_assums_concl t of
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1306
                      _ $ (Const ("Nominal.fresh", _) $ _ $ _) =>
ee9c7fa80d21 Extended strong induction rule with additional
berghofe
parents: 19649
diff changeset
  1307
                        asm_simp_tac (simpset_of thy9 addsimps fresh_aux) i
ee9c7fa80d21 Extended strong induction rule with additiona