--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Nominal/nominal_inductive2.ML Tue Oct 21 21:20:17 2008 +0200
@@ -0,0 +1,487 @@
+(* Title: HOL/Nominal/nominal_inductive2.ML
+ ID: $Id$
+ Author: Stefan Berghofer, TU Muenchen
+
+Infrastructure for proving equivariance and strong induction theorems
+for inductive predicates involving nominal datatypes.
+Experimental version that allows to avoid lists of atoms.
+*)
+
+signature NOMINAL_INDUCTIVE2 =
+sig
+ val prove_strong_ind: string -> (string * string list) list -> theory -> Proof.state
+end
+
+structure NominalInductive2 : NOMINAL_INDUCTIVE2 =
+struct
+
+val inductive_forall_name = "HOL.induct_forall";
+val inductive_forall_def = thm "induct_forall_def";
+val inductive_atomize = thms "induct_atomize";
+val inductive_rulify = thms "induct_rulify";
+
+fun rulify_term thy = MetaSimplifier.rewrite_term thy inductive_rulify [];
+
+val atomize_conv =
+ MetaSimplifier.rewrite_cterm (true, false, false) (K (K NONE))
+ (HOL_basic_ss addsimps inductive_atomize);
+val atomize_intr = Conv.fconv_rule (Conv.prems_conv ~1 atomize_conv);
+fun atomize_induct ctxt = Conv.fconv_rule (Conv.prems_conv ~1
+ (Conv.params_conv ~1 (K (Conv.prems_conv ~1 atomize_conv)) ctxt));
+
+val perm_bool = mk_meta_eq (thm "perm_bool");
+val perm_boolI = thm "perm_boolI";
+val (_, [perm_boolI_pi, _]) = Drule.strip_comb (snd (Thm.dest_comb
+ (Drule.strip_imp_concl (cprop_of perm_boolI))));
+
+fun mk_perm_bool pi th = th RS Drule.cterm_instantiate
+ [(perm_boolI_pi, pi)] perm_boolI;
+
+fun mk_perm_bool_simproc names = Simplifier.simproc_i
+ (theory_of_thm perm_bool) "perm_bool" [@{term "perm pi x"}] (fn thy => fn ss =>
+ fn Const ("Nominal.perm", _) $ _ $ t =>
+ if the_default "" (try (head_of #> dest_Const #> fst) t) mem names
+ then SOME perm_bool else NONE
+ | _ => NONE);
+
+fun transp ([] :: _) = []
+ | transp xs = map hd xs :: transp (map tl xs);
+
+fun add_binders thy i (t as (_ $ _)) bs = (case strip_comb t of
+ (Const (s, T), ts) => (case strip_type T of
+ (Ts, Type (tname, _)) =>
+ (case NominalPackage.get_nominal_datatype thy tname of
+ NONE => fold (add_binders thy i) ts bs
+ | SOME {descr, index, ...} => (case AList.lookup op =
+ (#3 (the (AList.lookup op = descr index))) s of
+ NONE => fold (add_binders thy i) ts bs
+ | SOME cargs => fst (fold (fn (xs, x) => fn (bs', cargs') =>
+ let val (cargs1, (u, _) :: cargs2) = chop (length xs) cargs'
+ in (add_binders thy i u
+ (fold (fn (u, T) =>
+ if exists (fn j => j < i) (loose_bnos u) then I
+ else AList.map_default op = (T, [])
+ (insert op aconv (incr_boundvars (~i) u)))
+ cargs1 bs'), cargs2)
+ end) cargs (bs, ts ~~ Ts))))
+ | _ => fold (add_binders thy i) ts bs)
+ | (u, ts) => add_binders thy i u (fold (add_binders thy i) ts bs))
+ | add_binders thy i (Abs (_, _, t)) bs = add_binders thy (i + 1) t bs
+ | add_binders thy i _ bs = bs;
+
+fun mk_set T [] = Const ("{}", HOLogic.mk_setT T)
+ | mk_set T (x :: xs) =
+ Const ("insert", T --> HOLogic.mk_setT T --> HOLogic.mk_setT T) $ x $
+ mk_set T xs;
+
+fun split_conj f names (Const ("op &", _) $ p $ q) _ = (case head_of p of
+ Const (name, _) =>
+ if name mem names then SOME (f p q) else NONE
+ | _ => NONE)
+ | split_conj _ _ _ _ = NONE;
+
+fun strip_all [] t = t
+ | strip_all (_ :: xs) (Const ("All", _) $ Abs (s, T, t)) = strip_all xs t;
+
+(*********************************************************************)
+(* maps R ... & (ALL pi_1 ... pi_n z. P z (pi_1 o ... o pi_n o t)) *)
+(* or ALL pi_1 ... pi_n z. P z (pi_1 o ... o pi_n o t) *)
+(* to R ... & id (ALL z. P z (pi_1 o ... o pi_n o t)) *)
+(* or id (ALL z. P z (pi_1 o ... o pi_n o t)) *)
+(* *)
+(* where "id" protects the subformula from simplification *)
+(*********************************************************************)
+
+fun inst_conj_all names ps pis (Const ("op &", _) $ p $ q) _ =
+ (case head_of p of
+ Const (name, _) =>
+ if name mem names then SOME (HOLogic.mk_conj (p,
+ Const ("Fun.id", HOLogic.boolT --> HOLogic.boolT) $
+ (subst_bounds (pis, strip_all pis q))))
+ else NONE
+ | _ => NONE)
+ | inst_conj_all names ps pis t u =
+ if member (op aconv) ps (head_of u) then
+ SOME (Const ("Fun.id", HOLogic.boolT --> HOLogic.boolT) $
+ (subst_bounds (pis, strip_all pis t)))
+ else NONE
+ | inst_conj_all _ _ _ _ _ = NONE;
+
+fun inst_conj_all_tac k = EVERY
+ [TRY (EVERY [etac conjE 1, rtac conjI 1, atac 1]),
+ REPEAT_DETERM_N k (etac allE 1),
+ simp_tac (HOL_basic_ss addsimps [@{thm id_apply}]) 1];
+
+fun map_term f t u = (case f t u of
+ NONE => map_term' f t u | x => x)
+and map_term' f (t $ u) (t' $ u') = (case (map_term f t t', map_term f u u') of
+ (NONE, NONE) => NONE
+ | (SOME t'', NONE) => SOME (t'' $ u)
+ | (NONE, SOME u'') => SOME (t $ u'')
+ | (SOME t'', SOME u'') => SOME (t'' $ u''))
+ | map_term' f (Abs (s, T, t)) (Abs (s', T', t')) = (case map_term f t t' of
+ NONE => NONE
+ | SOME t'' => SOME (Abs (s, T, t'')))
+ | map_term' _ _ _ = NONE;
+
+(*********************************************************************)
+(* Prove F[f t] from F[t], where F is monotone *)
+(*********************************************************************)
+
+fun map_thm ctxt f tac monos opt th =
+ let
+ val prop = prop_of th;
+ fun prove t =
+ Goal.prove ctxt [] [] t (fn _ =>
+ EVERY [cut_facts_tac [th] 1, etac rev_mp 1,
+ REPEAT_DETERM (FIRSTGOAL (resolve_tac monos)),
+ REPEAT_DETERM (rtac impI 1 THEN (atac 1 ORELSE tac))])
+ in Option.map prove (map_term f prop (the_default prop opt)) end;
+
+fun abs_params params t =
+ let val vs = map (Var o apfst (rpair 0)) (rename_wrt_term t params)
+ in (list_all (params, t), (rev vs, subst_bounds (vs, t))) end;
+
+fun inst_params thy (vs, p) th cts =
+ let val env = Pattern.first_order_match thy (p, prop_of th)
+ (Vartab.empty, Vartab.empty)
+ in Thm.instantiate ([],
+ map (Envir.subst_vars env #> cterm_of thy) vs ~~ cts) th
+ end;
+
+fun prove_strong_ind s avoids thy =
+ let
+ val ctxt = ProofContext.init thy;
+ val ({names, ...}, {raw_induct, intrs, elims, ...}) =
+ InductivePackage.the_inductive ctxt (Sign.intern_const thy s);
+ val ind_params = InductivePackage.params_of raw_induct;
+ val raw_induct = atomize_induct ctxt raw_induct;
+ val elims = map (atomize_induct ctxt) elims;
+ val monos = InductivePackage.get_monos ctxt;
+ val eqvt_thms = NominalThmDecls.get_eqvt_thms ctxt;
+ val _ = (case names \\ foldl (apfst prop_of #> add_term_consts) [] eqvt_thms of
+ [] => ()
+ | xs => error ("Missing equivariance theorem for predicate(s): " ^
+ commas_quote xs));
+ val induct_cases = map fst (fst (RuleCases.get (the
+ (Induct.lookup_inductP ctxt (hd names)))));
+ val induct_cases' = if null induct_cases then replicate (length intrs) ""
+ else induct_cases;
+ val raw_induct' = Logic.unvarify (prop_of raw_induct);
+ val elims' = map (Logic.unvarify o prop_of) elims;
+ val concls = raw_induct' |> Logic.strip_imp_concl |> HOLogic.dest_Trueprop |>
+ HOLogic.dest_conj |> map (HOLogic.dest_imp ##> strip_comb);
+ val ps = map (fst o snd) concls;
+
+ val _ = (case duplicates (op = o pairself fst) avoids of
+ [] => ()
+ | xs => error ("Duplicate case names: " ^ commas_quote (map fst xs)));
+ val _ = (case map fst avoids \\ induct_cases of
+ [] => ()
+ | xs => error ("No such case(s) in inductive definition: " ^ commas_quote xs));
+ fun mk_avoids params name sets =
+ let
+ val (_, ctxt') = ProofContext.add_fixes_i
+ (map (fn (s, T) => (Name.binding s, SOME T, NoSyn)) params) ctxt;
+ fun mk s =
+ let
+ val t = Syntax.read_term ctxt' s;
+ val t' = list_abs_free (params, t) |>
+ funpow (length params) (fn Abs (_, _, t) => t)
+ in (t', HOLogic.dest_setT (fastype_of t)) end
+ handle TERM _ =>
+ error ("Expression " ^ quote s ^ " to be avoided in case " ^
+ quote name ^ " is not a set type");
+ val ps = map mk sets
+ in
+ case duplicates op = (map snd ps) of
+ [] => ps
+ | Ts => error ("More than one set in case " ^ quote name ^
+ " for type(s) " ^ commas_quote (map (Syntax.string_of_typ ctxt') Ts))
+ end;
+
+ val prems = map (fn (prem, name) =>
+ let
+ val prems = map (incr_boundvars 1) (Logic.strip_assums_hyp prem);
+ val concl = incr_boundvars 1 (Logic.strip_assums_concl prem);
+ val params = Logic.strip_params prem
+ in
+ (params,
+ if null avoids then
+ map (fn (T, ts) => (mk_set T ts, T))
+ (fold (add_binders thy 0) (prems @ [concl]) [])
+ else case AList.lookup op = avoids name of
+ NONE => []
+ | SOME sets =>
+ map (apfst (incr_boundvars 1)) (mk_avoids params name sets),
+ prems, strip_comb (HOLogic.dest_Trueprop concl))
+ end) (Logic.strip_imp_prems raw_induct' ~~ induct_cases');
+
+ val atomTs = distinct op = (maps (map snd o #2) prems);
+ val atoms = map (fst o dest_Type) atomTs;
+ val ind_sort = if null atomTs then HOLogic.typeS
+ else Sign.certify_sort thy (map (fn a => Sign.intern_class thy
+ ("fs_" ^ Sign.base_name a)) atoms);
+ val fs_ctxt_tyname = Name.variant (map fst (term_tfrees raw_induct')) "'n";
+ val fs_ctxt_name = Name.variant (add_term_names (raw_induct', [])) "z";
+ val fsT = TFree (fs_ctxt_tyname, ind_sort);
+
+ val inductive_forall_def' = Drule.instantiate'
+ [SOME (ctyp_of thy fsT)] [] inductive_forall_def;
+
+ fun lift_pred' t (Free (s, T)) ts =
+ list_comb (Free (s, fsT --> T), t :: ts);
+ val lift_pred = lift_pred' (Bound 0);
+
+ fun lift_prem (t as (f $ u)) =
+ let val (p, ts) = strip_comb t
+ in
+ if p mem ps then
+ Const (inductive_forall_name,
+ (fsT --> HOLogic.boolT) --> HOLogic.boolT) $
+ Abs ("z", fsT, lift_pred p (map (incr_boundvars 1) ts))
+ else lift_prem f $ lift_prem u
+ end
+ | lift_prem (Abs (s, T, t)) = Abs (s, T, lift_prem t)
+ | lift_prem t = t;
+
+ fun mk_fresh (x, T) = HOLogic.mk_Trueprop
+ (NominalPackage.fresh_star_const T fsT $ x $ Bound 0);
+
+ val (prems', prems'') = split_list (map (fn (params, sets, prems, (p, ts)) =>
+ let
+ val params' = params @ [("y", fsT)];
+ val prem = Logic.list_implies
+ (map mk_fresh sets @
+ map (fn prem =>
+ if null (term_frees prem inter ps) then prem
+ else lift_prem prem) prems,
+ HOLogic.mk_Trueprop (lift_pred p ts));
+ in abs_params params' prem end) prems);
+
+ val ind_vars =
+ (DatatypeProp.indexify_names (replicate (length atomTs) "pi") ~~
+ map NominalAtoms.mk_permT atomTs) @ [("z", fsT)];
+ val ind_Ts = rev (map snd ind_vars);
+
+ val concl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
+ (map (fn (prem, (p, ts)) => HOLogic.mk_imp (prem,
+ HOLogic.list_all (ind_vars, lift_pred p
+ (map (fold_rev (NominalPackage.mk_perm ind_Ts)
+ (map Bound (length atomTs downto 1))) ts)))) concls));
+
+ val concl' = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
+ (map (fn (prem, (p, ts)) => HOLogic.mk_imp (prem,
+ lift_pred' (Free (fs_ctxt_name, fsT)) p ts)) concls));
+
+ val (vc_compat, vc_compat') = map (fn (params, sets, prems, (p, ts)) =>
+ map (fn q => abs_params params (incr_boundvars ~1 (Logic.list_implies
+ (List.mapPartial (fn prem =>
+ if null (ps inter term_frees prem) then SOME prem
+ else map_term (split_conj (K o I) names) prem prem) prems, q))))
+ (maps (fn (t, T) => map (fn (u, U) => HOLogic.mk_Trueprop
+ (NominalPackage.fresh_star_const U T $ u $ t)) sets)
+ (ts ~~ binder_types (fastype_of p)) @
+ map (fn (u, U) => HOLogic.mk_Trueprop (Const (@{const_name finite},
+ HOLogic.mk_setT U --> HOLogic.boolT) $ u)) sets) |>
+ split_list) prems |> split_list;
+
+ val perm_pi_simp = PureThy.get_thms thy "perm_pi_simp";
+ val pt2_atoms = map (fn a => PureThy.get_thm thy
+ ("pt_" ^ Sign.base_name a ^ "2")) atoms;
+ val eqvt_ss = Simplifier.theory_context thy HOL_basic_ss
+ addsimps (eqvt_thms @ perm_pi_simp @ pt2_atoms)
+ addsimprocs [mk_perm_bool_simproc ["Fun.id"],
+ NominalPermeq.perm_simproc_app, NominalPermeq.perm_simproc_fun];
+ val fresh_star_bij = PureThy.get_thms thy "fresh_star_bij";
+ val pt_insts = map (NominalAtoms.the_atom_info thy #> #pt_inst) atoms;
+ val at_insts = map (NominalAtoms.the_atom_info thy #> #at_inst) atoms;
+ val dj_thms = maps (NominalAtoms.the_atom_info thy #> #dj_thms) atoms;
+ val finite_ineq = map2 (fn th => fn th' => th' RS (th RS
+ @{thm pt_set_finite_ineq})) pt_insts at_insts;
+ val perm_set_forget =
+ map (fn th => th RS @{thm dj_perm_set_forget}) dj_thms;
+ val perm_freshs_freshs = atomTs ~~ map2 (fn th => fn th' => th' RS (th RS
+ @{thm pt_freshs_freshs})) pt_insts at_insts;
+
+ fun obtain_fresh_name ts sets (T, fin) (freshs, ths1, ths2, ths3, ctxt) =
+ let
+ val thy = ProofContext.theory_of ctxt;
+ (** protect terms to avoid that fresh_star_prod_set interferes with **)
+ (** pairs used in introduction rules of inductive predicate **)
+ fun protect t =
+ let val T = fastype_of t in Const ("Fun.id", T --> T) $ t end;
+ val p = foldr1 HOLogic.mk_prod (map protect ts);
+ val atom = fst (dest_Type T);
+ val {at_inst, ...} = NominalAtoms.the_atom_info thy atom;
+ val fs_atom = PureThy.get_thm thy
+ ("fs_" ^ Sign.base_name atom ^ "1");
+ val avoid_th = Drule.instantiate'
+ [SOME (ctyp_of thy (fastype_of p))] [SOME (cterm_of thy p)]
+ ([at_inst, fin, fs_atom] MRS @{thm at_set_avoiding});
+ val (([cx], th1 :: th2 :: ths), ctxt') = Obtain.result
+ (fn _ => EVERY
+ [rtac avoid_th 1,
+ full_simp_tac (HOL_ss addsimps [@{thm fresh_star_prod_set}]) 1,
+ full_simp_tac (HOL_basic_ss addsimps [@{thm id_apply}]) 1,
+ rotate_tac 1 1,
+ REPEAT (etac conjE 1)])
+ [] ctxt;
+ val (Ts1, _ :: Ts2) = take_prefix (not o equal T) (map snd sets);
+ val pTs = map NominalAtoms.mk_permT (Ts1 @ Ts2);
+ val (pis1, pis2) = chop (length Ts1)
+ (map Bound (length pTs - 1 downto 0));
+ val _ $ (f $ (_ $ pi $ l) $ r) = prop_of th2
+ val th2' =
+ Goal.prove ctxt [] []
+ (list_all (map (pair "pi") pTs, HOLogic.mk_Trueprop
+ (f $ fold_rev (NominalPackage.mk_perm (rev pTs))
+ (pis1 @ pi :: pis2) l $ r)))
+ (fn _ => cut_facts_tac [th2] 1 THEN
+ full_simp_tac (HOL_basic_ss addsimps perm_set_forget) 1) |>
+ Simplifier.simplify eqvt_ss
+ in
+ (freshs @ [term_of cx],
+ ths1 @ ths, ths2 @ [th1], ths3 @ [th2'], ctxt')
+ end;
+
+ fun mk_ind_proof thy thss =
+ Goal.prove_global thy [] prems' concl' (fn {prems = ihyps, context = ctxt} =>
+ let val th = Goal.prove ctxt [] [] concl (fn {context, ...} =>
+ rtac raw_induct 1 THEN
+ EVERY (maps (fn (((((_, sets, oprems, _),
+ vc_compat_ths), vc_compat_vs), ihyp), vs_ihypt) =>
+ [REPEAT (rtac allI 1), simp_tac eqvt_ss 1,
+ SUBPROOF (fn {prems = gprems, params, concl, context = ctxt', ...} =>
+ let
+ val (cparams', (pis, z)) =
+ chop (length params - length atomTs - 1) params ||>
+ (map term_of #> split_last);
+ val params' = map term_of cparams'
+ val sets' = map (apfst (curry subst_bounds (rev params'))) sets;
+ val pi_sets = map (fn (t, _) =>
+ fold_rev (NominalPackage.mk_perm []) pis t) sets';
+ val (P, ts) = strip_comb (HOLogic.dest_Trueprop (term_of concl));
+ val gprems1 = List.mapPartial (fn (th, t) =>
+ if null (term_frees t inter ps) then SOME th
+ else
+ map_thm ctxt' (split_conj (K o I) names)
+ (etac conjunct1 1) monos NONE th)
+ (gprems ~~ oprems);
+ val vc_compat_ths' = map2 (fn th => fn p =>
+ let
+ val th' = gprems1 MRS inst_params thy p th cparams';
+ val (h, ts) =
+ strip_comb (HOLogic.dest_Trueprop (concl_of th'))
+ in
+ Goal.prove ctxt' [] []
+ (HOLogic.mk_Trueprop (list_comb (h,
+ map (fold_rev (NominalPackage.mk_perm []) pis) ts)))
+ (fn _ => simp_tac (HOL_basic_ss addsimps
+ (fresh_star_bij @ finite_ineq)) 1 THEN rtac th' 1)
+ end) vc_compat_ths vc_compat_vs;
+ val (vc_compat_ths1, vc_compat_ths2) =
+ chop (length vc_compat_ths - length sets) vc_compat_ths';
+ val vc_compat_ths1' = map
+ (Conv.fconv_rule (Conv.arg_conv (Conv.arg_conv
+ (Simplifier.rewrite eqvt_ss)))) vc_compat_ths1;
+ val (pis', fresh_ths1, fresh_ths2, fresh_ths3, ctxt'') = fold
+ (obtain_fresh_name ts sets)
+ (map snd sets' ~~ vc_compat_ths2) ([], [], [], [], ctxt');
+ fun concat_perm pi1 pi2 =
+ let val T = fastype_of pi1
+ in if T = fastype_of pi2 then
+ Const ("List.append", T --> T --> T) $ pi1 $ pi2
+ else pi2
+ end;
+ val pis'' = fold_rev (concat_perm #> map) pis' pis;
+ val ihyp' = inst_params thy vs_ihypt ihyp
+ (map (fold_rev (NominalPackage.mk_perm [])
+ (pis' @ pis) #> cterm_of thy) params' @ [cterm_of thy z]);
+ fun mk_pi th =
+ Simplifier.simplify (HOL_basic_ss addsimps [@{thm id_apply}]
+ addsimprocs [NominalPackage.perm_simproc])
+ (Simplifier.simplify eqvt_ss
+ (fold_rev (mk_perm_bool o cterm_of thy)
+ (pis' @ pis) th));
+ val gprems2 = map (fn (th, t) =>
+ if null (term_frees t inter ps) then mk_pi th
+ else
+ mk_pi (the (map_thm ctxt (inst_conj_all names ps (rev pis''))
+ (inst_conj_all_tac (length pis'')) monos (SOME t) th)))
+ (gprems ~~ oprems);
+ val perm_freshs_freshs' = map (fn (th, (_, T)) =>
+ th RS the (AList.lookup op = perm_freshs_freshs T))
+ (fresh_ths2 ~~ sets);
+ val th = Goal.prove ctxt'' [] []
+ (HOLogic.mk_Trueprop (list_comb (P $ hd ts,
+ map (fold_rev (NominalPackage.mk_perm []) pis') (tl ts))))
+ (fn _ => EVERY ([simp_tac eqvt_ss 1, rtac ihyp' 1] @
+ map (fn th => rtac th 1) fresh_ths3 @
+ [REPEAT_DETERM_N (length gprems)
+ (simp_tac (HOL_basic_ss
+ addsimps [inductive_forall_def']
+ addsimprocs [NominalPackage.perm_simproc]) 1 THEN
+ resolve_tac gprems2 1)]));
+ val final = Goal.prove ctxt'' [] [] (term_of concl)
+ (fn _ => cut_facts_tac [th] 1 THEN full_simp_tac (HOL_ss
+ addsimps vc_compat_ths1' @ fresh_ths1 @
+ perm_freshs_freshs') 1);
+ val final' = ProofContext.export ctxt'' ctxt' [final];
+ in resolve_tac final' 1 end) context 1])
+ (prems ~~ thss ~~ vc_compat' ~~ ihyps ~~ prems'')))
+ in
+ cut_facts_tac [th] 1 THEN REPEAT (etac conjE 1) THEN
+ REPEAT (REPEAT (resolve_tac [conjI, impI] 1) THEN
+ etac impE 1 THEN atac 1 THEN REPEAT (etac @{thm allE_Nil} 1) THEN
+ asm_full_simp_tac (simpset_of thy) 1)
+ end);
+
+ in
+ thy |>
+ ProofContext.init |>
+ Proof.theorem_i NONE (fn thss => ProofContext.theory (fn thy =>
+ let
+ val ctxt = ProofContext.init thy;
+ val rec_name = space_implode "_" (map Sign.base_name names);
+ val ind_case_names = RuleCases.case_names induct_cases;
+ val induct_cases' = InductivePackage.partition_rules' raw_induct
+ (intrs ~~ induct_cases);
+ val thss' = map (map atomize_intr) thss;
+ val thsss = InductivePackage.partition_rules' raw_induct (intrs ~~ thss');
+ val strong_raw_induct =
+ mk_ind_proof thy thss' |> InductivePackage.rulify;
+ val strong_induct =
+ if length names > 1 then
+ (strong_raw_induct, [ind_case_names, RuleCases.consumes 0])
+ else (strong_raw_induct RSN (2, rev_mp),
+ [ind_case_names, RuleCases.consumes 1]);
+ val ([strong_induct'], thy') = thy |>
+ Sign.add_path rec_name |>
+ PureThy.add_thms [(("strong_induct", #1 strong_induct), #2 strong_induct)];
+ val strong_inducts =
+ ProjectRule.projects ctxt (1 upto length names) strong_induct'
+ in
+ thy' |>
+ PureThy.add_thmss [(("strong_inducts", strong_inducts),
+ [ind_case_names, RuleCases.consumes 1])] |> snd |>
+ Sign.parent_path
+ end))
+ (map (map (rulify_term thy #> rpair [])) vc_compat)
+ end;
+
+
+(* outer syntax *)
+
+local structure P = OuterParse and K = OuterKeyword in
+
+val _ =
+ OuterSyntax.command "nominal_inductive2"
+ "prove strong induction theorem for inductive predicate involving nominal datatypes" K.thy_goal
+ (P.name -- Scan.optional (P.$$$ "avoids" |-- P.enum1 "|" (P.name --
+ (P.$$$ ":" |-- P.and_list1 P.term))) [] >> (fn (name, avoids) =>
+ Toplevel.print o Toplevel.theory_to_proof (prove_strong_ind name avoids)));
+
+end;
+
+end