| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/Isabelle/HOL/Nominal/ (Beweissystem Isabelle Version 2025-1©) Datei vom 16.11.2025 mit Größe 24 kB |
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Quelle nominal_inductive2.ML Sprache: SML |
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(* Title: HOL/Nominal/nominal_inductive2.ML
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 option -> (string * string list) list -> local_theory -> Proof.state end structure NominalInductive2 : NOMINAL_INDUCTIVE2 = struct val inductive_forall_def = @{thm HOL.induct_forall_def}; val inductive_atomize = @{thms induct_atomize}; val inductive_rulify = @{thms induct_rulify}; fun rulify_term thy = Simplifier.rewrite_term thy inductive_rulify []; fun atomize_conv ctxt = Simplifier.rewrite_cterm (true, false, false) (K (K NONE)) (put_simpset HOL_basic_ss ctxt addsimps inductive_atomize); fun atomize_intr ctxt = Conv.fconv_rule (Conv.prems_conv ~1 (atomize_conv ctxt)); fun atomize_induct ctxt = Conv.fconv_rule (Conv.prems_conv ~1 (Conv.params_conv ~1 (Conv.prems_conv ~1 o atomize_conv) ctxt)); fun fresh_postprocess ctxt = Simplifier.full_simplify (put_simpset HOL_basic_ss ctxt addsimps [@{thm fresh_star_set_eq}, @{thm fresh_star_Un_elim}, @{thm fresh_star_insert_elim}, @{thm fresh_star_empty_elim}]); fun preds_of ps t = inter (op = o apsnd dest_Free) ps (Term.add_frees t []); val perm_bool = mk_meta_eq @{thm perm_bool_def}; val perm_boolI = @{thm perm_boolI}; val (_, [perm_boolI_pi, _]) = Drule.strip_comb (Thm.dest_arg (Drule.strip_imp_concl (Thm.cprop_of perm_boolI))); fun mk_perm_bool ctxt pi th = th RS infer_instantiate ctxt [(#1 (dest_Var (Thm.term_of perm_boolI_pi)), pi)] perm_boolI fun mk_perm_bool_simproc names = Simplifier.make_simproc \<^context> {name = "perm_bool", kind = Simproc, lhss = [\<^term>\<open>perm pi x\<close>], proc = fn _ => fn _ => fn ct => (case Thm.term_of ct of Const (\<^const_name>\<open>Nominal.perm\<close>, _) $ _ $ t => if member (op =) names (the_default "" (try (dest_Const_name o head_of) t)) then SOME perm_bool else NONE | _ => NONE), identifier = []}; 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 NominalDatatype.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 split_conj f names (Const (\<^const_name>\<open>HOL.conj\<close>, _) $ p $ q) _ = (case head_of p Const (name, _) => if member (op =) names name then SOME (f p q) else NONE | _ => NONE) | split_conj _ _ _ _ = NONE; fun strip_all [] t = t | strip_all (_ :: xs) (Const (\<^const_name>\<open>All\<close>, _) $ 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 (\<^const_name>\<open>HOL.conj\<close>, _) $ p $ q) _ = (case head_of p of Const (name, _) => if member (op =) names name then SOME (HOLogic.mk_conj (p, Const (\<^const_name>\<open>Fun.id\<close>, 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 (\<^const_name>\<open>Fun.id\<close>, HOLogic.boolT --> HOLogic.boolT) $ (subst_bounds (pis, strip_all pis t))) else NONE | inst_conj_all _ _ _ _ _ = NONE; fun inst_conj_all_tac ctxt k = EVERY [TRY (EVERY [eresolve_tac ctxt [conjE] 1, resolve_tac ctxt [conjI] 1, assume_tac ctxt 1]), REPEAT_DETERM_N k (eresolve_tac ctxt [allE] 1), simp_tac (put_simpset HOL_basic_ss ctxt 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 = Thm.prop_of th; fun prove t = Goal.prove ctxt [] [] t (fn {context = goal_ctxt, ...} => EVERY [cut_facts_tac [th] 1, eresolve_tac goal_ctxt [rev_mp] 1, REPEAT_DETERM (FIRSTGOAL (resolve_tac goal_ctxt monos)), REPEAT_DETERM (resolve_tac goal_ctxt [impI] 1 THEN (assume_tac goal_ctxt 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)) (Term.variant_bounds t params) in (Logic.list_all (params, t), (vs, subst_bounds (rev vs, t))) end; fun inst_params thy (vs, p) th cts = let val env = Pattern.first_order_match thy (p, Thm.prop_of th) (Vartab.empty, Vartab.empty) in Thm.instantiate (TVars.empty, Vars.make (map (dest_Var o Envir.subst_term env) vs ~~ cts)) end; fun prove_strong_ind s alt_name avoids lthy = let val thy = Proof_Context.theory_of lthy; val ({names, ...}, {raw_induct, intrs, elims, ...}) = Inductive.the_inductive_global lthy (Sign.intern_const thy s); val ind_params = Inductive.params_of raw_induct; val raw_induct = atomize_induct lthy raw_induct; val elims = map (atomize_induct lthy) elims; val monos = Inductive.get_monos lthy; val eqvt_thms = NominalThmDecls.get_eqvt_thms lthy; val _ = (case subtract (op =) (fold (Term.add_const_names o Thm.prop_of) eqvt_thms []) names o [] => () | xs => error ("Missing equivariance theorem for predicate(s): " ^ commas_quote xs)); val induct_cases = map (fst o fst) (fst (Rule_Cases.get (the (Induct.lookup_inductP lthy (hd names))))); val induct_cases' = if null induct_cases then replicate (length intrs) "" else induct_cases; val (raw_induct', ctxt') = lthy |> yield_singleton (Variable.import_terms false) (Thm.prop_of raw_induct); 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 apply2 fst) avoids of [] => () | xs => error ("Duplicate case names: " ^ commas_quote (map fst xs))); val _ = (case subtract (op =) induct_cases (map fst avoids) of [] => () | xs => error ("No such case(s) in inductive definition: " ^ commas_quote xs)); fun mk_avoids params name sets = let val (_, ctxt') = Proof_Context.add_fixes (map (fn (s, T) => (Binding.name s, SOME T, NoSyn)) params) lthy; fun mk s = let val t = Syntax.read_term ctxt' s; val t' = fold_rev absfree 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"); fun add_set p [] = [p] | add_set (t, T) ((u, U) :: ps) = if T = U then let val S = HOLogic.mk_setT T in (Const (\<^const_name>\<open>sup\<close>, S --> S --> S) $ u $ t, T) :: ps end else (u, U) :: add_set (t, T) ps in fold (mk #> add_set) sets [] 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) => (HOLogic.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 dest_Type_name atomTs; val ind_sort = if null atomTs then \<^sort>\<open>type\<close> else Sign.minimize_sort thy (Sign.certify_sort thy (map (fn a => Sign.intern_class thy ("fs_" ^ Long_Name.base_name a)) atoms)); val (fs_ctxt_tyname, _) = Name.variant "'n" (Variable.names_of ctxt'); val ([fs_ctxt_name], ctxt'') = Variable.variant_fixes ["z"] ctxt'; val fsT = TFree (fs_ctxt_tyname, ind_sort); val inductive_forall_def' = Thm.instantiate' [SOME (Thm.global_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 member (op =) ps p then HOLogic.mk_induct_forall fsT $ 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 (NominalDatatype.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 (preds_of ps prem) then prem else lift_prem prem) prems, HOLogic.mk_Trueprop (lift_pred p ts)); in abs_params params' prem end) prems); val ind_vars = (Case_Translation.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 (NominalDatatype.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 (map_filter (fn prem => if null (preds_of ps 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 (NominalDatatype.fresh_star_const U T $ u $ t)) sets) (ts ~~ binder_types (fastype_of p)) @ map (fn (u, U) => HOLogic.mk_Trueprop (Const (\<^const_name>\<open>finite\<close>, HOLogic.mk_setT U --> HOLogic.boolT) $ u)) sets) |> split_list) prems |> split_list; val perm_pi_simp = Global_Theory.get_thms thy "perm_pi_simp"; val pt2_atoms = map (fn a => Global_Theory.get_thm thy ("pt_" ^ Long_Name.base_name a ^ "2")) atoms; fun eqvt_ss ctxt = put_simpset HOL_basic_ss ctxt addsimps (eqvt_thms @ perm_pi_simp @ pt2_atoms) |> Simplifier.add_proc (mk_perm_bool_simproc [\<^const_name>\<open>Fun.id\<close>]) |> Simplifier.add_proc NominalPermeq.perm_app_simproc |> Simplifier.add_proc NominalPermeq.perm_fun_simproc; val fresh_star_bij = Global_Theory.get_thms thy "fresh_star_bij"; val pt_insts = map (NominalAtoms.pt_inst_of thy) atoms; val at_insts = map (NominalAtoms.at_inst_of thy) atoms; val dj_thms = maps (fn a => map (NominalAtoms.dj_thm_of thy a) (remove (op =) a atoms)) 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 = Proof_Context.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 (\<^const_name>\<open>Fun.id\<close>, T --> T) $ t end; val p = foldr1 HOLogic.mk_prod (map protect ts); val atom = dest_Type_name T; val {at_inst, ...} = NominalAtoms.the_atom_info thy atom; val fs_atom = Global_Theory.get_thm thy ("fs_" ^ Long_Name.base_name atom ^ "1"); val avoid_th = Thm.instantiate' [SOME (Thm.global_ctyp_of thy (fastype_of p))] [SOME (Thm.global_cterm_of thy p)] ([at_inst, fin, fs_atom] MRS @{thm at_set_avoiding}); val (([(_, cx)], th1 :: th2 :: ths), ctxt') = Obtain.result (fn ctxt' => EVERY [resolve_tac ctxt' [avoid_th] 1, full_simp_tac (put_simpset HOL_ss ctxt' addsimps [@{thm fresh_star_prod_set}]) 1, full_simp_tac (put_simpset HOL_basic_ss ctxt' addsimps [@{thm id_apply}]) 1, rotate_tac 1 1, REPEAT (eresolve_tac ctxt' [conjE] 1)]) [] ctxt; val (Ts1, _ :: Ts2) = chop_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) = Thm.prop_of th2 val th2' = Goal.prove ctxt' [] [] (Logic.list_all (map (pair "pi") pTs, HOLogic.mk_Trueprop (f $ fold_rev (NominalDatatype.mk_perm (rev pTs)) (pis1 @ pi :: pis2) l $ r))) (fn {context = goal_ctxt, ...} => cut_facts_tac [th2] 1 THEN full_simp_tac (put_simpset HOL_basic_ss goal_ctxt addsimps perm_set_forget) 1) |> Simplifier.simplify (eqvt_ss ctxt') in (freshs @ [Thm.term_of cx], ths1 @ ths, ths2 @ [th1], ths3 @ [th2'], ctxt') end; fun mk_ind_proof ctxt thss = Goal.prove ctxt [] prems' concl' (fn {prems = ihyps, context = goal_ctxt} => let val th = Goal.prove goal_ctxt [] [] concl (fn {context = goal_ctxt1, ...} => resolve_tac goal_ctxt1 [raw_induct] 1 THEN EVERY (maps (fn (((((_, sets, oprems, _), vc_compat_ths), vc_compat_vs), ihyp), vs_ihypt) => [REPEAT (resolve_tac goal_ctxt1 [allI] 1), simp_tac (eqvt_ss goal_ctxt1) 1, SUBPROOF (fn {prems = gprems, params, concl, context = goal_ctxt2, ...} => let val (cparams', (pis, z)) = chop (length params - length atomTs - 1) (map #2 params) ||> (map Thm.term_of #> split_last); val params' = map Thm.term_of cparams' val sets' = map (apfst (curry subst_bounds (rev params'))) sets; val pi_sets = map (fn (t, _) => fold_rev (NominalDatatype.mk_perm []) pis t) sets'; val (P, ts) = strip_comb (HOLogic.dest_Trueprop (Thm.term_of concl)); val gprems1 = map_filter (fn (th, t) => if null (preds_of ps t) then SOME th else map_thm goal_ctxt2 (split_conj (K o I) names) (eresolve_tac goal_ctxt2 [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 (Thm.concl_of th')) in Goal.prove goal_ctxt2 [] [] (HOLogic.mk_Trueprop (list_comb (h, map (fold_rev (NominalDatatype.mk_perm []) pis) ts))) (fn {context = goal_ctxt3, ...} => simp_tac (put_simpset HOL_basic_ss goal_ctxt3 addsimps (fresh_star_bij @ finite_ineq)) 1 THEN resolve_tac goal_ctxt3 [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 goal_ctxt2))))) vc_compat_ths1; val (pis', fresh_ths1, fresh_ths2, fresh_ths3, ctxt'') = fold (obtain_fresh_name ts sets) (map snd sets' ~~ vc_compat_ths2) ([], [], [], [], goal_ctxt2); fun concat_perm pi1 pi2 = let val T = fastype_of pi1 in if T = fastype_of pi2 then Const (\<^const_name>\<open>append\<close>, 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 (NominalDatatype.mk_perm []) (pis' @ pis) #> Thm.global_cterm_of thy) params' @ [Thm.global_cterm_of thy z]); fun mk_pi th = Simplifier.simplify (put_simpset HOL_basic_ss ctxt'' addsimps [@{thm id_apply}] |> Simplifier.add_proc NominalDatatype.perm_simproc) (Simplifier.simplify (eqvt_ss ctxt'') (fold_rev (mk_perm_bool ctxt'' o Thm.cterm_of ctxt'') (pis' @ pis) th)); val gprems2 = map (fn (th, t) => if null (preds_of ps t) then mk_pi th else mk_pi (the (map_thm ctxt'' (inst_conj_all names ps (rev pis'')) (inst_conj_all_tac ctxt'' (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 (NominalDatatype.mk_perm []) pis') (tl ts)))) (fn {context = goal_ctxt4, ...} => EVERY ([simp_tac (eqvt_ss goal_ctxt4) 1, resolve_tac goal_ctxt4 [ihyp'] 1] @ map (fn th => resolve_tac goal_ctxt4 [th] 1) fresh_ths3 @ [REPEAT_DETERM_N (length gprems) (simp_tac (put_simpset HOL_basic_ss goal_ctxt4 addsimps [inductive_forall_def'] |> Simplifier.add_proc NominalDatatype.perm_simproc) 1 THEN resolve_tac goal_ctxt4 gprems2 1)])); val final = Goal.prove ctxt'' [] [] (Thm.term_of concl) (fn {context = goal_ctxt5, ...} => cut_facts_tac [th] 1 THEN full_simp_tac (put_simpset HOL_ss goal_ctxt5 addsimps vc_compat_ths1' @ fresh_ths1 @ perm_freshs_freshs') 1); val final' = Proof_Context.export ctxt'' goal_ctxt2 [final]; in resolve_tac goal_ctxt2 final' 1 end) goal_ctxt1 1]) (prems ~~ thss ~~ vc_compat' ~~ ihyps ~~ prems''))) in cut_facts_tac [th] 1 THEN REPEAT (eresolve_tac goal_ctxt [conjE] 1) THEN REPEAT (REPEAT (resolve_tac goal_ctxt [conjI, impI] 1) THEN eresolve_tac goal_ctxt [impE] 1 THEN assume_tac goal_ctxt 1 THEN REPEAT (eresolve_tac goal_ctxt @{thms allE_Nil} 1) THEN asm_full_simp_tac goal_ctxt 1) end) |> fresh_postprocess ctxt |> singleton (Proof_Context.export ctxt lthy); in ctxt'' |> Proof.theorem NONE (fn thss => fn lthy1 => let val rec_name = space_implode "_" (map Long_Name.base_name names); val rec_qualified = Binding.qualify false rec_name; val ind_case_names = Rule_Cases.case_names induct_cases; val induct_cases' = Inductive.partition_rules' raw_induct (intrs ~~ induct_cases); val thss' = map (map (atomize_intr lthy1)) thss; val thsss = Inductive.partition_rules' raw_induct (intrs ~~ thss'); val strong_raw_induct = mk_ind_proof lthy1 thss' |> Inductive.rulify lthy1; val strong_induct_atts = map (Attrib.internal \<^here> o K) [ind_case_names, Rule_Cases.consumes (~ (Thm.nprems_of strong_raw_induct))]; val strong_induct = if length names > 1 then strong_raw_induct else strong_raw_induct RSN (2, rev_mp); val (induct_name, inducts_name) = case alt_name of NONE => (rec_qualified (Binding.name "strong_induct"), rec_qualified (Binding.name "strong_inducts")) | SOME s => (Binding.name s, Binding.name (s ^ "s")); val ((_, [strong_induct']), lthy2) = lthy1 |> Local_Theory.note ((induct_name, strong_induct_atts), [strong_induct]); val strong_inducts = Project_Rule.projects lthy2 (1 upto length names) strong_induct' in lthy2 |> Local_Theory.notes [((inducts_name, []), strong_inducts |> map (fn th => ([th], [Attrib.internal \<^here> (K ind_case_names), Attrib.internal \<^here> (K (Rule_Cases.consumes (1 - Thm.nprems_of th)))])))] |> snd end) (map (map (rulify_term thy #> rpair [])) vc_compat) end; (* outer syntax *) val _ = Outer_Syntax.local_theory_to_proof \<^command_keyword>\<open>nominal_inductive2\<close> "prove strong induction theorem for inductive predicate involving nominal dataty (Parse.name -- Scan.option (\<^keyword>\<open>(\<close> |-- Parse.!!! (Parse.name --| \<^keyword>\<open>)\<close> (Scan.optional (\<^keyword>\<open>avoids\<close> |-- Parse.enum1 "|" (Parse.name -- (\<^keyword>\<open>:\<close> |-- Parse.and_list1 Parse.term))) []) >> (fn ((name, rule_name), avo prove_strong_ind name rule_name avoids)); end ¤ Dauer der Verarbeitung: 0.2 Sekunden (vorverarbeitet) ¤*© Formatika GbR, Deutschland |
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2026-03-28