--- a/Nominal/induction_schema.ML Tue Dec 28 19:51:25 2010 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,401 +0,0 @@
-(* Title: HOL/Tools/Function/induction_schema.ML
- Author: Alexander Krauss, TU Muenchen
-
-A method to prove induction schemas.
-*)
-
-signature INDUCTION_SCHEMA =
-sig
- val mk_ind_tac : (int -> tactic) -> (int -> tactic) -> (int -> tactic)
- -> Proof.context -> thm list -> tactic
- val induction_schema_tac : Proof.context -> thm list -> tactic
- val setup : theory -> theory
-end
-
-
-structure Induction_Schema : INDUCTION_SCHEMA =
-struct
-
-open Function_Lib
-
-type rec_call_info = int * (string * typ) list * term list * term list
-
-datatype scheme_case = SchemeCase of
- {bidx : int,
- qs: (string * typ) list,
- oqnames: string list,
- gs: term list,
- lhs: term list,
- rs: rec_call_info list}
-
-datatype scheme_branch = SchemeBranch of
- {P : term,
- xs: (string * typ) list,
- ws: (string * typ) list,
- Cs: term list}
-
-datatype ind_scheme = IndScheme of
- {T: typ, (* sum of products *)
- branches: scheme_branch list,
- cases: scheme_case list}
-
-val ind_atomize = Raw_Simplifier.rewrite true @{thms induct_atomize}
-val ind_rulify = Raw_Simplifier.rewrite true @{thms induct_rulify}
-
-fun meta thm = thm RS eq_reflection
-
-val sum_prod_conv = Raw_Simplifier.rewrite true
- (map meta (@{thm split_conv} :: @{thms sum.cases}))
-
-fun term_conv thy cv t =
- cv (cterm_of thy t)
- |> prop_of |> Logic.dest_equals |> snd
-
-fun mk_relT T = HOLogic.mk_setT (HOLogic.mk_prodT (T, T))
-
-fun dest_hhf ctxt t =
- let
- val ((vars, imp), ctxt') = Function_Lib.focus_term t ctxt
- in
- (ctxt', vars, Logic.strip_imp_prems imp, Logic.strip_imp_concl imp)
- end
-
-fun mk_scheme' ctxt cases concl =
- let
- fun mk_branch concl =
- let
- val (_, ws, Cs, _ $ Pxs) = dest_hhf ctxt concl
- val (P, xs) = strip_comb Pxs
- in
- SchemeBranch { P=P, xs=map dest_Free xs, ws=ws, Cs=Cs }
- end
-
- val (branches, cases') = (* correction *)
- case Logic.dest_conjunctions concl of
- [conc] =>
- let
- val _ $ Pxs = Logic.strip_assums_concl conc
- val (P, _) = strip_comb Pxs
- val (cases', conds) =
- take_prefix (Term.exists_subterm (curry op aconv P)) cases
- val concl' = fold_rev (curry Logic.mk_implies) conds conc
- in
- ([mk_branch concl'], cases')
- end
- | concls => (map mk_branch concls, cases)
-
- fun mk_case premise =
- let
- val (ctxt', qs, prems, _ $ Plhs) = dest_hhf ctxt premise
- val (P, lhs) = strip_comb Plhs
-
- fun bidx Q =
- find_index (fn SchemeBranch {P=P',...} => Q aconv P') branches
-
- fun mk_rcinfo pr =
- let
- val (_, Gvs, Gas, _ $ Phyp) = dest_hhf ctxt' pr
- val (P', rcs) = strip_comb Phyp
- in
- (bidx P', Gvs, Gas, rcs)
- end
-
- fun is_pred v = exists (fn SchemeBranch {P,...} => v aconv P) branches
-
- val (gs, rcprs) =
- take_prefix (not o Term.exists_subterm is_pred) prems
- in
- SchemeCase {bidx=bidx P, qs=qs, oqnames=map fst qs(*FIXME*),
- gs=gs, lhs=lhs, rs=map mk_rcinfo rcprs}
- end
-
- fun PT_of (SchemeBranch { xs, ...}) =
- foldr1 HOLogic.mk_prodT (map snd xs)
-
- val ST = Balanced_Tree.make (uncurry SumTree.mk_sumT) (map PT_of branches)
- in
- IndScheme {T=ST, cases=map mk_case cases', branches=branches }
- end
-
-fun mk_completeness ctxt (IndScheme {cases, branches, ...}) bidx =
- let
- val SchemeBranch { xs, ws, Cs, ... } = nth branches bidx
- val relevant_cases = filter (fn SchemeCase {bidx=bidx', ...} => bidx' = bidx) cases
-
- val allqnames = fold (fn SchemeCase {qs, ...} => fold (insert (op =) o Free) qs) relevant_cases []
- val (Pbool :: xs') = map Free (Variable.variant_frees ctxt allqnames (("P", HOLogic.boolT) :: xs))
- val Cs' = map (Pattern.rewrite_term (ProofContext.theory_of ctxt) (filter_out (op aconv) (map Free xs ~~ xs')) []) Cs
-
- fun mk_case (SchemeCase {qs, oqnames, gs, lhs, ...}) =
- HOLogic.mk_Trueprop Pbool
- |> fold_rev (fn x_l => curry Logic.mk_implies (HOLogic.mk_Trueprop(HOLogic.mk_eq x_l)))
- (xs' ~~ lhs)
- |> fold_rev (curry Logic.mk_implies) gs
- |> fold_rev mk_forall_rename (oqnames ~~ map Free qs)
- in
- HOLogic.mk_Trueprop Pbool
- |> fold_rev (curry Logic.mk_implies o mk_case) relevant_cases
- |> fold_rev (curry Logic.mk_implies) Cs'
- |> fold_rev (Logic.all o Free) ws
- |> fold_rev mk_forall_rename (map fst xs ~~ xs')
- |> mk_forall_rename ("P", Pbool)
- end
-
-fun mk_wf R (IndScheme {T, ...}) =
- HOLogic.Trueprop $ (Const (@{const_name wf}, mk_relT T --> HOLogic.boolT) $ R)
-
-fun mk_ineqs R (IndScheme {T, cases, branches}) =
- let
- fun inject i ts =
- SumTree.mk_inj T (length branches) (i + 1) (foldr1 HOLogic.mk_prod ts)
-
- val thesis = Free ("thesis", HOLogic.boolT) (* FIXME *)
-
- fun mk_pres bdx args =
- let
- val SchemeBranch { xs, ws, Cs, ... } = nth branches bdx
- fun replace (x, v) t = betapply (lambda (Free x) t, v)
- val Cs' = map (fold replace (xs ~~ args)) Cs
- val cse =
- HOLogic.mk_Trueprop thesis
- |> fold_rev (curry Logic.mk_implies) Cs'
- |> fold_rev (Logic.all o Free) ws
- in
- Logic.mk_implies (cse, HOLogic.mk_Trueprop thesis)
- end
-
- fun f (SchemeCase {bidx, qs, oqnames, gs, lhs, rs, ...}) =
- let
- fun g (bidx', Gvs, Gas, rcarg) =
- let val export =
- fold_rev (curry Logic.mk_implies) Gas
- #> fold_rev (curry Logic.mk_implies) gs
- #> fold_rev (Logic.all o Free) Gvs
- #> fold_rev mk_forall_rename (oqnames ~~ map Free qs)
- in
- (HOLogic.mk_mem (HOLogic.mk_prod (inject bidx' rcarg, inject bidx lhs), R)
- |> HOLogic.mk_Trueprop
- |> export,
- mk_pres bidx' rcarg
- |> export
- |> Logic.all thesis)
- end
- in
- map g rs
- end
- in
- map f cases
- end
-
-
-fun mk_ind_goal thy branches =
- let
- fun brnch (SchemeBranch { P, xs, ws, Cs, ... }) =
- HOLogic.mk_Trueprop (list_comb (P, map Free xs))
- |> fold_rev (curry Logic.mk_implies) Cs
- |> fold_rev (Logic.all o Free) ws
- |> term_conv thy ind_atomize
- |> Object_Logic.drop_judgment thy
- |> HOLogic.tupled_lambda (foldr1 HOLogic.mk_prod (map Free xs))
- in
- SumTree.mk_sumcases HOLogic.boolT (map brnch branches)
- end
-
-fun mk_induct_rule ctxt R x complete_thms wf_thm ineqss
- (IndScheme {T, cases=scases, branches}) =
- let
- val n = length branches
- val scases_idx = map_index I scases
-
- fun inject i ts =
- SumTree.mk_inj T n (i + 1) (foldr1 HOLogic.mk_prod ts)
- val P_of = nth (map (fn (SchemeBranch { P, ... }) => P) branches)
-
- val thy = ProofContext.theory_of ctxt
- val cert = cterm_of thy
-
- val P_comp = mk_ind_goal thy branches
-
- (* Inductive Hypothesis: !!z. (z,x):R ==> P z *)
- val ihyp = Term.all T $ Abs ("z", T,
- Logic.mk_implies
- (HOLogic.mk_Trueprop (
- Const (@{const_name Set.member}, HOLogic.mk_prodT (T, T) --> mk_relT T --> HOLogic.boolT)
- $ (HOLogic.pair_const T T $ Bound 0 $ x)
- $ R),
- HOLogic.mk_Trueprop (P_comp $ Bound 0)))
- |> cert
-
- val aihyp = Thm.assume ihyp
-
- (* Rule for case splitting along the sum types *)
- val xss = map (fn (SchemeBranch { xs, ... }) => map Free xs) branches
- val pats = map_index (uncurry inject) xss
- val sum_split_rule =
- Pat_Completeness.prove_completeness thy [x] (P_comp $ x) xss (map single pats)
-
- fun prove_branch (bidx, (SchemeBranch { P, xs, ws, Cs, ... }, (complete_thm, pat))) =
- let
- val fxs = map Free xs
- val branch_hyp = Thm.assume (cert (HOLogic.mk_Trueprop (HOLogic.mk_eq (x, pat))))
-
- val C_hyps = map (cert #> Thm.assume) Cs
-
- val (relevant_cases, ineqss') =
- (scases_idx ~~ ineqss)
- |> filter (fn ((_, SchemeCase {bidx=bidx', ...}), _) => bidx' = bidx)
- |> split_list
-
- fun prove_case (cidx, SchemeCase {qs, gs, lhs, rs, ...}) ineq_press =
- let
- val case_hyps =
- map (Thm.assume o cert o HOLogic.mk_Trueprop o HOLogic.mk_eq) (fxs ~~ lhs)
-
- val cqs = map (cert o Free) qs
- val ags = map (Thm.assume o cert) gs
-
- val replace_x_ss = HOL_basic_ss addsimps (branch_hyp :: case_hyps)
- val sih = full_simplify replace_x_ss aihyp
-
- fun mk_Prec (idx, Gvs, Gas, rcargs) (ineq, pres) =
- let
- val cGas = map (Thm.assume o cert) Gas
- val cGvs = map (cert o Free) Gvs
- val import = fold Thm.forall_elim (cqs @ cGvs)
- #> fold Thm.elim_implies (ags @ cGas)
- val ipres = pres
- |> Thm.forall_elim (cert (list_comb (P_of idx, rcargs)))
- |> import
- in
- sih
- |> Thm.forall_elim (cert (inject idx rcargs))
- |> Thm.elim_implies (import ineq) (* Psum rcargs *)
- |> Conv.fconv_rule sum_prod_conv
- |> Conv.fconv_rule ind_rulify
- |> (fn th => th COMP ipres) (* P rs *)
- |> fold_rev (Thm.implies_intr o cprop_of) cGas
- |> fold_rev Thm.forall_intr cGvs
- end
-
- val P_recs = map2 mk_Prec rs ineq_press (* [P rec1, P rec2, ... ] *)
-
- val step = HOLogic.mk_Trueprop (list_comb (P, lhs))
- |> fold_rev (curry Logic.mk_implies o prop_of) P_recs
- |> fold_rev (curry Logic.mk_implies) gs
- |> fold_rev (Logic.all o Free) qs
- |> cert
-
- val Plhs_to_Pxs_conv =
- foldl1 (uncurry Conv.combination_conv)
- (Conv.all_conv :: map (fn ch => K (Thm.symmetric (ch RS eq_reflection))) case_hyps)
-
- val res = Thm.assume step
- |> fold Thm.forall_elim cqs
- |> fold Thm.elim_implies ags
- |> fold Thm.elim_implies P_recs (* P lhs *)
- |> Conv.fconv_rule (Conv.arg_conv Plhs_to_Pxs_conv) (* P xs *)
- |> fold_rev (Thm.implies_intr o cprop_of) (ags @ case_hyps)
- |> fold_rev Thm.forall_intr cqs (* !!qs. Gas ==> xs = lhss ==> P xs *)
- in
- (res, (cidx, step))
- end
-
- val (cases, steps) = split_list (map2 prove_case relevant_cases ineqss')
-
- val bstep = complete_thm
- |> Thm.forall_elim (cert (list_comb (P, fxs)))
- |> fold (Thm.forall_elim o cert) (fxs @ map Free ws)
- |> fold Thm.elim_implies C_hyps
- |> fold Thm.elim_implies cases (* P xs *)
- |> fold_rev (Thm.implies_intr o cprop_of) C_hyps
- |> fold_rev (Thm.forall_intr o cert o Free) ws
-
- val Pxs = cert (HOLogic.mk_Trueprop (P_comp $ x))
- |> Goal.init
- |> (Simplifier.rewrite_goals_tac (map meta (branch_hyp :: @{thm split_conv} :: @{thms sum.cases}))
- THEN CONVERSION ind_rulify 1)
- |> Seq.hd
- |> Thm.elim_implies (Conv.fconv_rule Drule.beta_eta_conversion bstep)
- |> Goal.finish ctxt
- |> Thm.implies_intr (cprop_of branch_hyp)
- |> fold_rev (Thm.forall_intr o cert) fxs
- in
- (Pxs, steps)
- end
-
- val (branches, steps) =
- map_index prove_branch (branches ~~ (complete_thms ~~ pats))
- |> split_list |> apsnd flat
-
- val istep = sum_split_rule
- |> fold (fn b => fn th => Drule.compose_single (b, 1, th)) branches
- |> Thm.implies_intr ihyp
- |> Thm.forall_intr (cert x) (* "!!x. (!!y<x. P y) ==> P x" *)
-
- val induct_rule =
- @{thm "wf_induct_rule"}
- |> (curry op COMP) wf_thm
- |> (curry op COMP) istep
-
- val steps_sorted = map snd (sort (int_ord o pairself fst) steps)
- in
- (steps_sorted, induct_rule)
- end
-
-
-fun mk_ind_tac comp_tac pres_tac term_tac ctxt facts =
- (ALLGOALS (Method.insert_tac facts)) THEN HEADGOAL (SUBGOAL (fn (t, i) =>
- let
- val (ctxt', _, cases, concl) = dest_hhf ctxt t
- val scheme as IndScheme {T=ST, branches, ...} = mk_scheme' ctxt' cases concl
- val ([Rn,xn], ctxt'') = Variable.variant_fixes ["R","x"] ctxt'
- val R = Free (Rn, mk_relT ST)
- val x = Free (xn, ST)
- val cert = cterm_of (ProofContext.theory_of ctxt)
-
- val ineqss = mk_ineqs R scheme
- |> map (map (pairself (Thm.assume o cert)))
- val complete =
- map_range (mk_completeness ctxt scheme #> cert #> Thm.assume) (length branches)
- val wf_thm = mk_wf R scheme |> cert |> Thm.assume
-
- val (descent, pres) = split_list (flat ineqss)
- val newgoals = complete @ pres @ wf_thm :: descent
-
- val (steps, indthm) =
- mk_induct_rule ctxt'' R x complete wf_thm ineqss scheme
-
- fun project (i, SchemeBranch {xs, ...}) =
- let
- val inst = (foldr1 HOLogic.mk_prod (map Free xs))
- |> SumTree.mk_inj ST (length branches) (i + 1)
- |> cert
- in
- indthm
- |> Drule.instantiate' [] [SOME inst]
- |> simplify SumTree.sumcase_split_ss
- |> Conv.fconv_rule ind_rulify
- end
-
- val res = Conjunction.intr_balanced (map_index project branches)
- |> fold_rev Thm.implies_intr (map cprop_of newgoals @ steps)
- |> Drule.generalize ([], [Rn])
-
- val nbranches = length branches
- val npres = length pres
- in
- Thm.compose_no_flatten false (res, length newgoals) i
- THEN term_tac (i + nbranches + npres)
- THEN (EVERY (map (TRY o pres_tac) ((i + nbranches + npres - 1) downto (i + nbranches))))
- THEN (EVERY (map (TRY o comp_tac) ((i + nbranches - 1) downto i)))
- end))
-
-
-fun induction_schema_tac ctxt =
- mk_ind_tac (K all_tac) (assume_tac APPEND' Goal.assume_rule_tac ctxt) (K all_tac) ctxt;
-
-val setup =
- Method.setup @{binding induction_schema} (Scan.succeed (RAW_METHOD o induction_schema_tac))
- "proves an induction principle"
-
-end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Nominal/nominal_induct.ML Thu Dec 30 10:00:09 2010 +0000
@@ -0,0 +1,185 @@
+(* Author: Christian Urban and Makarius
+
+The nominal induct proof method.
+*)
+
+structure NominalInduct:
+sig
+ val nominal_induct_tac: Proof.context -> bool -> (binding option * (term * bool)) option list list ->
+ (string * typ) list -> (string * typ) list list -> thm list -> thm list -> int -> Rule_Cases.cases_tactic
+
+ val nominal_induct_method: (Proof.context -> Proof.method) context_parser
+end =
+
+struct
+
+(* proper tuples -- nested left *)
+
+fun tupleT Ts = HOLogic.unitT |> fold (fn T => fn U => HOLogic.mk_prodT (U, T)) Ts;
+fun tuple ts = HOLogic.unit |> fold (fn t => fn u => HOLogic.mk_prod (u, t)) ts;
+
+fun tuple_fun Ts (xi, T) =
+ Library.funpow (length Ts) HOLogic.mk_split
+ (Var (xi, (HOLogic.unitT :: Ts) ---> Term.range_type T));
+
+val split_all_tuples =
+ Simplifier.full_simplify (HOL_basic_ss addsimps
+ @{thms split_conv split_paired_all unit_all_eq1})
+(*
+ @{thm fresh_unit_elim}, @{thm fresh_prod_elim}] @
+ @{thms fresh_star_unit_elim} @ @{thms fresh_star_prod_elim})
+*)
+
+
+(* prepare rule *)
+
+fun inst_mutual_rule ctxt insts avoiding rules =
+ let
+ val (nconcls, joined_rule) = Rule_Cases.strict_mutual_rule ctxt rules;
+ val concls = Logic.dest_conjunctions (Thm.concl_of joined_rule);
+ val (cases, consumes) = Rule_Cases.get joined_rule;
+
+ val l = length rules;
+ val _ =
+ if length insts = l then ()
+ else error ("Bad number of instantiations for " ^ string_of_int l ^ " rules");
+
+ fun subst inst concl =
+ let
+ val vars = Induct.vars_of concl;
+ val m = length vars and n = length inst;
+ val _ = if m >= n + 2 then () else error "Too few variables in conclusion of rule";
+ val P :: x :: ys = vars;
+ val zs = drop (m - n - 2) ys;
+ in
+ (P, tuple_fun (map #2 avoiding) (Term.dest_Var P)) ::
+ (x, tuple (map Free avoiding)) ::
+ map_filter (fn (z, SOME t) => SOME (z, t) | _ => NONE) (zs ~~ inst)
+ end;
+ val substs =
+ map2 subst insts concls |> flat |> distinct (op =)
+ |> map (pairself (Thm.cterm_of (ProofContext.theory_of ctxt)));
+ in
+ (((cases, nconcls), consumes), Drule.cterm_instantiate substs joined_rule)
+ end;
+
+fun rename_params_rule internal xs rule =
+ let
+ val tune =
+ if internal then Name.internal
+ else fn x => the_default x (try Name.dest_internal x);
+ val n = length xs;
+ fun rename prem =
+ let
+ val ps = Logic.strip_params prem;
+ val p = length ps;
+ val ys =
+ if p < n then []
+ else map (tune o #1) (take (p - n) ps) @ xs;
+ in Logic.list_rename_params (ys, prem) end;
+ fun rename_prems prop =
+ let val (As, C) = Logic.strip_horn prop
+ in Logic.list_implies (map rename As, C) end;
+ in Thm.equal_elim (Thm.reflexive (Drule.cterm_fun rename_prems (Thm.cprop_of rule))) rule end;
+
+
+(* nominal_induct_tac *)
+
+fun nominal_induct_tac ctxt simp def_insts avoiding fixings rules facts =
+ let
+ val thy = ProofContext.theory_of ctxt;
+ val cert = Thm.cterm_of thy;
+
+ val ((insts, defs), defs_ctxt) = fold_map Induct.add_defs def_insts ctxt |>> split_list;
+ val atomized_defs = map (map (Conv.fconv_rule Induct.atomize_cterm)) defs;
+
+ val finish_rule =
+ split_all_tuples
+ #> rename_params_rule true
+ (map (Name.clean o ProofContext.revert_skolem defs_ctxt o fst) avoiding);
+
+ fun rule_cases ctxt r =
+ let val r' = if simp then Induct.simplified_rule ctxt r else r
+ in Rule_Cases.make_nested (Thm.prop_of r') (Induct.rulified_term r') end;
+ in
+ (fn i => fn st =>
+ rules
+ |> inst_mutual_rule ctxt insts avoiding
+ |> Rule_Cases.consume (flat defs) facts
+ |> Seq.maps (fn (((cases, concls), (more_consumes, more_facts)), rule) =>
+ (PRECISE_CONJUNCTS (length concls) (ALLGOALS (fn j =>
+ (CONJUNCTS (ALLGOALS
+ let
+ val adefs = nth_list atomized_defs (j - 1);
+ val frees = fold (Term.add_frees o prop_of) adefs [];
+ val xs = nth_list fixings (j - 1);
+ val k = nth concls (j - 1) + more_consumes
+ in
+ Method.insert_tac (more_facts @ adefs) THEN'
+ (if simp then
+ Induct.rotate_tac k (length adefs) THEN'
+ Induct.fix_tac defs_ctxt k
+ (List.partition (member op = frees) xs |> op @)
+ else
+ Induct.fix_tac defs_ctxt k xs)
+ end)
+ THEN' Induct.inner_atomize_tac) j))
+ THEN' Induct.atomize_tac) i st |> Seq.maps (fn st' =>
+ Induct.guess_instance ctxt
+ (finish_rule (Induct.internalize more_consumes rule)) i st'
+ |> Seq.maps (fn rule' =>
+ CASES (rule_cases ctxt rule' cases)
+ (Tactic.rtac (rename_params_rule false [] rule') i THEN
+ PRIMITIVE (singleton (ProofContext.export defs_ctxt ctxt))) st'))))
+ THEN_ALL_NEW_CASES
+ ((if simp then Induct.simplify_tac ctxt THEN' (TRY o Induct.trivial_tac)
+ else K all_tac)
+ THEN_ALL_NEW Induct.rulify_tac)
+ end;
+
+
+(* concrete syntax *)
+
+local
+
+val avoidingN = "avoiding";
+val fixingN = "arbitrary"; (* to be consistent with induct; hopefully this changes again *)
+val ruleN = "rule";
+
+val inst = Scan.lift (Args.$$$ "_") >> K NONE ||
+ Args.term >> (SOME o rpair false) ||
+ Scan.lift (Args.$$$ "(") |-- (Args.term >> (SOME o rpair true)) --|
+ Scan.lift (Args.$$$ ")");
+
+val def_inst =
+ ((Scan.lift (Args.binding --| (Args.$$$ "\<equiv>" || Args.$$$ "==")) >> SOME)
+ -- (Args.term >> rpair false)) >> SOME ||
+ inst >> Option.map (pair NONE);
+
+val free = Args.context -- Args.term >> (fn (_, Free v) => v | (ctxt, t) =>
+ error ("Bad free variable: " ^ Syntax.string_of_term ctxt t));
+
+fun unless_more_args scan = Scan.unless (Scan.lift
+ ((Args.$$$ avoidingN || Args.$$$ fixingN || Args.$$$ ruleN) -- Args.colon)) scan;
+
+
+val avoiding = Scan.optional (Scan.lift (Args.$$$ avoidingN -- Args.colon) |--
+ Scan.repeat (unless_more_args free)) [];
+
+val fixing = Scan.optional (Scan.lift (Args.$$$ fixingN -- Args.colon) |--
+ Parse.and_list' (Scan.repeat (unless_more_args free))) [];
+
+val rule_spec = Scan.lift (Args.$$$ "rule" -- Args.colon) |-- Attrib.thms;
+
+in
+
+val nominal_induct_method =
+ Args.mode Induct.no_simpN -- (Parse.and_list' (Scan.repeat (unless_more_args def_inst)) --
+ avoiding -- fixing -- rule_spec) >>
+ (fn (no_simp, (((x, y), z), w)) => fn ctxt =>
+ RAW_METHOD_CASES (fn facts =>
+ HEADGOAL (nominal_induct_tac ctxt (not no_simp) x y z w facts)));
+
+end
+
+end;