wenzelm@24830: (* Title: Tools/induct.ML wenzelm@24830: Author: Markus Wenzel, TU Muenchen wenzelm@24830: wenzelm@26924: Proof by cases, induction, and coinduction. wenzelm@24830: *) wenzelm@24830: wenzelm@24830: signature INDUCT_DATA = wenzelm@24830: sig wenzelm@24830: val cases_default: thm wenzelm@24830: val atomize: thm list wenzelm@24830: val rulify: thm list wenzelm@24830: val rulify_fallback: thm list berghofe@34907: val dest_def: term -> (term * term) option berghofe@34907: val trivial_tac: int -> tactic wenzelm@24830: end; wenzelm@24830: wenzelm@24830: signature INDUCT = wenzelm@24830: sig wenzelm@24830: (*rule declarations*) wenzelm@24830: val vars_of: term -> term list wenzelm@24830: val dest_rules: Proof.context -> wenzelm@24861: {type_cases: (string * thm) list, pred_cases: (string * thm) list, wenzelm@24861: type_induct: (string * thm) list, pred_induct: (string * thm) list, wenzelm@24861: type_coinduct: (string * thm) list, pred_coinduct: (string * thm) list} wenzelm@24830: val print_rules: Proof.context -> unit wenzelm@24830: val lookup_casesT: Proof.context -> string -> thm option wenzelm@24861: val lookup_casesP: Proof.context -> string -> thm option wenzelm@24830: val lookup_inductT: Proof.context -> string -> thm option wenzelm@24861: val lookup_inductP: Proof.context -> string -> thm option wenzelm@24830: val lookup_coinductT: Proof.context -> string -> thm option wenzelm@24861: val lookup_coinductP: Proof.context -> string -> thm option wenzelm@24830: val find_casesT: Proof.context -> typ -> thm list wenzelm@24861: val find_casesP: Proof.context -> term -> thm list wenzelm@24830: val find_inductT: Proof.context -> typ -> thm list wenzelm@24861: val find_inductP: Proof.context -> term -> thm list wenzelm@24830: val find_coinductT: Proof.context -> typ -> thm list wenzelm@24861: val find_coinductP: Proof.context -> term -> thm list wenzelm@24830: val cases_type: string -> attribute wenzelm@24861: val cases_pred: string -> attribute wenzelm@27140: val cases_del: attribute wenzelm@24830: val induct_type: string -> attribute wenzelm@24861: val induct_pred: string -> attribute wenzelm@27140: val induct_del: attribute wenzelm@24830: val coinduct_type: string -> attribute wenzelm@24861: val coinduct_pred: string -> attribute wenzelm@27140: val coinduct_del: attribute berghofe@34907: val map_simpset: (simpset -> simpset) -> Context.generic -> Context.generic berghofe@34907: val add_simp_rule: attribute berghofe@34907: val no_simpN: string wenzelm@24830: val casesN: string wenzelm@24830: val inductN: string wenzelm@24830: val coinductN: string wenzelm@24830: val typeN: string wenzelm@24861: val predN: string wenzelm@24830: val setN: string wenzelm@24830: (*proof methods*) wenzelm@24830: val fix_tac: Proof.context -> int -> (string * typ) list -> int -> tactic berghofe@34907: val add_defs: (binding option * (term * bool)) option list -> Proof.context -> wenzelm@24830: (term option list * thm list) * Proof.context wenzelm@24830: val atomize_term: theory -> term -> term berghofe@34907: val atomize_cterm: conv wenzelm@24830: val atomize_tac: int -> tactic wenzelm@24830: val inner_atomize_tac: int -> tactic wenzelm@24830: val rulified_term: thm -> theory * term wenzelm@24830: val rulify_tac: int -> tactic berghofe@34907: val simplified_rule: Proof.context -> thm -> thm berghofe@34907: val simplify_tac: Proof.context -> int -> tactic berghofe@34907: val trivial_tac: int -> tactic berghofe@34907: val rotate_tac: int -> int -> int -> tactic wenzelm@24830: val internalize: int -> thm -> thm wenzelm@26940: val guess_instance: Proof.context -> thm -> int -> thm -> thm Seq.seq wenzelm@26924: val cases_tac: Proof.context -> term option list list -> thm option -> wenzelm@24830: thm list -> int -> cases_tactic wenzelm@27323: val get_inductT: Proof.context -> term option list list -> thm list list berghofe@34907: val induct_tac: Proof.context -> bool -> (binding option * (term * bool)) option list list -> wenzelm@26924: (string * typ) list list -> term option list -> thm list option -> wenzelm@26924: thm list -> int -> cases_tactic wenzelm@26924: val coinduct_tac: Proof.context -> term option list -> term option list -> thm option -> wenzelm@26924: thm list -> int -> cases_tactic wenzelm@24830: val setup: theory -> theory wenzelm@24830: end; wenzelm@24830: wenzelm@32171: functor Induct(Data: INDUCT_DATA): INDUCT = wenzelm@24830: struct wenzelm@24830: wenzelm@24830: wenzelm@24830: (** misc utils **) wenzelm@24830: wenzelm@24830: (* encode_type -- for indexing purposes *) wenzelm@24830: wenzelm@24830: fun encode_type (Type (c, Ts)) = Term.list_comb (Const (c, dummyT), map encode_type Ts) wenzelm@24830: | encode_type (TFree (a, _)) = Free (a, dummyT) wenzelm@24830: | encode_type (TVar (a, _)) = Var (a, dummyT); wenzelm@24830: wenzelm@24830: wenzelm@24830: (* variables -- ordered left-to-right, preferring right *) wenzelm@24830: wenzelm@24830: fun vars_of tm = wenzelm@24830: rev (distinct (op =) (Term.fold_aterms (fn (t as Var _) => cons t | _ => I) tm [])); wenzelm@24830: wenzelm@24830: local wenzelm@24830: wenzelm@24830: val mk_var = encode_type o #2 o Term.dest_Var; wenzelm@24830: wenzelm@24830: fun concl_var which thm = mk_var (which (vars_of (Thm.concl_of thm))) handle Empty => wenzelm@24830: raise THM ("No variables in conclusion of rule", 0, [thm]); wenzelm@24830: wenzelm@24830: in wenzelm@24830: wenzelm@24830: fun left_var_prem thm = mk_var (hd (vars_of (hd (Thm.prems_of thm)))) handle Empty => wenzelm@24830: raise THM ("No variables in major premise of rule", 0, [thm]); wenzelm@24830: wenzelm@24830: val left_var_concl = concl_var hd; wenzelm@24830: val right_var_concl = concl_var List.last; wenzelm@24830: wenzelm@24830: end; wenzelm@24830: wenzelm@24830: wenzelm@24830: berghofe@34907: (** constraint simplification **) berghofe@34907: berghofe@34907: (* rearrange parameters and premises to allow application of one-point-rules *) berghofe@34907: berghofe@34907: fun swap_params_conv ctxt i j cv = berghofe@34907: let berghofe@34907: fun conv1 0 ctxt = Conv.forall_conv (cv o snd) ctxt berghofe@34907: | conv1 k ctxt = berghofe@34907: Conv.rewr_conv @{thm swap_params} then_conv berghofe@34907: Conv.forall_conv (conv1 (k-1) o snd) ctxt berghofe@34907: fun conv2 0 ctxt = conv1 j ctxt berghofe@34907: | conv2 k ctxt = Conv.forall_conv (conv2 (k-1) o snd) ctxt berghofe@34907: in conv2 i ctxt end; berghofe@34907: berghofe@34907: fun swap_prems_conv 0 = Conv.all_conv berghofe@34907: | swap_prems_conv i = berghofe@34907: Conv.implies_concl_conv (swap_prems_conv (i-1)) then_conv berghofe@34907: Conv.rewr_conv Drule.swap_prems_eq berghofe@34907: berghofe@34907: fun drop_judgment ctxt = ObjectLogic.drop_judgment (ProofContext.theory_of ctxt); berghofe@34907: berghofe@34907: fun find_eq ctxt t = berghofe@34907: let berghofe@34907: val l = length (Logic.strip_params t); berghofe@34907: val Hs = Logic.strip_assums_hyp t; berghofe@34907: fun find (i, t) = berghofe@34907: case Data.dest_def (drop_judgment ctxt t) of berghofe@34907: SOME (Bound j, _) => SOME (i, j) berghofe@34907: | SOME (_, Bound j) => SOME (i, j) berghofe@34907: | _ => NONE berghofe@34907: in berghofe@34907: case get_first find (map_index I Hs) of berghofe@34907: NONE => NONE berghofe@34907: | SOME (0, 0) => NONE berghofe@34907: | SOME (i, j) => SOME (i, l-j-1, j) berghofe@34907: end; berghofe@34907: berghofe@34907: fun mk_swap_rrule ctxt ct = case find_eq ctxt (term_of ct) of berghofe@34907: NONE => NONE berghofe@34907: | SOME (i, k, j) => SOME (swap_params_conv ctxt k j (K (swap_prems_conv i)) ct); berghofe@34907: berghofe@34907: val rearrange_eqs_simproc = Simplifier.simproc berghofe@34907: (Thm.theory_of_thm Drule.swap_prems_eq) "rearrange_eqs" ["all t"] berghofe@34907: (fn thy => fn ss => fn t => berghofe@34907: mk_swap_rrule (Simplifier.the_context ss) (cterm_of thy t)) berghofe@34907: berghofe@34907: (* rotate k premises to the left by j, skipping over first j premises *) berghofe@34907: berghofe@34907: fun rotate_conv 0 j 0 = Conv.all_conv berghofe@34907: | rotate_conv 0 j k = swap_prems_conv j then_conv rotate_conv 1 j (k-1) berghofe@34907: | rotate_conv i j k = Conv.implies_concl_conv (rotate_conv (i-1) j k); berghofe@34907: berghofe@34907: fun rotate_tac j 0 = K all_tac berghofe@34907: | rotate_tac j k = SUBGOAL (fn (goal, i) => CONVERSION (rotate_conv berghofe@34907: j (length (Logic.strip_assums_hyp goal) - j - k) k) i); berghofe@34907: berghofe@34907: (* rulify operators around definition *) berghofe@34907: berghofe@34907: fun rulify_defs_conv ctxt ct = berghofe@34907: if exists_subterm (is_some o Data.dest_def) (term_of ct) andalso berghofe@34907: not (is_some (Data.dest_def (drop_judgment ctxt (term_of ct)))) berghofe@34907: then berghofe@34907: (Conv.forall_conv (rulify_defs_conv o snd) ctxt else_conv berghofe@34907: Conv.implies_conv (Conv.try_conv (rulify_defs_conv ctxt)) berghofe@34907: (Conv.try_conv (rulify_defs_conv ctxt)) else_conv berghofe@34907: Conv.first_conv (map Conv.rewr_conv Data.rulify) then_conv berghofe@34907: Conv.try_conv (rulify_defs_conv ctxt)) ct berghofe@34907: else Conv.no_conv ct; berghofe@34907: berghofe@34907: berghofe@34907: wenzelm@24830: (** induct data **) wenzelm@24830: wenzelm@24830: (* rules *) wenzelm@24830: wenzelm@30560: type rules = (string * thm) Item_Net.T; wenzelm@24830: wenzelm@33373: fun init_rules index : rules = wenzelm@33373: Item_Net.init wenzelm@33373: (fn ((s1, th1), (s2, th2)) => s1 = s2 andalso Thm.eq_thm_prop (th1, th2)) wenzelm@33373: (single o index); wenzelm@24830: wenzelm@27140: fun filter_rules (rs: rules) th = wenzelm@30560: filter (fn (_, th') => Thm.eq_thm_prop (th, th')) (Item_Net.content rs); wenzelm@27140: wenzelm@30560: fun lookup_rule (rs: rules) = AList.lookup (op =) (Item_Net.content rs); wenzelm@24830: wenzelm@24830: fun pretty_rules ctxt kind rs = wenzelm@30560: let val thms = map snd (Item_Net.content rs) wenzelm@32091: in Pretty.big_list kind (map (Display.pretty_thm ctxt) thms) end; wenzelm@24830: wenzelm@24830: wenzelm@24830: (* context data *) wenzelm@24830: wenzelm@33519: structure InductData = Generic_Data wenzelm@24830: ( berghofe@34907: type T = (rules * rules) * (rules * rules) * (rules * rules) * simpset; wenzelm@24830: val empty = wenzelm@24830: ((init_rules (left_var_prem o #2), init_rules (Thm.major_prem_of o #2)), wenzelm@24830: (init_rules (right_var_concl o #2), init_rules (Thm.major_prem_of o #2)), berghofe@34907: (init_rules (left_var_concl o #2), init_rules (Thm.concl_of o #2)), berghofe@34907: empty_ss addsimprocs [rearrange_eqs_simproc] addsimps [Drule.norm_hhf_eq]); wenzelm@24830: val extend = I; berghofe@34907: fun merge (((casesT1, casesP1), (inductT1, inductP1), (coinductT1, coinductP1), simpset1), berghofe@34907: ((casesT2, casesP2), (inductT2, inductP2), (coinductT2, coinductP2), simpset2)) = wenzelm@30560: ((Item_Net.merge (casesT1, casesT2), Item_Net.merge (casesP1, casesP2)), berghofe@34907: (Item_Net.merge (inductT1, inductT2), Item_Net.merge (inductP1, inductP2)), berghofe@34907: (Item_Net.merge (coinductT1, coinductT2), Item_Net.merge (coinductP1, coinductP2)), berghofe@34907: merge_ss (simpset1, simpset2)); wenzelm@24830: ); wenzelm@24830: wenzelm@27140: val get_local = InductData.get o Context.Proof; wenzelm@24830: wenzelm@24830: fun dest_rules ctxt = berghofe@34907: let val ((casesT, casesP), (inductT, inductP), (coinductT, coinductP), _) = get_local ctxt in wenzelm@30560: {type_cases = Item_Net.content casesT, wenzelm@30560: pred_cases = Item_Net.content casesP, wenzelm@30560: type_induct = Item_Net.content inductT, wenzelm@30560: pred_induct = Item_Net.content inductP, wenzelm@30560: type_coinduct = Item_Net.content coinductT, wenzelm@30560: pred_coinduct = Item_Net.content coinductP} wenzelm@24830: end; wenzelm@24830: wenzelm@24830: fun print_rules ctxt = berghofe@34907: let val ((casesT, casesP), (inductT, inductP), (coinductT, coinductP), _) = get_local ctxt in wenzelm@24830: [pretty_rules ctxt "coinduct type:" coinductT, wenzelm@24861: pretty_rules ctxt "coinduct pred:" coinductP, wenzelm@24830: pretty_rules ctxt "induct type:" inductT, wenzelm@24861: pretty_rules ctxt "induct pred:" inductP, wenzelm@24830: pretty_rules ctxt "cases type:" casesT, wenzelm@24861: pretty_rules ctxt "cases pred:" casesP] wenzelm@24830: |> Pretty.chunks |> Pretty.writeln wenzelm@24830: end; wenzelm@24830: wenzelm@24867: val _ = wenzelm@24830: OuterSyntax.improper_command "print_induct_rules" "print induction and cases rules" wenzelm@24830: OuterKeyword.diag (Scan.succeed (Toplevel.no_timing o Toplevel.unknown_context o wenzelm@24867: Toplevel.keep (print_rules o Toplevel.context_of))); wenzelm@24830: wenzelm@24830: wenzelm@24830: (* access rules *) wenzelm@24830: wenzelm@24830: val lookup_casesT = lookup_rule o #1 o #1 o get_local; wenzelm@24861: val lookup_casesP = lookup_rule o #2 o #1 o get_local; wenzelm@24830: val lookup_inductT = lookup_rule o #1 o #2 o get_local; wenzelm@24861: val lookup_inductP = lookup_rule o #2 o #2 o get_local; wenzelm@24830: val lookup_coinductT = lookup_rule o #1 o #3 o get_local; wenzelm@24861: val lookup_coinductP = lookup_rule o #2 o #3 o get_local; wenzelm@24830: wenzelm@24830: wenzelm@24830: fun find_rules which how ctxt x = wenzelm@30560: map snd (Item_Net.retrieve (which (get_local ctxt)) (how x)); wenzelm@24830: wenzelm@24830: val find_casesT = find_rules (#1 o #1) encode_type; wenzelm@24861: val find_casesP = find_rules (#2 o #1) I; wenzelm@24830: val find_inductT = find_rules (#1 o #2) encode_type; wenzelm@24861: val find_inductP = find_rules (#2 o #2) I; wenzelm@24830: val find_coinductT = find_rules (#1 o #3) encode_type; wenzelm@24861: val find_coinductP = find_rules (#2 o #3) I; wenzelm@24830: wenzelm@24830: wenzelm@24830: wenzelm@24830: (** attributes **) wenzelm@24830: wenzelm@24830: local wenzelm@24830: wenzelm@24830: fun mk_att f g name arg = wenzelm@27140: let val (x, thm) = g arg in (InductData.map (f (name, thm)) x, thm) end; wenzelm@27140: wenzelm@27140: fun del_att which = Thm.declaration_attribute (fn th => InductData.map (which (pairself (fn rs => wenzelm@33373: fold Item_Net.remove (filter_rules rs th) rs)))); wenzelm@24830: berghofe@34907: fun map1 f (x, y, z, s) = (f x, y, z, s); berghofe@34907: fun map2 f (x, y, z, s) = (x, f y, z, s); berghofe@34907: fun map3 f (x, y, z, s) = (x, y, f z, s); berghofe@34907: fun map4 f (x, y, z, s) = (x, y, z, f s); wenzelm@24830: wenzelm@33373: fun add_casesT rule x = map1 (apfst (Item_Net.update rule)) x; wenzelm@33373: fun add_casesP rule x = map1 (apsnd (Item_Net.update rule)) x; wenzelm@33373: fun add_inductT rule x = map2 (apfst (Item_Net.update rule)) x; wenzelm@33373: fun add_inductP rule x = map2 (apsnd (Item_Net.update rule)) x; wenzelm@33373: fun add_coinductT rule x = map3 (apfst (Item_Net.update rule)) x; wenzelm@33373: fun add_coinductP rule x = map3 (apsnd (Item_Net.update rule)) x; wenzelm@24830: wenzelm@33368: val consumes0 = Rule_Cases.consumes_default 0; wenzelm@33368: val consumes1 = Rule_Cases.consumes_default 1; wenzelm@24830: wenzelm@24830: in wenzelm@24830: wenzelm@24830: val cases_type = mk_att add_casesT consumes0; wenzelm@24861: val cases_pred = mk_att add_casesP consumes1; wenzelm@27140: val cases_del = del_att map1; wenzelm@27140: wenzelm@24830: val induct_type = mk_att add_inductT consumes0; wenzelm@24861: val induct_pred = mk_att add_inductP consumes1; wenzelm@27140: val induct_del = del_att map2; wenzelm@27140: wenzelm@24830: val coinduct_type = mk_att add_coinductT consumes0; wenzelm@24861: val coinduct_pred = mk_att add_coinductP consumes1; wenzelm@27140: val coinduct_del = del_att map3; wenzelm@24830: berghofe@34907: fun map_simpset f = InductData.map (map4 f); berghofe@34907: fun add_simp_rule (ctxt, thm) = berghofe@34907: (map_simpset (fn ss => ss addsimps [thm]) ctxt, thm); berghofe@34907: wenzelm@24830: end; wenzelm@24830: wenzelm@24830: wenzelm@24830: wenzelm@24830: (** attribute syntax **) wenzelm@24830: berghofe@34907: val no_simpN = "no_simp"; wenzelm@24830: val casesN = "cases"; wenzelm@24830: val inductN = "induct"; wenzelm@24830: val coinductN = "coinduct"; wenzelm@24830: wenzelm@24830: val typeN = "type"; wenzelm@24861: val predN = "pred"; wenzelm@24830: val setN = "set"; wenzelm@24830: wenzelm@24830: local wenzelm@24830: wenzelm@24830: fun spec k arg = wenzelm@24830: Scan.lift (Args.$$$ k -- Args.colon) |-- arg || wenzelm@24830: Scan.lift (Args.$$$ k) >> K ""; wenzelm@24830: wenzelm@30528: fun attrib add_type add_pred del = wenzelm@30528: spec typeN Args.tyname >> add_type || wenzelm@24861: spec predN Args.const >> add_pred || wenzelm@27140: spec setN Args.const >> add_pred || wenzelm@30528: Scan.lift Args.del >> K del; wenzelm@24830: wenzelm@24830: in wenzelm@24830: wenzelm@30528: val attrib_setup = wenzelm@30722: Attrib.setup @{binding cases} (attrib cases_type cases_pred cases_del) wenzelm@30722: "declaration of cases rule" #> wenzelm@30722: Attrib.setup @{binding induct} (attrib induct_type induct_pred induct_del) wenzelm@30722: "declaration of induction rule" #> wenzelm@30722: Attrib.setup @{binding coinduct} (attrib coinduct_type coinduct_pred coinduct_del) berghofe@34907: "declaration of coinduction rule" #> berghofe@34907: Attrib.setup @{binding induct_simp} (Scan.succeed add_simp_rule) berghofe@34907: "declaration of rules for simplifying induction or cases rules"; wenzelm@24830: wenzelm@24830: end; wenzelm@24830: wenzelm@24830: wenzelm@24830: wenzelm@24830: (** method utils **) wenzelm@24830: wenzelm@24830: (* alignment *) wenzelm@24830: wenzelm@24830: fun align_left msg xs ys = wenzelm@24830: let val m = length xs and n = length ys haftmann@33957: in if m < n then error msg else (take n xs ~~ ys) end; wenzelm@24830: wenzelm@24830: fun align_right msg xs ys = wenzelm@24830: let val m = length xs and n = length ys haftmann@33957: in if m < n then error msg else (drop (m - n) xs ~~ ys) end; wenzelm@24830: wenzelm@24830: wenzelm@24830: (* prep_inst *) wenzelm@24830: wenzelm@32432: fun prep_inst ctxt align tune (tm, ts) = wenzelm@24830: let wenzelm@32432: val cert = Thm.cterm_of (ProofContext.theory_of ctxt); wenzelm@24830: fun prep_var (x, SOME t) = wenzelm@24830: let wenzelm@24830: val cx = cert x; wenzelm@26626: val xT = #T (Thm.rep_cterm cx); wenzelm@24830: val ct = cert (tune t); wenzelm@32432: val tT = #T (Thm.rep_cterm ct); wenzelm@24830: in wenzelm@32432: if Type.could_unify (tT, xT) then SOME (cx, ct) wenzelm@24830: else error (Pretty.string_of (Pretty.block wenzelm@24830: [Pretty.str "Ill-typed instantiation:", Pretty.fbrk, wenzelm@32432: Syntax.pretty_term ctxt (Thm.term_of ct), Pretty.str " ::", Pretty.brk 1, wenzelm@32432: Syntax.pretty_typ ctxt tT])) wenzelm@24830: end wenzelm@24830: | prep_var (_, NONE) = NONE; wenzelm@24830: val xs = vars_of tm; wenzelm@24830: in wenzelm@24830: align "Rule has fewer variables than instantiations given" xs ts wenzelm@24830: |> map_filter prep_var wenzelm@24830: end; wenzelm@24830: wenzelm@24830: wenzelm@24830: (* trace_rules *) wenzelm@24830: wenzelm@24830: fun trace_rules _ kind [] = error ("Unable to figure out " ^ kind ^ " rule") wenzelm@24830: | trace_rules ctxt _ rules = Method.trace ctxt rules; wenzelm@24830: wenzelm@24830: wenzelm@24830: wenzelm@24830: (** cases method **) wenzelm@24830: wenzelm@24830: (* wenzelm@24830: rule selection scheme: wenzelm@24830: cases - default case split wenzelm@24861: `A t` cases ... - predicate/set cases wenzelm@24830: cases t - type cases wenzelm@24830: ... cases ... r - explicit rule wenzelm@24830: *) wenzelm@24830: wenzelm@24830: local wenzelm@24830: wenzelm@24830: fun get_casesT ctxt ((SOME t :: _) :: _) = find_casesT ctxt (Term.fastype_of t) wenzelm@24830: | get_casesT _ _ = []; wenzelm@24830: wenzelm@24861: fun get_casesP ctxt (fact :: _) = find_casesP ctxt (Thm.concl_of fact) wenzelm@24861: | get_casesP _ _ = []; wenzelm@24830: wenzelm@24830: in wenzelm@24830: wenzelm@26924: fun cases_tac ctxt insts opt_rule facts = wenzelm@24830: let wenzelm@24830: val thy = ProofContext.theory_of ctxt; wenzelm@24830: wenzelm@24830: fun inst_rule r = wenzelm@33368: if null insts then `Rule_Cases.get r wenzelm@24830: else (align_left "Rule has fewer premises than arguments given" (Thm.prems_of r) insts wenzelm@32432: |> maps (prep_inst ctxt align_left I) wenzelm@33368: |> Drule.cterm_instantiate) r |> pair (Rule_Cases.get r); wenzelm@24830: wenzelm@24830: val ruleq = wenzelm@24830: (case opt_rule of wenzelm@24830: SOME r => Seq.single (inst_rule r) wenzelm@24830: | NONE => wenzelm@24861: (get_casesP ctxt facts @ get_casesT ctxt insts @ [Data.cases_default]) wenzelm@24830: |> tap (trace_rules ctxt casesN) wenzelm@24830: |> Seq.of_list |> Seq.maps (Seq.try inst_rule)); wenzelm@24830: in wenzelm@24830: fn i => fn st => wenzelm@24830: ruleq wenzelm@33368: |> Seq.maps (Rule_Cases.consume [] facts) wenzelm@24830: |> Seq.maps (fn ((cases, (_, more_facts)), rule) => berghofe@34907: CASES (Rule_Cases.make_common (thy, berghofe@34907: Thm.prop_of (Rule_Cases.internalize_params rule)) cases) wenzelm@24830: (Method.insert_tac more_facts i THEN Tactic.rtac rule i) st) wenzelm@24830: end; wenzelm@24830: wenzelm@24830: end; wenzelm@24830: wenzelm@24830: wenzelm@24830: wenzelm@24830: (** induct method **) wenzelm@24830: wenzelm@24830: val conjunction_congs = [@{thm Pure.all_conjunction}, @{thm imp_conjunction}]; wenzelm@24830: wenzelm@24830: wenzelm@24830: (* atomize *) wenzelm@24830: wenzelm@24830: fun atomize_term thy = wenzelm@24830: MetaSimplifier.rewrite_term thy Data.atomize [] wenzelm@24830: #> ObjectLogic.drop_judgment thy; wenzelm@24830: wenzelm@24830: val atomize_cterm = MetaSimplifier.rewrite true Data.atomize; wenzelm@24830: wenzelm@24830: val atomize_tac = Simplifier.rewrite_goal_tac Data.atomize; wenzelm@24830: wenzelm@24830: val inner_atomize_tac = wenzelm@24830: Simplifier.rewrite_goal_tac (map Thm.symmetric conjunction_congs) THEN' atomize_tac; wenzelm@24830: wenzelm@24830: wenzelm@24830: (* rulify *) wenzelm@24830: wenzelm@24830: fun rulify_term thy = wenzelm@24830: MetaSimplifier.rewrite_term thy (Data.rulify @ conjunction_congs) [] #> wenzelm@24830: MetaSimplifier.rewrite_term thy Data.rulify_fallback []; wenzelm@24830: wenzelm@24830: fun rulified_term thm = wenzelm@24830: let wenzelm@24830: val thy = Thm.theory_of_thm thm; wenzelm@24830: val rulify = rulify_term thy; wenzelm@24830: val (As, B) = Logic.strip_horn (Thm.prop_of thm); wenzelm@24830: in (thy, Logic.list_implies (map rulify As, rulify B)) end; wenzelm@24830: wenzelm@24830: val rulify_tac = wenzelm@24830: Simplifier.rewrite_goal_tac (Data.rulify @ conjunction_congs) THEN' wenzelm@24830: Simplifier.rewrite_goal_tac Data.rulify_fallback THEN' wenzelm@24830: Goal.conjunction_tac THEN_ALL_NEW wenzelm@24830: (Simplifier.rewrite_goal_tac [@{thm Pure.conjunction_imp}] THEN' Goal.norm_hhf_tac); wenzelm@24830: wenzelm@24830: berghofe@34907: (* simplify *) berghofe@34907: berghofe@34907: fun simplify_conv ctxt ct = berghofe@34907: if exists_subterm (is_some o Data.dest_def) (term_of ct) then berghofe@34907: (Conv.try_conv (rulify_defs_conv ctxt) then_conv berghofe@34907: Simplifier.full_rewrite (Simplifier.context ctxt (#4 (get_local ctxt)))) ct berghofe@34907: else Conv.all_conv ct; berghofe@34907: berghofe@34907: fun simplified_rule ctxt thm = berghofe@34907: Conv.fconv_rule (Conv.prems_conv ~1 (simplify_conv ctxt)) thm; berghofe@34907: berghofe@34907: fun simplify_tac ctxt = CONVERSION (simplify_conv ctxt); berghofe@34907: berghofe@34907: val trivial_tac = Data.trivial_tac; berghofe@34907: berghofe@34907: wenzelm@24830: (* prepare rule *) wenzelm@24830: wenzelm@32432: fun rule_instance ctxt inst rule = wenzelm@32432: Drule.cterm_instantiate (prep_inst ctxt align_left I (Thm.prop_of rule, inst)) rule; wenzelm@24830: wenzelm@24830: fun internalize k th = wenzelm@24830: th |> Thm.permute_prems 0 k wenzelm@24830: |> Conv.fconv_rule (Conv.concl_conv (Thm.nprems_of th - k) atomize_cterm); wenzelm@24830: wenzelm@24830: wenzelm@24830: (* guess rule instantiation -- cannot handle pending goal parameters *) wenzelm@24830: wenzelm@24830: local wenzelm@24830: wenzelm@32032: fun dest_env thy env = wenzelm@24830: let wenzelm@24830: val cert = Thm.cterm_of thy; wenzelm@24830: val certT = Thm.ctyp_of thy; wenzelm@32032: val pairs = Vartab.dest (Envir.term_env env); wenzelm@32032: val types = Vartab.dest (Envir.type_env env); wenzelm@24830: val ts = map (cert o Envir.norm_term env o #2 o #2) pairs; wenzelm@24830: val xs = map2 (curry (cert o Var)) (map #1 pairs) (map (#T o Thm.rep_cterm) ts); wenzelm@32032: in (map (fn (xi, (S, T)) => (certT (TVar (xi, S)), certT T)) types, xs ~~ ts) end; wenzelm@24830: wenzelm@24830: in wenzelm@24830: wenzelm@26940: fun guess_instance ctxt rule i st = wenzelm@24830: let wenzelm@26940: val thy = ProofContext.theory_of ctxt; wenzelm@26626: val maxidx = Thm.maxidx_of st; wenzelm@24830: val goal = Thm.term_of (Thm.cprem_of st i); (*exception Subscript*) wenzelm@29276: val params = rev (Term.rename_wrt_term goal (Logic.strip_params goal)); wenzelm@24830: in wenzelm@24830: if not (null params) then wenzelm@24830: (warning ("Cannot determine rule instantiation due to pending parameter(s): " ^ wenzelm@26940: commas_quote (map (Syntax.string_of_term ctxt o Syntax.mark_boundT) params)); wenzelm@24830: Seq.single rule) wenzelm@24830: else wenzelm@24830: let wenzelm@24830: val rule' = Thm.incr_indexes (maxidx + 1) rule; wenzelm@24830: val concl = Logic.strip_assums_concl goal; wenzelm@24830: in wenzelm@32032: Unify.smash_unifiers thy [(Thm.concl_of rule', concl)] (Envir.empty (Thm.maxidx_of rule')) wenzelm@24830: |> Seq.map (fn env => Drule.instantiate (dest_env thy env) rule') wenzelm@24830: end wenzelm@24830: end handle Subscript => Seq.empty; wenzelm@24830: wenzelm@24830: end; wenzelm@24830: wenzelm@24830: wenzelm@24830: (* special renaming of rule parameters *) wenzelm@24830: wenzelm@24830: fun special_rename_params ctxt [[SOME (Free (z, Type (T, _)))]] [thm] = wenzelm@24830: let wenzelm@26712: val x = Name.clean (ProofContext.revert_skolem ctxt z); wenzelm@24830: fun index i [] = [] wenzelm@24830: | index i (y :: ys) = wenzelm@24830: if x = y then x ^ string_of_int i :: index (i + 1) ys wenzelm@24830: else y :: index i ys; wenzelm@24830: fun rename_params [] = [] wenzelm@24830: | rename_params ((y, Type (U, _)) :: ys) = wenzelm@24830: (if U = T then x else y) :: rename_params ys wenzelm@24830: | rename_params ((y, _) :: ys) = y :: rename_params ys; wenzelm@24830: fun rename_asm A = wenzelm@24830: let wenzelm@24830: val xs = rename_params (Logic.strip_params A); wenzelm@24830: val xs' = wenzelm@28375: (case filter (fn x' => x' = x) xs of wenzelm@24830: [] => xs | [_] => xs | _ => index 1 xs); wenzelm@24830: in Logic.list_rename_params (xs', A) end; wenzelm@24830: fun rename_prop p = wenzelm@24830: let val (As, C) = Logic.strip_horn p wenzelm@24830: in Logic.list_implies (map rename_asm As, C) end; wenzelm@24830: val cp' = cterm_fun rename_prop (Thm.cprop_of thm); wenzelm@24830: val thm' = Thm.equal_elim (Thm.reflexive cp') thm; wenzelm@33368: in [Rule_Cases.save thm thm'] end wenzelm@24830: | special_rename_params _ _ ths = ths; wenzelm@24830: wenzelm@24830: wenzelm@24830: (* fix_tac *) wenzelm@24830: wenzelm@24830: local wenzelm@24830: wenzelm@24830: fun goal_prefix k ((c as Const ("all", _)) $ Abs (a, T, B)) = c $ Abs (a, T, goal_prefix k B) wenzelm@24830: | goal_prefix 0 _ = Term.dummy_pattern propT wenzelm@24830: | goal_prefix k ((c as Const ("==>", _)) $ A $ B) = c $ A $ goal_prefix (k - 1) B wenzelm@24830: | goal_prefix _ _ = Term.dummy_pattern propT; wenzelm@24830: wenzelm@24830: fun goal_params k (Const ("all", _) $ Abs (_, _, B)) = goal_params k B + 1 wenzelm@24830: | goal_params 0 _ = 0 wenzelm@24830: | goal_params k (Const ("==>", _) $ _ $ B) = goal_params (k - 1) B wenzelm@24830: | goal_params _ _ = 0; wenzelm@24830: wenzelm@24830: fun meta_spec_tac ctxt n (x, T) = SUBGOAL (fn (goal, i) => wenzelm@24830: let wenzelm@24830: val thy = ProofContext.theory_of ctxt; wenzelm@24830: val cert = Thm.cterm_of thy; wenzelm@24830: wenzelm@24830: val v = Free (x, T); wenzelm@24830: fun spec_rule prfx (xs, body) = wenzelm@24830: @{thm Pure.meta_spec} wenzelm@26712: |> Thm.rename_params_rule ([Name.clean (ProofContext.revert_skolem ctxt x)], 1) wenzelm@24830: |> Thm.lift_rule (cert prfx) wenzelm@24830: |> `(Thm.prop_of #> Logic.strip_assums_concl) wenzelm@24830: |-> (fn pred $ arg => wenzelm@24830: Drule.cterm_instantiate wenzelm@24830: [(cert (Term.head_of pred), cert (Logic.rlist_abs (xs, body))), wenzelm@24830: (cert (Term.head_of arg), cert (Logic.rlist_abs (xs, v)))]); wenzelm@24830: wenzelm@24830: fun goal_concl k xs (Const ("all", _) $ Abs (a, T, B)) = goal_concl k ((a, T) :: xs) B wenzelm@24830: | goal_concl 0 xs B = wenzelm@24830: if not (Term.exists_subterm (fn t => t aconv v) B) then NONE wenzelm@24830: else SOME (xs, Term.absfree (x, T, Term.incr_boundvars 1 B)) wenzelm@24830: | goal_concl k xs (Const ("==>", _) $ _ $ B) = goal_concl (k - 1) xs B wenzelm@24830: | goal_concl _ _ _ = NONE; wenzelm@24830: in wenzelm@24830: (case goal_concl n [] goal of wenzelm@24830: SOME concl => wenzelm@24830: (compose_tac (false, spec_rule (goal_prefix n goal) concl, 1) THEN' rtac asm_rl) i wenzelm@24830: | NONE => all_tac) wenzelm@24830: end); wenzelm@24830: wenzelm@24832: fun miniscope_tac p = CONVERSION o wenzelm@26568: Conv.params_conv p (K (MetaSimplifier.rewrite true [Thm.symmetric Drule.norm_hhf_eq])); wenzelm@24830: wenzelm@24830: in wenzelm@24830: wenzelm@24830: fun fix_tac _ _ [] = K all_tac wenzelm@24830: | fix_tac ctxt n xs = SUBGOAL (fn (goal, i) => wenzelm@24830: (EVERY' (map (meta_spec_tac ctxt n) xs) THEN' wenzelm@24832: (miniscope_tac (goal_params n goal) ctxt)) i); wenzelm@24830: wenzelm@24830: end; wenzelm@24830: wenzelm@24830: wenzelm@24830: (* add_defs *) wenzelm@24830: wenzelm@24830: fun add_defs def_insts = wenzelm@24830: let berghofe@34907: fun add (SOME (_, (t, true))) ctxt = ((SOME t, []), ctxt) berghofe@34907: | add (SOME (SOME x, (t, _))) ctxt = wenzelm@28083: let val ([(lhs, (_, th))], ctxt') = wenzelm@30211: LocalDefs.add_defs [((x, NoSyn), (Thm.empty_binding, t))] ctxt wenzelm@24830: in ((SOME lhs, [th]), ctxt') end berghofe@34907: | add (SOME (NONE, (t as Free _, _))) ctxt = ((SOME t, []), ctxt) berghofe@34907: | add (SOME (NONE, (t, _))) ctxt = berghofe@34907: let berghofe@34907: val ([s], _) = Name.variants ["x"] (Variable.names_of ctxt); berghofe@34907: val ([(lhs, (_, th))], ctxt') = berghofe@34907: LocalDefs.add_defs [((Binding.name s, NoSyn), berghofe@34907: (Thm.empty_binding, t))] ctxt berghofe@34907: in ((SOME lhs, [th]), ctxt') end wenzelm@24830: | add NONE ctxt = ((NONE, []), ctxt); wenzelm@24830: in fold_map add def_insts #> apfst (split_list #> apsnd flat) end; wenzelm@24830: wenzelm@24830: wenzelm@24830: (* induct_tac *) wenzelm@24830: wenzelm@24830: (* wenzelm@24830: rule selection scheme: wenzelm@24861: `A x` induct ... - predicate/set induction wenzelm@24830: induct x - type induction wenzelm@24830: ... induct ... r - explicit rule wenzelm@24830: *) wenzelm@24830: wenzelm@24830: fun get_inductT ctxt insts = wenzelm@32188: fold_rev (map_product cons) (insts |> map wenzelm@27323: ((fn [] => NONE | ts => List.last ts) #> wenzelm@27323: (fn NONE => TVar (("'a", 0), []) | SOME t => Term.fastype_of t) #> wenzelm@27323: find_inductT ctxt)) [[]] wenzelm@33368: |> filter_out (forall Rule_Cases.is_inner_rule); wenzelm@24830: wenzelm@24861: fun get_inductP ctxt (fact :: _) = map single (find_inductP ctxt (Thm.concl_of fact)) wenzelm@24861: | get_inductP _ _ = []; wenzelm@24830: berghofe@34907: fun induct_tac ctxt simp def_insts arbitrary taking opt_rule facts = wenzelm@24830: let wenzelm@24830: val thy = ProofContext.theory_of ctxt; wenzelm@24830: wenzelm@24830: val ((insts, defs), defs_ctxt) = fold_map add_defs def_insts ctxt |>> split_list; berghofe@34907: val atomized_defs = map (map (Conv.fconv_rule atomize_cterm)) defs; wenzelm@24830: wenzelm@24830: fun inst_rule (concls, r) = wenzelm@33368: (if null insts then `Rule_Cases.get r wenzelm@24830: else (align_left "Rule has fewer conclusions than arguments given" wenzelm@24830: (map Logic.strip_imp_concl (Logic.dest_conjunctions (Thm.concl_of r))) insts wenzelm@32432: |> maps (prep_inst ctxt align_right (atomize_term thy)) wenzelm@33368: |> Drule.cterm_instantiate) r |> pair (Rule_Cases.get r)) wenzelm@24830: |> (fn ((cases, consumes), th) => (((cases, concls), consumes), th)); wenzelm@24830: wenzelm@24830: val ruleq = wenzelm@24830: (case opt_rule of wenzelm@33368: SOME rs => Seq.single (inst_rule (Rule_Cases.strict_mutual_rule ctxt rs)) wenzelm@24830: | NONE => wenzelm@24861: (get_inductP ctxt facts @ wenzelm@24830: map (special_rename_params defs_ctxt insts) (get_inductT ctxt insts)) wenzelm@33368: |> map_filter (Rule_Cases.mutual_rule ctxt) wenzelm@24830: |> tap (trace_rules ctxt inductN o map #2) wenzelm@24830: |> Seq.of_list |> Seq.maps (Seq.try inst_rule)); wenzelm@24830: berghofe@34907: fun rule_cases ctxt rule = berghofe@34907: let val rule' = (if simp then simplified_rule ctxt else I) berghofe@34907: (Rule_Cases.internalize_params rule); berghofe@34907: in Rule_Cases.make_nested (Thm.prop_of rule') (rulified_term rule') end; wenzelm@24830: in wenzelm@24830: (fn i => fn st => wenzelm@24830: ruleq wenzelm@33368: |> Seq.maps (Rule_Cases.consume (flat defs) facts) wenzelm@24830: |> Seq.maps (fn (((cases, concls), (more_consumes, more_facts)), rule) => wenzelm@24830: (PRECISE_CONJUNCTS (length concls) (ALLGOALS (fn j => wenzelm@24830: (CONJUNCTS (ALLGOALS berghofe@34907: let berghofe@34907: val adefs = nth_list atomized_defs (j - 1); berghofe@34907: val frees = fold (Term.add_frees o prop_of) adefs []; berghofe@34907: val xs = nth_list arbitrary (j - 1); berghofe@34907: val k = nth concls (j - 1) + more_consumes berghofe@34907: in berghofe@34907: Method.insert_tac (more_facts @ adefs) THEN' berghofe@34907: (if simp then berghofe@34907: rotate_tac k (length adefs) THEN' berghofe@34907: fix_tac defs_ctxt k berghofe@34907: (List.partition (member op = frees) xs |> op @) berghofe@34907: else berghofe@34907: fix_tac defs_ctxt k xs) berghofe@34907: end) wenzelm@24830: THEN' inner_atomize_tac) j)) wenzelm@24830: THEN' atomize_tac) i st |> Seq.maps (fn st' => wenzelm@26940: guess_instance ctxt (internalize more_consumes rule) i st' wenzelm@32432: |> Seq.map (rule_instance ctxt (burrow_options (Variable.polymorphic ctxt) taking)) wenzelm@24830: |> Seq.maps (fn rule' => berghofe@34907: CASES (rule_cases ctxt rule' cases) wenzelm@24830: (Tactic.rtac rule' i THEN wenzelm@24830: PRIMITIVE (singleton (ProofContext.export defs_ctxt ctxt))) st')))) berghofe@34907: THEN_ALL_NEW_CASES berghofe@34907: ((if simp then simplify_tac ctxt THEN' (TRY o trivial_tac) berghofe@34907: else K all_tac) berghofe@34907: THEN_ALL_NEW rulify_tac) wenzelm@24830: end; wenzelm@24830: wenzelm@24830: wenzelm@24830: wenzelm@24830: (** coinduct method **) wenzelm@24830: wenzelm@24830: (* wenzelm@24830: rule selection scheme: wenzelm@24861: goal "A x" coinduct ... - predicate/set coinduction wenzelm@24830: coinduct x - type coinduction wenzelm@24830: coinduct ... r - explicit rule wenzelm@24830: *) wenzelm@24830: wenzelm@24830: local wenzelm@24830: wenzelm@24830: fun get_coinductT ctxt (SOME t :: _) = find_coinductT ctxt (Term.fastype_of t) wenzelm@24830: | get_coinductT _ _ = []; wenzelm@24830: wenzelm@24861: fun get_coinductP ctxt goal = find_coinductP ctxt (Logic.strip_assums_concl goal); wenzelm@24861: wenzelm@24861: fun main_prop_of th = wenzelm@33368: if Rule_Cases.get_consumes th > 0 then Thm.major_prem_of th else Thm.concl_of th; wenzelm@24830: wenzelm@24830: in wenzelm@24830: wenzelm@26924: fun coinduct_tac ctxt inst taking opt_rule facts = wenzelm@24830: let wenzelm@24830: val thy = ProofContext.theory_of ctxt; wenzelm@24830: wenzelm@24830: fun inst_rule r = wenzelm@33368: if null inst then `Rule_Cases.get r wenzelm@32432: else Drule.cterm_instantiate (prep_inst ctxt align_right I (main_prop_of r, inst)) r wenzelm@33368: |> pair (Rule_Cases.get r); wenzelm@24830: wenzelm@24830: fun ruleq goal = wenzelm@24830: (case opt_rule of wenzelm@24830: SOME r => Seq.single (inst_rule r) wenzelm@24830: | NONE => wenzelm@24861: (get_coinductP ctxt goal @ get_coinductT ctxt inst) wenzelm@24830: |> tap (trace_rules ctxt coinductN) wenzelm@24830: |> Seq.of_list |> Seq.maps (Seq.try inst_rule)); wenzelm@24830: in wenzelm@24830: SUBGOAL_CASES (fn (goal, i) => fn st => wenzelm@24830: ruleq goal wenzelm@33368: |> Seq.maps (Rule_Cases.consume [] facts) wenzelm@24830: |> Seq.maps (fn ((cases, (_, more_facts)), rule) => wenzelm@26940: guess_instance ctxt rule i st wenzelm@32432: |> Seq.map (rule_instance ctxt (burrow_options (Variable.polymorphic ctxt) taking)) wenzelm@24830: |> Seq.maps (fn rule' => berghofe@34907: CASES (Rule_Cases.make_common (thy, berghofe@34907: Thm.prop_of (Rule_Cases.internalize_params rule')) cases) wenzelm@24830: (Method.insert_tac more_facts i THEN Tactic.rtac rule' i) st))) wenzelm@24830: end; wenzelm@24830: wenzelm@24830: end; wenzelm@24830: wenzelm@24830: wenzelm@24830: wenzelm@24830: (** concrete syntax **) wenzelm@24830: wenzelm@27809: structure P = OuterParse; wenzelm@27809: wenzelm@24830: val arbitraryN = "arbitrary"; wenzelm@24830: val takingN = "taking"; wenzelm@24830: val ruleN = "rule"; wenzelm@24830: wenzelm@24830: local wenzelm@24830: wenzelm@24830: fun single_rule [rule] = rule wenzelm@24830: | single_rule _ = error "Single rule expected"; wenzelm@24830: wenzelm@24830: fun named_rule k arg get = wenzelm@24830: Scan.lift (Args.$$$ k -- Args.colon) |-- Scan.repeat arg :|-- wenzelm@24830: (fn names => Scan.peek (fn context => Scan.succeed (names |> map (fn name => wenzelm@24830: (case get (Context.proof_of context) name of SOME x => x wenzelm@24830: | NONE => error ("No rule for " ^ k ^ " " ^ quote name)))))); wenzelm@24830: wenzelm@24861: fun rule get_type get_pred = wenzelm@24830: named_rule typeN Args.tyname get_type || wenzelm@24861: named_rule predN Args.const get_pred || wenzelm@24861: named_rule setN Args.const get_pred || wenzelm@24830: Scan.lift (Args.$$$ ruleN -- Args.colon) |-- Attrib.thms; wenzelm@24830: wenzelm@24861: val cases_rule = rule lookup_casesT lookup_casesP >> single_rule; wenzelm@24861: val induct_rule = rule lookup_inductT lookup_inductP; wenzelm@24861: val coinduct_rule = rule lookup_coinductT lookup_coinductP >> single_rule; wenzelm@24830: wenzelm@24830: val inst = Scan.lift (Args.$$$ "_") >> K NONE || Args.term >> SOME; wenzelm@24830: berghofe@34907: val inst' = Scan.lift (Args.$$$ "_") >> K NONE || berghofe@34907: Args.term >> (SOME o rpair false) || berghofe@34907: Scan.lift (Args.$$$ "(") |-- (Args.term >> (SOME o rpair true)) --| berghofe@34907: Scan.lift (Args.$$$ ")"); berghofe@34907: wenzelm@24830: val def_inst = wenzelm@28083: ((Scan.lift (Args.binding --| (Args.$$$ "\" || Args.$$$ "==")) >> SOME) berghofe@34907: -- (Args.term >> rpair false)) >> SOME || berghofe@34907: inst' >> Option.map (pair NONE); wenzelm@24830: wenzelm@27370: val free = Args.context -- Args.term >> (fn (_, Free v) => v | (ctxt, t) => wenzelm@27370: error ("Bad free variable: " ^ Syntax.string_of_term ctxt t)); wenzelm@24830: wenzelm@24830: fun unless_more_args scan = Scan.unless (Scan.lift wenzelm@24830: ((Args.$$$ arbitraryN || Args.$$$ takingN || Args.$$$ typeN || wenzelm@24861: Args.$$$ predN || Args.$$$ setN || Args.$$$ ruleN) -- Args.colon)) scan; wenzelm@24830: wenzelm@24830: val arbitrary = Scan.optional (Scan.lift (Args.$$$ arbitraryN -- Args.colon) |-- wenzelm@27809: P.and_list1' (Scan.repeat (unless_more_args free))) []; wenzelm@24830: wenzelm@24830: val taking = Scan.optional (Scan.lift (Args.$$$ takingN -- Args.colon) |-- wenzelm@24830: Scan.repeat1 (unless_more_args inst)) []; wenzelm@24830: wenzelm@24830: in wenzelm@24830: wenzelm@30722: val cases_setup = wenzelm@30722: Method.setup @{binding cases} wenzelm@30722: (P.and_list' (Scan.repeat (unless_more_args inst)) -- Scan.option cases_rule >> wenzelm@30722: (fn (insts, opt_rule) => fn ctxt => wenzelm@30722: METHOD_CASES (fn facts => Seq.DETERM (HEADGOAL (cases_tac ctxt insts opt_rule facts))))) wenzelm@30722: "case analysis on types or predicates/sets"; wenzelm@24830: wenzelm@30722: val induct_setup = wenzelm@30722: Method.setup @{binding induct} berghofe@34907: (Args.mode no_simpN -- (P.and_list' (Scan.repeat (unless_more_args def_inst)) -- berghofe@34907: (arbitrary -- taking -- Scan.option induct_rule)) >> berghofe@34907: (fn (no_simp, (insts, ((arbitrary, taking), opt_rule))) => fn ctxt => wenzelm@30722: RAW_METHOD_CASES (fn facts => berghofe@34907: Seq.DETERM (HEADGOAL (induct_tac ctxt (not no_simp) insts arbitrary taking opt_rule facts))))) wenzelm@30722: "induction on types or predicates/sets"; wenzelm@24830: wenzelm@30722: val coinduct_setup = wenzelm@30722: Method.setup @{binding coinduct} wenzelm@30722: (Scan.repeat (unless_more_args inst) -- taking -- Scan.option coinduct_rule >> wenzelm@30722: (fn ((insts, taking), opt_rule) => fn ctxt => wenzelm@30722: RAW_METHOD_CASES (fn facts => wenzelm@30722: Seq.DETERM (HEADGOAL (coinduct_tac ctxt insts taking opt_rule facts))))) wenzelm@30722: "coinduction on types or predicates/sets"; wenzelm@24830: wenzelm@24830: end; wenzelm@24830: wenzelm@24830: wenzelm@24830: wenzelm@24830: (** theory setup **) wenzelm@24830: wenzelm@30722: val setup = attrib_setup #> cases_setup #> induct_setup #> coinduct_setup; wenzelm@24830: wenzelm@24830: end;