| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/Isabelle/HOL/Nominal/ (Beweissystem Isabelle Version 2025-1©) Datei vom 16.11.2025 mit Größe 6 kB |
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Quelle nominal_induct.ML Sprache: SML |
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(* Author: Christian Urban and Makarius
The nominal induct proof method. *) structure NominalInduct: sig val nominal_induct_tac: bool -> (binding option * (term * bool)) option list list -> (string * typ) list -> (string * typ) list list -> thm list -> thm list -> int -> context_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_case_prod (Var (xi, (HOLogic.unitT :: Ts) ---> Term.range_type T)); fun split_all_tuples ctxt = Simplifier.full_simplify (put_simpset HOL_basic_ss ctxt addsimps [@{thm split_conv}, @{thm split_paired_all}, @{thm unit_all_eq1}, @{thm fresh_unit_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 (fn (t, u) => (#1 (dest_Var t), Thm.cterm_of ctxt u)); in (((cases, nconcls), consumes), infer_instantiate ctxt substs joined_rule) end; fun rename_params_rule internal xs rule = let val tune = if internal then Name.internal else perhaps (try Name.dest_internal); 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.renamed_prop (rename_prems (Thm.prop_of rule)) rule end; (* nominal_induct_tac *) fun nominal_induct_tac simp def_insts avoiding fixings rules facts i (ctxt, st) = let 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 ctxt))) defs; val finish_rule = split_all_tuples defs_ctxt #> rename_params_rule true (map (Name.clean o Variable.revert_fixed 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 ctxt (Thm.prop_of r') (Induct.rulified_term ctxt r') end; fun context_tac _ _ = rules |> inst_mutual_rule ctxt insts avoiding |> Rule_Cases.consume ctxt (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 Thm.prop_of) adefs []; val xs = nth_list fixings (j - 1); val k = nth concls (j - 1) + more_consumes in Method.insert_tac ctxt (more_facts @ adefs) THEN' (if simp then Induct.rotate_tac k (length adefs) THEN' Induct.arbitrary_tac defs_ctxt k (List.partition (member op = frees) xs |> op @) else Induct.arbitrary_tac defs_ctxt k xs) end) THEN' Induct.inner_atomize_tac defs_ctxt) j)) THEN' Induct.atomize_tac ctxt) i st |> Seq.maps (fn st' => Induct.guess_instance ctxt (finish_rule (Induct.internalize ctxt more_consumes rule)) i st' |> Seq.maps (fn rule' => CONTEXT_CASES (rule_cases ctxt rule' cases) (resolve_tac ctxt [rename_params_rule false [] rule'] i THEN PRIMITIVE (singleton (Proof_Context.export defs_ctxt ctxt))) (ctxt, st')))); in (context_tac CONTEXT_THEN_ALL_NEW ((if simp then Induct.simplify_tac ctxt THEN' (TRY o Induct.trivial_tac ctxt) else K all_tac) THEN_ALL_NEW Induct.rulify_tac ctxt)) i (ctxt, st) 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.$$$ ")"); val def_inst = ((Scan.lift (Args.binding --| (Args.$$$ "\ -- (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 : (Proof.context -> Proof.method) context_parser = Scan.lift (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 _ => fn facts => (nominal_induct_tac (not no_simp) x y z w facts 1)); end; end; ¤ Dauer der Verarbeitung: 0.17 Sekunden (vorverarbeitet) ¤*© Formatika GbR, Deutschland |
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2026-03-28