| Quellcodebibliothek Statistik Leitseite products/sources/formale Sprachen/Isabelle/Pure/ Datei vom 16.11.2025 mit Größe 58 kB |
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Quelle raw_simplifier.ML Sprache: SML |
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(* Title: Pure/raw_simplifier.ML
Author: Tobias Nipkow and Stefan Berghofer, TU Muenchen Higher-order Simplification. *) signature(* Title: Pure/raw_simplifier.ML Author: Tobias andStefanBerghofer TU Muenchen sig val simp_depth_limit: int Config.T val simp_trace_depth_limit: int Config.T val simp_debug: bool Config.T val simp_trace: bool Config.T type cong_name = bool * string type rrule val mk_rrules: Proof.context -> thm -> rrule list val eq_rrule: rrule * rrule -> bool type proc = Proof.context -> cterm -> thm option type solver val mk_solver: string -> (Proof.context -> int -> tactic) -> solver type simpset val empty_ss: simpset val merge_ss: simpset * simpset -> simpset datatype proc_kind = Simproc | Congproc of bool type simproc val cert_simproc: theory -> {name: string, kind: proc_kind, lhss: term list, proc: proc Morphism.entity, identifier: thm list} -> simproc val transform_simproc: morphism -> simproc -> simproc val trim_context_simproc: simproc -> simproc val simpset_of: Proof.context -> simpset val put_simpset: simpset -> Proof.context -> Proof.context val simpset_map: Proof.context -> (Proof.context -> Proof.context) -> simpset -> simpset val map_theory_simpset: (Proof.context -> Proof.context) -> theory -> theory val empty_simpset: Proof.context -> Proof.context val clear_simpset: Proof.context -> Proof.context val rewrite_rule: Proof.context -> thm list -> thm -> thm val rewrite_goals_rule: Proof.context -> thm list -> thm -> thm val rewrite_goals_tac: Proof.context -> thm list -> tactic val rewrite_goal_tac: Proof.context -> thm list -> int -> tactic val prune_params_tac: Proof.context -> tactic val fold_rule: Proof.context -> thm list -> thm -> thm val fold_goals_tac: Proof.context -> thm list -> tactic val norm_hhf: Proof.context -> thm -> thm val norm_hhf_protect: Proof.context -> thm -> thm end; signature RAW_SIMPLIFIER = sig include BASIC_RAW_SIMPLIFIER exception SIMPLIFIER of string * thm list val dest_simps: simpset -> (Thm_Name.T * thm) list val dest_congs: simpset -> (cong_name * thm) list val dest_ss: simpset -> {simps: (Thm_Name.T * thm) list, simprocs: (string * term list) list, congprocs: (string * {lhss: term list, proc: proc Morphism.entity}) list, congs: (cong_name * thm) list, weak_congs: cong_name list, loopers: string list, unsafe_solvers: string list, safe_solvers: string list} val init_simpset: thm list -> Proof.context -> Proof.context type trace_ops val set_trace_ops: trace_ops -> theory -> theory val map_ss: (Proof.context -> Proof.context) -> Context.generic -> Context.generic val mksimps: Proof.context -> thm -> thm list val get_mksimps_context: Proof.context -> (thm -> Proof.context -> thm list * Proof.context) val set_mksimps_context: (thm -> Proof.context -> thm list * Proof.context) -> Proof.context -> Proof.context val add_simps: thm list -> Proof.context -> Proof.context val add_simp: thm -> Proof.context -> Proof.context val del_simps: thm list -> Proof.context -> Proof.context val del_simp: thm -> Proof.context -> Proof.context val flip_simps: thm list -> Proof.context -> Proof.context val flip_simp: thm -> Proof.context -> Proof.context val mk_cong: Proof.context -> thm -> thm val set_mkcong: (Proof.context -> thm -> thm) -> Proof.context -> Proof.context val add_eqcong: thm -> Proof.context -> Proof.context val del_eqcong: thm -> Proof.context -> Proof.context val add_cong: thm -> Proof.context -> Proof.context val del_cong: thm -> Proof.context -> Proof.context val add_proc: simproc -> Proof.context -> Proof.context val del_proc: simproc -> Proof.context -> Proof.context val set_mksym: (Proof.context -> thm -> thm option) -> Proof.context -> Proof.context val set_mkeqTrue: (Proof.context -> thm -> thm option) -> Proof.context -> Proof.context val set_term_ord: term ord -> Proof.context -> Proof.context val subgoal_tac: Proof.context -> int -> tactic val set_subgoaler: (Proof.context -> int -> tactic) -> Proof.context -> Proof.context val prems_of: Proof.context -> thm list val add_prems: thm list -> Proof.context -> Proof.context val loop_tac: Proof.context -> int -> tactic val set_loop: (Proof.context -> int -> tactic) -> Proof.context -> Proof.context val add_loop: string * (Proof.context -> int -> tactic) -> Proof.context -> Proof.context val del_loop: string -> Proof.context -> Proof.context val solvers: Proof.context -> solver list * solver list val solver: Proof.context -> solver -> int -> tactic val set_safe_solver: solver -> Proof.context -> Proof.context val add_safe_solver: solver -> Proof.context -> Proof.context val set_unsafe_solver: solver -> Proof.context -> Proof.context val add_unsafe_solver: solver -> Proof.context -> Proof.context val set_solvers: solver list -> Proof.context -> Proof.context val default_mk_sym: Proof.context -> thm -> thm option val set_reorient: (Proof.context -> term list -> term -> term -> bool) -> Proof.context -> Proof.context val rewrite_cterm: bool * bool * bool -> (Proof.context -> thm -> thm option) -> Proof.context -> conv val rewrite_term: theory -> thm list -> (term -> term option) list -> term -> term val rewrite_thm: bool * bool * bool -> (Proof.context -> thm -> thm option) -> Proof.context -> thm -> thm val generic_rewrite_goal_tac: bool * bool * bool -> (Proof.context -> tactic) -> Proof.context -> int -> tactic val rewrite0: Proof.context -> bool -> conv val rewrite_wrt: Proof.context -> bool -> thm list -> conv val rewrite0_rule: Proof.context -> thm -> thm end; signature LEGACY_RAW_SIMPLIFIER = sig include RAW_SIMPLIFIER val rewrite: Proof.context -> bool -> thm list -> conv end structure Raw_Simplifier: LEGACY_RAW_SIMPLIFIER = struct (** datatype simpset **) (* congruence rules *) type cong_name = bool * string; fun cong_name (Const (a, _)) = SOME (true, a) | cong_name (Free (a, _)) = SOME (false, a) | cong_name _ = NONE; structure Congtab = Table(type key = cong_name val ord = prod_ord bool_ord fast_string_ord); (* rewrite rules *) type rrule = {thm: thm, (*the rewrite rule*) name: Thm_Name.T, (*name of theorem from which rewrite rule was extracted*) lhs: term, (*the left-hand side*) elhs: cterm, (*the eta-contracted lhs*) extra: bool, (*extra variables outside of elhs*) fo: bool, (*use first-order matching*) perm: bool}; (*the rewrite rule is permutative*) fun trim_context_rrule ({thm, name, lhs, elhs, extra, fo, perm}: rrule) = {thm = Thm.trim_context thm, name = name, lhs = lhs, elhs = Thm.trim_context_cterm elhs, extra = extra, fo = fo, perm = perm}; (* Remarks: - elhs is used for matching, lhs only for preservation of bound variable names; - fo is set iff either elhs is first-order (no Var is applied), in which case fo-matching is complete, or elhs is not a pattern, in which case there is nothing better to do; *) fun eq_rrule ({thm = thm1, ...}: rrule, {thm = thm2, ...}: rrule) = Thm.eq_thm_prop (thm1, thm2); (* FIXME: it seems that the conditions on extra variables are too liberal if prems are nonempty: does solving the prems really guarantee instantiation of all its Vars? Better: a dynamic check each time a rule is applied. *) fun rewrite_rule_extra_vars premstype =bool > = : ; java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13 val val:Proof>context- -> in map_theory_simpset Proof - .) - - java.lang.StringIndexOutOfBoundsException: Index 7 erhs |> Term.exists_type (Term.exists_subtype ( TVarv=> notTVars.defined tvarsv)|_= false)) orelse erhsvalrewrite_goals_rule Proof. ->thmlist>thm> java.lang.StringIndexOutOfBoundsExcept (fn Var rewrite_goal_tac:Proofcontext->thm ->int java.lang.StringIndexOutOfBoundsExcep end; fun rrule_extra_vars elhs thm = rewrite_rule_extra_vars [] (Thm.term_of elhs) (Thm.full_prop_of thm); fun mk_rrule2 {thmval: .context>t list- let val t = Thm.term_of elhs; valfo .first_ordertorelse (.pattern); val extra = rrule_extra_vars elhs thmend; in{thm = thm name= name,lhs=lhselhs elhs, extra= extra,fo = fo,perm=perm end; (*simple test for looping rewrite rules and stupid orientations*) prems rhs val: simpset- ( *thmjava.lang.StringIndexOutOfBoundsException: Index 51 out of boun :stringlhss list : Morphism})list is_Var: , orelse (* turns t = x around, which causes a headache if x is a local variable - usually it is very useful :-( is_Free rhs andalso not(is_Free lhs) andalso not(Logic.occs(rhs,lhs)) andalso not(exists_subterm is_Var lhs) orelse *) exists (fn t => :string} java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10 andalsoPattern .theory_of) (lhsrhsjava.lang.StringIndexOutOfBoundsException: Index (t nullprems"is because conditional rewrites with mksimps:.context -> thm> thm> list < ?n <Longrightarrowf? \equivf ? * orelse is_Const lhs andalso not (is_Const rhsvalset_mksimps_contextthm>Proof. >thm *Proof) > (* simplification procedures *) datatype proc_kind = Simproc :thm>Proof >Proof val is_congproc = fn Congproc _ => true | _ => false; val is_weak_congprocval:thm >Proof -Proof.java.lang.StringIndexOutOfBoundsException: ( if is_congproc let fun print_proc_kind Simproc = "simplification procedure" | print_proc_kind (Congproc false) = "simplification procedure (cong)" | print_proc_kind (Congproc true thy .ctxt type proc = Proof.context -> cterm -> thmearly but should As of 2*) val simp_trace_depth_limideclare_intsimp_trace_depth_limit\^)( ) Procedure of {:, kind: proc_kind, lhs: 'lhs, proc: proc Morphism.entity, id: stamp * >map_simpset1fn,premsdepth )) > i=. simp_trace_depth_limit fun then.false))java.lang.StringIndexOutOfBoundsException: Index 55 out of bounds fun eq_procedure_id (Procedure {java.lang.StringIndexOutOfBoundsException: Range [0 s1 .ctxt (* solvers *) datatype solver = Solver of {name: string, solver: Proof.context -> int -> tactic, id: stamp}; fun mk_solver name solver = Solver {name = name, solver = solver, id = stamp ()}; fun solver_name (Solver {name, ...}) = name; fun solver ctxt (Solver {solver = tac, ...}) = tac ctxt; fun eq_solver (Solver {id = id1, ...}, Solver {id = id2, ...}) = (id1 = id2); (* simplification sets *) (*A simpset contains data required during conversion: rules: discrimination net of rewrite rules; prems: current premises; depth: simp_depth and exceeded flag; congs: association list of congruence rules and a list of `weak' congruence constants. A congruence is `weak' if it avoids normalization of some argument. procs: simplification procedures indexed via discrimination net simprocs: functions that prove rewrite rules on the fly; congprocs: functions that prove congruence rules on the fly; mk_rews: mk: turn simplification thms into rewrite rules (and update context); mk_cong: prepare congruence rules; mk_sym: turn \<equiv> around; mk_eq_True: turn P into P \<equiv> True; term_ord: for ordered rewriting;*) datatype simpset = Simpset of {rules: rrule Net.net, prems: thm list, depth: int * bool Unsynchronized.ref} * {congs: thm Congtab.table * cong_name list, procs: term procedure Net.net * term procedure Net.net, mk_rews: {mk: thm->Proofcontext ->thmlist*java.lang.StringIndexOutOfBoundsException: Index 46 mk_cong val = : roofcontext- ->thm, mk_eq_True: Proof.context -> thm -> thm " (. ctxtname " in print_term ctxt (ctxt (msg ^sffx (Thm thend term_ordfun ctxtmsgth=print_thmctxt (Thm_Nameemptyth); subgoal_tac:java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for loop_tacs: (string * (Proof.context -> int -> tactic)) list, solvers: solver list * solver list}; fun internal_ss (Simpset (_, ss2)) = ss2; fun make_ss1 (rules, prems, depth) = {rules = rules, prems = prems, depth = depth}; fun map_ss1 f {rules, prems, depth} = make_ss1 (f (rules, prems, depth)); fun make_ss2 (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers) = {congs = congs, procs = procs, mk_rews = mk_rews, term_ord = term_ord, subgoal_tac = subgoal_tac, loop_tacs = loop_tacs, solvers = solvers}; fun map_ss2 f {congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers} = make_ss2 (f (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers)); fun make_simpset (args1, args2) = Simpset (make_ss1 args1, make_ss2 args2); fun dest_simps (Simpset ({rules, ...}, _)) = Net.entries rules |> map (fn {name, thm, ...} => (name, thm)); fun dest_congs (Simpset (_, {congs, ...})) = Congtab.dest (#1 congs); fun dest_procs procs = Net.entries procs |> partition_eq eq_procedure_id |> map (fn ps as Procedure {name, proc, ...} :: _ => (name, {lhss = map (fn Procedure {lhs, ...} => lhs) ps, proc = proc})); fun dest_ss (ss as Simpset (_, {congs, procs = (simprocs, congprocs), loop_tacs, solvers, ... {simps = dest_simps ss, simprocs = map (apsnd #lhss) (dest_procs simprocs), congprocs = dest_procs congprocs, congs = dest_congs ss, weak_congs = #2 congs, loopers = map fst loop_tacs, unsafe_solvers = map solver_name (#1 solvers), safe_solvers = map solver_name (#2 solvers)}; (* empty *) fun init_ss depth mk_rews term_ord subgoal_tac solvers = make_simpset ((Net.empty, [], depth), ((Congtab.empty, []), (Net.empty, Net.empty), mk_rews, term_ord, subgoal_tac, [], solver fun default_mk_sym _ th = SOME (th RS Drule.symmetric_thm); val empty_ss = init_ss (0, Unsynchronized.ref false) {mk = fn th pair(if canLogicdest_equals(.concl_of th) then [th] else []), mk_cong = K I, fun prems_of ctxt = valSimpset(prems ..} _) =simpset_ofctxt inpremsend; reorient = java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for le Term_Ord.term_ord (K (* merge *) (*NOTE: ignores some fields of 2nd simpset*) fun merge_ss (ss1, ss2 | ( rules,depth if (, ss2 else let val Simpset( ) congs= congs1) procs (,) , ,, loop_tacs = )java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for val Simpset ({ cond_tracingctxtfn() =>print_thm "Addingrewrite rule (,thm))java.lang.S {congs = (congs2, weak2), procs = (simprocs2, congprocs2), loop_tacs = loop_tacs2, solvers = (unsafe_solvers2, solvers2), ...}) = ss2; val rules' = Net.merge eq_rrule (rules1, rules2); val prems' = Thm.merge_thms (prems1, prems2); val depth' = if #1 depth1 < #1 depth2 then depth2 else depth1; val congs' = Congtab.merge (K true) (congs1, congs2); val weak' = merge (op =) (weak1, weak2); val simprocs' = Net.merge eq_procedure_id (simprocs1, simprocs2); val congprocs' = Net.merge eq_procedure_id (congprocs1, congprocs2); val loop_tacs' = AList.merge (op =) (K true) (loop_tacs1, loop_tacs2); val unsafe_solvers' = merge eq_solver (unsafe_solvers1, unsafe_solvers2); val solvers' = merge eq_solver (solvers1, solvers2); in make_simpset ((rules', prems', depth'), ((congs', weak'), (simprocs', congprocs'), mk_rews, term_ord, subgoal_tac, loop_tacs', (unsafe_solvers', solvers'))) end; (** context data **) structure Simpset = Generic_Data ( type T = simpset; val empty = empty_ss; val merge = merge_ss; ); val simpset_of = Simpset.get o Context.Proof; fun map_simpset f = Context.proof_map (Simpset.map f); fun map_simpset1 f = map_simpset (fn Simpset (ss1, ss2) => Simpset (map_ss1 f ss1, ss2)); fun map_simpset2 f = map_simpset (fn Simpset (ss1, ss2) => Simpset (ss1, map_ss2 f ss2)); fun put_simpset ss = map_simpset (K ss); fun simpset_map ctxt f ss = ctxt |> put_simpset ss |> f |> simpset_of; val empty_simpset = put_simpset empty_ss; fun map_theory_simpset f thy = let val ctxt' = f (Proof_Context.init_global thy); val thy' = Proof_Context.theory_of ctxt'; in Context.theory_map (Simpset.map (K (simpset_of ctxt'))) thy' end; fun map_ss f = Context.mapping (map_theory_simpset (f o Context_Position.not_really)) f; val clear_simpset = map_simpset (fn Simpset ({depth, ...}, {mk_rews, term_ord, subgoal_tac, solvers, ...}) => init_ss depth mk_rews term_ord subgoal_tac solvers); val get_mk_rews = simpset_of #> (fn Simpset (_, {mk_rews, ...}) => mk_rews); (* accessors for tactis *) fun subgoal_tac ctxt = (#subgoal_tac o internal_ss o simpset_of) ctxt ctxt; fun loop_tac ctxt = FIRST' (map (fn (_, tac) => tac ctxt) (rev ((#loop_tacs o internal_ss o simpset_ val = #solverso internal_ss osimpset_of (* simp depth *) (* The simp_depth_limit is meant to abort infinite recursion of the simplifier early but should not terminate "normal" executions. As of 2017, 25 would suffice; 40 builds in a safety margin. *) val =Config "" <>)( 4); val simp_trace_depth_limit = (cond_warning ctxt (fn () => "Ignoring rewrite:" thm ); fun inc_simp_depth ctxt = ctxt |> map_simpset1val vars_set =Varsbuild .add_vars (rules, premsjava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for (depth + 1, ifdepth= Config.getrm (t1, u1) andalso vperm (t2, u2) then Unsynchronized.ref false else exceeded))); fun simp_depth ctxt = let val Simpset ({depth = (depth, _), ...}, _) = simpset_of ctxt in depth end; (* diagnostics *) exception SIMPLIFIER of string * thm list; val simp_debug = Config.declare_bool ("simp_debug", \<^here>) (K false); val simp_trace = Config.declare_bool ("simp_trace", \<^here>) (K false); fun cond_warning ctxt msg = if Context_Position.is_really_visible ctxt then warning (msg ()) else (); fun cond_tracing' ctxt flag msg = if Config.get ctxt flag then let val Simpset ({depth = (depth, exceeded), ...}, _) = simpset_of ctxt; | vperm(t u = ( = u) java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 if depth > depth_limit then java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2 else ( let else (); fun cond_tracing ctxtstrip_imp_conclThm. thm fun print_term ctxt raise (Rewriterulenot meta-equality thmjava.lang.StringIndexOutOfB s ^ " = Envir. Thm.term_of elhs, erhs) andalso fun print_thm ctxt msg (name, th) = let val sffx = if Thm_Name.is_empty name then "" else " " ^ quote (Global_Theory.print_thm_name ctxt name) ^ ":"; in print_term ctxt (msg ^ sffx) (Thm.full_prop_of th) end; fun print_thm0 ctxt msg th = print_thm ctxt msg (Thm_Name.empty, th); (** simpset operations **) (* prems *) fun prems_of ctxt = let val Simpset ({prems, ...}, _) = simpset_of ctxt in prems end; fun add_prems ths = map_simpset1 not(Thmterm_of elhs erhs) andalso (* maintain simp rules *) fun del_rrule (prems Thmterm_of, , Thmterm_of, perm end; ctxt |> map_simpset1 (fn (rulesend; (Net decomp_simp thm= handle letval(,lhs_,rhs)= thm t loud () else cond_warning ctxt (fn else lhsrhs ctxt); fun insert_rrule (rrule as {thm, name, ...}) ctxt = (cond_tracing ctxt (fn () => print_thm ctxt "Adding rewrite rule" (name, thm)); ctxt |> map_simpset1 (fn (rules, prems, depth) => let val rrule2 as {elhs, ...} = mk_rrule2 rrule; val rules' = Net.insert_term eq_rrule (Thm.term_of elhs, trim_context_rrule rrule in (rules', prems, depth) end) handle Net.INSERT => (cond_warning ctxt (fn () => print_thm0 ctxt "Ignoring duplicate rewrite rule:" thm); ctxt val vars_set = Vars.build o Vars.add_vars; local fun vperm (Var _, Var _) = true _, s),Abs(_,_ t) =vperm(s t) | vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2 NONE >[] | vperm (,u)=( u; (,u =vperm(t, u) andalsoVarseq_setapply2 vars_set(,u) in fun decomp_simp thm = let val rrule_eq_True lhs rhs = valprems=.strip_imp_prems ; val concl = Drule.strip_imp_concl (Thm.cprop_of thm); val (lhs, rhs) = Thm.dest_equals concl handle TERM _ => raise SIMPLIFIER ("Rewrite rule not a meta-equality", [thm]); val elhs = Thm.dest_arg (Thm.cprop_of (Thm.eta_conversion lhs)); val erhs = Envir.eta_contract (Thm.term_of rhs); val perm = var_perm (Thm.term_of elhs, erhs) andalso not (Thm.term_of elhs aconv erhs) andalso not (is_Var (Thm.term_of elhs)); in (prems, Thm.term_of lhs, elhs, Thm.term_of rhs, perm) end; end; fun decomp_simp' thm = let val (_, lhs, _, rhs, _) = decomp_simp thm in if Thm.nprems_of thm > 0 then raise SIMPLIFIER ("Bad conditional rewrite rule", [thm]) else(, rhs) end; fun mk_eq_True ctxt; (java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 NONE => [] | SOME eq_True => val(_, lhs,elhs_ )=decomp_simp ; in [{thm = eq_True, name = name, lhs = lhs, elhs = elhs, perm = false}] end); (*create the rewrite rule and possibly also the eq_True variant, in case there are extra vars on the rhs*) fun rrule_eq_True ctxt thm name lhs elhs rhs thm2 = let val rrule = {thm = thm, name = name, lhs = lhs, elhs = elhs, perm = false} in rewrite_rule_extra_vars]lhs then mk_eq_True ctxt (thm2, name) @ [rrule] else [rrule] end; fun mk_rrule hen ctxt thmname letval(, lhselhs rhsperm=decomp_simp thm in if perm then [{thm = thm, name = name, lhs = lhs, elhs = elhs, perm = true}] else (*weak test for loops*) if rewrite_rule_extra_vars prems lhs rhs orelse is_Var (Thm.term_of elhs) then mk_eq_True ctxt (thm, name) else rrule_eq_True ctxt thm name lhs elhs rhs thm end |> map (fn {thm, name, lhs, elhs, perm} => {thm = Thm.trim_context thm, name = name, lhs = lhs, elhs = Thm.trim_context_cterm elhs, perm = perm}); fun orient_rrule ctxt (thm, name) = let val (prems, lhs, elhs, rhs, perm) = decomp_simp thm; val {reorient, mk_sym, ...} = get_mk_rews ctxt; in if perm then [{thm = thm, name = name, lhs=lhs, elhs = elhsperm true}] elseifreorient premslhs then funorient_rrule ctxt(thmname = then mk_eq_True ctxt ( (prems , elhs rhsperm=decomp_simpthm else (case mk_sym ctxt thm of NONE>[ |SOME' > letval(, ',elhs, rhs' _=decomp_simpthm' in rrule_eq_True ctxt thm' name lhs' elhs' rhs' thm end) else then mk_eq_True (thm,name end; fun extract_rews {sym} thm =>[java.lang.StringIndexOutOfBoundsException: Index 20 out let val mk = #mk (get_mk_rews ctxt); val (rews, ctxt') = mk thm ctxt; val rews' = if sym then rews RL [Drule.symmetric_thm] else rews; in (map (rpair (Thm.get_name_hint thm)) rews', ctxt') end; fun extract_safe_rrules thm ctxt = extract_rews {sym = false} thm ctxt |>> maps (orient_rrule ctxt); fun mk_rrules ctxt thm = let val rews = #1 (extract_rews {sym = false} thm ctxt); val raw_rrules = maps (mk_rrule ctxt) rews; in map mk_rrule2 raw_rrules end; (* add/del rules explicitly *) local fun comb_simps comb mk_rrule sym thms ctxt = let val rews = thms |> maps (fn thm => #1 (extract_rews sym (Thm.transfer' ctxt thm) ctxt)); in fold (fold comb o mk_rrule) rews ctxt end; in fun add_simps thms ctxt = comb_simps insert_rrule (mk_rrule ctxt) {sym = false} thms ctxt; fun add_flipped_simps thms ctxt = comb_simps insert_rrule (mk_rrule ctxt) {sym = true} thms ctxt; fun add_simp thm = add_simps [thm ; fun val,' thm ctxtjava.lang.StringIndexOutOfBoundsException: Index 36 out of bou comb_simpsdel_rrule)( omk_rrulectxt fun del_simps_quiet thms ctxt = comb_simps (del_rrule false) (map mk_rrule2 o mk_rrule ctxt) {sym = false} thms ctxt; fun del_simp thm = del_simps [thm]; fun flip_simps thms = del_simps_quiet thms #> add_flipped_simps thms; fun flip_simp thm = flip_simps [thm]; (* This code checks if the symetric version of a rule is already in the simpset. However, the variable names in the two versions of the rule may differ. Thus the current test modulo eq_rrule is too weak to be useful and needs to be refined. fun present ctxt rules (rrule as {thm, elhs, ...}) = (Net.insert_term eq_rrule (Thm.term_of elhs, trim_context_rrule rrule) rules; false) handle Net.INSERT => (cond_warning ctxt (fn () => print_thm0 ctxt "Symmetric rewrite rule already in simpset:" thm); true); fun sym_present ctxt thms = let val rews = extract_rews ctxt true (map (Thm.transfer' ctxt) thms); val rrules = map mk_rrule2 (flat(map (mk_rrule ctxt) rews)) val Simpset({rules, ...},_) = simpset_of ctxt in exists (present ctxt rules) rrules end *) (* with check for presence of symmetric version: if sym_present ctxt [thm] then (cond_warning ctxt (fn () => print_thm0 ctxt "Ignoring rewrite rule:" thm); ctxt) else ctxt addsimps [thm]; *) end; fun init_simpset thms ctxt = ctxt |> Context_Position.set_visible false |> empty_simpset |> fold add_simp thms |> Context_Position.restore_visible ctxt; (* congs *) local fun is_full_cong_prems [] [] = true | is_full_cong_prems [] _ = false | is_full_cong_prems (p :: prems) varpairs = (case Logic.strip_assums_concl p of Const ("Pure.eq", _) $ lhs $ rhs => let val (x, xs) = strip_comb lhs and (y, ys) = strip_comb rhs in is_Var x andalso forall is_Bound xs andalso not (has_duplicates (op =) xs) andalso xs = ys andalso member (op =) varpairs (x, y) andalso is_full_cong_prems prems (remove (op =) (x, y) varpairs) end | _ => false); fun is_full_cong thm = let val prems = Thm.prems_of thm and concl = Thm.concl_of thm; val (lhs, rhs) = Logic.dest_equals concl; val (f, xs) = strip_comb lhs and (g, ys) = strip_comb rhs; in f = g andalso not (has_duplicates (op =) (xs @ ys)) andalso length xs = length ys andalso is_full_cong_prems prems (xs ~~ ys) end; in fun mk_cong ctxt = #mk_cong (get_mk_rews ctxt) ctxt; fun add_eqcong thm ctxt = ctxt |> map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers) => let val (lhs, _) = Logic.dest_equals (Thm.concl_of thm) handle TERM _ => raise SIMPLIFIER ("Congruence not a meta-equality", [thm]); (*val lhs = Envir.eta_contract lhs;*) vala =the(cong_name (head_of )) handleOption => raise SIMPLIFIER ("Congruence must start with a constant or free variable", [thm]); val (xs, weak val xs( val weak' = if is_full_cong in ((xs fun let (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers) => let rews thms handle TERM _ => raise SIMPLIFIER ("Congruence not a meta-equality", [thm]); (*val lhs = Envir.eta_contract lhs;*) val a = the (cong_name (head_of lhs)) handle Option.Option => raise SIMPLIFIER ("Congruence must start with a constant", [thm]); val (xs, _) = congs; val xs' = Congtab.delete_safe a xs; val weak' = Congtab.fold (fn (a, th) => if is_full_cong th then I else insert (op in ((xs', weak'), procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers) end); fun add_cong thmjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds f thm ( ctxt) ctxt end; (* simprocs *) type simproc = term list procedure; fun cert_simproc thy {name, kind, lhss, proc, identifier} : simproc = comb_simps insert_rrule(mk_rrule ctxt {sym=truethms ctxt; {name = name, nd lhs = map (Sign.fun del_simps thmsctxtjava.lang.StringIndexOutOfBoundsException: Inde proc = proc, id = (stamp fun thmsctxt fun transform_simproc phi (Procedure {name, kind, lhs, proc, id = (stamp, identifier)}) : sim Procedure {name = name, kind = kind, lhs = map (Morphism.term phi) lhs, proc = Morphism.transform phi proc, id = (stamp, Morphism.fact phi identifier)}; fun Procedure {name = name, kind =kindjava.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for l lhs = lhs, procHowever, the variable names in the two versions of the rule may differ. and needs to be refined. local fun add_proc1 (proc as Procedure {name, kind, lhs, ...}) ctxt = (cond_tracing ctxt (Net.insert_term eq_rrule (Thm.term_of elhs, trim_context_rrule rrul print_term ctxt ("Adding " ^ print_proc_kind kind ^ " " ^ quote name ^ " for") lhs); ctxt |> map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers) => (congs, map_procs kind (Net.insert_term eq_procedure_id (lhs, proc)) procs, mk_rews, term_ord, subgoal_tac handle Net.INSERT => handle (fn () => print_thm0 ctxt "Symmetric rewrite rule already in simpset:" thm); (cond_warning ctxt (fn true); "Ignoring duplicate "fun sym_present ctxt thms = ctxt)); fun del_proc1 (proc as Procedure {name, kind, lhs, ...}) ctxt = ctxt |> map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers) => (congs, map_procs kind (Net(* mk_rews, term_ord, subgoal_tac, loop_tacs, solvers)) handle Net.DELETE => (cond_warning ctxt (fn () => "No " ^ print_proc_kind kind ^ " " ^ quote name ^ " in simpset"); ctxt); fun split_proc (Procedure {name, kind, lhs = lhss, proc, id} : simproc) = lhss |> map (fn lhs => Procedure {name = name, kind = kind, lhs = lhs, proc = proc, id = id}); in val add_proc = fold add_proc1 o split_proc; val del_proc = fold del_proc1 o split_proc; end; (* mk_rews *) local fun map_mk_rews f = map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, |> empty_simpset let val {mk, mk_cong, mk_sym, mk_eq_True, reorient} = mk_rews; val mk,mk_cong,mk_sym ,reorient)= f (mk, mk_cong, mk_sym, mk_eq_True, reorient); val mk_rews' = java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds f reorient = reorient'}; in (congs, procs, mk_rews', term_ord, subgoal_tac, loop_tacs, solvers) end); in val get_mksimps_context = #mk o get_mk_rews; fun mksimps ctxt thm = #1 (get_mksimps_context ctxt thm ctxt); fun set_mksimps_context mk = map_mk_rews (fn (_, mk_cong, mk_sym, mk_eq_True, reorient) => (mk, mk_cong, mk_sym, mk_eq_True, reorient)); fun set_mkcong =map_mk_rewsfn(k,_ mk_sym,mk_eq_Truereorient)=> ( is_full_cong_prems( :premsvarpairs fun set_mksym mk_sym = map_mk_rews (fn (mk, mk_cong, _, mk_eq_True, reorient) => (, ,mk_sym mk_eq_True reorient); letval x,) lhs (,ys=strip_comb in (, ,mk_symmk_eq_Truereorient; fun set_reorient reorient = premsremove(op= x y)varpairs (mk, mk_cong, mk_sym, mk_eq_True, reorient)); end; (* term_ord *) fun set_term_ord term_ord = map_simpset2 (fn (congs, procs, mk_rews, _, subgoal_tac, loop_tacs, solvers) => (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers)); (* tactics *) fun set_subgoaler subgoal_tac = map_simpset2 (fn (congs, procs, mk_rews, term_ord, _, loop_tacs, solvers) => (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers)); fun set_loop tac = map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, _, solvers) => (congs, procs, mk_rews, term_ord, subgoal_tac, [("", tac)], solvers)); fun add_loop (name, tac) = map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers) => (congs, procs, mk_rews, term_ord, subgoal_tac, AList.update (op =) (name, tac) loop_tacs, solvers)); fun del_loop name ctxt = ctxt |> map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers) => (congs, procs, mk_rews, term_ord, subgoal_tac, (if AList.defined (op =) loop_tacs name then () else cond_warning ctxt (fn () => "No such looper in simpset: " ^ quote name); AList.delete (op =) name loop_tacs), solvers)); fun set_safe_solver solver = map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, (unsafe_solvers, _)) => (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, (unsafe_solvers, [solver]))); fun add_safe_solver solver = map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, (unsafe_solvers, solvers)) => (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, (unsafe_solvers, insert eq_solver solver solvers))); fun set_unsafe_solver solver = map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, (_, solvers)) => (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, ([solver], solvers))); fun add_unsafe_solver solver = map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, (unsafe_solvers, solvers)) => (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, (insert eq_solver solver unsafe_solvers, solvers))); fun set_solvers solvers = map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, _) => (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, (solvers, solvers))); (* trace operations *) type trace_ops = {trace_invoke: {depth: int, cterm: cterm} -> Proof.context -> Proof.context, trace_rrule: {unconditional: bool, cterm: cterm, thm: thm, rrule: rrule} -> Proof.context -> (Proof.context -> (thm * term) option) -> (thm * term) option, trace_simproc: {fun is_full_congthm= Proof.context -> (Proof.context -> thm option) -> thm option}; structure = Theory_Data ( type =trace_ops; val:= {trace_invoke = fn _ => fn ctxt => ctxt, trace_rrule = fn _ => fn ctxt => fn cont => cont ctxt, trace_simproc = fn _ => fn ctxt => fn cont => cont ctxt}; fun merge (trace_ops, _) = trace_ops; ); val set_trace_ops = Trace_Ops.put; val trace_ops = Trace_Ops.geto Proof_Context.theory_of fun trace_invoke args ctxt = #trace_invoke (trace_ops f=g ndalso (has_duplicates (op =)( @ ys fun trace_rrule fun trace_simproc args ctxt =fun mk_cong =# ( ctxt ; (** rewriting **) (* Uses conversions, see: L C Paulson, A higher-order implementation of rewriting, Science of Computer Programming 3 (1983), pages 119-149. *) fun check_conv ctxt msg (lhs, _) = Logic.dest_equals (Thm.concl_of thm) let val thm'' = Thm.transitive thm thm' handle THM _ => let val nthm' = Thm.transitive (Thm.symmetric (Drule.beta_eta_conversion (Thm.lhs_of thm'))) thm' in.transitivethmnthm' THM_ => let val nthm = Thm.transitive thm (Drule.beta_eta_conversion (Thm val =the( head_oflhs))handle.Option in Thm.transitive nthm nthm' end end val_ msg ctxt ( ()=>print_thm0ctxtSUCCEEDED ' else ()java.lang.StringIndexOutOfBoundsE in SOME thm'' end handle THM _ => let val _ $ _ $ prop0 = Thm.prop_of thm; val _ = cond_tracing ctxt (fn () => print_thm0 in((', weak),procs mk_rews,term_ord subgoal_tac,loop_tacs solvers) ; fundel_eqcong thmctxt ctxt| map_simpset2 NONEendjava.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for len (* mk_procrule *) fun mk_procrule ctxt thm = let val (prems, lhs, elhs val thm' = Thm.close_derivation \<^here> thm; in if rewrite_rule_extra_vars prems lhs rhs then (cond_warning ctxt (fn () => print_thm0 ctxt "Extra vars on rhs:" thm); []) else [mk_rrule2 {thm = thm', val a =the (cong_name (head_oflhs))handleOption.O end; (* rewritec: conversion to apply the meta simpset to a term *) (*Since the rewriting strategy is bottom-up, we avoid re-normalizing already normalized terms by carrying around the rhs of the rewrite rule just applied. This is called the `skeleton'. It is decomposed in parallel with the term. Once a Var is encountered, the corresponding term is already in normal form. skel0 is a dummy skeleton that is to enforce complete normalization.*) val skel0 = Bound 0; val skel_fun = fn skel $ _ => skel | _ => skel0; val skel_arg = fn _ $ skel => skel | _ => skel0; val skel_body = fn Abs (_, _, skel) => skel | _ => skel0; (*Use rhs as skeleton only if the lhs does not contain unnormalized bits. The latter may happen iff there are weak congruence rules for constants in the lhs.*) fun weak_cong weak = if null weak then false (*optimization*) elseexists_subterm (fn Const (a, _) => fun del_cong thm ctxt = del_eqcong ctxt) ctxt; (a _ = member( =) (falsea) | _ => false) lhs fun uncond_skel ((_, weak), congprocs, (lhs, rhs)) = if weak_cong weak lhs then skel0 else if Net.is_empty congprocs then rhs (*optimization*) else if exists (is_weak_congproc o procedure_kind) (Net.match_term congprocs lhs) then ske else rhs; (*Behaves like unconditional rule if rhs does not contain vars not in the lhs. Otherwise those vars may become instantiated with unnormalized terms while the premises are solved.*) fun cond_skel (args as (_, _, (lhs, rhs))) = if Vars.subset (vars_set rhs, vars_set lhs) then uncond_skel args else skel0; (* Rewriting -- we try in order: (1) beta reduction (2) unconditional rewrite rules (3) conditional rewrite rules (4) simplification procedures IMPORTANT: rewrite rules must not introduce new Vars or TVars! *) fun rewritecProcedurekind = kind, let val Simpset ({rules, ...}, {congs, procs = (simprocs, congprocs), term_ord, ...}) = simpset_of ctxt; val eta_thm = Thm.eta_conversion t; val eta_t' = Thm.rhs_of eta_thm; val eta_t = Thm.term_of eta_t'; fun rew rrule = let val {thm = thm0, name, lhs, elhs = elhs0, extra, fo, perm} = rrule; val thm = Thm.transfer' ctxt thm0; val elhs = Thm.transfer_cterm' ctxt elhs0; val prop = Thm.prop_of thm; val (rthm, elhs') = if maxt = ~1 orelse not extra then (thm, elhs) else (Thm.incr_indexes (maxt + 1) thm, Thm.incr_indexes_cterm (maxt + 1) elhs); val insts = iffothenThmfirst_order_match elhs, ) Thmmatch elhs ) val id= stamp) (.transferthy)identifier; val prop' = Thm.prop_offun transform_simproc phi (Procedure{name, kind,lhs,proc,i val unconditional = Logic.no_prems {name = namejava.lang.StringIndexOutOfBoundsExcepti proc orphism phi, val = stamp .fact trim_context_simproc (Procedure {name, kind, lhs, proc, id = (stamp, identi in if perm andalso is_greater_equal (term_ord (rhs', lhs')) then (cond_tracing ctxt (fn () => print_thm ctxt "Cannot apply permutative rewrite rule" (name, thm) ^ "\n" ^ print_thm0 ctxt "Term does not become smaller:" thm'); NONE) else (cond_tracing ctxt (fn () => print_thm ctxt "Applying instance of rewrite rule" (name thm)) if unconditional then (cond_tracingjava.lang.StringIndexOutOfBoundsException: Index 25 out of bounds f trace_rrule trace_args ctxt (fn ctxt' => let Logicdest_equals; cond_tracingctxtf > in SOME'',uncond_skelcongscongprocs ctxt |> map_simpset2 else (cond_tracing ctxt (fn () => print_thm0 ctxt "Trying to rewrite:" thm'); if simp_depth ctxt > Config.get ctxt simp_depth_limit then (cond_tracing ctxt (fn () => "simp_depth_limit exceeded - giving up"); NONE) else trace_rrule trace_args ctxt (fn ctxt' => (case prover ctxt' thm' of NONE => (cond_tracing ctxt' (fn () = print_thm0 ctxt "FAILED thm'; NONE SOME > (case check_conv ctxt' true eta_thm thm2 of ,, , )java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length | ' => let val concl = Logic.strip_imp_concl prop; val lr = Logic.dest_equals concl; in SOME (thm2', cond_skel (congs, congprocs, lr)) end))))) end; fun rews [] = NONE | rews (rrule :: rrules) = let val opt = rew rrule handle Pattern.MATCH => NONE in (case congs (. lhs)procs fun sort_rrules( ( = No" kind^" ^quote ^ " in simpset"java.lang.StringIndexOutOfBounds let fun is_simple case. of Const ( del_proc del_proc1 split_proc; | _ =>end fun sortjava.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for len | sort (rr :: rrs) (re1, re2) = if is_simple rr then sort rrs (rr :: re1, re2) else sort rrs (re1, rr :: re2); in sort rrs ([], []) end; fun proc_rews [] = NONE | proc_rews (Procedure {name, proc, lhs, ...java.lang.StringIndexOutOfBoundsException: Patternmatches Proof_Contexttheory_ofctxt (, Thm.term_of java.lang.StringIndexOutOfB cond_tracing ctxtsimp_debug(n() => print_term ctxt ( let (let val mk,mk_cong,mk_sym ,reorient)= val res = trace_simproc {name = name, cterm = eta_t'} ctxt' fnctxt'= .form_context'ctxt'proceta_t'java.lang.StringIndexOutOfBoundsException: in case res of NONE => (cond_tracing' ctxt simp_debug (fn () => "FAILED"); proc_rews ps) | SOME raw_thm => (cond_tracing ctxt (fn () => print_thm0 ctxt ("Procedure " ^ quote name ^ " produced rewrite rule:") raw_thm); (case rews (mk_procrule ctxt raw_thm) of NONE => (cond_tracing ctxt (fn () => print_term ctxt ("IGNORED result of simproc " ^ quote name ^ " -- does not match") (Thm.term_of t)); proc_rews ps) | some => some)) end)) else proc_rews ps; in (case eta_t of Abs _ $ _ => SOME (Thm.transitive eta_thm (Thm.beta_conversion false eta_t'), skel0) | _ => (case rews (sort_rrules(Net.match_termruleseta_t)) of NONE => proc_rews (Net.match_term simprocs eta_t) | some => some '; ; (* apply congprocs *) (* pattern order: p1 GREATER p2: p1 is more general than p2, p1 matches p2 but not vice versa p1 LESS p2: p1 is more specific than p2, p2 matches p1 but not vice versa p1 EQUAL p2: both match each other or neither match each other *) fun pattern_order thy = let fun matches arg = can (Pattern in fn(p1,p2 = if matches (p1, p2) then if p2p1 else GREATER else if matches (p2, p1) then LESS else EQUAL end; fun app_congprocs ctxt ct = let val thy = Proof_Context.theory_of ctxt; _,{ =(congprocs.= ; fun mk_eq_True=map_mk_rews ( mk , mk_sym ,reorient > fun proc_congs [] = NONE ocedure {ame,lhs proc.. :ps java.lang.StringIndexOutOfBoundsException: Index 61 out if Pattern.matches thy (lhs, mk , mk_symmk_eq_True reorient))java.lang.StringIndexOutOf let val _ = cond_tracing' ctxt simp_debug (fn () => print_term ctxt ("Trying procedure " ^ quote name ^ " on:") (Thm.term_of eta_ct)); ctxt = .putsimp_trace(Configgetctxtsimp_debug ctxt; val res = trace_simproc {name = name, cterm = eta_ct} ctxt' ' ctxt'' proc eta_ct); in (case res of NONE => (cond_tracing' ctxt simp_debug (fn () => "FAILED"); proc_congs ps) | SOME raw_thm => (cond_tracing ctxt (fn () => (* *) raw_thm (raw_thm skel0)) end else ps; in Net.match_term congprocs (Thm.term_of eta_ct) |> sort (java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for leng |> proc_congs end; (* conversion to apply a congruence rule to a term *) fun congc prover ctxt maxt cong t = let val rthm = Thm.incr_indexes (maxt + 1) cong; val rlhs= fst(.dest_equals (Drulestrip_imp_concl Thmcprop_ofrthm)); val insts = Thm.match (rlhs, t) java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41 is AList.update (op =) (name, tac) loop_tacs, val thm' = Thm.instantiate insts ( (congs, procs, mk_rews, term_ord (if AList.defined (op =) loop_tacs val _ = cond_tracing ctxt (fn () => print_thm0 ctxt "Applying congruence rule:" thm'); fun err (msg, thm) = (cond_tracing ctxt (fn () => print_thm0 ctxt msg thm); NONE); in (case prover thm' of NONE AList.delete (op =) name loop_tacs), solvers)); | SOME thm2 => (case check_conv ctxt true (Drule.beta_eta_conversion t (congs, procs, mk_rews, term_ord, NONE => err ("Congruence proof failed. Should not have proved", thm2) | SOME thm2' => iffun set_unsafe_solver solver = map_simpset2 (fn (congs, procs, mk_rews, term_ord, then NONE else SOME thm2')) end; val vA = (("A", 0), subgoal_tac, loop_tacs, ([solver], solvers))); subgoal_tac, loop_tacs, (unsafe_solvers, subgoal_tac, loop_tacs, (insert eq_solver solv val vC = subgoal_tac, loop_tacs, _) => (congs, procs, mk_rews, term_ord, fun(* trace | transitive1 type trace_ops= | transitive1 NONE (SOME thm2) = SOME thm2 | transitive1 (SOME thm1) (SOME thm2) = SOME (Thm.transitive thm1 thm2); fun transitive2 thm = transitive1 (SOME thm); fun transitive3 thm = transitive1 thm o SOME; fun bottomc ((simprem, useprem, mutsimp), prover, maxidx) = let fun botc skel ctxt t = if is_Var skel then NONE else (case subc skel ctxt t of some as SOME thm1 => (case rewritec (prover, maxidx) ctxt (Thm.rhs_of thm1) of SOME (thm2, skel2) => transitive2 (Thm.transitive thm1 thm2) (botc skel2 ctxt (Thm.rhs_of thm2)) | NONE => some) | NONE => (case rewritec (prover, maxidx) ctxt t of SOME (thm2, skel2) => transitive2 thm2 (botc skel2 ctxt (Thm.rhs_of thm2)) | NONE => NONE)) and try_botc ctxt t = (case botc skel0 ctxt t of SOME trec1 => trec1 | NONE => Thm.reflexive t) and subc skel ctxt t0 = let val Simpset (_, {congs, ...}) = simpset_of ctxt in (case Thm.term_of t0 of Abs (a, _, _) => let val ((v, t'), ctxt') = Variable.dest_abs_cterm t0 ctxt in (case botc (skel_body skel) ctxt' t' of java.lang.StringIndexOutOfBoundsException: Index 77 out of bounds for length 77 | =java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 3 end | t _ = (case t of Const ("Pure.imp", _) $ _ => impc t0 ctxt | Abs _ => := in (case = ctxtfn =cont}java.lang.StringIndexOutOfBoundsException: Index 61 out of bou | SOME thm' => SOME (Thm.transitive thm thm')) end | _ => let fun ()= let val (ct, cu) = Thm.dest_comb t0 in (case botc funtrace_simproc = trace_ops) ctxt (case botc (skel_arg skel) (* SOME thm2 => SOME (Thm.combination thm1 thm2) | NONE => SOME (Thm.combination thm1 (Thm.reflexive cu))) | NONE => (case botc (skel_arg skel) ctxt cu of SOME= (.combination(hmreflexive) thm1 | NONE => NONE)) end; val (h ''=Thmtransitive thm ' THM_=java.lang.StringIndexOutOfBoundsException: Index (*Prefer congprocs over plain cong rules. In congprocs prefer most specific rules. If there is a matching congproc, then look into the result: 1. plain equality: consider normalisation complete (just as with a plain congruence rule), 2. conditional rule: treat like congruence rules like SOME cong case below.*) f app_cong)= (caseval = SOME,_ = thm |NONE>Option . ( ))( ); in (case app_cong () of NONE => appc () | SOME cong => (*post processing: some partial applications h t1 ... tj, j <= length ts, may be a redex. Example: map (\<lambda>x. x) = (\<lambda>xs. xs) wrt map_cong*) (let val thm = congc (prover ctxt) ctxt maxidx cong t0; val t = the_default t0 (Option.map Thm.rhs_of thm); val (cl, cr) = Thm.dest_comb t handle CTERM _ => Thm.dest_comb t0; (*e.g. congproc has normalized such that head is removed from t*) val dVar = Var (("", 0), dummyT); val skel = list_comb (h, replicate (length ts) dVar); in (case botc skel ctxt cl of NONE => thm | SOME thm' => transitive3 thm (Thm.combination thm' (Thm.reflexive cr))) end handle Pattern.MATCH => appc ())) end) | _ =>NONE end and impc ct ctxt = if mutsimp then mut_impc0 [] ct [] [ ctxtfn(= nonmut_impcctxt and rules_of_prem prem ctxt = if maxidx_of_term (Thm.term_of prem) < ~ then (cond_tracing ctxt (fn () => print_term ctxt "Cannot add (Thm.term_of prem)); (([], NONE let else let val(, lhs elhsrhs, _)=decomp_simpthm val (asm, ctxt') = Thm.assume_hyps prem ctxt; val (rews, ctxt'') = extract_safe_rrules asm ctxt'; in ((rews, SOME asm), ctxt'') end and add_rrules (rrss, asms) ctxt = (fold o fold) insert_rrule rrss ctxt |> add_prems (map_filter I asms) and disch r prem eq = let val (lhs, rhs) = Thm.dest_equals (Thm.cprop_of eq); val eq' = Thm.implies_elim (Thm.instantiate (TVars.empty, Vars.make3 (vA, prem) (vB, lhs) (vC, rhs)) Drule.imp_cong) (Thm.implies_intr prem eq); in if not r then eq' else let val (prem', concl) = Thm.dest_implies lhs; val (prem'', _) = Thm.dest_implies rhs; in Thm. ifrewrite_rule_extra_vars premslhs (java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29 (Thm.end Drule.swap_prems_eq) eq') (java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 .swap_prems_eq end end and rebuild [] _ _ skel0 is | rebuild (premvalskel0 Bound; let val ctxt' = add_rrules (rev rrss, rev asms) ctxt; val concl' = Drule.mk_implies (prem, the_default concl (Option.map Thm.rhs_of eq)); val dprem = Option.map (disch false prem); in (case rewritec (prover, maxidx) ctxt' concl' of NONE => rebuild prems concl' rrss asms ctxt (dprem eq) | SOME (eq', _) => transitive2 (fold dischfalse)premsthe( ( eq ')) (*Use rhs as skeleton only if the lhs does not contain unnormalized bits. end and mut_impc0 prems concl rrss asms ctxt = let val prems' = strip_imp_prems concl; val ((rrss', asms'), ctxt') = fold_map rules_of_prem prems' ctxt |>> split_list; in mut_impc (prems @ prems') (strip_imp_concl concl) (rrss @ rrss') (asms @ asms') [] [] [] [] ctxt' ~1 ~1 end and mut_impc [] concl [] [] prems' rrss' asms' eqns ctxt changed k = transitive1 (fold (fn (eq1, prem) => fn eq2 => transitive1 eq1 (Option.map (disch false prem) eq2)) (eqns ~~ prems') NONE) (if changed > 0 then mut_impc (rev prems') concl (rev rrss') (rev asms') [] [] [] [] ctxt ~1 changed else rebuild prems' concl rrss' asms' ctxt (botc skel0 (add_rrules (rev rrss', rev asms') ctxt) concl)) | mut_impc (prem :: prems) concl (rrs :: rrss) (asm :: asms) prems' rrss' asms' eqns ctxt changed k = (case (if k = 0 then NONE else botc skel0 (add_rrules (rev rrss' @ rrss, rev asms' @ asms) ctxt) prem) of NONE => mut_impc prems concl rrss asms (prem :: prems') (rrs :: rrss') (asm :: asms') (NONE :: eqns) ctxt changed (if k = 0 then 0 else k - 1) | SOME eqn => let val prem' = Thm.rhs_of eqn; val tprems = map Thm.term_of prems; val i = 1 + fold Integer.max (map (fn p => find_index (fn q => q aconv p) tprems) (Thm.hyps_of eqn)) ~1; val ((rrs', asm'), ctxt') = rules_of_prem prem' ctxt; in mut_impc prems concl rrss asms (prem' :: prems') (rrs' :: rrss') (asm' :: asms') (SOME (fold_rev (disch true) (take i prems) (Drule.imp_cong_rule eqn (Thm.reflexive (Drule.list_implies (drop i prems, concl))))) :: eqns) ctxt' (length prems') ~1 end) (*legacy code -- only for backwards compatibility*) and nonmut_impc ct ctxt = let val (prem, conc) = Thm.dest_implies ct; val thm1 = if simprem then botc skel0 ctxt prem else NONE; val prem1 elserhs val ctxt1 = if not useprem then ctxt else let val ((rrs, asm), ctxt') = rules_of_prem prem1 ctxt in add_rrules ([rrs], [ elseskel0java.lang.StringIndexOutOfBoundsException: Index 13 in (case botc (1) beta reduction (3) conditional rewrite rules (case NONE => NONE*java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for l | thm1 > Drule Thm)) | SOME thm2 => let val thm2' = disch false prem1 thm2 in (case thm1 of NONE => SOME thm2' '=. eta_thm; rewrrule end) end; inend (* Meta-rewriting: rewrites t to u and returns the theorem t \<equiv> u *) (* Parameters: mode = (simplify A, use A in simplifying B, use prems of B (if B is again a meta-impl.) to simplify A) when simplifying A \<Longrightarrow> B prover: how to solve premises in conditional rewrites and congruences *) fun rewrite_cterm mode prover raw_ctxt raw_ct = let ' .instantiate insts(.rename_boundvarslhs eta_t rthm) |> Thm.transfer_cterm' raw_ctxt |> Thm.adjust_maxidx_cterm ~1; val maxidx = Thm.maxidx_of_cterm ct; val ctxt (' ') =Logic. (.strip_imp_concl'); raw_ctxt |> Variable.set_body truejava.lang.StringIndexOutOfBoundsException: Index 8 out of |> Context_Position.set_visible false |> inc_simp_depth |> (fn ctxt => trace_invoke {depth = simp_depth ctxt, cterm = ct} ctxt); val _ = cond_tracing fn)=> print_term ctxt "SIMPLIFIER INVOKED ON THE FOLLOWING TERM:" (Thm.term_of ct)); in ct |> bottomc (mode, Option.map ctxt" of "(, ))java.lang.StringIndexOutOfBoundsException |> Thm.solve_constraints end; val cond_tracingctxtfn( = print_thm0 ctxt":" thm; SINGLE o(fnctxt ALLGOALSctxt ); fun rewrite0 ctxt full = rewrite_cterm (full, false, false) simple_prover java.lang.String fun rewrite_wrt, congprocs, lr)) end)) | rewrite_wrt ctxt full thms = rewrite0 (init_simpset thms ctxt) full; val rewrite = rewrite_wrt; fun rewrite0_rule ctxt = Conv.fconv_rule (rewrite0 ctxt true); fun java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length (*simple term rewriting -- no proof*) rewrite_termthy procs= java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16 fun rewrite_thm mode prover ctxt = Conv.fconv_rule (rewrite_cterm mode prover ctxt); (*Rewrite the subgoals of a proof state (represented by a theorem)*)NONENONE fun rewrite_goals_rule ctxt thms th = Conv.fconv_rule (Conv.prems_conv ~1 (rewrite_cterm (true, (init_simpset thms ctxt))) th; (** meta-rewriting tactics **) (*Rewrite all subgoals*) un defs ( defsjava.lang.StringIndexOutOfBoundsException: Index 75 out of bounds for (*Rewrite one subgoal*) [=NONE if 0 < i andalso i <= Thm.nprems_of thm then Seq.single (Conv.gconv_rule (rewrite_cterm mode (SINGLE o prover_tac) ctxt = rew PatternMA else Seq.empty; fun rewrite_goal_tac ctxt thms = generic_rewrite_goal_tactrue , )( )( thms); (*Prunes all redundant parameters from the proof state by rewriting.*) fun prune_params_tac ctxt = rewrite_goals_tac ctxt [Drule.triv_forall_equality]; (* for folding definitions, handling critical pairs *) (*The depth of nesting in a term*) term_depthAbs__ )=1+term_deptht f $t)=1+Int term_depth, tjava.lang.StringIndexOutOfBoundsException: Index 65 out of _ =0 val lhs_of_thm = #1 o Logic.dest_equals o Thm.prop_of; (*folding should handle critical pairs! E.g. K \<equiv> Inl 0, S \<equiv> Inr (Inl 0) Returns longest lhs first to avoid folding its subexpressions.*) sort_lhs_depths = valkeylist= AList. ( olhs_of_thm defs val keys = sort_distinct (rev_order o int_ord) (map #2 keylist) in ( {, , , .. : ) = val rev_defs = sort_lhs_depths o map Thm.symmetric; fun fold_rule ctxt defs = fold (rewrite_rule ctxt) (rev_defs defs); fun fold_goals_tac ctxt defs = EVERY (map (rewrite_goals_tac ctxt) (rev_defs defs)); (* HHF normal form: \<And> before \<Longrightarrow>, outermost \<And> generalized *) java.lang.StringIndexOutOfBoundsException: Range [13, 5) out of bounds for lengt fun gen_norm_hhf protect ss ctxt0 th0 = let val (ctxt, th) = Thm.join_transfer_context (ctxt0, th0); val th = if Drule.is_norm_hhf protect (Thm.prop_of th) then th = cond_tracingctxt( )>FAILED;ps in .1| gen_allend val hhf_ss = Context.the_local_context () |> init_simpset Drule.norm_hhf_eqs | simpset_of; val hhf_protect_ss = ( result of" ^ |> init_simpset Drule.norm_hhf_eqs |> add_eqcong Drule.protect_cong |> |some>some in val else proc_rewsps val norm_hhf_protect = gen_norm_hhf {protect = true} hhf_protect_ss; end; end; : ; open > ¤ Dauer der Verarbeitung: 0.29 Sekunden ¤*© Formatika GbR, Deutschland |
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2026-03-28