| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/Isabelle/HOL/ (Beweissystem Isabelle Version 2025-1©) Datei vom 16.11.2025 mit Größe 24 kB |
|
Quelle raw_simplifier.ML Sprache: SML |
|||||||||
|
AuthorNipkow , Higher-order Simplification. *) signature BASIC_RAW_SIMPLIFIER = sig val simp_depth_limitjava.lang.StringIndexOutOfBoundsException: Index 3 out of bou val val add_simps: val add_simp: thm list -> Proof val del_simp: thm -> Proof.context val flip_si val simp_debug: bool Config. val subgoal_tac: Proof val set_subgoaler: (Proof.context -> int val simp_traceall its Vars? Better: a dynamic check each *) cong_name bool *string type rrule val mk_rrules: Proof.context -> thm -> rrule list val eq_rrule: rrule * rrule->bool type valelhss elhs:prems typesolver 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 simpset_map .context - (Proof.context -> Proof.) - simpset->simpset valmap_theory_simpset:(.context->Proofcontext - theory>theory val empty_simpset: Proof.context -> Proof.context val clear_simpset: Proof.context -> Proof.context fn > (.defined v >falseorelse :Proofcontext>thm - ->thm val rewrite_goals_tac: Proof.context -> thm list -> tactic valrewrite_goal_tac . - thm list ->tactic val prune_params_tac: Proof.context -> tactic val fold_rulejava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for fold_goals_tac Proof - hmlist - tactic val java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5 =Pattern notPattern t; end signature RAW_SIMPLIFIER = sig include BASIC_RAW_SIMPLIFIER exception SIMPLIFIER of string * thm, , =elhs , }end val dest_simps:fundefault_reorientctxt lhs = dest_congs simpset - cong_name ) list val dest_ss: simpset -> {simps: (Thm_Name.T * thm) list, simprocs: (string * term list) list, congprocs ( * {lhss: term, procproc.entity , congs: (cong_name * thm) list, weak_congscong_namelist java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10 unsafe_solvers is_Free rhs andalso not(is_Free lhs) andalso not andalso not(exists_subter safe_solvers list val init_simpset: thm list orelse type trace_ops val set_trace_ops: trace_ops -> theory -> theory nullprems Pattern.matches(Proof_Context ct val map_ss: (Proof *hecondition" " necessarybecauseconditionalrewrites valmksimps Proof - - thm val get_mksimps_context: Proof.context -> (thm -> the rhs is an instance of the lhs; example: ?m\> : ( - Proof.ontext- list .context- Proof.context -> Proof.context val add_simps: java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds fo valadd_simp - .context- .context val del_simps: thm list ->java.lang.StringIndexOutOfBoundsException: Index 0 out of b val del_simp: thm -> Proof.context -> Proof.context flip_simps list- .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 prems elhs erhs = let val elhss = elhs :: prems; val tvars = TVars.build (fold TVars.add_tvars elhss); val vars = Vars.build (fold Vars.add_vars elhss); in erhs |> Term.exists_type (Term.exists_subtype (fn TVar v => not (TVars.defined tvars v) | _ => false)) orelse erhs |> Term.exists_subterm (fn Var v => not (Vars.defined vars v) | _ => false) end; fun rrule_extra_vars elhs thm = rewrite_rule_extra_vars [] (Thm.term_of elhs) (Thm.full_prop_of thm); fun mk_rrule2 {thm, name, lhs, elhs, perm} = let val t = Thm.term_of elhs; val fo = Pattern.first_order t orelse not (Pattern.pattern t); val extra = rrule_extra_vars elhs thm; in {thm = thm, name = name, lhs = lhs, elhs = elhs, extra = extra, fo = fo, perm = perm} end; (*simple test for looping rewrite rules and stupid orientations*) fun default_reorient ctxt prems lhs rhs = rewrite_rule_extra_vars prems lhs rhs orelse is_Var (head_of lhs) 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 => Logic.occs (lhs, t)) (rhs :: prems) orelse null prems andalso Pattern.matches (Proof_Context.theory_of ctxt) (lhs, rhs) (*the condition "null prems" is necessary because conditional rewrites with extra variables in the conditions may terminate although the rhs is an instance of the lhs; example: ?m < ?n \<Longrightarrow> f ?n \<equiv> f ?m *) orelse is_Const lhs andalso not (is_Const rhs); (* simplification procedures *) datatype proc_kind = Simproc | Congproc of bool; val is_congproc = fn Congproc _ => true | _ => false; val is_weak_congproc = fn Congproc weak => weak | _ => false; fun map_procs kind f (simprocs, congprocs) = if is_congproc kind then (simprocs, f congprocs) else (f simprocs, congprocs); fun print_proc_kind Simproc = "simplification procedure" | print_proc_kind (Congproc false) = "simplification procedure (cong)" | print_proc_kind (Congproc true) = "simplification procedure (weak cong)"; type proc = Proof.context -> cterm -> thm option; datatype 'lhs procedure = Procedure of {name: string, kind: proc_kind, lhs: 'lhs, proc: proc Morphism.entity, id: stamp * thm list}; fun procedure_kind (Procedure {kind, ...}) = kind; fun procedure_lhs (Procedure {lhs, ...}) = lhs; fun eq_procedure_id (Procedure {id = (s1, ths1), ...}, Procedure {id = (s2, ths2), ...}) = s1 = s2 andalso eq_list Thm.eq_thm_prop (ths1, ths2); (* 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 -> Proof.context -> thm list * Proof.context, mk_cong: Proof.context -> thm -> thm, mk_sym: Proof.context -> thm -> thm option, mk_eq_True: Proof.context -> thm -> thm option, reorient: Proof.context -> term list -> term -> term -> bool}, term_ord: term ord, subgoal_tac: Proof.context -> int -> tactic, 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 can Logic.dest_equals (Thm.concl_of th) then [th] else []), mk_cong = K I, mk_sym = default_mk_sym, mk_eq_True = K (K NONE), reorient = default_reorient} Term_Ord.term_ord (K (K no_tac)) ([], []); (* merge *) (*NOTE: ignores some fields of 2nd simpset*) fun merge_ss (ss1, ss2) = if pointer_eq (ss1, ss2) then ss1 else let val Simpset ({rules = rules1, prems = prems1, depth = depth1}, {congs = (congs1, weak1), procs = (simprocs1, congprocs1), mk_rews, term_ord, subgoal_tac, loop_tacs = loop_tacs1, solvers = (unsafe_solvers1, solvers1)}) = ss1; val Simpset ({rules = rules2, prems = prems2, depth = depth2}, {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 fun map_procs kindf (improcs,congprocs)= java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5 val ctxt' = f (Proof_Context.init_global thy); val thy' =Proof_Contexttheory_of '; option; 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 solvers = #solvers o internal_ss o simpset_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 simp_depth_limit = Config. t = Config. ("simp_trace_depth_limit", \<^here> K1) fun inc_simp_depth name stringjava.lang.StringIndexOutOfBoundsException: Index 17 o ctxt| map_simpset1 (fn (rules prems, (depth, exceeded)=> (rules, prems, (depth if depth =Configgetctxtsimp_trace_depth_limit then Unsynchronizedref 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; val depth_limit =Configget ctxt simp_trace_depth_limit; in if depth java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for leng if procs: simplification procedures indexed via discrimination net else (tracing (enclose congprocs: functions that prove congruence rules on the fly; end else (); fun term_ord: for ordered rewriting;*) fun mk .- Proof.context, s ^ "\n" ^ Syntax.string_of_term ctxt t; fun print_thm ctxt msg (name, th) = let val sffx= if mk_symProof. ->thm option else""^quoteGlobal_Theoryprint_thm_name )^:"; in print_termmsg ) (.full_prop_of) ; funprint_thm0 msg., h) (** simpset operations **) (* prems *) => if . Thm) ctxt let {,..},_ ctxt end fun add_prems ths = map_simpset1 (fn (rules, prems, depth) => (rules, ths @ prems, depth)); (* maintain simp rules *) fun del_rrule loudfun del_rrule loud ctxt>map_simpset1(fn(, prems ) => (Net.delete_term pointer_eq(ss1) then ss1 handle Net. let (f notloudthen () else cond_warning ctxt { (, weak1)procs =(simprocs1 congprocs1,mk_rews term_ord subgoal_t ctxt; fun insert_rrule (rrule as {thm, name, ...}) ctxt = ( ( )= ctxt "name ); ctxt |> map_simpset1 (fn (rules, prems, depth) => solvers ointernal_ss in (java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 handle Net.val simp_depth_limit .declare_int(simp_depth_limit,\^here K 4; print_thm0ctxtIgnoringduplicate rule" thm);ctxt)java.lang.StringIndexOutOfBoundsE . oVars; local fun vperm (Var _, Var _) = true . ctxt simp_trace_depth_limit | vperm (t1 $ t2,java.lang.StringIndexOutOfBoundsException: Range [33, 20) out of bo ,)t u; fun var_perm (t, u) = vperm (t, u) andalso Vars.eq_set (apply2 vars_set (t, u)); in fun decomp_simp thm = let val end val . (Thmcprop_of); val ( SIMPLIFIER" not a meta-equality",[]); val elhs = Thm.dest_arg (Thm.cprop_of (Thm.eta_conversion lhs)); valerhs= eta_contract(Thm.term_of rhs); val perm = var_perm (java.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for l . aconvjava.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for leng java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25 in,. lhselhs. rhsperm)end end fun 'thm = _ , _ , _ =decomp_simp in if (if no then() else(, ) end; fun mk_eq_True java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds fo (case #mk_eq_True, ,)= (,t = ] | SOME eq_True vperm( u t=u) letfunvar_permt ) (. (apply2vars_set t ); in [{thm = eq_True, name = name, lhs = lhs, (*create the rewrite rule and possibly also the eq_True variant, in case there are extra vars on the rhs*) fun ctxtthmname elhs thm2 let val rrule = {thm = prems Logicstrip_imp_premsprop if rewrite_rule_extra_vars [] lhs rhs then mk_eq_Truejava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for else lhsjava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for len end fun mk_rrule ctxt (thm, name) = let val (prems, lhs, elhs, rhs, perm) = decomp_simp thm in if permlet _, lhs , ,_ eq_True else (*weak test for loops*) if rewrite_rule_extra_vars prems lhs rhs orelse is_Var (Thmif [ lhsrhsjava.lang.StringInd t mk_eq_True (, ) else rrule_eq_True prems, , , ) java.lang.StringIndexOutOfBoundsException: Index 60 ou end |> map (fn {thm, name, lhs, elhs, perm} => {thm ,elhs , =true ctxt rhs (, )= let val(,lhs,, ) = ; val {reorient, mk_sym, else in = ] thm = _ lhs ' ',_ thmjava.lang.StringIndexOutOfBoundsException: Index 64 out of bounds fo then ctxtthm ) else (case mk_sym ctxt NONE>] | SOME thm' => let val (java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for leng in rrule_eq_True ctxt thm' name lhs' elhsjava.lang.StringIndexOutOfBoundsException: else rrule_eq_True ctxt thm name lhs elhs rhs end fun extract_rews {sym} thm ctxt = let val mk = #mk (rews ctxt)= mkthm; val rews' = if sym then rews RL [Drule.symmetric_thm] else rews; in (map (rpair (Thm.get_name_hint thm)u ( true mapmk_rrule2 ctxt) {sym = false} thms ctxt; funand needs to java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds fo (Net.insert_term eq_rrule (Thm.term_of elhs false) fun mk_rrules ctxt thm = let val rews = cong_namelhs .Option val ( ctxt; in map mk_rrule2 raw_rrules end; (* add/del rules explicitly *) local fun java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5 val =java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length |> maps (fn thm => #1 (extract_rews sym (Thm.java.lang.StringIndexOutOfBoundsException: In in fold (fold comb o mk_rrule) in fun add_simps thms ctxt = comb_simps insert_rrule (mk_rrule ctxt) {sym = falsefundel_cong ctxt=del_eqcong(mk_cong fun add_flipped_simps thms ctxt = ) =} thms fun add_simp , fundel_simps = comb_simps (del_rrule true) (map mk_rrule2 o mk_rrule ctxt) {sym = false} thms ctxt; fundel_simps_quiet = comb_simps (java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for fun fun flip_simp , (* 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 java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 > |> fold add_simp java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds fo |> Context_Position.restore_visible ctxtval(' ' ',mk_eq_True' ' java.lang.StringIndex (* congs *) local fun is_full_cong_prems | is_full_cong_premsmk_cong ( (k ,mk_sym , reorient > |is_full_cong_prems p: ) = java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 Const ("Pure.eq", _) $ lhsmkmk_cong ,,reorient) val(,xs=strip_comb andy ) rhs mkmk_cong , , )) not (has_duplicates member (op =) varpairs (x, y) andalso is_full_cong_prems ( ( )(,y)) end | _ => false); java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 22 let val structureTrace_Ops val (lhs, rhs) = Logic T= trace_ops val (f, xs) = strip_comb lhs and (g, ys) = strip_comb rhs val empty T java.lang.StringIndexOutO in Proof_Context; a not op xsys xs =length andalso is_full_cong_prems prems (xs ~~ ys) end; in fun ctxt mk_congget_mk_rewsctxt)ctxt fun add_eqcong thm ctxt = java.lang.StringIndexOutOfBoundsException: Index 0 out of b (fn (congs, procs L C Paulson, A higher-order implementation Science of Computer Programming let valjava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length handle TERM _ => raise SIMPLIFIER ( Thm nthmhandle java.lang.StringIndexOutOfBoundsExcepti (*val lhs = Envir.eta_contract lhs;*) vala= cong_name( Option > raise SIMPLIFIER ("Congruence must start with a constant or free variable", [thm]); val (xs, weak) = congs; _=if then cond_tracingfn > ctxt " ""thm)else(; val weak' = if is_full_cong thm then weak xs' , ,subgoal_tac ,solversend) del_eqcong = | (fn (congs, procsin ; let val (lhs, _) = Logic.dest_equals java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17 (*val lhs = Envir.eta_contract lhs;*) = . java.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 6 raise SIMPLIFIER ("Congruence mustjava.lang.StringIndexOutOfBoundsException: Index alized terms by carrying around the rhs of the rewrite rule just val xs' = Congtab.delete_safe with the term. Once a Var is encountered, the corr val weak' = Congtab.fold (fn (a,java.lang.StringIndexOutOfBoundsException: Index in fun lhs fun add_cong thm ctxt = add_eqcong (mk_cong ctxt exists_subterm (mk_cong thm; end|Free,_ >member op) eak, java.lang.StringIndexOutOfBoundsException: Index 52 out o (* simprocs *) type simproc = (3) conditional rewrite rules fun cert_simproc thy {name,java.lang.StringIndexOutOfBoundsException: Index 0 out o {name = name, lhs = map .first_order_match(',eta_t' proc else.match(',eta_t'; =( (,mapThm thy) )}; name ,, (stamp, identifier:= Procedure , kind = kind, lhs = map (Morphism.term phi) lhs, =M.transform proc id=(,Morphism phi identifier)}; funrewrite,); Procedure {name = name, kind = kind, lhs = lhs, proc = Morphism.entity_reset_context proc, id = (stamp, map Thm.trim_context identifier)}; local fun add_proc1 (procval lr = . prop ( (n ()= print_term (thm' (, congprocs, lr)) end)) ='"thm) NONE) (fn (congs| thm2=java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds (congs, map_procs kind (Net.insert_term eq_procedure_id (lhs, proc)) procs, mk_rews term_ord subgoal_tac,loop_tacs solvers) handle Net.INSERT => (cond_warning ctxt (fn () => "Ignoring duplicate " ^ print_proc_kind kind ^ " " ^ quote name); ctxt)); fun del_proc1 (proc SOMEthm2= ctxt |> map_simpset2 java.lang.StringIndexOutOfBoundsException: Range [32, 6) out of bounds for lengt (, map_procskind Netdelete_termeq_procedure_id(, proc) procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers)) handle Net.DELETE => cond_warningctxt(fn( > " ^print_proc_kind ""^ name); 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 ( Thmprop_ofthmof val =fold osplit_proc ; (* mk_rews *) local fun if.(. )lhst)then map_simpset2 (fn (congs, procs('ctxt ( )=> let val let val(' mk_cong' ',mk_eq_True' ')java.lang.StringIndexOutOfBoundsException: Range [6 f (mk, mk_cong, mk_sym( ' >Morphism ' ) val mk_rews' = {mk . eta_t) java.lang.StringIndexOutOfBoundsException: Index 62 reorient=reorient}java.lang.StringIndexOutOfBoundsException: Index 30 out of bou in (congs endjava.lang.StringIndexOutOfBoundsException: Range [6, 7) out of bounds in val get_mksimps_context = #mk o val get_mksimps_context = #mk o get_mk_rews fun mksimps ctxt thm = #1 (get_mksimps_context ctxt java.lang.StringIndexOutOfBoundsExce fun (mk ( )> fun set_mkcong mk_cong = map_mk_rews (fn (mk, _, mk_sym, if matches(p2, ) thenEQUAL (mk, mk_cong, mk_sym, java.lang.StringIndexOutOfBoundsException: Index 29 out of bo fun set_mksym mk_sym valSimpset( procs (, congprocs), ..}) =simpset_ofctxt (mk fun set_mkeqTruemk_eq_True map_mk_rews (n(, mk_cong mk_sym,_ reorient)=java.lang.Strin (mk, mk_cong, | proc_congs (Pr{ame ,, .}: ) = fun set_reorient reorient = map_mk_rews (fn (mk, mk_cong, mk_sym, mk_eq_True, _) => (,mk_cong , ,reorient; end; (* term_ord *) fun set_term_ordval'Config simp_trace . )ctxtjava.lang.StringIndexOutOfBoundsExc map_simpset2 (fn (congs, procs, (fn ctxt'' => Morphism.form_contextproceta_ct (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers)); tactics fun set_subgoaler subgoal_tac =SOME,)) (congs, procs, mk_rews, term_ord, proc_congspsjava.lang.StringIndexOutOfBoundsExcept 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 Thm.(. )java.lang.StringIndexOutOfBoundsException: Index 81 out of bounds for len map_simpset2 (* Thm.match can raise Pattern.MATCH; (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 *) java.lang.StringIndexOutOfBoundsException: Range [16, 17) out of bounds for leng {trace_invoke: {depth: int, cterm: cterm} -> Proof.context -> Proof.context, trace_rrule: {unconditional: bool, cterm: cterm, thm: thm, rrule: rrule} -> Proof.context -> (Proof NONE= NONE) trace_simproc: {name: string, cterm: cterm} -> Proof.context -> (Proof.context -> thm option) -> thm $=> structure Trace_Ops = Theory_Data ( type T = trace_ops; valempty T = {trace_invoke = fn _ => fn ctxt => ctxt, trace_rrule = fn _ => fn ctxt => fn cont => cont ctxt, trace_simproc= fn_ = fnctxt => fn cont= ctxt; fun merge (trace_ops, _) = trace_ops; ); val set_trace_ops = Trace_Ops.put; val trace_ops = Trace_Ops.get o Proof_Context.theory_of; fun trace_invoke args ctxt = #trace_invoke (trace_ops ctxt) appc fun trace_rrule args ctxt = #trace_rrule (trace_ops ctxt) args ctxt; fun argsctxt #trace_simproc( ctxt args; (** rewriting **) * Uses conversions, see: L Cjava.lang.StringIndexOutOfBoundsException: Index 85 out of bounds for length 8 Science of thm1 > SOMEThmcombination (hm. ct thm1) *) fun check_conv ctxt msg thm thm' = let valthm .transitivethmthmhandle > let val nthm' = Thm.transitive (Thm.symmetric (Drule.beta_eta_conversion (Thm.lhs_of thm'))) thm' in Thm unapp_cong ( = nthm Thm.transitive thm (Drule.beta_eta_conversion (Thm (thm )> SOME in Thm.transitive nthm nthm' end end val _ = if msg then NONE = .mapPartial(Congtablookup(stcongs cong_nameh)java.lang.StringI in SOME thm'' end _ ) let val _ $ _ $ prop0 = Thm.prop_of thm; val _ = cond_tracing ( ( > print_thm0 ctxt "Proved wrong theorem (bad subgoaler?)" thm' ^ "\n" elsenonmu print_term>1 java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10 (* mk_procrule *) fun mk_procrule ctxt thm = java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5 prems,, rhs _) thm val thm' = Thm.close_derivation \< in rewrite_rule_extra_vars rhs then (cond_warning ctxt (fn () => print_thm0 ctxt " (hm.transitive else [mk_rrule2 {thm = thm', name = Thm_Name.empty, lhs = lhs, elhs = elhs, perm = f end; (* rewritec: conversion to apply the meta simpset to a term *) (*Since the rewriting strategy is bottom-up, we avoid re-normalizing alreadyDrule) 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.*) = 0 val skel_fun = fn skel $ _ => skel | _ => skel0; val skel_arg = fn _ $ skel => skel | _ => skel0; val skel_body = fn ( false) ( transitive3(prem) eq) (*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_congjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for if null weak then false (*optimization*) else exists_subterm (fn Const (a, _) => member (op =) weak (true, transitive1 (fold (fn (eq1, prem) => fn eq2 => transitiv | Free (a, _) => member (op =) weak (false, a) | _ => false) lhs fun uncond_skel ((_, weak), congprocs, (lhs, rhs prems' rrss' asms' eqns ctxt changed k 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 (rrs :: rrss') (asm :: asms') (NON ; (*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 ; (* 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 rewritec (prover, maxt) ctxt t = let val SOMEthm1'= SOME(.imp_cong_rule thm1'(.reflexive conc)) simpset_of ctxt; val eta_thm = Thm.eta_conversion t; valeta_t Thmrhs_of val eta_t = Thm.term_of eta_t'; funrew = let val {thm = thm0, name, lhs, elhs = elhs0, extra, fo, perm} = rrule; val thm = Thm.transfer' ctxt thm0; val elhs = Thm.transfer_cterm' in try_botc ; val prop = Thm.prop_of thm; val (rthm, elhs') = if maxt = ~1 orelse not extra then (thm, elhs) else (Thm. use prems of B (if B is again a meta-impl.) to simplify A) val insts = if fo then Thm.first_order_match (elhs', eta_t') else Thm.match (elhs', eta_t'); valthm=Thm Thm eta_t) val prop' = Thm.prop_of thm'; val unconditional = Logic.no_prems prop'; vallhs,rhs Logicdest_equalsLogic prop) val trace_args = {unconditional = unconditional, cterm = eta_t', thm = thm' raw_ctxt in if perm andalso is_greater_equal (term_ord (rhs', lhs')) then (cond_tracing ctxt (fn () => print_thm ctxt "Cannot apply permutative rewrite rule print_thm0 ctxt "Term does not become smaller:" thm') cond_tracing ctxt( () ja NONE) else (cond_tracing ctxt (fn () => print_thm "pplyinginstanceof rewriterule"(amethm; if unconditional ( ( ) = print_thm0 Rewriting ') trace_rrule trace_args ctxt (fn ctxt' (fn => ALLGOALS (resolve_tac ctxt (prems_of let val lr = Logic.dest_equals prop; val SOME thm'' = check_conv ctxt' false eta_thm thm'; in SOME (thm'', uncond_skel (congsjava.lang.StringIndexOutOfBoundsException: Index 0 else (cond_tracing ctxt (fn () => print_thm0 ctxt "Trying to rewrite:" thm'); if simp_depth ctxt >( then (cond_tracing ctxt fun rules else trace_rrule trace_args ctxt (fn ctxt' => (case java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length NONE => (cond_tracing ctxt' (fn () => print_thm0 ctxt' "FAILED" thm'); NONE) | SOME thm2 => (case check_conv ctxt' true eta_thm thm2 of => java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34 java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 35 let val concl = rewrite_goals_tacctxt = PRIMITIVE (ewrite_goals_rulectxtdefs); val lr = Logic.dest_equals concl; in SOME (thm2', cond_skel (congs, congprocs, lr)) end))))) end; funrews] NONE | rews (rrule :: rrules) = letvalopt rrulehandle. = java.lang.StringIndexOutOfBoundsException: Index 62 out of in (case opt of NONE => rews rrules | some => some) end fun sort_rrules (true, false false Kno_tac init_simpsetthms ctxtjava.lang.StringIndexOu let fun is_simple ({thm, ...}: rrule) = fun ( (, , t) term_depth t Const ("Pure.eq", |term_depth ( t + .max ( f term_depth) | _ => false); fun sort [] (re1, re2) = re1 @ re2 | sort (rr :: |term_depth ; if is_simple rr then sort rrs ( Returns fun sort_lhs_depthsdefs in sort rrs ([ letval maketerm_depth )java.lang.StringIndexOutOfBoundsException: Range fun proc_rews [] = NONE |proc_rewsProcedurenameproc lhs.}::psjava.lang.StringIndexOutOfBoundsException: I if Pattern.matches (Proof_Context.theory_of ctxt) (lhs, Thm.term_of t)java.lang.String (cond_tracing' ctxt simp_debug (fn () => print_term ctxt ("Trying procedure " ^ quote name ^ " on:") eta_t); (let val ctxt' = Config.put simp_trace (Config.get ctxt simp_debug) ctxt val res = trace_simproc {name = name, cterm = eta_t'} ctxt' 'java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13 in case reselse NONE=(' simp_debug fn()=> "") proc_rews ) | SOME raw_thm => (cond_tracing ctxt (fn () => print_thm0 ctxt ("Procedure " th'|>Thmadjust_maxidx_thm ~ >Variable. ctxt end; (case rews>; NONE => (cond_tracing ctxt (fn () => print_term ctxt (IGNORED simproc ^quotename^ " -- does not match") (Thm.term_of t)); proc_rews ps) = )) java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 else ; in (case eta_t of structureBasic_Raw_Simplifier BASIC_RAW_SIMPLIFIER=Raw_Simplifier | _=> (case rews (sort_rrules (Net.match_term rules eta_t)) of NONE => proc_rews (Net.match_term simprocs eta_t) | some => some)) end; (* 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.match thy arg) (Vartab.empty, Vartab.empty); in fn (p1, p2) => if matches (p1, p2) then if matches (p2, p1) then EQUAL 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; val Simpset (_, {procs = (_, congprocs), ...}) = simpset_of ctxt; val eta_ct = Thm.rhs_of (Thm.eta_conversion ct); fun proc_congs [] = NONE | proc_congs (Procedure {name, lhs, proc, ...} :: ps) = if Pattern.matches thy (lhs, Thm.term_of ct) then let val _ = cond_tracing' ctxt simp_debug (fn () => print_term ctxt ("Trying procedure " ^ quote name ^ " on:") (Thm.term_of eta_ct)); val ctxt' = Config.put simp_trace (Config.get ctxt simp_debug) ctxt; val res = trace_simproc {name = name, cterm = eta_ct} ctxt' (fn ctxt'' => Morphism.form_context' 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 () => print_thm0 ctxt ("Procedure " ^ quote name ^ " produced congruence rule:") raw_thm); SOME (raw_thm, skel0))) end else proc_congs ps; in Net.match_term congprocs (Thm.term_of eta_ct) |> sort (pattern_order thy o apply2 procedure_lhs) |> 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 (Thm.dest_equals (Drule.strip_imp_concl (Thm.cprop_of rthm))); val insts = Thm.match (rlhs, t) (* Thm.match can raise Pattern.MATCH; is handled when congc is called *) val thm' = Thm.instantiate insts (Thm.rename_boundvars (Thm.term_of rlhs) (Thm.term_of t) rthm); 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 => err ("Congruence proof failed. Could not prove", thm') | SOME thm2 => (case check_conv ctxt true (Drule.beta_eta_conversion t) thm2 of NONE => err ("Congruence proof failed. Should not have proved", thm2) | SOME thm2' => if op aconv (apply2 Thm.term_of (Thm.dest_equals (Thm.cprop_of thm2'))) then NONE else SOME thm2')) end; val vA = (("A", 0), propT); val vB = (("B", 0), propT); val vC = (("C", 0), propT); fun transitive1 NONE NONE = NONE | transitive1 (SOME thm1) NONE = SOME thm1 | 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 SOME thm => SOME (Thm.abstract_rule a v thm) | NONE => NONE) end | t $ _ => (case t of Const ("Pure.imp", _) $ _ => impc t0 ctxt | Abs _ => let val thm = Thm.beta_conversion false t0 in (case subc skel0 ctxt (Thm.rhs_of thm) of NONE => SOME thm | SOME thm' => SOME (Thm.transitive thm thm')) end | _ => let fun appc () = let val (ct, cu) = Thm.dest_comb t0 in (case botc (skel_fun skel) ctxt ct of SOME thm1 => (case botc (skel_arg skel) ctxt cu of 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 thm1 => SOME (Thm.combination (Thm.reflexive ct) thm1) | NONE => NONE)) end; val (h, ts) = strip_comb t; (*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.*) fun app_cong () = (case app_congprocs ctxt t0 of SOME (thm, _) => SOME thm | NONE => Option.mapPartial (Congtab.lookup (fst congs)) (cong_name h)); 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 [] [] ctxt else nonmut_impc ct ctxt and rules_of_prem prem ctxt = if maxidx_of_term (Thm.term_of prem) <> ~1 then (cond_tracing ctxt (fn () => print_term ctxt "Cannot add premise as rewrite rule because it contains (type) unk (Thm.term_of prem)); (([], NONE), ctxt)) else let 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.transitive (Thm.transitive (Thm.instantiate (TVars.empty, Vars.make3 (vA, prem') (vB, prem) (vC, concl)) Drule.swap_prems_eq) eq') (Thm.instantiate (TVars.empty, Vars.make3 (vA, prem) (vB, prem'') (vC, concl)) Drule.swap_prems_eq) end end and rebuild [] _ _ _ _ eq = eq | rebuild (prem :: prems) concl (_ :: rrss) (_ :: asms) ctxt eq = 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 (disch false) prems (the (transitive3 (dprem eq) eq'))) (mut_impc0 (rev prems) (Thm.rhs_of eq') (rev rrss) (rev asms) ctxt)) 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 = the_default prem (Option.map Thm.rhs_of thm1); val ctxt1 = if not useprem then ctxt else let val ((rrs, asm), ctxt') = rules_of_prem prem1 ctxt in add_rrules ([rrs], [asm]) ctxt' end; in (case botc skel0 ctxt1 conc of NONE => (case thm1 of NONE => NONE | SOME thm1' => SOME (Drule.imp_cong_rule thm1' (Thm.reflexive conc))) | SOME thm2 => let val thm2' = disch false prem1 thm2 in (case thm1 of NONE => SOME thm2' | SOME thm1' => SOME (Thm.transitive (Drule.imp_cong_rule thm1' (Thm.reflexive conc)) thm2')) end) end; in try_botc end; (* 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 val ct = raw_ct |> Thm.transfer_cterm' raw_ctxt |> Thm.adjust_maxidx_cterm ~1; val maxidx = Thm.maxidx_of_cterm ct; val ctxt = raw_ctxt |> Variable.set_body true |> Context_Position.set_visible false |> inc_simp_depth |> (fn ctxt => trace_invoke {depth = simp_depth ctxt, cterm = ct} ctxt); val _ = cond_tracing ctxt (fn () => print_term ctxt "SIMPLIFIER INVOKED ON THE FOLLOWING TERM:" (Thm.term_of ct)); in ct |> bottomc (mode, Option.map (Drule.flexflex_unique (SOME ctxt)) oo prover, maxidx) ctxt |> Thm.solve_constraints end; val simple_prover = SINGLE o (fn ctxt => ALLGOALS (resolve_tac ctxt (prems_of ctxt))); fun rewrite0 ctxt full = rewrite_cterm (full, false, false) simple_prover ctxt; fun rewrite_wrt _ _ [] = Thm.reflexive | 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 rewrite_rule ctxt = Conv.fconv_rule o rewrite_wrt ctxt true; (*simple term rewriting -- no proof*) fun rewrite_term thy rules procs = Pattern.rewrite_term thy (map decomp_simp' rules) procs; 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)*) fun rewrite_goals_rule ctxt thms th = Conv.fconv_rule (Conv.prems_conv ~1 (rewrite_cterm (true, true, true) simple_prover (init_simpset thms ctxt))) th; (** meta-rewriting tactics **) (*Rewrite all subgoals*) fun rewrite_goals_tac ctxt defs = PRIMITIVE (rewrite_goals_rule ctxt defs); (*Rewrite one subgoal*) fun generic_rewrite_goal_tac mode prover_tac ctxt i thm = if 0 < i andalso i <= Thm.nprems_of thm then Seq.single (Conv.gconv_rule (rewrite_cterm mode (SINGLE o prover_tac) ctxt) i thm) else Seq.empty; fun rewrite_goal_tac ctxt thms = generic_rewrite_goal_tac (true, false, false) (K no_tac) (init_simpset thms ctxt); (*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*) fun term_depth (Abs (_, _, t)) = 1 + term_depth t | term_depth (f $ t) = 1 + Int.max (term_depth f, term_depth t) | term_depth _ = 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.*) fun sort_lhs_depths defs = let val keylist = AList.make (term_depth o lhs_of_thm) defs val keys = sort_distinct (rev_order o int_ord) (map #2 keylist) in map (AList.find (op =) keylist) keys end; 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 *) local 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 else Conv.fconv_rule (rewrite_cterm (true, false, false) (K (K NONE)) (put_simpset ss ctxt)) th; in th' |> Thm.adjust_maxidx_thm ~1 |> Variable.gen_all ctxt end; val hhf_ss = Context.the_local_context () |> init_simpset Drule.norm_hhf_eqs |> simpset_of; val hhf_protect_ss = Context.the_local_context () |> init_simpset Drule.norm_hhf_eqs |> add_eqcong Drule.protect_cong |> simpset_of; in val norm_hhf = gen_norm_hhf {protect = false} hhf_ss; val norm_hhf_protect = gen_norm_hhf {protect = true} hhf_protect_ss; end; end; structure Basic_Raw_Simplifier: BASIC_RAW_SIMPLIFIER = Raw_Simplifier; open Basic_Raw_Simplifier; ¤ Diese beiden folgenden Angebotsgruppen bietet das Unternehmen0.26Angebot Wie Sie bei der Firma Beratungs- und Dienstleistungen beauftragen können ¤*Eine klare Vorstellung vom Zielzustand |
|
2026-03-28