| Quellcodebibliothek Statistik Leitseite products/sources/formale Sprachen/Isabelle/HOL/Tools/Sledgehammer/ (Beweissystem Isabelle Version 2025-1©) Datei vom 16.11.2025 mit Größe 22 kB |
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Quelle sledgehammer_mepo.ML Sprache: SML |
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(* Title: HOL/Tools/Sledgehammer/sledgehammer_mepo.ML
Author: Jia Meng, Cambridge University Computer Laboratory and NICTA Author: Jasmin Blanchette, TU Muenchen Sledgehammer's iterative relevance filter (MePo = Meng-Paulson). *) signature SLEDGEHAMMER_MEPO = sig type stature = ATP_Problem_Generate.stature type lazy_fact = Sledgehammer_Fact.lazy_fact type fact = Sledgehammer_Fact.fact type params = Sledgehammer_Prover.params type relevance_fudge = {local_const_multiplier : real, worse_irrel_freq : real, higher_order_irrel_weight : real, abs_rel_weight : real, abs_irrel_weight : real, theory_const_rel_weight : real, theory_const_irrel_weight : real, chained_const_irrel_weight : real, intro_bonus : real, elim_bonus : real, simp_bonus : real, local_bonus : real, assum_bonus : real, chained_bonus : real, max_imperfect : real, max_imperfect_exp : real, threshold_divisor : real, ridiculous_threshold : real} val trace : bool Config.T val pseudo_abs_name : string val default_relevance_fudge : relevance_fudge val mepo_suggested_facts : Proof.context -> params -> int -> relevance_fudge option -> term list -> term -> lazy_fact list -> fact list end; structure Sledgehammer_MePo : SLEDGEHAMMER_MEPO = struct open ATP_Problem_Generate open Sledgehammer_Util open Sledgehammer_Fact open Sledgehammer_Prover val trace = Attrib.setup_config_bool \<^binding>\<open>sledgehammer_mepo_trace\<close> (K fa fun trace_msg ctxt msg = if Config.get ctxt trace then tracing (msg ()) else () val sledgehammer_prefix = "Sledgehammer" ^ Long_Name.separator val pseudo_abs_name = sledgehammer_prefix ^ "abs" val theory_const_suffix = Long_Name.separator ^ " 1" type relevance_fudge = {local_const_multiplier : real, worse_irrel_freq : real, higher_order_irrel_weight : real, abs_rel_weight : real, abs_irrel_weight : real, theory_const_rel_weight : real, theory_const_irrel_weight : real, chained_const_irrel_weight : real, intro_bonus : real, elim_bonus : real, simp_bonus : real, local_bonus : real, assum_bonus : real, chained_bonus : real, max_imperfect : real, max_imperfect_exp : real, threshold_divisor : real, ridiculous_threshold : real} (* FUDGE *) val default_relevance_fudge = {local_const_multiplier = 1.5, worse_irrel_freq = 100.0, higher_order_irrel_weight = 1.05, abs_rel_weight = 0.5, abs_irrel_weight = 2.0, theory_const_rel_weight = 0.5, theory_const_irrel_weight = 0.25, chained_const_irrel_weight = 0.25, intro_bonus = 0.15, elim_bonus = 0.15, simp_bonus = 0.15, local_bonus = 0.55, assum_bonus = 1.05, chained_bonus = 1.5, max_imperfect = 11.5, max_imperfect_exp = 1.0, threshold_divisor = 2.0, ridiculous_threshold = 0.1} fun order_of_type (Type (\<^type_name>\<open>fun\<close>, [T1, T2])) = Int.max (order_of_type T1 + 1, order_of_type T2) | order_of_type (Type (_, Ts)) = fold (Integer.max o order_of_type) Ts 0 | order_of_type _ = 0 (* An abstraction of Isabelle types and first-order terms *) datatype pattern = PVar | PApp of string * pattern list datatype ptype = PType of int * typ list fun string_of_patternT (TVar _) = "_" | string_of_patternT (Type (s, ps)) = if null ps then s else s ^ string_of_patternsT ps | string_of_patternT (TFree (s, _)) = s and string_of_patternsT ps = "(" ^ commas (map string_of_patternT ps) ^ ")" fun string_of_ptype (PType (_, ps)) = string_of_patternsT ps (*Is the second type an instance of the first one?*) fun match_patternT (TVar _, _) = true | match_patternT (Type (s, ps), Type (t, qs)) = s = t andalso match_patternsT (ps, qs) | match_patternT (TFree (s, _), TFree (t, _)) = s = t | match_patternT (_, _) = false and match_patternsT (_, []) = true | match_patternsT ([], _) = false | match_patternsT (p :: ps, q :: qs) = match_patternT (p, q) andalso match_patternsT (ps, qs) fun match_ptype (PType (_, ps), PType (_, qs)) = match_patternsT (ps, qs) (* Is there a unifiable constant? *) fun pconst_mem f consts (s, ps) = exists (curry (match_ptype o f) ps) (map snd (filter (curry (op =) s o fst) consts)) fun pconst_hyper_mem f const_tab (s, ps) = exists (curry (match_ptype o f) ps) (these (Symtab.lookup const_tab s)) (* Pairs a constant with the list of its type instantiations. *) fun ptype thy const x = (if const then these (try (Sign.const_typargs thy) x) else []) fun rich_ptype thy const (s, T) = PType (order_of_type T, ptype thy const (s, T)) fun rich_pconst thy const (s, T) = (s, rich_ptype thy const (s, T)) fun string_of_hyper_pconst (s, ps) = s ^ "{" ^ commas (map string_of_ptype ps) ^ "}" fun patternT_eq (TVar _, TVar _) = true | patternT_eq (Type (s, Ts), Type (t, Us)) = s = t andalso patternsT_eq (Ts, Us) | patternT_eq (TFree (s, _), TFree (t, _)) = (s = t) | patternT_eq _ = false and patternsT_eq ([], []) = true | patternsT_eq ([], _) = false | patternsT_eq (_, []) = false | patternsT_eq (T :: Ts, U :: Us) = patternT_eq (T, U) andalso patternsT_eq (Ts, Us) fun ptype_eq (PType (m, Ts), PType (n, Us)) = m = n andalso patternsT_eq (Ts, Us) (* Add a pconstant to the table, but a [] entry means a standard connective, which we ignore. *) fun add_pconst_to_table (s, p) = Symtab.map_default (s, [p]) (insert ptype_eq p) (* Set constants tend to pull in too many irrelevant facts. We limit the damage by treating them more or less as if they were built-in but add their axiomatization at the end. *) val set_consts = [\<^const_name>\<open>Collect\<close>, \<^const_name>\<open>Set.member\<close>] val set_thms = @{thms Collect_mem_eq mem_Collect_eq Collect_cong} fun add_pconsts_in_term thy = let fun do_const const (x as (s, _)) ts = if member (op =) set_consts s then fold (do_term false) ts else (not (is_irrelevant_const s) ? add_pconst_to_table (rich_pconst thy const x)) #> fold (do_term false) ts and do_term ext_arg t = (case strip_comb t of (Const x, ts) => do_const true x ts | (Free x, ts) => do_const false x ts | (Abs (_, T, t'), ts) => ((null ts andalso not ext_arg) (* Since lambdas on the right-hand side of equalities are usually extensionalized later by "abs_extensionalize_term", we don't penalize them here. *) ? add_pconst_to_table (pseudo_abs_name, PType (order_of_type T + 1, []))) #> fold (do_term false) (t' :: ts) | (_, ts) => fold (do_term false) ts) and do_term_or_formula ext_arg T = if T = HOLogic.boolT then do_formula else do_term ext_arg and do_formula t = (case t of Const (\<^const_name>\<open>Pure.all\<close>, _) $ Abs (_, _, t') => do_formula t' | \<^Const_>\<open>Pure.imp for t1 t2\<close> => do_formula t1 #> do_formula t2 | Const (\<^const_name>\<open>Pure.eq\<close>, Type (_, [T, _])) $ t1 $ t2 => do_term_or_formula false T t1 #> do_term_or_formula true T t2 | \<^Const_>\<open>Trueprop for t1\<close> => do_formula t1 | \<^Const_>\<open>False\<close> => I | \<^Const_>\<open>True\<close> => I | \<^Const_>\<open>Not for t1\<close> => do_formula t1 | Const (\<^const_name>\<open>All\<close>, _) $ Abs (_, _, t') => do_formula t' | Const (\<^const_name>\<open>Ex\<close>, _) $ Abs (_, _, t') => do_formula t' | \<^Const_>\<open>conj for t1 t2\<close> => do_formula t1 #> do_formula t2 | \<^Const_>\<open>disj for t1 t2\<close> => do_formula t1 #> do_formula t2 | \<^Const_>\<open>implies for t1 t2\<close> => do_formula t1 #> do_formula t2 | Const (\<^const_name>\<open>HOL.eq\<close>, Type (_, [T, _])) $ t1 $ t2 => do_term_or_formula false T t1 #> do_term_or_formula true T t2 | Const (\<^const_name>\<open>If\<close>, Type (_, [_, Type (_, [T, _])])) $ t1 $ t2 $ t3 => do_formula t1 #> fold (do_term_or_formula false T) [t2, t3] | Const (\<^const_name>\<open>Ex1\<close>, _) $ Abs (_, _, t') => do_formula t' | Const (\<^const_name>\<open>Ball\<close>, _) $ t1 $ Abs (_, _, t') => do_formula (t1 $ Bound ~1) #> do_formula t' | Const (\<^const_name>\<open>Bex\<close>, _) $ t1 $ Abs (_, _, t') => do_formula (t1 $ Bound ~1) #> do_formula t' | (t0 as Const (_, \<^typ>\<open>bool\<close>)) $ t1 => do_term false t0 #> do_formula t1 (* theory constant *) | _ => do_term false t) in do_formula end fun pconsts_in_fact thy t = Symtab.fold (fn (s, pss) => fold (cons o pair s) pss) (Symtab.empty |> add_pconsts_in_term thy t) [] (* Inserts a dummy "constant" referring to the theory name, so that relevance takes the given theory into account. *) fun theory_constify ({theory_const_rel_weight, theory_const_irrel_weight, ...} : relev thy_name t = if exists (curry (op <) 0.0) [theory_const_rel_weight, theory_const_irrel_weight] then Const (thy_name ^ theory_const_suffix, \<^typ>\<open>bool\<close>) $ t else t fun theory_const_prop_of fudge th = theory_constify fudge (Thm.theory_base_name th) (Thm.prop_of th) fun pair_consts_fact thy fudge fact = (case fact |> snd |> theory_const_prop_of fudge |> pconsts_in_fact thy of [] => NONE | consts => SOME ((fact, consts), NONE)) (* A two-dimensional symbol table counts frequencies of constants. It's keyed first by constant name and second by its list of type instantiations. For the latter, we need a linear ordering on "pattern list". *) fun patternT_ord p = (case p of (Type (s, ps), Type (t, qs)) => (case fast_string_ord (s, t) of EQUAL => dict_ord patternT_ord (ps, qs) | ord => ord) | (TVar _, TVar _) => EQUAL | (TVar _, _) => LESS | (Type _, TVar _) => GREATER | (Type _, TFree _) => LESS | (TFree (s, _), TFree (t, _)) => fast_string_ord (s, t) | (TFree _, _) => GREATER) fun ptype_ord (PType (m, ps), PType (n, qs)) = (case dict_ord patternT_ord (ps, qs) of EQUAL => int_ord (m, n) | ord => ord) structure PType_Tab = Table(type key = ptype val ord = ptype_ord) fun count_fact_consts thy fudge = let fun do_const const (s, T) ts = (* Two-dimensional table update. Constant maps to types maps to count. *) PType_Tab.map_default (rich_ptype thy const (s, T), 0) (Integer.add 1) |> Symtab.map_default (s, PType_Tab.empty) #> fold do_term ts and do_term t = (case strip_comb t of (Const x, ts) => do_const true x ts | (Free x, ts) => do_const false x ts | (Abs (_, _, t'), ts) => fold do_term (t' :: ts) | (_, ts) => fold do_term ts) in do_term o theory_const_prop_of fudge o snd end fun pow_int _ 0 = 1.0 | pow_int x 1 = x | pow_int x n = if n > 0 then x * pow_int x (n - 1) else pow_int x (n + 1) / x (*The frequency of a constant is the sum of those of all instances of its type.*) fun pconst_freq match const_tab (c, ps) = PType_Tab.fold (fn (qs, m) => match (ps, qs) ? Integer.add m) (the (Symtab.lookup const_tab c)) (* A surprising number of theorems contain only a few significant constants. These include all induction rules and other general theorems. *) (* "log" seems best in practice. A constant function of one ignores the constant frequencies. Rare constants give more points if they are relevant than less rare ones. *) fun rel_weight_for _ freq = 1.0 + 2.0 / Math.ln (Real.fromInt freq + 1.0) (* Irrelevant constants are treated differently. We associate lower penalties to very rare constants and very common ones -- the former because they can't lead to the inclusion of too many new facts, and the latter because they are so common as to be of little interest. *) fun irrel_weight_for ({worse_irrel_freq, higher_order_irrel_weight, ...} : relevance_f freq = let val (k, x) = worse_irrel_freq |> `Real.ceil in (if freq < k then Math.ln (Real.fromInt (freq + 1)) / Math.ln x else rel_weight_for order freq / rel_weight_for order k) * pow_int higher_order_irrel_weight (order - 1) end fun multiplier_of_const_name local_const_multiplier s = if String.isSubstring "." s then 1.0 else local_const_multiplier (* Computes a constant's weight, as determined by its frequency. *) fun generic_pconst_weight local_const_multiplier abs_weight theory_const_weight chain weight_for f const_tab chained_const_tab (c as (s, PType (m, _))) = if s = pseudo_abs_name then abs_weight else if String.isSuffix theory_const_suffix s then theory_const_weight else multiplier_of_const_name local_const_multiplier s * weight_for m (pconst_freq (match_ptype o f) const_tab c) |> (if chained_const_weight < 1.0 andalso pconst_hyper_mem I chained_const_tab c then curry (op *) chained_const_weight else I) fun rel_pconst_weight ({local_const_multiplier, abs_rel_weight, theory_const_rel_wei ...} : relevance_fudge) const_tab = generic_pconst_weight local_const_multiplier abs_rel_weight theory_const_rel_weight rel_weight_for I const_tab Symtab.empty fun irrel_pconst_weight (fudge as {local_const_multiplier, abs_irrel_weight, theory_const_irrel_weight, chained_const_irrel_weight, ...}) const_tab chained_const generic_pconst_weight local_const_multiplier abs_irrel_weight theory_const_irrel_we chained_const_irrel_weight (irrel_weight_for fudge) swap const_tab chained_const_tab fun stature_bonus ({intro_bonus, ...} : relevance_fudge) (_, Intro) = intro_bonus | stature_bonus {elim_bonus, ...} (_, Elim) = elim_bonus | stature_bonus {simp_bonus, ...} (_, Simp) = simp_bonus | stature_bonus {local_bonus, ...} (Local, _) = local_bonus | stature_bonus {assum_bonus, ...} (Assum, _) = assum_bonus | stature_bonus {chained_bonus, ...} (Chained, _) = chained_bonus | stature_bonus _ _ = 0.0 fun is_odd_const_name s = s = pseudo_abs_name orelse String.isSuffix theory_const_suffix s fun fact_weight fudge stature const_tab rel_const_tab chained_const_tab fact_consts = (case fact_consts |> List.partition (pconst_hyper_mem I rel_const_tab) ||> filter_out (pconst_hyper_mem swap rel_const_tab) of ([], _) => 0.0 | (rel, irrel) => if forall (forall (is_odd_const_name o fst)) [rel, irrel] then 0.0 else let val irrel = irrel |> filter_out (pconst_mem swap rel) val rel_weight = 0.0 |> fold (curry (op +) o rel_pconst_weight fudge const_tab) rel val irrel_weight = ~ (stature_bonus fudge stature) |> fold (curry (op +) o irrel_pconst_weight fudge const_tab chained_const_tab) irrel val res = rel_weight / (rel_weight + irrel_weight) in if Real.isFinite res then res else 0.0 end) fun take_most_relevant ctxt max_facts remaining_max ({max_imperfect, max_imperfect_exp, ...} : relevance_fudge) (candidates : ((lazy_fact * (string * ptype) list) * real) list) = let val max_imperfect = Real.ceil (Math.pow (max_imperfect, Math.pow (Real.fromInt remaining_max / Real.fromInt max_facts, max_imperfect_exp))) val (perfect, imperfect) = candidates |> sort (Real.compare o swap o apply2 snd) |> chop_prefix (fn (_, w) => w > 0.99999) val ((accepts, more_rejects), rejects) = chop max_imperfect imperfect |>> append perfect |>> chop remaining_max in trace_msg ctxt (fn () => "Actually passed (" ^ string_of_int (length accepts) ^ " of " ^ string_of_int (length candidates) ^ "): " ^ (accepts |> map (fn ((((name, _), _), _), weight) => name () ^ " [" ^ Real.toString weight ^ "]") |> commas)); (accepts, more_rejects @ rejects) end fun if_empty_replace_with_scope thy facts sc tab = if Symtab.is_empty tab then Symtab.empty |> fold (add_pconsts_in_term thy) (map_filter (fn ((_, (sc', _)), th) => if sc' = sc then SOME (Thm.prop_of th) else NONE) facts) else tab fun consider_arities th = let fun aux _ _ NONE = NONE | aux t args (SOME tab) = (case t of t1 $ t2 => SOME tab |> aux t1 (t2 :: args) |> aux t2 [] | Const (s, _) => (if is_widely_irrelevant_const s then SOME tab else (case Symtab.lookup tab s of NONE => SOME (Symtab.update (s, length args) tab) | SOME n => if n = length args then SOME tab else NONE)) | _ => SOME tab) in aux (Thm.prop_of th) [] end (* FIXME: This is currently only useful for polymorphic type encodings. *) fun could_benefit_from_ext facts = fold (consider_arities o snd) facts (SOME Symtab.empty) |> is_none (* High enough so that it isn't wrongly considered as very relevant (e.g., for E weights), but low enough so that it is unlikely to be truncated away if few facts are included. *) val special_fact_index = 45 (* FUDGE *) fun eq_prod eqx eqy ((x1, y1), (x2, y2)) = eqx (x1, x2) andalso eqy (y1, y2) val really_hopeless_get_kicked_out_iter = 5 (* FUDGE *) fun relevance_filter ctxt thres0 decay max_facts (fudge as {threshold_divisor, ridiculous_threshold, ...}) facts hyp_ts concl_t = let val thy = Proof_Context.theory_of ctxt val const_tab = fold (count_fact_consts thy fudge) facts Symtab.empty val add_pconsts = add_pconsts_in_term thy val chained_ts = facts |> map_filter (try (fn ((_, (Chained, _)), th) => Thm.prop_of th)) val chained_const_tab = Symtab.empty |> fold add_pconsts chained_ts val goal_const_tab = Symtab.empty |> fold add_pconsts hyp_ts |> add_pconsts concl_t |> (fn tab => if Symtab.is_empty tab then chained_const_tab else tab) |> fold (if_empty_replace_with_scope thy facts) [Chained, Assum, Local] fun iter j remaining_max thres rel_const_tab hopeless hopeful = let val hopeless = hopeless |> j = really_hopeless_get_kicked_out_iter ? filter_out (fn (_, w) => w < 0.001) fun relevant [] _ [] = (* Nothing has been added this iteration. *) if j = 0 andalso thres >= ridiculous_threshold then (* First iteration? Try again. *) iter 0 max_facts (thres / threshold_divisor) rel_const_tab hopeless hopeful else [] | relevant candidates rejects [] = let val (accepts, more_rejects) = take_most_relevant ctxt max_facts remaining_max fudge candidates val sps = maps (snd o fst) accepts val rel_const_tab' = rel_const_tab |> fold add_pconst_to_table sps fun is_dirty (s, _) = Symtab.lookup rel_const_tab' s <> Symtab.lookup rel_const_tab s val (hopeful_rejects, hopeless_rejects) = (rejects @ hopeless, ([], [])) |-> fold (fn (ax as (_, consts), old_weight) => if exists is_dirty consts then apfst (cons (ax, NONE)) else apsnd (cons (ax, old_weight))) |>> append (more_rejects |> map (fn (ax as (_, consts), old_weight) => (ax, if exists is_dirty consts then NONE else SOME old_weight))) val thres = 1.0 - (1.0 - thres) * Math.pow (decay, Real.fromInt (length accepts)) val remaining_max = remaining_max - length accepts in trace_msg ctxt (fn () => "New or updated constants: " ^ commas (rel_const_tab' |> Symtab.dest |> subtract (eq_prod (op =) (eq_list ptype_eq)) (Symtab.dest rel_const_tab) |> map string_of_hyper_pconst)); map (fst o fst) accepts @ (if remaining_max = 0 then [] else iter (j + 1) remaining_max thres rel_const_tab' hopeless_rejects hopeful_rejects) end | relevant candidates rejects (((ax as (((_, stature), _), fact_consts)), cached_weight) :: hopeful) = let val weight = (case cached_weight of SOME w => w | NONE => fact_weight fudge stature const_tab rel_const_tab chained_const_tab fact_consts) in if weight >= thres then relevant ((ax, weight) :: candidates) rejects hopeful else relevant candidates ((ax, weight) :: rejects) hopeful end in trace_msg ctxt (fn () => "ITERATION " ^ string_of_int j ^ ": current threshold: " ^ Real.toString thres ^ ", constants: " ^ commas (rel_const_tab |> Symtab.dest |> filter (curry (op <>) [] o snd) |> map string_of_hyper_pconst)); relevant [] [] hopeful end fun uses_const s t = fold_aterms (curry (fn (Const (s', _), false) => s' = s | (_, b) => b)) t false fun uses_const_anywhere accepts s = exists (uses_const s o Thm.prop_of o snd) accepts orelse exists (uses_const s) (concl_t :: hyp_ts) fun add_set_const_thms accepts = exists (uses_const_anywhere accepts) set_consts ? append set_thms fun insert_into_facts accepts [] = accepts | insert_into_facts accepts ths = let val add = facts |> filter (member Thm.eq_thm_prop ths o snd) val (bef, after) = accepts |> filter_out (member Thm.eq_thm_prop ths o snd) |> take (max_facts - length add) |> chop special_fact_index in bef @ add @ after end fun insert_special_facts accepts = (* FIXME: get rid of "ext" here once it is treated as a helper *) [] |> could_benefit_from_ext accepts ? cons @{thm ext} |> add_set_const_thms accepts |> insert_into_facts accepts in facts |> map_filter (pair_consts_fact thy fudge) |> iter 0 max_facts thres0 goal_const_tab [] |> insert_special_facts |> tap (fn accepts => trace_msg ctxt (fn () => "Total relevant: " ^ string_of_int (length accepts))) end fun mepo_suggested_facts ctxt ({fact_thresholds = (thres0, thres1), ...} : params) max_fac hyp_ts concl_t facts = let val thy = Proof_Context.theory_of ctxt val fudge = fudge |> the_default default_relevance_fudge val decay = Math.pow ((1.0 - thres1) / (1.0 - thres0), 1.0 / Real.fromInt (max_facts + 1)) in trace_msg ctxt (fn () => "Considering " ^ string_of_int (length facts) ^ " facts"); (if thres1 < 0.0 then facts else if thres0 > 1.0 orelse thres0 > thres1 orelse max_facts <= 0 then [] else relevance_filter ctxt thres0 decay max_facts fudge facts hyp_ts (concl_t |> theory_constify fudge (Context.theory_base_name thy))) |> map fact_of_lazy_fact end end; ¤ Dauer der Verarbeitung: 0.24 Sekunden (vorverarbeitet) ¤*© Formatika GbR, Deutschland |
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2026-03-28