| Quellcodebibliothek Statistik Leitseite products/sources/formale Sprachen/Isabelle/HOL/Tools/Sledgehammer/ (Beweissystem Isabelle Version 2025-1©) Datei vom 16.11.2025 mit Größe 23 kB |
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SSL sledgehammer_isar.ML Sprache: SML |
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(* Title: HOL/Tools/Sledgehammer/sledgehammer_isar.ML
Author: Jasmin Blanchette, TU Muenchen Author: Steffen Juilf Smolka, TU Muenchen Isar proof reconstruction from ATP proofs. *) signature SLEDGEHAMMER_ISAR = sig type atp_step_name = ATP_Proof.atp_step_name type ('a, 'b) atp_step = ('a, 'b) ATP_Proof.atp_step type 'a atp_proof = 'a ATP_Proof.atp_proof type stature = ATP_Problem_Generate.stature type one_line_params = Sledgehammer_Proof_Methods.one_line_params val trace : bool Config.T type isar_params = bool * (string option * string option * string list) * Time.time * real option * bool * bool * (term, string) atp_step list * thm val proof_text : Proof.context -> bool -> bool option -> bool -> (unit -> isar_params) -> int -> one_line_params -> string val abduce_text : Proof.context -> term list -> string end; structure Sledgehammer_Isar : SLEDGEHAMMER_ISAR = struct open ATP_Util open ATP_Problem open ATP_Problem_Generate open ATP_Proof open ATP_Proof_Reconstruct open Sledgehammer_Util open Sledgehammer_Proof_Methods open Sledgehammer_Isar_Proof open Sledgehammer_Isar_Preplay open Sledgehammer_Isar_Compress open Sledgehammer_Isar_Minimize structure String_Redirect = ATP_Proof_Redirect( type key = atp_step_name val ord = fn ((s, _ : string list), (s', _)) => fast_string_ord (s, s') val string_of = fst) open String_Redirect val trace = Attrib.setup_config_bool \<^binding>\<open>sledgehammer_isar_trace\<close> (K fa val e_definition_rule = "definition" val e_skolemize_rule = "skolemize" val leo2_extcnf_forall_neg_rule = "extcnf_forall_neg" val satallax_skolemize_rule = "tab_ex" val vampire_choice_axiom_rule = "choice_axiom" val vampire_skolemisation_rule = "skolemisation" val veriT_la_generic_rule = "la_generic" val veriT_simp_arith_rule = "simp_arith" val veriT_skolemize_rules = Lethe_Proof.skolemization_steps val z3_skolemize_rule = Z3_Proof.string_of_rule Z3_Proof.Skolemize val z3_th_lemma_rule_prefix = Z3_Proof.string_of_rule (Z3_Proof.Th_Lemma "") val zipperposition_cnf_rule = "cnf" val symbol_introduction_rules = [e_definition_rule, e_skolemize_rule, leo2_extcnf_forall_neg_rule, satallax_skolemi spass_skolemize_rule, vampire_choice_axiom_rule, vampire_skolemisation_rule, z3_sko zipperposition_cnf_rule, zipperposition_define_rule] @ veriT_skolemize_rules fun is_ext_rule rule = (rule = leo2_extcnf_equal_neg_rule) val is_maybe_ext_rule = is_ext_rule orf String.isPrefix satallax_tab_rule_prefix val is_symbol_introduction_rule = member (op =) symbol_introduction_rules fun is_arith_rule rule = String.isPrefix z3_th_lemma_rule_prefix rule orelse rule = veriT_simp_arith_rule orelse rule = veriT_la_generic_rule fun raw_label_of_num num = (num, 0) fun label_of_clause [(num, _)] = raw_label_of_num num | label_of_clause c = (space_implode "___" (map (fst o raw_label_of_num o fst) c), 0) fun add_global_fact ss = apsnd (union (op =) ss) fun add_fact_of_dependency [(_, ss as _ :: _)] = add_global_fact ss | add_fact_of_dependency names = apfst (insert (op =) (label_of_clause names)) fun add_line_pass1 (line as (name, role, t, rule, [])) lines = (* No dependencies: lemma (for Z3), fact, conjecture, or (for Vampire) internal facts or definitions. *) if role = Conjecture orelse role = Negated_Conjecture then line :: lines else if t aconv \<^prop>\<open>True\<close> then map (replace_dependencies_in_line (name, [])) lines else if role = Definition orelse role = Lemma orelse role = Hypothesis orelse is_arith_rule rule then line :: lines else if role = Axiom then lines (* axioms (facts) need no proof lines *) else map (replace_dependencies_in_line (name, [])) lines | add_line_pass1 line lines = line :: lines fun add_lines_pass2 res [] = rev res | add_lines_pass2 res ((line as (name, role, t, rule, deps)) :: lines) = let fun normalize role = role = Conjecture ? (HOLogic.dest_Trueprop #> s_not #> HOLogic.mk_Trueprop) val norm_t = normalize role t val is_duplicate = exists (fn (prev_name, prev_role, prev_t, _, _) => (prev_role = Hypothesis andalso prev_t aconv t) orelse (member (op =) deps prev_name andalso Term.aconv_untyped (normalize prev_role prev_t, norm_t))) res fun looks_boring () = t aconv \<^prop>\<open>False\<close> orelse length deps < 2 fun is_symbol_introduction_line (_, _, _, rule', deps') = is_symbol_introduction_rule rule' andalso member (op =) deps' name fun is_before_symbol_introduction_rule () = exists is_symbol_introduction_line lines in if is_duplicate orelse (role = Plain andalso not (is_symbol_introduction_rule rule) andalso not (is_ext_rule rule) andalso not (is_arith_rule rule) andalso not (null lines) andalso looks_boring () andalso not (is_before_symbol_introduction_rule ())) then add_lines_pass2 res (map (replace_dependencies_in_line (name, deps)) lines) else add_lines_pass2 (line :: res) lines end type isar_params = bool * (string option * string option * string list) * Time.time * real option * bool * bool * (term, string) atp_step list * thm val basic_systematic_methods = [Metis_Method (NONE, NONE, []), Meson_Method, Blast_Method, SATx_Method, Argo_Method] val basic_simp_based_methods = [Auto_Method, Simp_Method, Fastforce_Method, Force_Method] val basic_arith_methods = [Linarith_Method, Presburger_Method, Algebra_Method] val arith_methods = basic_arith_methods @ basic_simp_based_methods @ basic_systematic_m val systematic_methods = basic_systematic_methods @ basic_arith_methods @ basic_simp_based_methods @ [Metis_Method (SOME full_typesN, NONE, []), Metis_Method (SOME no_typesN, NONE, [])] val rewrite_methods = basic_simp_based_methods @ basic_systematic_methods @ basic_arith val skolem_methods = Moura_Method :: systematic_methods fun isar_proof_text ctxt debug num_chained isar_proofs smt_proofs isar_params (one_line_params as ((used_facts, (_, one_line_play)), banner, subgoal, subgoal_count)) let val _ = if debug then writeln "Constructing Isar proof..." else () fun generate_proof_text () = let val (verbose, alt_metis_args, preplay_timeout, compress, try0, minimize, atp_proof0, goa isar_params () in if null atp_proof0 then one_line_proof_text one_line_params else let val systematic_methods' = insert (op =) (Metis_Method alt_metis_args) systematic_ fun massage_methods (meths as meth :: _) = if not try0 then [meth] else if smt_proofs then insert (op =) (SMT_Method (SMT_Verit "default")) meths else meths val (params, _, concl_t) = strip_subgoal goal subgoal ctxt val fixes = map (fn (s, T) => (Binding.name s, SOME T, NoSyn)) params val ctxt = ctxt |> Variable.set_body false |> Proof_Context.add_fixes fixes |> snd val do_preplay = preplay_timeout <> Time.zeroTime val compress = (case compress of NONE => if isar_proofs = NONE andalso do_preplay then 1000.0 else 10.0 | SOME n => n) fun is_fixed ctxt = Variable.is_declared ctxt orf Name.is_skolem fun introduced_symbols_of ctxt t = Term.add_frees t [] |> filter_out (is_fixed ctxt o fst) |> rev fun get_role keep_role ((num, _), role, t, rule, _) = if keep_role role then SOME ((raw_label_of_num num, t), rule) else NONE val trace = Config.get ctxt trace val string_of_atp_steps = let val to_string = ATP_Proof.string_of_atp_step (Syntax.string_of_term ctxt) I in enclose "[\n" "\n]" o cat_lines o map (enclose " " "," o to_string) end val atp_proof = atp_proof0 |> trace ? tap (tracing o prefix "atp_proof0 = " o string_of_atp_steps) |> distinct (op =) (* Zipperposition generates duplicate lines *) |> (fn lines => fold_rev add_line_pass1 lines []) |> add_lines_pass2 [] |> trace ? tap (tracing o prefix "atp_proof = " o string_of_atp_steps) val conjs = map_filter (fn (name, role, _, _, _) => if member (op =) [Conjecture, Negated_Conjecture] role then SOME name else NONE) atp_proof val assms = map_filter (Option.map fst o get_role (curry (op =) Hypothesis)) atp_proof fun add_lemma ((label, goal), rule) ctxt = let val (obtains, proof_methods) = (if is_symbol_introduction_rule rule then (introduced_symbols_of ctxt goal, skolem_meth else if is_arith_rule rule then ([], arith_methods) else ([], rewrite_methods)) ||> massage_methods val prove = Prove { qualifiers = [], obtains = obtains, label = label, goal = goal, subproofs = [], facts = ([], []), proof_methods = proof_methods, comment = ""} in (prove, ctxt |> not (null obtains) ? (Variable.add_fixes (map fst obtains) #> snd)) end val (lems, _) = fold_map add_lemma (map_filter (get_role (member (op =) [Definition, Lemma])) atp_proof) ctxt val bot = #1 (List.last atp_proof) val refute_graph = atp_proof |> map (fn (name, _, _, _, from) => (from, name)) |> make_refute_graph bot |> fold (Atom_Graph.default_node o rpair ()) conjs val axioms = axioms_of_refute_graph refute_graph conjs val tainted = tainted_atoms_of_refute_graph refute_graph conjs val is_clause_tainted = exists (member (op =) tainted) val steps = Symtab.empty |> fold (fn (name as (s, _), role, t, rule, _) => Symtab.update_new (s, (rule, t |> (if is_clause_tainted [name] then HOLogic.dest_Trueprop #> role <> Conjecture ? s_not #> fold exists_of (map Var (Term.add_vars t [])) #> HOLogic.mk_Trueprop else I)))) atp_proof fun is_referenced_in_step _ (Let _) = false | is_referenced_in_step l (Prove {subproofs, facts = (ls, _), ...}) = member (op =) ls l orelse exists (is_referenced_in_proof l) subproofs and is_referenced_in_proof l (Proof {steps, ...}) = exists (is_referenced_in_step l) steps (* We try to introduce pure lemmas (not "obtains") close to where they are used. *) fun insert_lemma_in_step lem (step as Prove {qualifiers, obtains, label, goal, subproofs, facts = (ls, gs), proof_methods, comment}) = let val l' = the (label_of_isar_step lem) in if member (op =) ls l' then [lem, step] else let val refs = map (is_referenced_in_proof l') subproofs in if length (filter I refs) = 1 then [Prove { qualifiers = qualifiers, obtains = obtains, label = label, goal = goal, subproofs = map2 (fn false => I | true => insert_lemma_in_proof lem) refs subproofs, facts = (ls, gs), proof_methods = proof_methods, comment = comment}] else [lem, step] end end and insert_lemma_in_steps lem [] = [lem] | insert_lemma_in_steps lem (step :: steps) = if not (null (obtains_of_isar_step lem)) orelse is_referenced_in_step (the (label_of_isar_step lem)) step then insert_lemma_in_step lem step @ steps else step :: insert_lemma_in_steps lem steps and insert_lemma_in_proof lem (proof as Proof {steps, ...}) = isar_proof_with_steps proof (insert_lemma_in_steps lem steps) val rule_of_clause_id = fst o the o Symtab.lookup steps o fst val finish_off = close_form #> rename_bound_vars fun prop_of_clause [(num, _)] = Symtab.lookup steps num |> the |> snd |> finish_off | prop_of_clause names = let val lits = map (HOLogic.dest_Trueprop o snd) (map_filter (Symtab.lookup steps o fst) names) in (case List.partition (can HOLogic.dest_not) lits of (negs as _ :: _, pos as _ :: _) => s_imp (Library.foldr1 s_conj (map HOLogic.dest_not negs), Library.foldr1 s_disj pos) | _ => fold (curry s_disj) lits \<^term>\<open>False\<close>) end |> HOLogic.mk_Trueprop |> finish_off fun maybe_show outer c = if outer andalso eq_set (op =) (c, conjs) then [Show] else [] fun isar_steps outer predecessor accum [] = accum |> (if tainted = [] then (* e.g., trivial, empty proof by Z3 *) cons (Prove { qualifiers = if outer then [Show] else [], obtains = [], label = no_label, goal = concl_t, subproofs = [], facts = sort_facts (the_list predecessor, []), proof_methods = massage_methods systematic_methods', comment = ""}) else I) |> rev | isar_steps outer _ accum (Have (id, (gamma, c)) :: infs) = let val l = label_of_clause c val t = prop_of_clause c val rule = rule_of_clause_id id val introduces_symbols = is_symbol_introduction_rule rule val deps = ([], []) |> fold add_fact_of_dependency gamma |> is_maybe_ext_rule rule ? add_global_fact [short_thm_name ctxt ext] |> sort_facts val meths = (if introduces_symbols then skolem_methods else if is_arith_rule rule then arith_methods else systematic_methods') |> massage_methods fun prove subproofs facts = Prove { qualifiers = maybe_show outer c, obtains = [], label = l, goal = t, subproofs = subproofs, facts = facts, proof_methods = meths, comment = ""} fun steps_of_rest step = isar_steps outer (SOME l) (step :: accum) infs in if is_clause_tainted c then (case gamma of [g] => if introduces_symbols andalso is_clause_tainted g andalso not (null accum) then let val fixes = introduced_symbols_of ctxt (prop_of_clause g) val subproof = Proof {fixes = fixes, assumptions = [], steps = rev accum} in isar_steps outer (SOME l) [prove [subproof] ([], [])] infs end else steps_of_rest (prove [] deps) | _ => steps_of_rest (prove [] deps)) else steps_of_rest (if introduces_symbols then (case introduced_symbols_of ctxt t of [] => prove [] deps | skos => Prove { qualifiers = [], obtains = skos, label = l, goal = t, subproofs = [], facts = deps, proof_methods = meths, comment = ""}) else prove [] deps) end | isar_steps outer predecessor accum (Cases cases :: infs) = let fun isar_case (c, subinfs) = isar_proof false [] [(label_of_clause c, prop_of_clause c)] [] subinfs val c = succedent_of_cases cases val l = label_of_clause c val t = prop_of_clause c val step = Prove { qualifiers = maybe_show outer c, obtains = [], label = l, goal = t, subproofs = map isar_case (filter_out (null o snd) cases), facts = sort_facts (the_list predecessor, []), proof_methods = massage_methods systematic_methods', comment = ""} in isar_steps outer (SOME l) (step :: accum) infs end and isar_proof outer fixes assumptions lems infs = let val steps = fold_rev insert_lemma_in_steps lems (isar_steps outer NONE [] infs) in Proof {fixes = fixes, assumptions = assumptions, steps = steps} end val canonical_isar_proof = refute_graph |> trace ? tap (tracing o prefix "Refute graph:\n" o string_of_refute_graph) |> redirect_graph axioms tainted bot |> trace ? tap (tracing o prefix "Direct proof:\n" o string_of_direct_proof) |> isar_proof true params assms lems |> postprocess_isar_proof_remove_show_stuttering |> postprocess_isar_proof_remove_unreferenced_steps I |> relabel_isar_proof_canonically val ctxt = ctxt |> enrich_context_with_local_facts canonical_isar_proof val preplay_data = Unsynchronized.ref Canonical_Label_Tab.empty val _ = fold_isar_steps (fn meth => K (set_preplay_outcomes_of_isar_step ctxt preplay_timeout preplay_data meth [])) (steps_of_isar_proof canonical_isar_proof) () fun str_of_preplay_outcome outcome = if Lazy.is_finished outcome then string_of_play_outcome (Lazy.force outcome) else "?" fun str_of_meth l meth = string_of_proof_method [] meth ^ " " ^ str_of_preplay_outcome (preplay_outcome_of_isar_step_for_method (!preplay_data) l meth) fun comment_of l = map (str_of_meth l) #> commas fun trace_isar_proof label proof = if trace then tracing (timestamp () ^ "\n" ^ label ^ ":\n\n" ^ string_of_isar_proof ctxt subgoal subgoal_count (comment_isar_proof comment_of proof) ^ "\n") else () fun comment_of l (meth :: _) = (case (verbose, Lazy.force (preplay_outcome_of_isar_step_for_method (!preplay_data) l meth)) of (false, Played _) => "" | (_, outcome) => string_of_play_outcome outcome) val (play_outcome, isar_proof) = canonical_isar_proof |> tap (trace_isar_proof "Original") |> compress_isar_proof ctxt compress preplay_timeout preplay_data |> tap (trace_isar_proof "Compressed") |> postprocess_isar_proof_remove_unreferenced_steps (do_preplay ? keep_fastest_method_of_isar_step (!preplay_data) #> minimize ? minimize_isar_step_dependencies ctxt preplay_data) |> tap (trace_isar_proof "Minimized") |> `(if do_preplay then preplay_outcome_of_isar_proof (!preplay_data) else K (Play_Timed_Out Time.zeroTime)) ||> (comment_isar_proof comment_of #> chain_isar_proof #> kill_useless_labels_in_isar_proof #> relabel_isar_proof_nicely #> rationalize_obtains_in_isar_proofs ctxt) in (case (num_chained, add_isar_steps (steps_of_isar_proof isar_proof) 0) of (0, 1) => one_line_proof_text (if is_less (play_outcome_ord (play_outcome, one_line_play)) then (case isar_proof of Proof {steps = [Prove {qualifiers = [Show], facts = (_, gfs), proof_methods = meth :: _, ...}], ...} => let val used_facts' = map_filter (fn s => if exists (fn (p, (sc, _)) => content_of_pretty p = s andalso sc = Chained) used_facts then NONE else SOME (Pretty.str s, (Global, General))) gfs in ((used_facts', (meth, play_outcome)), banner, subgoal, subgoal_count) end | _ => one_line_params) else one_line_params) ^ (if isar_proofs = SOME true then "\n(No Isar proof available)" else "") | (_, num_steps) => let val msg = (if verbose then [string_of_int num_steps ^ " step" ^ plural_s num_steps] else []) @ (if do_preplay then [string_of_play_outcome play_outcome] else []) in one_line_proof_text one_line_params ^ (if isar_proofs <> NONE orelse (case play_outcome of Played _ => true | _ => false) then "\n\nIsar proof" ^ (commas msg |> not (null msg) ? enclose " (" ")") ^ ":\n" ^ Active.sendback_markup_command (string_of_isar_proof ctxt subgoal subgoal_count isar_proof) else "") end) end end in if debug then generate_proof_text () else (case try generate_proof_text () of SOME s => s | NONE => one_line_proof_text one_line_params ^ (if isar_proofs = SOME true then "\nWarning: Isar proof construction failed" else "")) end fun isar_proof_would_be_a_good_idea (_, play) = (case play of Played _ => false | Play_Timed_Out time => time > Time.zeroTime | Play_Failed => true) fun proof_text ctxt debug isar_proofs smt_proofs isar_params num_chained (one_line_params as ((_, preplay), _, _, _)) = (if isar_proofs = SOME true orelse (isar_proofs = NONE andalso isar_proof_would_be_a_good_idea preplay) then isar_proof_text ctxt debug num_chained isar_proofs smt_proofs isar_params else one_line_proof_text) one_line_params fun abduce_text ctxt tms = "Candidate missing assumption" ^ plural_s (length tms) ^ ":\n" ^ cat_lines (map (Syntax.string_of_term ctxt) tms) end; ¤ Dauer der Verarbeitung: 0.16 Sekunden (vorverarbeitet) ¤*© Formatika GbR, Deutschland |
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2026-03-28