| Quellcodebibliothek Statistik Leitseite products/sources/formale Sprachen/Isabelle/FOLP/ (Beweissystem Isabelle Version 2025-1©) Datei vom 16.11.2025 mit Größe 6 kB |
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Quelle classical.ML Sprache: SML |
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(* Title: FOLP/classical.ML
Author: Lawrence C Paulson, Cambridge University Computer Laboratory Copyright 1992 University of Cambridge Like Provers/classical but modified because match_tac is unsuitable for proof objects. Theorem prover for classical reasoning, including predicate calculus, set theory, etc. Rules must be classified as intr, elim, safe, hazardous. A rule is unsafe unless it can be applied blindly without harmful results. For a rule to be safe, its premises and conclusion should be logically equivalent. There should be no variables in the premises that are not in the conclusion. *) signature CLASSICAL_DATA = sig val mp: thm (* [| P-->Q; P |] ==> Q *) val not_elim: thm (* [| ~P; P |] ==> R *) val swap: thm (* ~P ==> (~Q ==> P) ==> Q *) val sizef : thm -> int (* size function for BEST_FIRST *) val hyp_subst_tacs: Proof.context -> (int -> tactic) list end; (*Higher precedence than := facilitates use of references*) infix 4 addSIs addSEs addSDs addIs addEs addDs; signature CLASSICAL = sig type claset val empty_cs: claset val addDs : claset * thm list -> claset val addEs : claset * thm list -> claset val addIs : claset * thm list -> claset val addSDs: claset * thm list -> claset val addSEs: claset * thm list -> claset val addSIs: claset * thm list -> claset val print_cs: Proof.context -> claset -> unit val rep_cs: claset -> {safeIs: thm list, safeEs: thm list, hazIs: thm list, hazEs: thm list, safe0_brls:(bool*thm)list, safep_brls: (bool*thm)list, haz_brls: (bool*thm)list} val best_tac : Proof.context -> claset -> int -> tactic val contr_tac : Proof.context -> int -> tactic val fast_tac : Proof.context -> claset -> int -> tactic val inst_step_tac : Proof.context -> int -> tactic val joinrules : thm list * thm list -> (bool * thm) list val mp_tac: Proof.context -> int -> tactic val safe_tac : Proof.context -> claset -> tactic val safe_step_tac : Proof.context -> claset -> int -> tactic val slow_step_tac : Proof.context -> claset -> int -> tactic val step_tac : Proof.context -> claset -> int -> tactic val swapify : thm list -> thm list val swap_res_tac : Proof.context -> thm list -> int -> tactic val uniq_mp_tac: Proof.context -> int -> tactic end; functor Classical(Data: CLASSICAL_DATA): CLASSICAL = struct local open Data in (** Useful tactics for classical reasoning **) val imp_elim = make_elim mp; (*Solve goal that assumes both P and ~P. *) fun contr_tac ctxt = eresolve_tac ctxt [not_elim] THEN' assume_tac ctxt; (*Finds P-->Q and P in the assumptions, replaces implication by Q *) fun mp_tac ctxt i = eresolve_tac ctxt ([not_elim,imp_elim]) i THEN assume_tac ctxt i; (*Like mp_tac but instantiates no variables*) fun uniq_mp_tac ctxt i = ematch_tac ctxt ([not_elim,imp_elim]) i THEN uniq_assume_tac ctxt i (*Creates rules to eliminate ~A, from rules to introduce A*) fun swapify intrs = intrs RLN (2, [swap]); (*Uses introduction rules in the normal way, or on negated assumptions, trying rules in order. *) fun swap_res_tac ctxt rls = let fun tacf rl = resolve_tac ctxt [rl] ORELSE' eresolve_tac ctxt [rl RSN (2, swap)] in assume_tac ctxt ORELSE' contr_tac ctxt ORELSE' FIRST' (map tacf rls) end; (*** Classical rule sets ***) datatype claset = CS of {safeIs: thm list, safeEs: thm list, hazIs: thm list, hazEs: thm list, (*the following are computed from the above*) safe0_brls: (bool*thm)list, safep_brls: (bool*thm)list, haz_brls: (bool*thm)list}; fun rep_cs (CS x) = x; (*For use with biresolve_tac. Combines intrs with swap to catch negated assumptions. Also pairs elims with true. *) fun joinrules (intrs,elims) = map (pair true) (elims @ swapify intrs) @ map (pair false) intrs; (*Note that allE precedes exI in haz_brls*) fun make_cs {safeIs,safeEs,hazIs,hazEs} = let val (safe0_brls, safep_brls) = (*0 subgoals vs 1 or more*) List.partition Bires.no_subgoals (sort Bires.subgoals_ord (joinrules(safeIs, safeEs))) in CS{safeIs=safeIs, safeEs=safeEs, hazIs=hazIs, hazEs=hazEs, safe0_brls=safe0_brls, safep_brls=safep_brls, haz_brls = sort Bires.subgoals_ord (joinrules(hazIs, hazEs))} end; (*** Manipulation of clasets ***) val empty_cs = make_cs{safeIs=[], safeEs=[], hazIs=[], hazEs=[]}; fun print_cs ctxt (CS{safeIs,safeEs,hazIs,hazEs,...}) = writeln (cat_lines (["Introduction rules"] @ map (Thm.string_of_thm ctxt) hazIs @ ["Safe introduction rules"] @ map (Thm.string_of_thm ctxt) safeIs @ ["Elimination rules"] @ map (Thm.string_of_thm ctxt) hazEs @ ["Safe elimination rules"] @ map (Thm.string_of_thm ctxt) safeEs)); fun (CS{safeIs,safeEs,hazIs,hazEs,...}) addSIs ths = make_cs {safeIs=ths@safeIs, safeEs=safeEs, hazIs=hazIs, hazEs=hazEs}; fun (CS{safeIs,safeEs,hazIs,hazEs,...}) addSEs ths = make_cs {safeIs=safeIs, safeEs=ths@safeEs, hazIs=hazIs, hazEs=hazEs}; fun cs addSDs ths = cs addSEs (map make_elim ths); fun (CS{safeIs,safeEs,hazIs,hazEs,...}) addIs ths = make_cs {safeIs=safeIs, safeEs=safeEs, hazIs=ths@hazIs, hazEs=hazEs}; fun (CS{safeIs,safeEs,hazIs,hazEs,...}) addEs ths = make_cs {safeIs=safeIs, safeEs=safeEs, hazIs=hazIs, hazEs=ths@hazEs}; fun cs addDs ths = cs addEs (map make_elim ths); (*** Simple tactics for theorem proving ***) (*Attack subgoals using safe inferences*) fun safe_step_tac ctxt (CS{safe0_brls,safep_brls,...}) = FIRST' [uniq_assume_tac ctxt, uniq_mp_tac ctxt, biresolve_tac ctxt safe0_brls, FIRST' (hyp_subst_tacs ctxt), biresolve_tac ctxt safep_brls] ; (*Repeatedly attack subgoals using safe inferences*) fun safe_tac ctxt cs = DETERM (REPEAT_FIRST (safe_step_tac ctxt cs)); (*These steps could instantiate variables and are therefore unsafe.*) fun inst_step_tac ctxt = assume_tac ctxt APPEND' contr_tac ctxt; (*Single step for the prover. FAILS unless it makes progress. *) fun step_tac ctxt (cs as (CS{haz_brls,...})) i = FIRST [safe_tac ctxt cs, inst_step_tac ctxt i, biresolve_tac ctxt haz_brls i]; (*** The following tactics all fail unless they solve one goal ***) (*Dumb but fast*) fun fast_tac ctxt cs = SELECT_GOAL (DEPTH_SOLVE (step_tac ctxt cs 1)); (*Slower but smarter than fast_tac*) fun best_tac ctxt cs = SELECT_GOAL (BEST_FIRST (Thm.no_prems, sizef) (step_tac ctxt cs 1)); (*Using a "safe" rule to instantiate variables is unsafe. This tactic allows backtracking from "safe" rules to "unsafe" rules here.*) fun slow_step_tac ctxt (cs as (CS{haz_brls,...})) i = safe_tac ctxt cs ORELSE (assume_tac ctxt i APPEND biresolve_tac ctxt haz_brls i); end; end; ¤ Dauer der Verarbeitung: 0.15 Sekunden (vorverarbeitet) ¤*© Formatika GbR, Deutschland |
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2026-03-28