| Quellcodebibliothek Statistik Leitseite products/sources/formale Sprachen/Isabelle/HOL/Prolog/ (Beweissystem Isabelle Version 2025-1©) Datei vom 16.11.2025 mit Größe 6 kB |
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Quelle prolog.ML Sprache: SML |
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(* Title: HOL/Prolog/prolog.ML
Author: David von Oheimb (based on a lecture on Lambda Prolog by Nadathur) *) structure Prolog = struct exception not_HOHH; fun isD t = case t of Const(\<^const_name>\<open>Trueprop\<close>,_)$t => isD t | Const(\<^const_name>\<open>HOL.conj\<close> ,_)$l$r => isD l andalso isD r | Const(\<^const_name>\<open>HOL.implies\<close>,_)$l$r => isG l andalso isD r | Const(\<^const_name>\<open>Pure.imp\<close>,_)$l$r => isG l andalso isD r | Const(\<^const_name>\<open>All\<close>,_)$Abs(s,_,t) => isD t | Const(\<^const_name>\<open>Pure.all\<close>,_)$Abs(s,_,t) => isD t | Const(\<^const_name>\<open>HOL.disj\<close>,_)$_$_ => false | Const(\<^const_name>\<open>Ex\<close> ,_)$_ => false | Const(\<^const_name>\<open>Not\<close>,_)$_ => false | Const(\<^const_name>\<open>True\<close>,_) => false | Const(\<^const_name>\<open>False\<close>,_) => false | l $ r => isD l | Const _ (* rigid atom *) => true | Bound _ (* rigid atom *) => true | Free _ (* rigid atom *) => true | _ (* flexible atom, anything else *) and isG t = case t of Const(\<^const_name>\<open>Trueprop\<close>,_)$t => isG t | Const(\<^const_name>\<open>HOL.conj\<close> ,_)$l$r => isG l andalso isG r | Const(\<^const_name>\<open>HOL.disj\<close> ,_)$l$r => isG l andalso isG r | Const(\<^const_name>\<open>HOL.implies\<close>,_)$l$r => isD l andalso isG r | Const(\<^const_name>\<open>Pure.imp\<close>,_)$l$r => isD l andalso isG r | Const(\<^const_name>\<open>All\<close>,_)$Abs(_,_,t) => isG t | Const(\<^const_name>\<open>Pure.all\<close>,_)$Abs(_,_,t) => isG t | Const(\<^const_name>\<open>Ex\<close> ,_)$Abs(_,_,t) => isG t | Const(\<^const_name>\<open>True\<close>,_) => true | Const(\<^const_name>\<open>Not\<close>,_)$_ => false | Const(\<^const_name>\<open>False\<close>,_) => false | _ (* atom *) => true; val check_HOHH_tac1 = PRIMITIVE (fn thm => if isG (Thm.concl_of thm) then thm else raise not_HOHH); val check_HOHH_tac2 = PRIMITIVE (fn thm => if forall isG (Thm.prems_of thm) then thm else raise not_HOHH); fun check_HOHH thm = (if isD (Thm.concl_of thm) andalso forall isG (Thm.prems_of thm) then thm else raise not_HOHH); fun atomizeD ctxt thm = let fun at thm = case Thm.concl_of thm of _$(Const(\<^const_name>\<open>All\<close> ,_)$Abs(s,_,_))=> let val s' = if s="P" then "PP" else s in at(thm RS (Rule_Insts.read_instantiate ctxt [((("x", 0), Position.none), s')] [s'] spec) end | _$(Const(\<^const_name>\<open>HOL.conj\<close>,_)$_$_) => at(thm RS conjunct1)@at(thm RS con | _$(Const(\<^const_name>\<open>HOL.implies\<close>,_)$_$_) => at(thm RS mp) | _ => [thm] in map zero_var_indexes (at thm) end; val atomize_ss = (empty_simpset \<^context> |> Simplifier.set_mksimps (mksimps mksimps_pairs)) addsimps [ @{thm all_conj_distrib}, (* "(! x. P x & Q x) = ((! x. P x) & (! x. Q x))" *) @{thm imp_conjL} RS sym, (* "(D :- G1 :- G2) = (D :- G1 & G2)" *) @{thm imp_conjR}, (* "(D1 & D2 :- G) = ((D1 :- G) & (D2 :- G))" *) @{thm imp_all}] (* "((!x. D) :- G) = (!x. D :- G)" *) |> simpset_of; (*val hyp_resolve_tac = Subgoal.FOCUS_PREMS (fn {prems, ...} => resolve_tac (maps atomizeD prems) 1); -- is nice, but cannot instantiate unknowns in the assumptions *) fun hyp_resolve_tac ctxt = SUBGOAL (fn (subgoal, i) => let fun ap (Const(\<^const_name>\<open>All\<close>,_)$Abs(_,_,t))=(case ap t of (k,a,t) => (k+1,a ,t | ap (Const(\<^const_name>\<open>HOL.implies\<close>,_)$_$t) =(case ap t of (k,_,t) => (k,true ,t | ap t = (0,false,t); (* fun rep_goal (Const (@{const_name Pure.all},_)$Abs (_,_,t)) = rep_goal t | rep_goal (Const (@{const_name Pure.imp},_)$s$t) = (case rep_goal t of (l,t) => (s::l,t)) | rep_goal t = ([] ,t); val (prems, Const(@{const_name Trueprop}, _)$concl) = rep_goal (#3(dest_state (st,i))); *) val prems = Logic.strip_assums_hyp subgoal; val concl = HOLogic.dest_Trueprop (Logic.strip_assums_concl subgoal); fun drot_tac k i = DETERM (rotate_tac k i); fun spec_tac 0 i = all_tac | spec_tac k i = EVERY' [dresolve_tac ctxt [spec], drot_tac ~1, spec_tac (k-1)] i; fun dup_spec_tac k i = if k = 0 then all_tac else EVERY' [DETERM o (eresolve_tac ctxt [all_dupE]), drot_tac ~2, spec_tac (k-1)] i; fun same_head _ (Const (x,_)) (Const (y,_)) = x = y | same_head k (s$_) (t$_) = same_head k s t | same_head k (Bound i) (Bound j) = i = j + k | same_head _ _ _ = true; fun mapn f n [] = [] | mapn f n (x::xs) = f n x::mapn f (n+1) xs; fun pres_tac (k,arrow,t) n i = drot_tac n i THEN ( if same_head k t concl then dup_spec_tac k i THEN (if arrow then eresolve_tac ctxt [mp] i THEN drot_tac (~n) i else assume_tac ctxt i) else no_tac); val ptacs = mapn (fn n => fn t => pres_tac (ap (HOLogic.dest_Trueprop t)) n i) 0 prems; in Library.foldl (op APPEND) (no_tac, ptacs) end); fun ptac ctxt prog = let val proga = maps (atomizeD ctxt) prog (* atomize the prog *) in (REPEAT_DETERM1 o FIRST' [ resolve_tac ctxt [TrueI], (* "True" *) resolve_tac ctxt [conjI], (* "[| P; Q |] ==> P & Q" *) resolve_tac ctxt [allI], (* "(!!x. P x) ==> ! x. P x" *) resolve_tac ctxt [exI], (* "P x ==> ? x. P x" *) resolve_tac ctxt [impI] THEN' (* "(P ==> Q) ==> P --> Q" *) asm_full_simp_tac (put_simpset atomize_ss ctxt) THEN' (* atomize the asms *) (REPEAT_DETERM o (eresolve_tac ctxt [conjE])) (* split the asms *) ]) ORELSE' resolve_tac ctxt [disjI1,disjI2] (* "P ==> P | Q","Q ==> P | Q"*) ORELSE' ((resolve_tac ctxt proga APPEND' hyp_resolve_tac ctxt) THEN' (fn _ => check_HOHH_tac2)) end; fun prolog_tac ctxt prog = check_HOHH_tac1 THEN DEPTH_SOLVE (ptac ctxt (map check_HOHH prog) 1); val prog_HOHH = []; end; ¤ Dauer der Verarbeitung: 0.10 Sekunden (vorverarbeitet) ¤*© Formatika GbR, Deutschland |
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2026-03-28