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Quellcode-Bibliothek© Kompilation durch diese Firma[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]Datei: TEST.properties Sprache: PVSOriginal von: PVS© |
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% predicate_coordination.pvs - General Theory of Coordination for 3D Maneuvers %------------------------------------------------------------------------------ predicate_coordination: THEORY BEGIN IMPORTING definitions_3D s,v,nv, nw,vo,nvo, vi,nvi : VAR Vect3 eps : VAR Sign pr : VAR posreal l,l1,l2 : VAR real Criter: TYPE = [[Vect3,Vect3]->set[Vect3]] SignedCrit: TYPE = [Sign -> Criter] Vector_Predicate: TYPE+ = [[Vect3,Vect3]->set[Vect3]] Crit,Crit1,Crit2,Crit3: VAR Criter Scrit,Scrit1,Scrit2,Scrit3: VAR SignedCrit C : VAR Vector_Predicate % BASIC DEFINITIONS sum_closed?(C): bool = FORALL (s,v,nv,nw:Vect3): C(s,v)(nv) AND C(s,v)(nw) IMPLIES C(s,v)(nv+nw) symmetric?(C) : bool = FORALL (s,v,nv:Vect3): C(s,v)(nv) IFF C(-s,-v)(-nv) crit_sum_closed?(Crit): bool = FORALL (s,v,nv,nw:Vect3): Crit(s,v)(nv) AND Crit(s,v)(nw) IMPLIES Crit(s,v)(nv+nw) sum_independent?(Crit,C): bool = FORALL (v,s,nv,nw: Vect3): (Crit(s,v)(nv) AND Crit(s,v)(nw) AND C(s,v)(v) IMPLIES NOT C(s,v)(nv+nw)) open?(C): bool = FORALL (s,v,nv: Vect3): C(s,v)(nv) IMPLIES (EXISTS (epsilon:posreal): FORALL (nw: Vect3): norm(nw)<epsilon IMPLIES C(s,v)(nv+nw)) crit_independent_of_length?(Crit): bool = FORALL (v,s,nv: Vect3,pr: posreal): (Crit(s,v)(nv) IFF Crit(s,pr*v)(nv)) independent_of_length?(C): bool = FORALL (s,v,nv:Vect3,pr,pz:posreal): (C(s,v)(nv) IFF C(s,pz*v)(pr*nv)) coordinated?(Crit1,Crit2,C): bool = FORALL (vo,vi,nvo,nvi,s: Vect3): (C(s,vo-vi)(vo-vi) AND Crit1(s,vo-vi)(nvo-vi) AND Crit2(-s,vi-vo)(nvi-vo) IMPLIES NOT C(s,vo-vi)(nvo-nvi)) coordinated_symmetric: LEMMA symmetric?(C) IMPLIES (coordinated?(Crit1,Crit2,C) IFF coordinated?(Crit2,Crit1,C)) crit_symmetric?(Crit): bool = FORALL (v,s,nv: Vect3): (Crit(s,v)(nv) IFF Crit(-s,-v)(-nv)) sum_indep_coordinated: LEMMA crit_symmetric?(Crit) AND sum_independent?(Crit,C) AND sum_closed?(C) IMPLIES coordinated?(Crit,Crit,C) coordinated_sum_indep: LEMMA crit_symmetric?(Crit) AND crit_independent_of_length?(Crit) AND coordinated?(Crit,Crit,C) AND open?(C) AND independent_of_length?(C) IMPLIES sum_independent?(Crit,C) crit_antisymmetric?(Scrit): bool = FORALL (v,s,nv: Vect3, eps:Sign): (Scrit(eps)(s,v)(nv) IFF Scrit(-eps)(-s,-v)(-nv)) sum_indep_coordinated_antisym: LEMMA crit_antisymmetric?(Scrit) AND sum_independent?(Scrit(eps),C) AND sum_closed?(C) IMPLIES coordinated?(Scrit(eps),Scrit(-eps),C) coordinated_antisym_sum_indep: LEMMA crit_antisymmetric?(Scrit) AND crit_independent_of_length?(Scrit(eps)) AND coordinated?(Scrit(eps),Scrit(-eps),C) AND open?(C) AND independent_of_length?(C) IMPLIES sum_independent?(Scrit(eps),C) % The DERIVED Criterion deriv(Crit,l): Criter = (LAMBDA (s,v): (LAMBDA (nv): Crit(s,v)(nv-l*v))) deriv_0: LEMMA deriv(Crit,0) = Crit deriv_subset: LEMMA Crit(s,v)(-l*v) AND crit_sum_closed?(Crit) IMPLIES subset?(Crit(s,v),deriv(Crit,l)(s,v)) deriv_coordinated: LEMMA l1+l2 = 1 IMPLIES crit_symmetric?(Crit) AND sum_independent?(Crit,C) IMPLIES coordinated?(deriv(Crit,l1),deriv(Crit,l2),C) deriv_coordinated_1: LEMMA crit_symmetric?(Crit) AND sum_independent?(Crit,C) IMPLIES coordinated?(deriv(Crit,1),Crit,C) Comb(Crit1,Crit2): Criter = (LAMBDA (s,v): (LAMBDA (nv): Crit1(s,v)(nv) OR (Crit2(s,v)(nv Comb_coordinated: LEMMA sum_independent?(Crit1,C) AND crit_symmetric?(Crit1) AND coordinated?(Crit2,Crit3,C) AND sum_closed?(C) AND symmetric?(C) IMPLIES coordinated?(Comb(Crit1,Crit2),Comb(Crit1,Crit3),C) END predicate_coordination ¤ Dauer der Verarbeitung: 0.21 Sekunden (vorverarbeitet) ¤ |
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