A Modal Lambda Calculus with Iteration and Case Constructs
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Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. A Modal Lambda Calculus with Iteration and Case Constructs Pierre Leleu. N˚ 3322 Décembre 1997. THÈME 2. ISSN 0249-6399. apport de recherche.
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(24) !#"$%'&)(* #+, +-.&/+0%1(%0# * K*. 8", ,. M. . M. ). H EH. : *30 _QSQTQ . 0. . ( ) . *. H . 0 * I*. M. H EH. H EH. * * 0 = _QSQTQ. : *30 _QSQTQ. *. H . *. =. * . H. l :/ * =. Il : / * =. *. 8:9<>-=RLg l _XJ1= K1_XJ1T<FljPcWYg[>3U:PaJPcW]g[>3UiGHU:>]Pa>Flj<>3jJ}L>3_glT<_X>EPcWYg[>3U:ZYW Pa9<>t JLIHJ}&GHF<K>3\]TlRSPXGHJLF>V l : F H J =, l : F = H l : J = 8:9<>tPcWYg<GHF<K?_aT<I>2U JL_edR1U>-RSF"j¢¨PQRL_X>EPX9l>t JLIHJ}&GHF<KJLF<>2UV E XZY [ @ /b 8 *0 I /+E @ Ab ;S U 8 0 0 * I J TS U9S I l : / = d: RLUX> = @ * K Il : / E = hl j dRLUX> b JL : b ;S U = 8 ( . . ) ( . . . . . ). . . . : ¢¨P =. @/b. 8. ) . 0 * I/ E. . @AbnK TS U 8. ). ( ) (. . . . . * ) * . 0. *. E XZY [ l : TS UDS = I l : / = 0. J. ¨¢ P b JL : b K TS U = 8 0 l : * = I l : / E = Z[>9"8: R]9<IPaGH>2JL9<UTlJL> _T<PcK1JLW]95 $glPaG>9<F<>(Kg<_Xd_X>2T<RLUXIHUXUX>3>t>3U j5RS=FlRjRZlW§¢¨GPiP*UX>JLj>3g[G= L[>>3_k_XR}M>3PaJLF]JL=?PX_kIHU¯g<WLIH&V>OJ1GPXT<9R}_EP*_aPc>3W]lUXgl_kg"UG>2F<P(M KP:UGH_aPXKLT<J9]IP >2_a>3U-Zlj<TRSTl_aP M >(PaPaGUX9<J1G>=?F WGH3/I URSRL>2_a_EM >PXPXGHFlJJLRSF"PXPXUi9<T<J]@_kURSG>PIHlW§GHFW@j OQ5 >pe9O_a GH^fL>3j§rO 8_aVJL>= <MOPX>9lg<>P Pa9<_a>>tF<JSPkRSZ<IH>-jGL[>3_X>3FlMO>2UV 1 U`FlJSPXGNMO>2j Z[>O J1_X>1}PX9l>=?Jj<RLI<MOJL_a>:GHU`j<MG Lª>_a>F]P3 À§>9"RL>:MOJLF]Pa>OYPUcPkRLMkU GFlUPX>2RLj(JS "PcfJ-MOJ1F]PX>OYPkU RSFljJLTl_&=Jj<RLI_XTlI>2U 3 f 9O 3 g 9RSFlj 3 ^ JLg-9:RS_a>e>Ygl_X>2UXUX>3jGFRL>3_XW UXG=?g<IH>-:RW3IHG1>EGHFN5 ^À¹rQPB8C9 1 ¢FJ1T<_IHR1UcPPcfJ PcWYg<GFlK(_aT<IH>3U¯PX9<>EPX>3_X=U b TS U RSFlj bnK ;S U RL_X>ER*g<_aGJ1_XG[GHFlj>O>2j ZYW RSIH[PX9<>EGF"j>O>3U JSb [TPXS 9<U >e3 JLMO_JLF"bnUcPaK_XTTlS U MO9`PXJ1g"_a>3U3_¯¥MO8:J19<FlGNUcU`Pa_X=?T">3M RLPXJ1Fl_ U PRPX9lTRSS UYP JL_`M Pa>2TlRLRSMk9IH WLdLRLUX>i>:jJLJ-_`¢¨F<PfJLMP¯JLF<Fl>3U>3PXj_aTlRSM IHP2<SJL ">iPa9<U>9<=J1T<INÀÂj(j9<>>lF F<M>iJLJ1=?F<g<>TPXPa>3G_XFl= K J}RSL_a>->3_f = GHFlTjPaTlTlMORSPXIHGHLWª>e¡1GPXFl>3j<_X=TlM UPaGJS1 V>LPc`WY8:g[9<E> GN/U¯EF<YJLPXfGHJL>EFJLF<GNUIHW>2UXF<UX>3>>3F]jPXGNRSPaJIl j<JL>O_lRtF< >ETPaPX9<Tl>Q_X>ePa>G=?_a=g<UIH>b=?>TF]S U-PkR}UXPXTlGHMkJL9 FPaJL9l VR}RSP F / >E ]PaRS>FlFlBj UXGH/JLF JSf > PXg<9l_XGHUiJ}1UX>eWUcGHPaF>= PX9l>-RLUi JLR?IHJ}IHJL&K1GHGHF<M3K"RSIªf 8:_kRS9<=?>*>GHF]PXJL>3_a_X>2UcZ<Pa>3TjPQGN_XUi>2RL\]jT<>3GPX_&>-&J1G_IHVPa9<"JLFlK1jJLFlPX9<RL>(I"PajJ?>OlPX9<Fl> GPag<GJ1_XFJ1g"JS>3 _= PaG>2TU:PaTlfRS>*I$UGFlPaRSj<PXTl>*M PaRLGFl1j > PcWYg">2U&f>-MJLT<INjR1jJLg<P:9l>_a>*MOJL=?g<IH>OPa>IHW JL_a=RSIHG®3>3jGF 5 pe^¯<r O8¨ 1 ¦ T<_ dRLUX>(MJLFlUPX_aTlM PtMOJ1T<IHj¬PaRLL>?RLUERS_aKLT<=?>F]PtR PcWYg[> F]3IHG1>(GHF 5 pE^¯Qr O8C9iGHFlUPX>3R1j¬JL fR=RLg l U_XGHKLJ1Fl=«G"KLM3_aRSJLF]T<YP F"3j¦ PcF¬WYg"Pa9<>2UQ>PaMOJJ1F1PcPaWY_ag[RL>3_XU3W1tl ¢J1Fl_Ej>PX>29<j¬>?Pa¢¨9<P*>MOJ1_XFl>2jUcPaTl_XM T"PaM GJ1P3VFRL_aIT< IHPa>39<UQ> JLPcW]_*g[d>3RLU UXl> : >/ F"U= T<_aUX>(TlMkPX99lRSPXPE9lRSJ1P F<I/ W l RS: Fl/ j E = / GHE U RSRS_aFl>tj= J1T<T_&PaTlMkRS9<IHJLWGNMOj>E>O "JLF<_i>3RLjF[TlRS_aF<>tG J1F<_X>=>2j>3g<j0_a>39OUX>¦ F]PaFlRSMPX>-GHJLRSFK1RLUXIHGGF¥K1Y91PXPa9<IWGNUiRSGNIHU&>3JL]_XGNPXR}9lPaJL>3UKLJ1PaFl9<RS>-I"F<PXJSJ?PkR}Pa9<PaG>*J1Flg<U_aJLg[>_XPXGH>3U:>-UcPkR}Pa> @ hl j. ( ) (. . . . *. [ []\^0_%_%`%`. *.
(25) #&)(%( & &) & 7 . %(! ' . $#& !. 8:RLFl9lj> ¢¨UP WU36PX5 ^`>3= À¹rQRLPIH8!J}9Oi U:Pa9<>(UaRS=?>-ZlR1UGNM*UPaRLMk=RSF<GHg<T<INR}PaGJ1FlUQR1U&Pa9<> =?Jj<RSIMRLIHMT<IHTlUi¢Yu&GPa9<JLTP*dRLUX> { µ µ y z 2µ N z2|<~98 | 3 |z µ y $ k '&)(% & ! 'Z!('& , k !(' & F !+W. +T &;:Q % Q$<9q ! %1 ! ! > & ! 'Z!('& 4 k 1" &ZY&ZZ!('& k '&(Z#"& k ! !+ +0 '- * #+0Z k 1" &Z '=< % . . . . % ('&'- !+ k +0'&T:Q1 6 ;&)(&)+T k ( ]1" & +T &;:Q k Z!('& F +< k 1" & k (% J .
(26). . @AC > C;@ K C > K C;@ K K. @AC > K C;@ K C > C(@ K K. #"E !+0+T !+ 'Q !+ Q& ( * #+N !+ % #Q&D +0'&T:Q + ! "&)(& !+N %'=< q @AC > C;@ K @JC > G N 8 F C(@ K k @AC > G N 8 F C;@LK B # & D < &+0 !+ 6Q !+ +0'&;: !+0' 1" &Z '= <9q + ! " &( &D&;: & '- !+,#"&Z %' B% !1 # + q @AC(@ K @AC > C(@ K k @AC > C;@LK B # %1( &+ 1" &+0 !+ *(&)Y !+ ++T+-& &% $( !Y& ( 1 # + q r!9& r & (* #+ k I B (% #Q) &D "Q #)" +- k ( & & !+1" & &(% ' & !(' & @AC > G N 8 F C(@ K @AC > C;@ K k % #+ ( & 'T !+ ) &Y&) ; + !+W4% Q$ <$ !. DYB( q; r!9& r Y&) M1 !+ * +0'&;:1D !+T . % !+ & +-& r.
(27). q. . . .
(28). . .
(29). . .
(30). . . @JC > C > K ;C @ K. @AC > G > K (C @ K. { µV8:µ 9<GNU&GNU:>3R1UGHIWg<_XJ}1>3jZ]WGFlj<TlM PaGJ1FJ1FPa9<>tPcWYg<GHF<KtbcTljK1=>3F]P3 j<>F<8:JL9<PX>*>3UFlPaJS9<PXGH>tJLFPX>3_XJS= UbTlZlUc&PaG9<PaT>3PX_XGH> JLFd GHUEGHUQjU>OT<"Z"F<Uc>3PajGPaTR1PXUi>2jTlUX TlJ1RS_ IN¥i¢¨ »Qb JSPX>td Pa9lR}RSP_aV>tPX>3_X=UERSFlj N5GHUeR }RS_aGHRLZ<IH>L b . . d. N. . :f b = :g b = : b TS U = = b: K TS U = =. d. N. . b d N = f : g : b d N = b d N : b ;S U d N = = : hl j b d N : b K TS U d N =M= h: l j . dRL¢¨UXP > b b JSLJ dd NN ¢¨dP RLUX> VJS VJS lRLZ"JL_XJ}PX1T<>F"V R}PX>3IWPX9<>_XT<IH> JL &UXT<ZlUPXGPXT<PXGHJLFGNU UPXGHIRLj=?GNUXUXGZlI>1$G >1g<_XJ}}RLZ<I>&GPX9 Pa9<>PcWYg<GHF<K¬_aT<IH>3U-K1G1>F : hl j : hl j. d. N. . [. bDc bed.
(31) r.
(32) !#"$%'&)(* #+, +-.&/+0%1(%0#. { µ" µ & y k z !µ2 !+ (% w? &Z¶ Qy2y x 1) z &9²¹% µ ¥x y3zD ± . . :. T % = @. . Jd. . 8. F. F. @AG N 8 / b @/b d N 8. 8. J. J. { µV8:µ 9<GNU&GNU:>3R1UGHIWg<_XJ}1>3jZ]WGFlj<TlM PaGJ1FJ1FPa9<>*j>3_XGH}R}PXGHJLFJS @AG N 8 F Ab 8 J Fµ z3|<z µ2 ¢¨ @ GHU(R}RSIHG jUPaR1MkJS O M L J ] F a P O > Y a P U > 0 C ITITI C > M RSF"j ^ GNU RLFGF]Pa>KL>3_3 @ E j>F<JLPX>2U-PX9l> UUPaPaR1R1MkMk H@ ¡`G&? 9<^ >3_X>§PX9< >IHR1UcP^¹MJLF]PX>YPaU-9lR1> Z[>>F _X>3=J}1>3j
(33) VH> 0 C ISITI C > M E G W^ 5RLFlj§PX9<>>=?gPcW PaRL9<Fl>8:j9<3 3 ^ >*¢¨P JLGH9 TgFY9QLl>3_aJL_aT<_UXIG>1J1GF"-FUc8:PkIHRS>9<=?Fl>(M=>L_a1T<RLPXIHUe>39<UQRS>E_aPX_X>-9lTlRSF<I> PEJSPe3= TlRLglULT"gT> RS9 I¥<GP*UXZ[>R>3>3M3FZ<RSGTl Pt_XUXJ1>*== J1J1T<_XZ">_&JLPPcMOPXWYJ1J1g<== GHF<glKIPX>J*_aT<PaRLJLI>2_XgVUQ>(YRL=_XTl_X>-RI>2W?F<DU Z<JL3 Pe_a >3UXRSg<W]?Tg F]9OPkR* R}=?Y3 "¨Jj<Ucj<%P_X9 GHRLL Il>33PcFVYWY<Flg[Z[0j> >39OM/ RLJ3TldUXR1G>-F]UPaB>JSJ 9 PcPaJ(JERLg<PcWYg<g"IHW(>2/U Pa9<FI>EH _XT<IHD> J 3/^ RLJLFlTg j9fRLFÂU¯&= 9<TlGNMkMk99R1RSU¯_a>Fl>eJ-M3=RS.F J1_X3 >:G/ >L=?J_aj<>=?RSIJ}L8:>i9]PXT"9<U>E1I&J9<M3RS>IªFMO JLRLF]MPa>3>OjY&PPXGPXGH9I [RSF?>QRS9"glRg<LI>&GNM RS_aPX>GH>EJLFV}RS1_afGHRL>Z<PaI_X>2W U JLRL FljPX9<PX>Q9<PX>3>3W_X= >F"GHRSFZ<IHPX>t9<>ETlU:IHJYPXM3J?RSI[K1GMO1JL>tF]PaR(>OYPcWYP 9Og[>*»QMk9<>1>3>Mk_XYPXGH9<F<>3KI>2RLUXIUK1JLPX9<_aG>QPa9< JL=IH J}&GHF<K*GHFYL>_kUXGJ1FI>3==R1U_a>=RSGHF RSGH_aIW?UGH=?g<IH> { µ µ y z 2µ s "± {}y µ ± |<Dy . . . . . .
(34) . .
(35). . . @ N F #"&)+.& !#"&)( 1" &D& ) ( 1 # + N F & + ' #"& +0'&;: k @Jq/ ( F k 1" & (% J 8 +-#"&DQ& ) ( * #+ N 8 F &) + 8 H@/r $ k @ N 8 F I b 8 FIH J 1" &+A@AG N 8 F /b 8 J r $ k @ : b d = 8 J #"&)+X#"&)( & .!(' & F %0%"N#"Q@ E b 8 F H J +-/@ E ad 8 F $ p q/ "&)( & ^ k J Z+- k 1" & k (% P +-41" &(% & ^ Z#"&Z & !+T & &)( %0)" ^ #" @ E +0' !+0: , _ & k ( & )& (% #E% &% k : b d = r $ k @ h b 0 G;b 1 j 8 F 4 J #"&)+ @ /b 0 8 F +< @ /b 1 8 J r $ k @ k b 8 F 1" &+N#"&)(& !(' & J %0%" 1" @ E ob 8 F 4 J ^ $ p E q " &( & ^ , _ k F Z+- k #"& k (% P +-41" &(% & ^ Z#"&Z &% !+T & &)(Z 0)" 1" R@ +0' !+0 ) & & (% #E% &% kRk %?b r k(&) $ k @ +<H b 8 J #"&)+,#"&)(& Z!('& F %0%" #"R@ E b 8 F 4 J ^ $ p E q " &( & ^ , _ k J Z+- k #"& k (% P +< #"&)(% & ^ 1" &D & B% !+0'& &( %0%"4#" @ +0' !+0 ) & & (% #E% &% k %+-) b r k(&) $ k @ f b 8 F 1" &/+ @AC I Ab 8 F r $ k @ g b 8 F 1" &A+ @ Ab 8 F r k. $k. . . .
(36). . .
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(42). . . . . . .
(43) q?. #&)(%( & &) & $k. +- ( +- Z!('& / , 0 M 0 0 * I* 0 * I / q +< E XY [ @ E /b ;S U 8 I l : / = k ( ^ $ p q "&)(& ^ , _ k 1" &:Z!('& F S+- k 0 0 * I JWTS UDS #"& k (% P +<4 #"&)(% & ^ #"&D & B% !+0'& &( %0%" 1" 1" &D / +T ;& :Q k @ E +T !+ Y& k ( & &B (% #Q) &) k)hl jB/B& b k : b TS U = r $ k @ hl jA$%ob k : b K ;S U = 8 F 1" &+ #"&)( & ( &'T(& !(' &%* 0 q ITITI q * +- E XZY [ (+-SZ!('& / %0)" #" F , 0 l : * = I l : / = q@ E Ab 8 0 * I / +-5@ E /bnK TS U 8 0 l : WJ TS U9S =MI l : / = k ( ^ $ p q " &( & ^ , _ k 1" & Z!('& F S+< k 1" & k (% P +- #"&)(% & ^ S1" & & B%/ !+0'& &( %0%"4#" #"&Z +0'&T:Q k @ E +0' !+0: & k ( & &)(% #E% &% k)hl jA$% b k : b K TS U = r.
(44). @. /B& %0)"W1" F hl j. . . . b. k. * ). . : b M T S U " = 8 ). * . . ). . . . q @ E Il : / * = Il : / = . . . q * ITISI R b 8. . . ) . . . ( . . ) ( . *. M. . . .
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(52) q2o.
(53) !#"$%'&)(* #+, +-.&/+0%1(%0#. $8 H J( »QTl_RSPaP39<>&_i9<GHIGNMkTl9UPX_X_k>R}PXPaT<>E_aFlPX9<U >*?_aG>3 j<GPaTlUiM PaRLG_XJ1K1FT<=?=?>3>MkF]9"PRSGNF<U&GNR(U= _X>3IH>->OPQ}RST"_aU&GHRLjZ<>OIl>1Flª>tqEPXG 9<>-GPi GNTlU&FlRSM FPaGJ1RSF5ZlU PX<_kJ1RL_XMO=PXGHJL¡<FJL ¥PXPc>WY_a=g[> RLFl:j/X@ H G GPiGNU&RSFRSg<glIGNMRSPXGHJLFV lJL_a= b 8", : hl j dRLUX> b JL 8 : /XH / =MI 8 : /XHO/ = I 8 : /XHO/XHO/ =MI e_&= lJL_&GHFlUPaRSF"MO>L : <JL_a= f & N 8 / I N = H : ^ 8 »eR}P I ^ _$= H _ RLFlj : <JL_a= f N 8 / IJ: INRS= 8 / I N = = H : ^ 8 »eR}P IJ: 8 : / H / HO/ = I f & N 8 / I 8 / I N =_&= H / =. . . . . . . . . . . . . . . . . ')#& , $ !. aP»QUXJe>J}>3J1FZ>2PaRLRS>QG_aFIjGH>R}>2_ P UXM3/PX_X9<GH>3Z[>:M >&>3PaFlG9<J1j >F_aJL>:@< <PXPXqB9<9l9 >Q>:]&PXM9lJL9<>t=?JLIHM3g<>QRSTF<UXPk>OJ1R}P¯F<PaJLGNGMJ1 ªRSF _aI[>3GN j<U¥J1TlPa_X9<M =Pa>GU J1PX>3F3DC_X=_a¨T<F<IHJ1JL>3_X <U3=PX9<RSBE>:I<GHJ1LU]Z>3¨IFbcJ1>3F<REMOKEP PX9fIN>3RS_XRSF<= _aK1>eTlJSGHRSF K1JLJL>¯TlF<G_¯P`>/M_XPaRL>3JSIHg<¨MJL_XT<>2F<IUT">E>3UF]MO1PaJL&U3_a_a9l>3R}UXPg"U J1Fl>i>fj:9l>F"RRS1F]MO>>P &GPX98:9lPa9<RS>-PQJL=?Z>3bcRL>2FlM P:UiPXJ1>3T<_X_i=_aU3>3j8:TlMO9YPXTlGHJLU:Ff_a>tT<:I>2RSUiF]&P:GHPXI9<$>*GF"MMOJLJL=?_ag[g<JLT_kPkR}R}PXPa> GJ1U]F¨>OPaJglRS_X>F"PXUT<GHJL_aFFV:M3RS<F<_aJLJ1=F<GNMR?RSI[PX>2 J1Mk_X9<=F<GNU3M RLIVg"J1GF]PQJL `]GH>- PaM9<JL>F]PX_kMkRL9<MOJLPXGNGHMOJL>5FVYJS >tU1¨f>OJ1glT<RLIHjFlUX9lGJ1R1F >QRSPaIH9<J}>ti JLUIHTlJ}U&GHPXF<J K?L_a>3>3>jg TlMOUPXGHGH=?JLFlg<U IV> dR1U> ¢¨P_a>3j<>O>3U3 ¢Flj>3>3j G f> RSIHJ}>3j U1 b b hl j f I dFR1U> & F N 8b / I 8 /f IJ&: NRLg<g / N = / JS N f &N / H / F HKFIHKF . . . . . . 8. I 8. IJ:. 8 I 8. . . I. . 8. . I 8. I = 8. ZYW _a>3j<TlM PaGJ1FJL $Pa9<>(dRLUX>O¨_X>2j>O RLFlj Ab hl j dRLUX> f N 8 / I 8 / IJ: RSglgBN = JL b H I b hl j dRLUX> f N 8 / I : SR g<g N = JS b 8 FIHKF HKF _aRSR >3 PXj<PX>3>3Tl __XM = PaU1GJ1IHMOFVGJ111F]> PX_kh>QlRLM UXj Pa9<dGJLJ1RLTlF¬UXIH>(jGHFlRLRLUg<IGNgHjJ}> JS PXU19lIS>MOITJ1I dF]RLPXUX_kJL>LRLTl?M IHPaj8:GJ19"9<FlRGHUUtLJS>-> <PadRSJ=?R1Z[Ug<>>IH>?_aR>3UXj<d9<>ORLJ}iUX>3> U UePa¢¨PXPeJ 9"_XR}Z[>2P->ejG>ORSF INUXEJ1J(_a¢¨djPE>3RLj_EUXJY>OPX>3¨J_XUe>29lF<jRJL>OLPt>?>3UXU3>MO¥>3J1¢=F$FlT<1JSPX>>39l_aFlW>MO_¯>?F"R}JLPXJL ¯Tl_kPXj<_a9lRLU3> I UXGHFlMO8:>-9<RS> glgVU]<¨>O&9<glGNRLMkFl9UGNGHJLU&F F<JL_XPi>2jR TlPaMO>PX_aGHJL= F GHF_XT<MIH>RSFl9lJLRLF<U?GNMZ[RL>I">3 FJ1_X=Pa9<<JLj_aJLJYTl>2KLU:9<F<IHJSWPiUc_aPa>Tlg<j_aGH>3>3UXj >F]3 P&UX>RS>NFYW5 dPaÁ->_arL= oB8¨R}:P&5 Pa9<>-R1rLJLoBZ8¨bc:>2M 5 ]P&BtIH>rQLP>38CI/9 GH& ®3GHRSj<I PX$JLGHgJLF<PaFJLGPQF<3KPXZ[9<>G>2PtUR >J1M_a_XJLM>2F<>3UcK1PaUi_X_XT"GNTlM UQ>PaFlGPaJ1MJFl>Ui_a3>3=?UPX>JL_a_a_aGN>-M >*PQlg<Pa_k_a9<U>3Pe>MGHGH_XUXF1>2>PajIH_XWJTljM GPePaT"GMOJ1&>3F¬GHj¬I $_aZ]T<F<NW IJL>2PeUE5 ¾Z[GF§>(GHF[UMs}J1JLBr ==?8C9 >(gltR}8:PaRG9YZlWTlI>(UQG fPX&9<G>(Pa>(9_XU>2PXPXjGH9<ITl>M :RSPaGg<RSJ1F]glF¬P-IGNMYRSPX> PX_aGHJL&JLF<FTGHIK9&RL»QMOJ1FlJLFlj_aU=GNPaj9<RS>3GHIU_ &»QGHJLI _a&=GFlRSj<IHGTl®2MOR}>PXGHJLUXFIGHKLg<9]_aPJLg[Mk9l>_XRSPXF<GH>3K1U3>3 U(GF PX9l>T"UTlRLI&UXMk9<>3=?>3UJS ePX9<>g<_aJYJS UJS iPa9<>5df9YT<_kMk9¨hiJ1UaU>3_(RSF"j ]Pa_XJ1F<K . . . . . . [ []\^0_%_%`%`. . . .
(54) q3u. #&)(%( & &) &. F. @ : &N 8 : C = @ N : 8 I @ Ab 8 : = @Ab. U. :). I =. H. . = 8. J. FIHKJ GNU:F<JSPQRLFRLZlUcPa_aR1M PaGJ1F H F F HKJ H FIHKJ 3 U]¨UPX>3gT9 H J FIHKJ H F H J F F H H F J FIHKJ F J UP H F UcP UcP UF"j UFlj H F F H F J H F J H J F H F J. UXg ^ RLG_ I : : ^RLG_ _ :. J. F. @AC I g&f b 8 = @ g&f b b 8 N 8 b @AC I f g b 8 N : = @ f&g b b 8 N 8 IJ: b N = 8 @ /b d 8 @/b b K 8 @Jd 8 , : = = @ : b d = : b K d = 8 @AC > /b d 8 @/b 8 @Jd d K 8 @ /b d 8 g = A= : @ : b d = : b d K = 8 @ g b g d 8 @AC I Jb d 8 @JC > G N 8 /b d 8 f = : = @AC > N @ f b f d 8 8 I b &N 8 I d 8 @ h b 0 G(b 1 j 8 4 @ h b 0 G;b 1 j 8 4 0= : ) 1 = @ @ h ba0 G;bi1Dj ba0 8 h ba0 G;bi1Dj bi1 8 @ h b G b j 8 = @ h b G b j b 8 @Ab 0 b 0 K 8 @ /bi1 8 @ Ab b K 8 4 : = = @ h b 0 G(b 1 j h b 0 K G(b 1 j 8 4 @ b b K 8 @ /bi1 b 1 K 8 @ /ba0 8 @ /b b K 8 4 = : = @ h b 0 G(b 1 j h b 0 G(b 1 K j 8 4 @ b b K 8. g<g I : g<g _ : :. F. H. :C. _X>2U9. F. U. ^ JLg UF"j. H. H. H. F. H. H. H. H. H. F. F J. F. F. F. F. F F. F. J. lUP UcP H H UcP F J F YFlj UF"j H H UXFlj F J J $GHKLTl_X>?qVhi>3jTlMOPXGHJLF_XTlI>2U¯YGH=?g<IH>tPcW]g[>3U3g<_aJjTlM PQRLFlj=Jj<RLIG PcW K19">RF<L8:>3>_aV 9<RS>PX>-gl_aT<>3_Xjg[T"J1M UXPX>GHJLJSF EIJYPX9<JL>2g"UU>Q_al>3JLU_EPX_aGGHF"MOPXUcPkGHJLRSFlFlUM>LGN[UG PXJ>(g<_aRL>I1HJ}>fF]P >2jU]¨RS>OF¬glRLRLZlFlUcUPaGH_aJLR1F"M U PaGJ1PaJFPXMOJ_a>3Z[R}Pa> >U]F<¨>O> glRLCFlj_a>3>3j<jV>O">3> U&JL9<T<GNMkIN9j @ N 8 F I b H - 8 F I : &N 8 F I b N 8 FIHKJ = H 8 F I b &M3RS9lF<GHFlMk9JSPiGNUuRSIHt¥J}MOJLFYU]1>>Y_Xg"PXGHRSZ<FlI>*UXGJ1PXJF JLN $Pa8 9<F >-I Ib > PQQRS8:_aKL9YT<Tl=?Ue>3fF1>-P& JLJ1 _XZlRSGHFj RLU]g<¨g<>OIHG glM3R}RLPXFlGHUJLGHFJLFZ[>3JLM ¯RLRSTlFUX>ERLJLZlPXUc9<Pa_a>3R1_XM &PaGNGUXJ1>EFVQ>tYGHf=J1GHT<INRSIN_ajIW19l"R1>> @ d H b d J :b d = H : 8 F I:b : 8 < 9 E > k M < 9 L J N G O M & > L J
(55) U1¨>OglRLFlUXGJ1F?= RLIHUX= J*=?>3: RLFlU`>i= 9l8 R1>:PXJ 1>>3g(Pa_aR1Mk(JL ªPX9<>&PcWYg[>3UfJS ªPX9l>iPX>3_X=U3$¢F"j>>2j R Pa>_a=m8:9<M>tRLF _a>3JLjFlT"IW-M PXZ[GHJL> FU1_a¨>O>INR}glPXRLGHJLFlFj>2GHU&j*j<G ">OGlPF<9">2RLjU$Z]PcWYW?g"Pa> 9<F>-GHHKF >J_a> FlM8:>t9Y_XTlT<U IH>3U>fGHF&GH$I<GHKLj<Tl>Ol_X>F<>:Yq Re3 UXF<G=?JSPag<GJ1IH>EF PcJSW] "g[Pc>3WYU3g">2g<j _aJ_a>3jjTlT"M M PiPXGHRLJLFlF¥j =?RLFlJjj<RL¢¨P%IG 9 PcW 9 &¥9< >3GH_XKL>T<f_a>?>@ 9lR3 _XL>2> jTl1JLM PaIHT<GJ1F]F5PaRL_a_XT<GHIIHW5>3UEJL =?J1_*GPdPX>2R1j U>UXJLRL=?Flj> Pc¢¨%PWY9Eg[>3RSU(Flj§GF PXG9<K1>T<_X_X>TlNoI>2U3 §MJL8:=?9<gl>RSWPXGHZ<MRLGIHFGPcW¬Z[>_XTlGHI=>2UQ=? >2J1j_(GHRSdPXRL>3UXIW > _a>OPa_XGH>1>3j _XJ1=Y>3MOPXGHJLF¬@ o< . . . . . . . . . . . . . . [. bDc bed.
(56) qBP.
(57) !#"$%'&)(* #+, +-.&/+0%1(%0#. dRLUX> f N 8 * IJ: P ;S U b 0 ITISI b E XZY [ = JL : b TS U =P8 0 * K I l : / E = hl j dR1U> f N 8 * I : P TS U ba0 ITISI b E XY [ = JS : b TS U = H 8 * K IJ: b ;S U f N 8 * I ba0 ITISI f N 8 * I b E XZY [ = 8 0 * K I l : /+E = hl j dRLUX> f N 8 * IJ: N2U b 0 ITISI b [ = JS : b TS U = 8 0 * K I l : / E = hl j dR1U> f N 8 * I : N U ba0 ISITI b [ = JL : b ;S U = H 8 * K IJ: U f N 8 * I ba0 ITISI f N 8 * I b [ = 8 0 * K I l : / E = @ hl j ¢¨P f N 8 * IJ: P TS U ba0 ISITI b E XZY [ = JS : bnK ;S U = 8 0 l : * =MI l : /+E = hl j ¢¨P f N 8 * IJ: P TS U ba0 ISITI b E XZY [ = JL : bnK TS U = H 8 l : * = I : bnK ;S U : hl j ¢¨P f N 8 * I ba0 JL : bnK TS U = = ITISI : hl j ¢¨P f N 8 * I b E XZY [ JL : bnK TS U = =M=P8 0 l : * = I l : / E = @ hl j ¢¨P f N 8 * IJ: N U ba0 ITITI b [ = JS : bnK TS U =P8 0 l : * = I l : / E = hl j ¢¨P f N 8 * IJ: NU b 0 ITITI b [ = JS : bnK TS U = H 8 l : * = I : U : hl j ¢¨P f N 8 * I b 0 JS : bnK ;S U = =9ITITI : hl j ¢¨P f N 8 * I b [ JS : b K ;S U = = = 8 0 l : * = I l : / E = GK1T<_X>*@ Vhi>3jTlMOPXGHJLF_aT<I>2U JL_edR1U>-RSF"j¢¨P @ @ /b H bnK 8 hl j dRLUX> b JL : b ;S U = 8 0 * K I l : /+E = @ hl j dR1U> b JS : b TS U = H hl j dR1U> b K JL : b ;S U =P8 @ @ /b TS U H d ;S U 8 hl j dRLUX> b JL : b ;S U = 8 0 * K I l : /+E = @ hl j dRLUX> b JL : b ;S U = H hl j dRLUX> b JL : d TS U = 8 @ @ Ab H bnK 8 hl j ¢¨P b JL : bnK TS U =P8 0 l : * = I l : / E = @ hl j ¢¨P b JL : b K TS U = H hl j ¢¨P b K JS : b K TS U = 8 @ @ AbnK TS U H dcK TS U 8 hl j ¢¨P b JS : bnK ;S U = 8 0 l : * =MI l : / E = @ hl j ¢¨P b JS : b K ;S U = H hl j ¢¨P b JS : d K ;S U =P8 $GHKLTl_X>-o V¯dfJ1=g"R}PXGHZ<GHIG PcW _a>3jT"M PXGHJLF_aT<IH>3U JL_edR1U>tRSF"j¢¨P. @ hl j. !. @. . @. . . . . . . . . . . . . . . . ) . . . . . . ) . . . . . ) . . . *. ) * . . . !. @. * . . !. . . *. ) * . . . . . *. ) * . . !. . * . * . . . . !. . . ! . @. . . !. !. *. ) * . . ! . @. * . . . . . . . ( . . . . ) (. * . . . *. . . . . . . . . ) . . . . ) (. . . . ( . . . . . ) * . . . . * . . [ []\^0_%_%`%`. *. ) * . . . . . . .
(58) qO. #&)(%( & &) &. i» JLPXE>tÀ§Pa9l> R}Pi:RSF]>tP:9lU1R¨L>O>tglF<RLJ?Fl_aj>3>2RLjUXJL FJL_aPX=J UQMJLZ[=?>3M3g<RSTTlPaUX> >(U >(IHRLJL_XF<> KG F]J1PX_X>3=_X>2U3UcPaG/>3 j>LGF>Pagl9<RS>(FlPXj>_aR=PXUe>3_XPX= 9lRSb PtRLJL_X>* $PcGHFWYg[J1> F<>OF¤PXJLGJ1F]F<PaJ> MRLJLFl_aj¬_X>29lUGg[K1JL9<F">j_E>JLFl_kMj>t>_t&GRSPaZ"9UcPaPX_a9<R1>(M PEJLZUXWYbc>2F]M PaPR}¨IH>LPa>3>3IMk9<PXF<>3_XGN\]=T<U3>3iU3 ¾U Jj<RSIHIHJLGPcF<WKJL JLF<_aIHW=UUQ>39"_X1R>3LU:> 9<Fl>3J_X> UXg"R1>2UiMOR?GNRSPaIJ]YJ1GIV_XPXPaTlJ >*=?PX9"GR}P*GF"jj>3TlUX>M Pa_aGLJ1>2F U J1T<_i UXg"Uf>2T"MOUGNTlRSIVRLI"R}PXPX>e>3F1j<Pa>OGJ1lFVF<>QYPX9<GH=>EGH_aIN>RSIN_aR}IWPXGHJL J1F"_&U g<H _aJYj<RSTlF"M jPkU, Pa9<3 M>-JL_aFYT<LI>3>Y_aUX3/UGHJLgTTF 99 GNU&_a>3RUXg"MO>2J1M F]PaPXG_k1RL>M IHWPaGJ1R1FUPa_a9<T<>eIH>L_a > ">OG1>LLPX_kRSFlUXGPaG1> RLFljÀ§PX9<>t>-&_aG> IHVl>RSINUGJ(1>L&_XUGWYPX=?> =?@ >OAPa_XbGNMSPa_aH RLFlITUXITGPaI G1H >EMb IJ]E UT<8 _aF >3U JLJ1 _ H¹@ /b H b 0 8 F ITISI @ /b E 0 H b E 8 F* ^@ _XJ1/¿g"b GJ]1U>iGPXH PcGHJLWYFg<d GHF<@<K&8 oF bcTlGNU(Paj9<K1U>=?PXFGHI >¯@AF]}PaGRSU3> IH1G _aj/>3j< b JLTl_ M Pa_aH G>3J1j<F-d TlbcM TlPa8 jGF J1K1F= bc>3TlF]jPaKLU=?RS_a>3>&F1Pkg<U_X>2U¢>3F_X1gl>3jRS_XZYPXGNWMOTlUJ1IHRL=_3 >QG=? QRLUPaF<R1GHMkg< T<IN:R}@JPXGHJLG >F"U= JSGHU( Pa}9<RS>eIHG jUPaR1RLMkFlªj f g b. . . . . . . . % , P , M' %. . . . . . . . . . !. cP8:WY>-9lg[> >3jUe>OM"RSJSF<Fl >tJLPaF<9<PcGNf>(MJERLPXI$>bc_aTl =J1j<_XKLU=-=?U-l>M3F]JLRSPaIHF U J}V &Z"cGHGN> F<UiKj<RS>OPXPalJL9<=?F<>(>2GNT"j§M UETlZ]RLRLWFlI jGj<Fl>Ocj<GNlTlU&F<M MGPaPXRLGGHJ1F<JLFVJLFFl GHJLM3¦ RS_eFlI kPXM9< >?>?RLUXK1G=?RLGF§g<IHW]f/>?PcWY9lg[R>31j5><PXJMRSPaINRLMOLTl>?ITlGUF]Pa3 J¬UX>RL>4MM5 peJLT<^¯F]<Ptr]sPX9l8C9 > ± z µ ;6 | ¥2µ 3 ~L| µ { y @ Ab F & + Wb R}PXJ1=?GHM k Z!('& F !+ @ @ Ab F & + Wb MRSFlJLF<GNMRLI k Z!(' & F !+/@ . . . . . .
(59). .
(60). . . .
(61). . " &)& %0 & +01 ( & &#/+<&4$!Y1" & k ! !+ (% &%s% @ /b @ J J +- +N(%( @!(' & N 8 F @ @ /b N F J @ /b @ /b F HKJ @ Ad F F b , f bnK @ b: d = J @ g b F @AG N 8 F /b @AC I /b J F b , g bnK @ @ f b &N 8 F I b FIHKJ F @ /b @ /ba0 F @ Jb 1 J : ba0 G;bi1 = , : k dL0 G)%+-d1 = F @JC > /b @ h b 0 G;b 1 j F 4 J F @ /b @ /b F 4 J b , h b 0 G(b 1 j F 4 J b , h b 0 G;b 1 j @ @ %+<b J k b F @ Ab @ /b TS U & b k : b TS U = +- Y( & Q&T: hl jB/Bm 0 * I /+E @ & b k : b TS U = 0 * K I l : / E = hl j/Bm @ /b @ /bnK ;S U hl j6$)b k : bnK TS U = +- Y( & QT& : 0 * I/ E @ hl j6$%Rb k : b K ;S U = 0 l : * = Il : / E = . . . . .
(62). .
(63).
(64). . . . . .
(65).
(66).
(67). . .
(68). .
(69). .
(70). . .
(71). . .
(72). . .
(73). . .
(74). . . . . . . ( ) (. . . . . .
(75) . * . . .
(76). ( ) (. . . . *. ) * .
(77) . ( . . ) . . [. bDc bed.
(78) q}s.
(79) !#"$%'&)(* #+, +-.&/+0%1(%0#. { µµ y z µ2 . . b F @ cb F qb Z+< + Q%%1(1 # +N +- #"& +0 ! ( & 0* #+ %( &D#" + & (' 'T #& Hb U A&;:s' + 8 % #+ ' +0 "!)'% 1) &D k F k #"& k (% J H P r @ Ab F `@ /b 8 F +-#"&)( & +- (& 0)* #+,(% & #" +N&D$'&'- #& 'b r { µVµ À5>-J1F<IHW KLGHL>EPX9l>*U1>OPaMk9JS PX9<>-gl_XJYJS 6V @.
(80). . . .
(81). .
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