The Why/Krakatoa/Caduceus platform for deductive program verification
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(69) >A@W>OQRÁZJUHSJ2MOÅjÐ<hÐMOGIÁJU<hNW>OGI>ALUHSMO@ 0ë 6OíÊ {
(70) YCG(HS@lLU<?GUÐ<?VCHS>ALU<ÈWG]JELUBtM=GIVZ<?G(JpNf<?\hH{Èj\?>%LIHRM=@QK>A@CB ßOYW>OßO<Üò>=J>AQKJpMYWJU<?VLUM³VZ<}JpHSßO@8>AÌWJpLUG]>O\#LÐMZVZ<?QSJ6MOÅNWGUM=ßOG]>AгJë76OíÊ ö¯M´\#M=@W\#QSYWVZ<=Î(MOYCGNCQK>%LUÅÆMOGIÐ0HSJL]>AHSQRM=GU<}V LUMÍLUFW<âNCGUMMOÅMAÅ>OVZÇ%>A@j\#<?VÌj<?FW>ÇHRM=GI>OQ JpNf<?\hH{Èj\?>%LIHRM=@WJ6>A@WVÉNCGUM=NjMlJp<}J,>O@ÉMOGIHSßOHS@W>AQ¢>ANCNWGUMl>O\]F³ÌW>=Jp<}VÒMO@ >A@HR@lLU<?GUÐ<}VZHS>ALU<
(71) ÈWG]JELUB MOG]VZ<hG&JUNj<}\#HRÈj\h>ALUHSMO@ÙQS>O@CßOYW>OßO<=ÊfËL]J&г>AHS@Ù\]Fj>AG]>O\/LI<hGIHSJpLUHK\îHSJÇ=<hG]JU>ALUHSQRHRLEÁ fÐîYCQRLUHRBtNCGIM%ÇO<?G MOYZLINCYZL?ÎWÐYCQRLUHRBJUMOYWGI\h<
(72) HS@CNCYZL}ÎWM=@ZBLIFC<#B :WÁÒß=<h@C<?GI>ALUHSMO@MAůÈjGIJpLpBMOG]VZ<hG6ÐMZVZ<hQKJ?Ê PCYZLIYCGU<8òMOGIÄ HR@j\#QSYWVZ<?J³LUFC<XVZ<?ÇO<?QRM=NCÐ<h@lLMOÅ>O@HS@lLU<?ßOG]>%LU<}VÛYWJU<hG³<?@ÇlHSGIMO@CÐ<h@lL}Ê ¿Í<>OGU<>AQKJpMVZ<}JpHSßO@CHS@Cß³>A@ HSÐNWGUM%Ç=<?VÒJUYCNCNfMOGUL6ÅÆMOGó>AÌjJELIGI>=\/L6ÐMZVZ<?QRHS@CßjÎZÌlÁÉNCGUM%ÇHKVZHS@Cß Ý [àõBQRHSÄO<Þ2FCHSßOFC<?GpBQR<?ÇO<?QZÐMZVZ<?QSJ,>A@WVGI<#ÈW@W<hÐ<h@lL?Ê ÄO<?ÁHKJUJUYC<6ÅÆM=G(LUFC<óÅÆYZLUYCGI<HKJª>OQSJUM LUFC<Ü>AYZLIMOг>%LIHS\ßO<h@W<hG]>%LUHSMO@MOů>A@C@CMOLI>ALUHSMO@WJ?Ê=õ¯MO@Cß&LI<hGIÐ Nf<hG]JUNj<}\/LUHSÇO<
(73) HSJ,LUMî\#MO@lLIGUHSÌCYZLI< LUM ÜG]>A@WVÛD9FW>OQRQS<h@Cß=< 18MO@ (<hGIHRÈW<?V 2MOÅLEò>OGU< <?NjMlJpHRLUM=GUÁ «>8ÄO<?Áàß=M=>AQ2ÅÆM=GYWJ&HKJLIM ÌCYCHSQSV QSHRÌCG]>AGIHS<?JMAÅ2ÇO<?GUHRÈW<?V JUMAÅLEò6>AGI<OÊ [à>A@ÁNj<?MONCQS<FW>Ç=<óÌf<h<h@HR@Ç=MOQSÇO<?VHS@³LIFC<ÜVC<?JUHRß=@É>A@WVÉVZ<hÇ=<hQRB MONCÐ<h@lLMAÅCLIFC<,NCQK>%LUÅÆMOGIÐ>A@WVLUFC<\h>OJU<9JpLUYjVZHR<}WJ &Ê 6>AG]VZMOY¯@Î 2¢Ê MOQKVZMWÎ ÊOD9FW>OYWVZFW>OGUÁ=Î 2¢ÊD9MO@j\]FCMO@«Î Ê6D9MO@lLI< E<?>O@«Î,;jÊ BPÊ9D9MOYW\]FWMAL?Î9[ Ê A
(74) MOßOß=YCÁOÎ Ê AYZÅ×>Á=Î Ê ÜYC<h@WMAL?Î öÊ óYWÌj<?GpL}Î9;jÊ,Ã&>A@CHSßWÎ 2Ê9õ«<}JU\hYCÁO<?G?Î 8Ê9[âM%Á=Î Ê {
(75) YWVZMOL?ÎD
(76) Ê 2>OYCQSHR@«Î9;WÊ MOYWJIJU<hQtÎ Ê M=YWJIJp<hL?Î Ê óGIÌW>AHS@«Ê . . .
(77)
(78) . . . . !. ". '. #. %$. &. ¯¹ ¯·½# }i |=qpkO%j chd«ic_o=m]v}rWc
(79) ic_v?®Zc Üic j qErlx/ci{c?yrly±q%ch²=ic}djm/e/m]r=]c
(80) i ic}djm]yrlvOc}i aói i{c ¢v?Æc i â,râvh}mIqEAy{m 1v?u²%d xEv%v}&ehrkXe?©=©lyn/ehxEyv}r=]iâstr%xEmIqErlehxEyv}rle?(²?v}|=qErle?(v?r bAv?uRx (e#qEm v%v},uKv?q mInUo=rlv}v ? qpe?r=uKmIq ×??? Aió¢yy hxqEm}c«²Oi _9i mIqEy±°ln/ehxEyv}r v?uª`v?r=l|=rlnIxEyv}rle?«qEv ?~ qpehw&
(81) |=y{ r str%xEmIqE©OqEmIxpehxEyv?rlóyr O©Zm olm]vhqCi²?v}|=qErle?Wv?u¯l|=rlnIxEyv?re?WqEev hqpe?w&w&y)r ×??} ?? h% OiódWm]n]|O%mIq/cªbZi 1_vAk=e ?m8k=mÉ{eâ{v }y{z%|lmk=| ©OqEm]w&ymIqvhqpkOqEmÉ©Zv}±Ow&v?qE©=olm³wÜ|=±xEy×vhqxE]m k=e?r=î{eX{v }y{z%|lmÉEe?r=v?qxEm]]i1e?xEmUq xEo=m]y]c9e?xEmIqehqEyym]rk=mÉa9m]npolmUqEnUo=mÉmIr sr=uSv?qEwehxEy{z%|lm ×??} =i v?qEre#x/c%aói WqEv#Ay{ r ó©Zv}yr%xEmIq2©OqEev ?qpehw&yr v}ehqEmªev ?y{n?ifsr Ae#xEolm]we#xEyn]vhufqEev hqpe?w _v?rlxqE|=nIxEyv}rji ×??} ] l#h Aie#qEnUo=}c_9i{c}e?|=y{rOtv}o=qEy r =c_9i =a,m/e?v?rly)r ehgZv}|Ox¯²e/}e©OqEev hqpe?w& ªy±xEoeh{y{ehy{ r óe?rlk uRqpe?w&mn]v?rk=y±xEyv}r=]i sr |OqpkWc²Oi{cmI{ole?wc ic«m/kO]i 2/#xEoàsr%xEmIqEre#xEy{v?rehª_v}rOuKmIqEm]r=n]m v?r o=m]v?qEmIwô«qEv#Ay)r Éyr cy ?olmIq 9qpkOmIqdWev }yn]]i¯v}|lw&mî}?}vhudWm]nIxE|=qEm`v?xEmIyr _v?w&©l|OxEmIq,bOnIy{mIrln]m}icZbO©=qEy r }mIq ×h} Oió¢yy hxqEm}c¨ ²=i _9i{cehqEnpol?cZ_9i ¯|=xEy±×©=qEv#mUqªmIqEy±°n/e#xEyv}rvhu«_Ù©OqEev ?qpehw&]i«str j e/Ay{mI]cl²Oi{c bAnUoA|=xEm?c ic 2e#qErlmIxx/c?ic#m/kO]i h#xEo
(82) sr%xEmIqEre#xEy{v?rehA_v}rOuKmIqEm]r=n]m2v?r
(83) =v?qEwe? ¨ r }yrlm]mUqEy{r mUxEolvAk=]iv?{|=w&m,}}?
(84) vhu¢dWm]nIxE|=qEm,`vhxEm]yrî_v}w&©=|=xEmIq2bOnIy{mIrln]m}ic=bAm/ehxxEm}c óc%~bOc bA©=qEy)r ?mIq ×??? / Oh Aie#qEnUo=}cW_9icCa,v}|lmUx/cZ`
(85) i ,mUqEy°ln/ehxEyv?r³v?u²e/}e_2e#qpkÉeh©l©={mUxEgZm]ole#Ayv?q ªy±xEoÒjHqEj mIj ©Zm]nIx xEv³xqpehrlEe?nUxEy{v?rlehrkân/ehqpkâxEm/e#qE]iXstr j |=)r =c Üi
(86) ic¯e?rlkOAeAc«¢i{c«m]k=]i ¯?xEoXj s sr= xEmUqErehxEyv?re?j_v?r=uKmUqEm]rln]mv}r³bAv?uRx (e#qEm )r }yr=m]mIqEy)r &ehrklvhqEwe?jmIxEolvAkO ×b « } Uc «|lr=m}cOstrlk=y{e ×??} Oi v}{k=vOjHc,j bCij c(¢yy hxqEm}cª²Oi _9i lvhqEwe?,mUqEy°ln/ehxEyv?r v?u
(87) ¢vehxEy r ?¢v}yr%xqEev hqpe?w&]iÀsr ]hxEos srAxEmUqErehxEyv?re?Ob%Ow&©Zv}y|lwÛv}rÜ_v}w&©=|=xEmIq¢,qEy±xEolw&mUxEy{n?chv}r%xE©Zm]ymIq/c?=qpe?r=n]m ×h} .* E. )(. *. +. /.. -,. 10. 20. 43. 76. -5. /.. 98 3 -5!3. 5:. <;=:. /.. ?>. 43. )(. 5. 7.. A@. &3. 5. &.. ?;. 7.. 0. B@. /.. C@. )3. 76. 5. /.. E(. )3. D+. 7.. 5. ?;. :. /.. F0. G@. 20. 3. )(. : 5. /.. !3. H>. 5. 5. 76. 3. +. /.. &..
(88) Oió²}e?n]v?gl]c 9icOe#qEnUo=}cO_9icAaeh|lnpojc}`
(89) i Wlv?qEwehlmUqEy°ln/ehxEyv?rvhujeónIv}w&w&mIqEn]y{ehlwehqxn/e#qpk eh©l©={mUx ªy±xEow
(90) |l±xEy©lmxEv%v?]iÜsr W9c ?m]g=qpehy{n&mIxEolvAkOv}ev h ehrkÉbOvhuSx (ehqEm m]npolrlv?ev ?%i ¯v}|=w&m(O?/óv?ujdjm]nUxE|=qEmª`vhxEm]yr_v?w&©l|=xEmUq2bAn]ym]rlnIm}icObAxEy±qEy)r =c~cAbA©=qEy )r ?mIq ×?}h ]Oi ¨9|lgZmIqx/c ic¢ehqEnpol}c_9i î5n]e?m&xE|kAÉv?u,_Àv}|OqEn]m&n]vAk=m&}mIqEy±°n/jHe#j xEy{j v?r WxEolmbAnUo=v?qq e?y±xEmîe?c }vhqEyxEo=wiXstrX,y{npolmUqErlcy =c 9i ic m]np®mIqx/c 9ic«m/kO]i ¯hqpkXs str%xEmIqErlehxEyv}rle? _v?r=uSmIqEm]rlnImv}rÍbOvhuSx (ehqEm j r }yrlm]mUqEy{ r 8ehrkXlv?qEwehªmIxEo=vAk= ×b j « Uc9v}g={mIr c mUqEwe?r% ×?? ?}i 9|lgZmIqx/c icjehqEnpol}cW_9i bOm]©lehqpehxEyv?r
(91) ehreh O
(92) y uSv? qó kO m/k= |= nI xEym mIqEy±°n] ehxEyv}rW i mInU o=Prlyn/ e? M qEmI©Zv?qx/c%~9rlymIqEy±xE9ehqEy s ×h} i 9(. /.. !0. &.. 0. F3. @. 7.. &.. (. 0. @. ,. 3. (. (. /.. 3. 5. /.. 3. :5. H>. 5. -5.
(93)
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