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The Why/Krakatoa/Caduceus platform for deductive program verification

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(1)The Why/Krakatoa/Caduceus platform for deductive program verification Jean-Christophe Filliâtre, Claude Marché. To cite this version: Jean-Christophe Filliâtre, Claude Marché. The Why/Krakatoa/Caduceus platform for deductive program verification. 19th International Conference on Computer Aided Verification, Jul 2007, Berlin, Germany. �inria-00270820�. HAL Id: inria-00270820 https://hal.inria.fr/inria-00270820 Submitted on 7 Apr 2008. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(67) HK\#<}JhÎZGIÇlB’JI>%L}ÎCm •ªGIßOMWÎZòHRLUF8<?@W\#MZVZHS@Cß=J6MOÅNfMOQSÁ™ÐM=GUNWFCHS\JUMOGULIJ>=JJp<?<h@8>AÌfM%ÇO<OÊ 3 •ª@CFW>O@W\#<?Ð<h@lLIJîMAŚJUNj<}\#HRÈj\h>ALUHSMO@ QK>A@Cß=YW>Aß=<?JÌfMALIF ÅÆMOGÒD >A@WVÛ;l>Ç%^> «ß=FCM=JpLÇ%>AGIHRB >AÌCQS<?J?ÎC> lZHSMOг>%LIHS\ÜÐMZVZ<hQKJ 3 2™Nf<?\#HRÈj\?>AQSQRÁÜLUMÜÃGI>OÄ%>%LUMl>CÎ#ÐM=GU<,JUYCNCNfMOGUL¯ÅÆM=G;l>Ç%>

(68) D>AG]V&JUMOYCG]\# < #LUG]>A@jJU>=\/LUHSMO@jJ(0ë 9ítÊ G :jM=>%LIHR@WßAB’NjM=HR@lL>AGIH{LIFCÐ<#LUHK\ë <%í’Ê 3 2™YCNCNfMOGULÅÆMO; 2™<hÇ=<hG]>AQª\h>=Jp<³JpLUYWVCHR<}J&FW>ÇO<Ìf<h<?@´\hMO@WVCYW\/LI<?V ;=>Ç%>âD>AG]VÙ>ONCNCQS<#L]JNCGUM%ǙHKVZ<?VÍ̙Á ‘ llB >AQRLUMÚë =%í>A@WVÀöGUYjJELI<?VÀõ«M=ßOHK\â\#M=ÐNj>A@CHS<?J  LUFW>< 2Z\]FCM=GUGUB’¿Ù>OH{LI< ß=GI>ONCFZB’г>AGIÄlHS@Cß >AQSßOMOB GUHRLUFCÐ8Ι\#M=@WJpHKVZ<?GU<}V³>OJ,>\]FW>AQSQR<?@CßO<óÅÆMOG,NWGUM=ßOG]>AÐÇ=<hGIH{Èf\h>%LIHRM=@8ëR@ì ?%í  JUMOÐ<š>Ç™HRM=@CHK\hJ(<?ÐîB Ìj<}VCVZ<?V\#MZVZ<6NCGIM%ǙHSVC<?V&̙BÁ AÜ>OJIJU>OYCQRL2>Ç™HK>%LUHSMO@î\#MOÐNW>O@™ÁOΏòFCHK\]FQS<?>OVC<?VLUM>A@MOGIHRß=HR@W>OQ.

(69) >A@W>OQRÁZJUHSJ2MOÅjÐ<hÐMOGIÁJU<hNW>OGI>ALUHSMO@ 0ë 6Oí’Ê {

(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]>AгJšë76Oí’Ê ö¯M´\#M=@W\#QSYWVZ<=Î(MOYCGNCQK>%LUÅÆMOGIÐ0HSJL]>AHSQRM=GU<}V LUMÍLUFW<âNCGUM™MOŚMAÅ>OVZÇ%>A@j\#<?V“Ìj<?FW>Ç™HRM=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<=Êf˒L]J&г>AHS@Ù\]Fj>AG]>O\/LI<hGIHSJpLUHK\îHSJÇ=<hG]JU>ALUHSQRHRLEÁ fÐîYCQRLUHRBtNCGIM%ÇO<?G MOYZLINCYZL?ÎWÐYCQRLUHRB’JUMOYWGI\h<

(72) HS@CNCYZL}ÎWM=@ZBLIFC<#B :WÁÒß=<h@C<?GI>ALUHSMO@MAůÈjGIJpLpB’MOG]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%ǙHKVZHS@Cß Ý š[àõ•B’QRHSÄO<Þ2FCHSßOFC<?GpB’QR<?ÇO<?QZÐMZVZ<?QSJ,>A@WVGI<#ÈW@W<hÐ<h@lL?Ê ‘ ÄO<?ÁHKJUJUYC<6ÅÆM=G(LUFC<óÅÆYZLUYCGI<šHKJª>OQSJUM LUFC<Ü>AYZLIMOг>%LIHS\šßO<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 2™MOŘLEò>OGU< <?NjMlJpHRLUM=GUÁ «>8ÄO<?Áàß=M=>AQ2ÅÆM=GYWJ&HKJLIM ÌCYCHSQSV QSHRÌCG]>AGIHS<?JMAÅ2ÇO<?GUHRÈW<?V JUMAŘLEò6>AGI<OÊ [à>A@™ÁNj<?MONCQS<šFW>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 •šÊ6D9MO@lLI< E<?>O@«Î,;jÊ BPÊ9D9MOYW\]FWMAL?Î9[ Ê A

(74) MOßOß=YCÁOÎ Ê AšYZÅ×>Á=Î Ê ÜYC<h@WMAL?Î ö‡Ê ”óYWÌj<?GpL}Î9;jÊ,Ã&>A@CHSßWÎ 2•Ê9õ«<}JU\hYCÁO<?G?Î 8Ê9[âM%Á=Î ‘ Ê {

(75) YWVZMOL?ÎD

(76) ‡Ê œ2>OYCQSHR@«Î9;WÊ MOYWJIJU<hQtÎ Ê M=YWJIJp<hL?Î Ê óGIÌW>AHS@«Ê . . .  

(77) 

(78) . . . . !. ". '. #. %$. &. ¯¹ ¯·š½# ‹}i |=qpkO‡%j chd«iœc_o=m]v}rWc

(79) iœc_v?®Zc Üiœc j qErl†’x/ci{c?­yœrly±q‡%ch²=iœc}djm/e/›m]r=†]c

(80) i  iœc}djm]yœrlvOc}­i aói i{c ”¢v?—œ—Æc i â‘,râvh›}mIqE›Ay{m 1v?u²%d xEv%v}—œ†&ehr™kXe?©=©l—œyœn/ehxEyœv}r=†]iâstr%xEmIqErlehxEyœv}rle?—(²?v}|=qErle?—(v?r bAv?uRx (e#qEm  v%v}—œ†,uKv?q  mInUo=rlv}—œv ?‡  qpe?r=†’uKmIq ׃???Œ ƒAióˆ¢yœ—œ—œy hxqEm}c«²Oi _9i –mIqEy±°ln/ehxEyœv}r v?uª`v?r=‰ˆl|=rlnIxEyœv}rle?—”«qEv ?~ qpehw&†

(81) |=†y{ r str%xEmIqE©OqEmIxpehxEyœv?rl†óyœr  ‡O©Zm  olm]vhq‡Ci²?v}|=qErle?—Wv?u¯ˆl|=rlnIxEyœv?r™e?—W”•qEev hqpe?w&w&yœ)r  ˜Œ ׃??}„ ??Š hŒ%Ž „OiódWm]†n]|O‡%mIq/cªbZi 1_vAk=e ?m8k=mɗ{eâ—{v }y{z%|lmk=| ©OqEm]w&yœmIqvhqpkOqEmÉ©Zv}—±‡Ow&v?qE©=olm³wÜ|=—±xEyœ‰×†vhqxEž]m k=e?r=†î—{eX—{v }y{z%|lmɆEe?r=††v?qxEm]†]i1e?†’xEmUq †xEo=m]†yœ†]c9e?†’xEmIq”•ehqEyœ†yœm]rk=mÉa9m]npolmUqEnUo=mÉmIr sr=uSv?qEwehxEy{z%|lm ׃??}‚ Œ=i v?qEr™e#x/c%aói W”•qEv#›Ay{ r ó©Zv}yœr%xEmIq2©OqEev ?qpehw&†yœr v}ehqEmª—œev ?y{n?ifsr Ae#xEolm]we#xEyœn]†vhuf”•qEev hqpe?w _v?rl†’xqE|=nIxEyœv}rji ׃??} ‹]ƒ l‹#ƒh‚ ŽAiše#qEnUo=ž}c_9i{c}”•e?|=—œy{rO‰tv}o=qEyœ r =c_9i =a,m/e?†v?rlyœ)r ehgZv}|Ox¯²e/›}e©OqEev hqpe?w&† ªy±xEoeh—{y{eh†y{ r óe?rlk uRqpe?w&mn]v?r™k=y±xEyœv}r=†]i sr |OqpkWc•²Oi{cmI—{ole?wc  iœc«m/kO†]i 2‹/€#xEoàsr%xEmIqEr™e#xEy{v?r™eh—ª_v}rOuKmIqEm]r=n]m v?r  o=m]v?qEmIwô”«qEv#›Ayœ)r Éyœr cy ?olmIq 9qpkOmIqdWev }yœn]†]i–¯v}—œ|lw&mî„}‚?}„vhudWm]nIxE|=qEm`v?xEmI†yœr _v?w&©l|OxEmIq,bOnIy{mIrln]m}iœcZbO©=qEyœ r }mIq ׃h}Ž ‚Oióˆ¢yœ—œ—œy hxqEm}c™¨ ²=i _9i{c™ehqEnpolž?cZ_9i ¯|=—œxEy±‰×©=qEv#›mUqª›mIqEy±°™n/e#xEyœv}rvhu«_Ù©OqEev ?qpehw&†]i«str j e/›Ay{mI†]cl²Oi{c bAnUoA|=—œxEm?c iœc 2e#qErlmIxx/c?iœc#m/kO†]i h‚#xEo

(82) sr%xEmIqEr™e#xEy{v?r™eh—A_v}rOuKmIqEm]r=n]m2v?r

(83) ˆ=v?qEwe?— ¨ r }yœrlm]mUqEy{r  mUxEolvAk=†]i–v?—{|=w&m,„}„}?€

(84) vhu¢dWm]nIxE|=qEm,`vhxEm]†yœrî_v}w&©=|=xEmIq2bOnIy{mIrln]m}iœc=bAm/ehxxE—œm}c ‘óc%~bO‘šc bA©=qEyœ)r ?mIq ׃???Œ ‹/Ž OƒhŠ Aiše#qEnUo=ž}cW_9iœcCa,v}|l††mUx/cZ`

(85) i ,–mUqEyœ°ln/ehxEyœv?r³v?u²e/›}e_2e#qpkÉeh©l©=—{mUxE†gZm]ole#›Ayœv?q ªy±xEoÒjHqEj mIj †©Zm]nIx xEv³xqpehrl†Ee?nUxEy{v?rl†ehr™kân/ehqpkâxEm/e#qE†]iXstr j |=)r =c Üi –

(86) iœc¯”•e?rlkO‡AeAc«”¢i{c«m]k=†]i ¯Œ?xEoXj s sr=‰ xEmUqEr™ehxEyœv?r™e?—j_v?r=uKmUqEm]rln]mv}r³bAv?uRx (e#qEm )r }yœr=m]mIqEyœ)r &ehr™kˆlvhqEwe?—jmIxEolvAkO† ×b ˆ« }‚ Uc ”«|lr=m}cOstrlk=y{e ׃??}‚ €Oi v}—{k=vOjHc,j bCiœj c(ˆ¢yœ—œ—œy hxqEm}cª²Oi _9i ˆlvhqEwe?—,–mUqEyœ°ln/ehxEyœv?r v?u

(87) ˆ¢—œvehxEyœ r ?‰”¢v}yœr%x”•qEev hqpe?w&†]iÀsr ‹]€hxEošs srAxEmUqEr™ehxEyœv?r™e?—Ob%‡Ow&©Zv}†yœ|lwÛv}rÜ_v}w&©=|=xEmIq¢‘,qEy±xEolw&mUxEy{n?chv}r%xE©Zm]—œ—œyœmIq/c?ˆ=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) ŠOió²}e?n]v?gl†]c 9iœcOe#qEnUo=ž}cO_9iœcAaeh|lnpojc}`

(89) i Wˆlv?qEweh—l›mUqEyœ°ln/ehxEyœv?rvhujeónIv}w&w&mIqEn]y{eh—l†wehqxn/e#qpk eh©l©=—{mUx ªy±xEow

(90) |l—±xEyœ©l—œmšxEv%v?—œ†]iÜsr W‘9c— ?m]g=qpehy{n&mIxEolvAkOv}—œev h‡ ehr™kÉbOvhuSx (ehqEm m]npolrlv?—œev ?‡%i –¯v}—œ|=w&m(„O‹?‹/‚óv?ujdjm]nUxE|=qEmª`vhxEm]†yœr_v?w&©l|=xEmUq2bAn]yœm]rlnIm}iœcObAxEy±qE—œyœ)r =c~­cAbA©=qEyœ )r ?mIq ׃?}hŒ ‹]Oi ¨9|lgZmIqx/c  iœc¢ehqEnpolž}c•_9i î‘5n]e?†m&†’xE|™kA‡Év?u,_À†v}|OqEn]m&n]vAk=m&›}mIqEy±°™n/jHe#j xEy{j v?r WxEolmbAnUo=v?qq‰ e?y±xEmîe?c— }vhqEyœxEo=wiXstrX‘,y{npolmUqErlcy =c 9i ­iœc m]np®mIqx/c 9iœc«m/kO†]i ¯„hqpkXs str%xEmIqErlehxEyœv}rle?— _v?r=uSmIqEm]rlnImv}rÍbOvhuSx (ehqEm j r }yœrlm]mUqEy{ r 8ehr™kXˆlv?qEweh—ªmIxEo=vAk=† ×b j ˆ« Ž Uc­9v}g=—{mIr  c mUqEwe?r%‡ ׃??Ž ‹?‹}i 9|lgZmIqx/c  iœcjehqEnpolž}cW_9i bOm]©lehqpehxEyœv?r

(91) ehr™eh  —œ‡O

(92) † yœ † uSv? qó kO m/šk= |= nI xEyœ›m › mIqEy±°™n] ehxEyœv}rW i   mInU o=Prlyœn/ e?— M qEmI©Zv?qx/c%~9rlyœ›mIqE†y±xEž9”•ehqEyœ† s ׃h}   i 9(. /.. !0. &.. 0. F3. @. 7.. &.. (. 0. @. ,. 3. (. (. /.. 3. 5. /.. 3. :5. H>. 5. -5.

(93)

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