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()' &K3#%, +45  :;<=>@ABCŸðŒbð$ü\¦Ánìl� ‰ãÉÖóvéÿª_ð$ÿ2ð$az¬]BLñ&Â×9?ˆ°ªÿ˪_ð$ÿbð$Ú&ñ\þJÄeã¯R}F�ÿn uabð$¦[Kõ�˜#*8�>Ù“ÿÏãmbð$òû«ËçBõ�Ó”fó $ ÿ½&²�bð$š| “ß�_V¶d–“ÿ«o´bð$¡�Xîþ¤ˆoûy*B²gåÿcuÄ ð�0e‚˜²ƒ0e„˜²…‡ˆ‰¿ ô   €�‚ƒ„… †A‡Áˆ‰Š‹Œ�Ž��‘’“”•–—Á˜™š›œ@¿ ÀÁÂÿÿÿà ÄÅAÆÁÇÈÉÊË5%ÌÍÎÏÁ×ÿËËË 8c8c     ?€�‚ƒœ1„…ðù†‡÷ˆ ¿ÀÁÂdÃÄÅÆÇÈÉÊ0uËÐÌ0íìÿÍ@T‰Î€Ï€ÿÿÐyÿÑ2Ò NÓPÃÔÕ'Öp”×°<ÿÿØÙ'Úp”ÿA¨)BCD|¾E„|¾…†|¾‡s "ñ Œ�0e@žÿÿÿÿŸÿÿÿÿ  ¡Á¢ÿÿÿÿ£ÿÿÿÿ¤ ¥Á¦ÿÿÿÿ§ÿÿÿÿ¿ ÙÿÿÿÿÚÿÿÿÿÛ ÜÁÝÿÿÿÿÞÿÿÿÿß àÁáÿÿÿÿâÿÿÿÿÿÀÿÿÿÿÿÿÿÿ Âÿÿÿÿÿÿÿÿ Âÿÿÿÿÿÿÿÿ‰ÿÿÿÿŠÿÿÿÿ‹ ŒÂ�ÿÿÿÿ��‘’¿‚‚@ABÿÿÿC DEEFÅGHIJK5%LMNOÅPQRSTUWYÿÿÿÿZÿÿÿÿ[ \Å]ÿÿÿÿ^ÿÿÿÿ_ `ÅaÿÿÿÿbÿÿÿÿN€�‚ÿÿÿƒ „…E†Å‡ˆ‰Š‹5%Œ�Ž�Å�‘’“”•—™ÿÿÿÿšÿÿÿÿ› œÅ�ÿÿÿÿžÿÿÿÿŸ  Å¡ÿÿÿÿ¢ÿÿÿÿ¿NÀÁÂÿÿÿà ÄÅEÆÅÇÈÉÊË5%ÌÍÎÏÅÐÑÒÓÔÕ×ÙÿÿÿÿÚÿÿÿÿÛ ÜÅÝÿÿÿÿÞÿÿÿÿß àÅáÿÿÿÿâÿÿÿÿÿNÿÿÿ FÆ   5%  Æÿÿÿÿÿÿÿÿ Æÿÿÿÿÿÿÿÿ Æ!ÿÿÿÿ"ÿÿÿÿ?N@ABÿÿÿC DEFFÆGHIJK5%LMNOÆPQRSTUWYÿÿÿÿZÿÿÿÿ[ \Æ]ÿÿÿÿ^ÿÿÿÿ_ `Æaÿÿÿÿbÿÿÿÿ0ñ –––€Ì@ñ÷ð8ó€ó€Ð„úÎÙ Êš;_êŒ6Êš;úgþý4`d`dŒµ—¾ 0Âüÿÿ¸ÿÿÿpûppû@ <ý4dddd@—¡k 0t© µÿ <ý4!d!d@—Ãl 0t©<ý4BdBd@—Ãl 0t©úgþý4CdCd€!µ—¾ 0Pùÿÿ¼ÿÿÿpûl pûœˆ’‰2ºDEFAULTFONTSIZEº10‰.ºDEFAULTWIDTHº348‰0ºDEFAULTHEIGHTº200Šк___PPT10‹°Ö˜·D‹[SOrier Newð•ð•t©t©<—ô•¾ 0ô•Ö†·DCourier Newð•ð•t©t©<—ô•¾ 0ô•Ö1 pµpµŠ º___PPT9‹ìäÓäÓ0äÓ[äÓ\äÓ^äÓ˜äÓšz?ÙHÚ%º2005-9-16 ºNJPLS@StevensOÙ Ú=ðßMóO?Ÿ¨]Modular Verification of Concurrent Assembly Code with Dynamic Thread Creation and Termination¡^^Ÿ¨6Xinyu Feng Yale University Joint work with Zhong Shao¡(7ªH"óVBŸ¨ MotivationŸ ðProof-carrying code (PCC) In principle: verify any property on any code Real binaries & no loss of efficiency Embedded OS, device drivers& All safety & liveness properties& Formal, machine-checkable proofs In reality: only works for sequential code¡v.†+€ €Ìþ†€ €€Ìþª˜YóWCŸ¨ ChallengesŸ¨æChallenges for Proof-carrying concur. code A general framework for concurrent assembly code verification Lack of structures (e.g. cobegin/coend blocks) Specification/proof generation Spec inference, proof assistant, theorem prover¡ˆ+>/0+>€€ €Ìþ €€0 € ªàóXDŸ¨ Previous workŸ Rely-Guarantee (R-G) Method Shared memory concurrency Thread modular verification Only for higher-level code: cobegin/coend CCAP[Yu&Shao, ICFP 04] The first PCC framework supporting concurrent assembly code R-G method Only support static threads P1 || & || Pn¡ÒPaPPcPP6+Ìþ€€€G€€Ìþ €  € çÿ €  € çÿª,} yó^IŸ¨Concurrency ProgrammingŸ ¼cobegin/coend S::=& | cobegin P1 || P2 codend | & Higher-level, well-structured Only support properly nested concurrent code fork/join S::=& | tid := fork f(a) | join tid | & More flexible: improperly nested code OSes/Java/& ¡n YC�C�G�Ìþ ÌþG�ÌþP C�€€ÌþG�Ìþ€ÌþG�Ìþ€Ìþ7€ªb a+ó Ÿ¨Our Contributions¡(Ÿ¨ÿA new PCC framework: CMAP Verification of general properties Dynamic thread creation/termination Generalize the Rely-Guarantee method Modular verification Realistic features Multiple instantiations of thread code Thread argument passing, thread-local data¡pG%(R#€$€Ìþ%€(€R € óŸ¨Outline of This TalkŸ¨“Background: the Rely-Guarantee Method Challenges for Dynamic Thread Creation/Termination Our Approach The CMAP Framework Conclusion and Future Work¡”&ÌþnóŸ¨The Rely-Guarantee MethodŸª óŸ¨The Rely-Guarantee MethodŸ ~Thread + Thread Environment Rely and Guarantee A, G: State ®ð State ®ð Prop Thread Modularity Non-Interference (interface compatibility): "ði,j. i¹ðj Þð Gi Þð Aj Safety of each thread Ti: (Ai, Gi)¡/ZZZ,ZZZ Z/ €€,€ €‚ˆ‚çÿ€‚ˆ‚çÿ€ € €€çÿ€€çÿ€€çÿ€ª>”!óŸ 0GCD Example [Yu&Shao 04]¡  Ÿª óŸ¨Outline of This TalkŸ¨“Background: the Rely-Guarantee Method Challenges for Dynamic Thread Creation/Termination Our Approach The CMAP Framework Conclusion and Future Work¡*”&–––þ3Ìþ;óŸ¨Concurrency ProgrammingŸ ¼cobegin/coend S::=& | cobegin P1 || P2 codend | & Higher-level, well-structured Only support properly nested concurrent code fork/join S::=& | tid := fork f(a) | join tid | & More flexible: improperly nested code OSes/Java/& ¡n YC�C�G�Ìþ ÌþG�ÌþP C�€€ÌþG�Ìþ€ÌþG�Ìþ€Ìþ7€ªb a+ó Ÿ¨Static and Dynamic ThreadsŸª ó Ÿ¨ ChallengesŸ ¦First attempt Check NI between all static threads Ti: (Ai, Gi) "ði,j. i¹ðj Þð Gi Þð Aj ¡æ$!€€Ìþ €€€çÿ€€çÿ€€çÿ€ €‚ˆ‚çÿ€‚ˆ‚çÿ€€ªF;ó%Ÿ¨Challenges: Changing Env. IªŸ ¢A-B: initialize data d no other threads will change d A : d = d B-C: collaborate with T3 to process d T3 may change d Still do not allow other threads change d C-D: T3 terminates No other threads can change d¡ð*&: ‚‚€ €çÿ€€ €çÿ8€€ €çÿ € € ó'Ÿ¨Challenges: Changing Env. IªŸª ó(Ÿ¨Challenges: Changing Env. IIªŸ¨�T2 and T3 have no overlap in their lifetime non-interference between all threads? Only check those that overlap? How to specify the overlapping?¡l,E  çÿ çÿ#E€ €ó;0Ÿ¨#Challenges: multiple instantiations¡$$(Ÿª ó:/Ÿ¨Challenges: ModularityŸª ó)Ÿ¨Outline of This TalkŸ¨“Background: the Rely-Guarantee Method Challenges for Dynamic Thread Creation/Termination Our Approach The CMAP Framework Conclusion and Future Work¡*”Y–––þ Ìþ.ó#Ÿ¨Our Approach (1)Ÿ rProblems for checking NI of static threads Changing environment Multiple instantiations Modularity issues CMAP:  lazy checking At each step, all live (dynamic) threads do not interfere¡d+?:+?€€€Ìþ€ó$Ÿ¨Our Approach (2)Ÿª óŸ¨Our Approach (3)Ÿ¨6Borrow ideas from typechecking data heaps (as in TAL):¡77ª ó+ Ÿ¨Our Approach (4)Ÿ¨Thread Termination: exit¡Aó,!Ÿ¨Our Approach (5)Ÿ¨Thread Creation: fork f(a)¡ Aó2'Ÿ¨Our Approach (6)Ÿª ó3(Ÿ¨Our Approach (7)Ÿ¨Queue Extensionó=2Ÿ¨Our Approach (8)Ÿ¨ Queue Updateó?3Ÿ¨Our Approach (9)Ÿª ó4)Ÿ¨Our Approach (10)Ÿ ¼Check static threads ßðàðLazy Check Changing Env. ßðàð Changing (A, G) Multiple instantiation ßðàð Not care Modularity ßðàð Certify only once General Enough Language (higher-level/assembly) Thread Model (preemptive/non-preemptive)¡¢"dJ €€„Ìþ€ „Ìþ€„Ìþ€€J€€ª+±óB5Ÿ FExample  Unbounded Thread CreationŸª óC6Ÿ FExample  Unbounded Thread CreationŸ¨GSpecification of Child: Ax: Gx: Non-interference between children: ¡R0€€çÿ€€çÿ)€ª"(óD7Ÿ FExample  Unbounded Thread CreationŸ¨How to specify the main thread?óE8Ÿª Ÿª óYEŸ¨Outline of This TalkŸ¨“Background: the Rely-Guarantee Method Challenges for Dynamic Thread Creation/Termination Our Approach The CMAP Framework Conclusion and Future Work¡*”f–––þÌþó[GŸ¨The CMAP FrameworkŸ¨×The abstract machine The verification logic Specification language Inference rules Soundness proof Example programs Unbounded dynamic thread creation Readers/Writers problem Lock-free program All implemented in Coq!¡t,P7PPLPP,7€L€€ó@4Ÿ¨The CMAP Framework - Machine¡(Ÿª ó]HŸ¨The CMAP FrameworkŸ ®The paper on CMAP (Feng&Shao ICFP 05): http://flint.cs.yale.edu/publications/cmap.html¡\(0€GÌþ)€GÌþª, (ó6+Ÿ¨ ConclusionŸ jProblems for unbounded dynamic thread creation Changing environment (fork/exit) Multiple instantiation of thread code No previously known modular verification method Our approach INV: active threads in the system do not interfere Combine the type-based proof technique with R-G method Unify thread s assumption/guarantee with env. s guarantee/assumption Thread modularity + code/proof reuse The CMAP framework and its Coq implementation ¡¼/ZwZ Z3Z|Z%Z.ZZ/w €3€|€% € . €  € ª"FióM>Ÿ¨ Future WorkŸ¨¥Certified Thread Libraries fork, yield, exit join, lock, monitors Surface language Higher-level specifications Partially infer A and G Certifying compilation to CMAP¡ˆ'SÌþ€,€‚€‚€óK=ó Ÿ¨Assembly Code VerificationŸ Why assembly code? Higher assurance (remove compiler from TCB) Critical components of OS kernel, embedded sys. Proof-Carrying Code (machine code + safety proof) Verification of general properties Type Safety (no stuck) Resource Consumption & Partial/Total Correctness¡TŽ#HŽ#€H€óŸ¨Assembly Code VerificationŸ ÔHarder than higher-level program verification Lack of abstractions Lack of structures (while, if& then& else, cobegin/coend) Many PCC frameworks Most of them only support sequential programs None of them support dynamic thread creation¡ž.M[.)C GÌþ€€ÿþ.€-€ÌþóŸ¨Concurrency VerificationŸ¨Multiple Control Flow (threads) interleaved execution interference on shared resource Cannot check all possible interleaving The number of possible traces is exponential in the number of threads Existing Work Most of them are at higher-level cobegin/coend¡Ž Z7Z'ZFZZ/Z 7'€F€€! €  A€ ó Ÿ¨%Concurrent Assembly Code VerificationŸ ÜCCAP [Yu and Shao, ICFP 04] The first PCC framework supporting concurrent assembly code Rely-Guarantee Method (Jones, 1983) The best-studied concurrency verification method for shared memory model Only support static threads P1 || & || Pn¡’`I`€I€€Ìþ €  € çÿ €  € çÿª, Ûó>1Ÿ¨ Related WorkŸ úRely-Guarantee Method Model Checking Pre-fixed upper bound of number of threads (SPIN, Java Pathfinder,& ) Not compositional (3VMC, SPIN, Java Pathfinder,& ) No dynamic thread creation (CIRC& ) Type Systems [Flanagan et al.] race-free, safe-lock, atomicity¡ª%ZšZZ Z%, €€ €ó5*Ÿ¨ Related WorkŸ RSeparation Logic [O Hearn 04, Bornat et al. 05] Not as general as R-G No dynamic thread creation Depends on the language constructs: conditional critical sections (ccs) ¡J0yyª4€óSAŸ¨Motivation - Previous workŸ BPCC systems Mostly for sequential code CCAP [Yu&Shao, ICFP04] Only static threads: P1 || & || Pn Shared memory concurrency verification Rely-Guarantee method Only for properly-nested code: cobegin/coend Model Checking No explicit formal proof Various limitations, e.g. non-compositional ¡ Z2Z$Z'ZZ.ZZEZZ  €€€€ €çÿ € €çÿ' € €.€€E€ € ª4-*Á/ðàóóóAóIóQóTóUó\ êøBï  0`ð ÿÿÿ–––ÝÝÝä¨33ÌÿPPÿÏ`ð 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ðzˆr‰öº SOURCEºÚ\documentclass{slides}\pagestyle{empty} \usepackage{latexsym} \usepackage{amssymb} \usepackage{latexsym} \usepackage{amssymb} \usepackage{amsmath} \usepackage[dvips]{color} \usepackage{../../share/proof} \let\cmttdfl\ttdefault \let\cmsfdfl\sfdefault \input bnf \input ../../share/infrule %% generic axiom & inference rule stuff \input ../../share/fontname %% New Font Names \input local \begin{document} $G \Rightarrow (A_{0} \land \ldots \land A_{99})$ \end{document} ‰6ºEXTERNALNAMEºtxp_fig‰$º BLENDº False‰0ºTRANSPARENTº False‰,ºKEEPFILESº False‰.ºDEBUGPAUSEº False‰*ºRESOLUTIONº600‰*ºTIMEOUTº (none)‰&ºBOXWIDTHº348‰(ºBOXHEIGHTº200‰"ºBOXFONTº10‰(ºBOXWRAPº False‰Lº2WORKAROUNDTRANSPARENCYBUGº False‰Dº*ALLOWFONTSUBSTITUTIONº False‰6ºBITMAPFORMATºpngmono‰(ºORIGWIDTHº201‰6ºPICTUREFILESIZEº3986ð¢ ð à ðH€°±²¿�ƒ¿ Àÿ?„†"ñ¿‚‚ðP ð ÀV ð,$ñDÿÿÿ 0 ðcŸ¨!But main cannot satisfy such a G!¡&"0 2"€G€ÌþðH ð ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿ3fãâÇ3fÌÌ™3f3f€ˆËŠÃº___PPT10‹£+õ.ΰDñO'ñ ²ÿÿÿÿ=ñ @Bñ Dñ 'ñ –ÿÿÿÿ=ñ @BñAñ?%ñ,(ñ <ñ +O%ñ,(ñ <ñ +DñA'ñ =ñ%ñ(ñÿÿÿÿDñé'ñ =ñ%ñ(ñDñ‘'ñ =ñA@Bñ�Bñ Bñ°Bñ0Bñ%ñ(ñDñø'ñ =ñ1ñ :ñBñvisible*ño3ñ>ñ+Bñ#style.visibility<ñû*ÿÿÿÿÿÿÿÿ%ñ(ñó+8+0+0 +î|(ï € 0 úðòPðñð~ð( ð ðð‚¢ ð ƒ ð0€è¾²¿�ƒ¿ÀÿðŠ Ð À ð"Ÿ¨Rmain: int i:=0; while (i<100){ data[i]:=0; fork(child, i); i++ }¡’S0 2€C€�C�€C€�C�€C€�C�€C€�C�ªHð¶ðl ð ± €—  ð ð± €— ð,$ñDÿÿÿ 0ðÌ¢ ð ³ ðB€ɲ�‚ƒ„¿�ÿÿ¿Àÿð` ± €—  ðRŸ (A , G )¡& 0 2 �G�þðfB ðB “ ð6…D¿ÀË>Ñÿð ` ð¬ðl ð ß �Å ððß �Åð,$ñDÿÿÿ 0ð¢ ð ³ ðB€ìͲ�‚ƒ„¿�ÿÿ¿Àÿð` ß �Å ðHŸ¨(A, G)¡&0 2�G�þðfB ðB “ ð6…D¿ÀË>Ñÿð @` @ð¸ðl ð J `0  ððJ `0 ð,$ñDÿÿÿ 0ðÈ¢ ð à ðH€Ò²�‚ƒ„¿�ÿÿ¿Àÿˆð` J `0  ðHŸ¨(A, G)¡&0 2�G�þðlB ð B £ ð<…D¿ÀË>Ñÿˆð Á ` Á 𬠲 ð  Ó ð^€€…‡A Á�ƒ¿Àÿ¿txp_figð9@ð ˆ ‰˜º SOURCEº|\documentclass{slides}\pagestyle{empty} \usepackage{latexsym} \usepackage{amssymb} \usepackage{latexsym} \usepackage{amssymb} \usepackage{amsmath} \usepackage[dvips]{color} \usepackage{../../share/proof} \let\cmttdfl\ttdefault \let\cmsfdfl\sfdefault \input bnf \input ../../share/infrule %% generic axiom & inference rule stuff \input ../../share/fontname %% New Font Names \input local \begin{document} $$ \begin{array}{l} A \equiv \forall k. \var{i} \le k < 100\Rightarrow \var{data}[k] = \var{data}'[k] \\ G \equiv \forall k. 0\le k < \var{i}\Rightarrow \var{data}[k] = \var{data}'[k] \\ \\ A' \equiv \forall k. \var{i+1} \le k < 100 \Rightarrow\var{data}[k] = \var{data}'[k] \\ G' \equiv \forall k. 0\le k < \var{i+1} \Rightarrow \var{data}[k] = \var{data}'[k] \\ \end{array} $$ \end{document} ‰6ºEXTERNALNAMEºtxp_fig‰$º BLENDº False‰0ºTRANSPARENTº False‰,ºKEEPFILESº False‰.ºDEBUGPAUSEº False‰*ºRESOLUTIONº600‰*ºTIMEOUTº (none)‰&ºBOXWIDTHº348‰(ºBOXHEIGHTº200‰"ºBOXFONTº10‰(ºBOXWRAPº False‰Lº2WORKAROUNDTRANSPARENCYBUGº False‰Dº*ALLOWFONTSUBSTITUTIONº False‰6ºBITMAPFORMATºpngmono‰(ºORIGWIDTHº436‰8ºPICTUREFILESIZEº 30026ðàðl ð ú `à  ððú `à ð,$ñDÿÿÿ 0ðö¢ ð ³ ðB€Ôá²�‚ƒ„¿�ÿÿ¿Àÿð` ú `à ð,$ñDÿÿÿ 0 ðHŸ¨(A, G)¡&0 2�G�þðfB ðB “ ð6…D¿ÀË>Ñÿð b ` b ðîðz ð ú `à  ð ðˆðð `Ö ð,$ñDÿÿÿ 0ðö¢ ð ³ ðB€dæ²�‚ƒ„¿�ÿÿ¿Àÿð` ú `à 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IªŸ ¢A-B: initialize data d no other threads will change d A : d = d B-C: collaborate with T3 to process d T3 may change d Still do not allow other threads change d C-D: T3 terminates No other threads can change d¡ð*&: ‚‚€ €çÿ€€ €çÿ8€€ €çÿ € € ó'Ÿ¨Challenges: Changing Env. IªŸª ó(Ÿ¨Challenges: Changing Env. IIªŸ¨�T2 and T3 have no overlap in their lifetime non-interference between all threads? Only check those that overlap? How to specify the overlapping?¡l,E  çÿ çÿ#E€ €ó;0Ÿ¨#Challenges: multiple instantiations¡$$(Ÿª ó:/Ÿ¨Challenges: ModularityŸª ó)Ÿ¨Outline of This TalkŸ¨“Background: the Rely-Guarantee Method Challenges for Dynamic Thread Creation/Termination Our Approach The CMAP Framework Conclusion and Future Work¡*”Y–––þ Ìþ.ó#Ÿ¨Our Approach (1)Ÿ rProblems for checking NI of static threads Changing environment Multiple instantiations Modularity issues CMAP:  lazy checking At each step, all live (dynamic) threads do not interfere¡d+?:+?€€€Ìþ€ó$Ÿ¨Our Approach (2)Ÿª óŸ¨Our Approach (3)Ÿ¨6Borrow ideas from typechecking data heaps (as in TAL):¡77ª ó+ Ÿ¨Our Approach (4)Ÿ¨Thread Termination: exit¡Aó,!Ÿ¨Our Approach (5)Ÿ¨Thread Creation: fork f(a)¡ Aó2'Ÿ¨Our Approach (6)Ÿª ó3(Ÿ¨Our Approach (7)Ÿ¨Queue Extensionó=2Ÿ¨Our Approach (8)Ÿ¨ Queue Updateó?3Ÿ¨Our Approach (9)Ÿª ó4)Ÿ¨Our Approach (10)Ÿ ¼Check static threads ßðàðLazy Check Changing Env. ßðàð Changing (A, G) Multiple instantiation ßðàð Not care Modularity ßðàð Certify only once General Enough Language (higher-level/assembly) Thread Model (preemptive/non-preemptive)¡¢"dJ €€„Ìþ€ „Ìþ€„Ìþ€€J€€ª+±óB5Ÿ FExample  Unbounded Thread CreationŸª óC6Ÿ FExample  Unbounded Thread CreationŸ¨GSpecification of Child: Ax: Gx: Non-interference between children: ¡R0€€çÿ€€çÿ)€ª"(óD7Ÿ FExample  Unbounded Thread CreationŸ¨How to specify the main thread?óE8Ÿª Ÿª óYEŸ¨Outline of This TalkŸ¨“Background: the Rely-Guarantee Method Challenges for Dynamic Thread Creation/Termination Our Approach The CMAP Framework Conclusion and Future Work¡*”f–––þÌþó[GŸ¨The CMAP FrameworkŸ¨×The abstract machine The verification logic Specification language Inference rules Soundness proof Example programs Unbounded dynamic thread creation Readers/Writers problem Lock-free program All implemented in Coq!¡t,P7PPLPP,7€L€€ó@4Ÿ¨The CMAP Framework - Machine¡(Ÿª ó]HŸ¨The CMAP FrameworkŸ ®The paper on CMAP (Feng&Shao ICFP 05): http://flint.cs.yale.edu/publications/cmap.html¡\(0€GÌþ)€GÌþª, (ó6+Ÿ¨ ConclusionŸ jProblems for unbounded dynamic thread creation Changing environment (fork/exit) Multiple instantiation of thread code No previously known modular verification method Our approach INV: active threads in the system do not interfere Combine the type-based proof technique with R-G method Unify thread s assumption/guarantee with env. s guarantee/assumption Thread modularity + code/proof reuse The CMAP framework and its Coq implementation ¡¼/ZwZ Z3Z|Z%Z.ZZ/w €3€|€% € . €  € ª"FióM>Ÿ¨ Future WorkŸ¨¥Certified Thread Libraries fork, yield, exit join, lock, monitors Surface language Higher-level specifications Partially infer A and G Certifying compilation to CMAP¡ˆ'SÌþ€,€‚€‚€óK=/ð¨óóAóIóQóUó\ êr¯}õÙ‹}™Ñ^Å1  !"#$%&'(þÿÿÿþÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿþÿÕÍÕœ.“—+,ù®DÕÍÕœ.“—+,ù®àœˆ�¨ÄÌÔÜ ä ìô ü   ¨On-screen Show Yale UniversityÍÑÙ)Ø 5ArialËÎÌå HelveticaTahoma WingdingsTimes New Roman Courier NewComic Sans MSSymbol Wingdings 3BlendsMicrosoft ¹«Ê½ 3.0^Modular Verification of Concurrent Assembly Code with Dynamic Thread Creation and Termination Motivation ChallengesPrevious workConcurrency ProgrammingOur ContributionsOutline of This TalkThe Rely-Guarantee MethodThe Rely-Guarantee MethodGCD Example [Yu&Shao¡¯04]Outline of This TalkConcurrency ProgrammingStatic and Dynamic Threads ChallengesChallenges: Changing Env. IChallenges: Changing Env. IChallenges: Changing Env. II$Challenges: multiple instantiationsChallenges: ModularityOutline of This TalkOur Approach (1)Our Approach (2)Our Approach (3)Our Approach (4)Our Approach (5)Our Approach (6)Our Approach (7)Our Approach (8)Our Approach (9)Our Approach (10)%Example ¨C Unbounded Thread Creation%Example ¨C Unbounded Thread Creation%Example ¨C Unbounded Thread Creation Slide 34Outline of This TalkThe CMAP FrameworkThe CMAP Framework - MachineThe CMAP Framework Conclusion Future Work Slide 41  Fonts Used Design TemplateEmbedded OLE Servers Slide Titles)< 8@ _PID_HLINKS¨Aô*+285,20,Example  Unbounded Thread Creation303,23,Modularity297,33,The CMAP Approach297,33,The CMAP Approach297,33,The CMAP Approach304,22,Changing Environment297,33,The CMAP Approachö"_À‘ã©Ñ ôXinyu FengXinyu Feng