iccad08-tutorial-ALL [Compatibility Mode]

Chaowang

Description

Program verification using Verrification--Connditioon geenerraationnShuvendu LahiriSoftware Reliability ResearchMicrosoft Research, Redmond5Outline From Programs to SMT formulas Straight line programs Annotations Loops and Procedures Modeeling loww-levell CC proggrrams HAVOC toolkit Challenges for scalable and automated verification6Program Correctness: Hoare Triple Hoare triple{P} S {Q}P, Q : predicates/propertyS : a prrogramm From a state satisfying P, if S executes, then either: Either S does not terminate, or S terminates in a state satisfying Q7Program verification Formula{ b.f = 5 } a.f = 5 { a.f + b.f = 10 }is valid iffSelect(f1,b) = 5 ∧ f2 = Store(f1,a,5) ⇒ Select(f2,a) + Select(f2,b) = 10is validtheory of equality: f, =theory of arithmetic: 5, 10, +theory of arrays: Select, Store• [Nelson & Oppen ’79]8Satisfiability-Modulo-Theory (SMT) Boolean satisfiability solving + theoryreasoning Ground theoriesEquality, arithmetic, Select/Store NP-cocomplletete loggics Phenomenal progress in the past few yearsYices [Dutretre&deMoura’06], Z3 [deMoura&Bjorner’07]9Simple prog. language (BoogiePL)[Leino et al.‘05] Commandsx := E evaluate E and change x to that valuehavoc x change x to an arbitrary valueasssert E if E holds, terminate; otherwise, go wrongassume E if E holds, terminate; otherwise, blockS ; T execute S, then Tgoto A or B; change point of control to block A or ...

Informations

• Publié par: Phawyug
• Nombre de lectures: 11
• Langue: English

Extrait

Shuvendu Lahiri

 

Software Reliability Research

Microsoft Research, Redmond

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HAVOC toolkit

 

 

Challenges for scalable and automated verification

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From a state satisfying P, if S executes, then either:  Either S does not terminate, or  S terminates in a state satisfying Q

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Select(f1,b) = 5∧f2 = Store(f1,a,5)⇒Select(f2,a) + Select(f2,b) = 10

is valid

theory of equality: f, =  

theory of arithmetic: 5, 10, +

theory of arrays:

 [Nelson & Oppen ’79]

Select, Store

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-com

e

e

o

cs

Phenomenal progress in the past few years  Yices [Dutretre&deMoura’06],  Z3 [deMoura&Bjorner’07]

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 if E holds, terminate; otherwise, go wrong  assumeE  if E holds, terminate; otherwise, block  S ; T  execute S, then T  gotoAorB;  change point of control to block A or block B, choosing blindly

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var y: int;

var a: [int] int;

start:

y := 10;

a[y] := 20;

y := a[10];

// array variable

// assignment to scalar

// sugar for a := update(a, y, 20) ;

//read from a map

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Else:

After:

  goto

; After

assume¬P ; [[T]]; gotoAfter

…

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assumeP; S;assertQ

Task: Transform a program withassume/saestr a formula  Known asVerification Condition(VC) generation

into

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if it terminates, terminates in Q

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