lec32a-HoareLogicInvariants.pdf

lec32a-HoareLogicInvariants.pdf - BITS Pilani Pilani Campus...

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BITS Pilani Pilani Campus MODULE: PROGRAM VERIFICATION Floyd-Hoare Logic: Verifying Loops: Loop Invariants Sundar B. CS&IS, BITS Pilani 0 20-11-2016 CS/IS F214 Logic in Computer Science
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Hoare Logic Basic Method Hoare Logic reduces basic correctness argument for a program /* Precondition: Input x satisfies some properties */ A(x) /* Postcondition: Running A on x results in ... */ to each statement in a program: /* p0 */ S1 /* p1 */ S2 /* p2 * / ... /* pN */ 20-11-2016 1 Sundar B. CS&IS, BITS Pilani such that pN is the required post-condition and p0 is the given precondition. How would this approach work for iterative statements (i.e. loops)? How many iterations will one go through?
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Hoare Logic Rule for Iterations Invariants Rule for Iterative Statement < φ B, S , φ> ----------------------------------------- <φ, while B do { S } , φ   B> Alternatively /* Precondition: φ */ while (B) do { /* φ B */ S /* φ */ } /* Postcondition: φ   B */ 20-11-2016 2 Sundar B. CS&IS, BITS Pilani This premise states that φ remains invariant (i.e. unchanged) over one iteration.
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