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?
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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