Quantitative Strongest Post

We present a novel strongest-postcondition-style calculus for quantitative reasoning about non-deterministic programs with loops. Whereas existing quantitative weakest pre allows reasoning about the value of a quantity after a program terminates on a given initial state, quantitative strongest post allows reasoning about the value that a quantity had before the program was executed and reached a given final state. We show how strongest post enables reasoning about the flow of quantitative information through programs. Similarly to weakest liberal preconditions, we also present a quantitative strongest liberal post. As a byproduct, we obtain the entirely unexplored notion of strongest liberal postconditions and show how these foreshadow a potential new program logic — partial incorrectness logic — which would be a more liberal version of O’Hearn’s recent incorrectness logic. This is joint work with Linpeng Zhang. It is to appear at OOPSLA 2022. A preprint is available here: https: //arxiv. org/pdf/2202. 06765. pdf

Authors

• Benjamin Lucien Kaminski

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