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Quantitative strongest post: a calculus for reasoning about the flow of quantitative information

2022; Association for Computing Machinery; Volume: 6; Issue: OOPSLA1 Linguagem: Inglês

10.1145/3527331

2475-1421

Linpeng Zhang, Benjamin Lucien Kaminski,

Formal Methods in Verification

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 develop 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.