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

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...

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Veröffentlicht in:Proceedings of ACM on programming languages Jg. 6; H. OOPSLA1; S. 1 - 29
Hauptverfasser: Zhang, Linpeng, Kaminski, Benjamin Lucien
Format: Journal Article
Sprache:Englisch
Veröffentlicht: 29.04.2022
ISSN:2475-1421, 2475-1421
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Abstract 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.
AbstractList 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.
Author Zhang, Linpeng
Kaminski, Benjamin Lucien
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  givenname: Benjamin Lucien
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