Quantitative Separation Logic

Abstract: We present quantitative separation logic (QSL). In contrast to classical separation logic, QSL employs quantities which evaluate to real numbers instead of predicates which evaluate to Boolean values. The connectives of classical separation logic, separating conjunction and separating implication, are lifted from predicates to quantities. This extension is conservative: Both connectives are backward compatible to their classical analogs and obey the same laws, e.g. modus ponens, adjointness, etc. Furthermore, we present a weakest precondition calculus for quantitative reasoning about probabilistic pointer programs in QSL. This calculus is a conservative extension of both Ishtiaq's, O'Hearn's and Reynolds' separation logic for heap-manipulating programs and Kozen's / McIver and Morgan's weakest preexpectations for probabilistic programs. Our calculus preserves O'Hearn's frame rule, which enables local reasoning - a key principle of separation logic. Finally, we briefly touch upon open questions regarding lower bounds on weakest preexpectations and intensional completeness of our calculus.

formal languages and automata theorylogic in computer sciencelogic

Audience: researchers in the discipline

Online Worldwide Seminar on Logic and Semantics (OWLS)

Series comments: The Online Worldwide Seminar on Logic and Semantics is a new series of research talks, highlighting the most exciting recent work in the international computer science logic community. The scope of the seminar series is roughly that of the major computer science logic conferences such as LICS, ICALP and FSCD. It takes place on most Wednesdays, with a focus every other week on the work of young researchers.

In this time of restricted international travel, a key aim of this series is to provide a forum for the informal discussion and social interaction that is so important for the progress of science. To facilitate this, the seminar incorporates in virtual form a number of features more normally associated with physical meetings.

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