TY  - JOUR
N1  - © 2019 Copyright held by the owner/author(s). This work is licensed under a Creative Commons Attribution 4.0 license.
Y1  - 2019/01//
AV  - public
VL  - 3
TI  - Quantitative Separation Logic - A Logic for Reasoning about Probabilistic Programs
A1  - Batz, K
A1  - Kaminski, BL
A1  - Katoen, J-P
A1  - Matheja, C
A1  - Noll, T
JF  - Proceedings of the ACM on Programming Languages
UR  - http://dx.doi.org/10.1145/3290347
ID  - discovery10089701
N2  - We present quantitative separation logic ($\mathsf{QSL}$). In contrast to classical separation logic, $\mathsf{QSL}$ 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 develop a weakest precondition calculus for quantitative reasoning about probabilistic pointer programs in $\mathsf{QSL}$. This calculus is a conservative extension of both Reynolds' separation logic for heap-manipulating programs and Kozen's / McIver and Morgan's weakest preexpectations for probabilistic programs. Soundness is proven with respect to an operational semantics based on Markov decision processes. Our calculus preserves O'Hearn's frame rule, which enables local reasoning. We demonstrate that our calculus enables reasoning about quantities such as the probability of terminating with an empty heap, the probability of reaching a certain array permutation, or the expected length of a list.
ER  -