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Divergences on monads for relational program logics

Published online by Cambridge University Press:  31 July 2023

Tetsuya Sato Open the ORCID record for Tetsuya Sato [Opens in a new window]  and
Shin-ya Katsumata Open the ORCID record for Shin-ya Katsumata [Opens in a new window]
Tetsuya Sato
Affiliation:
Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo, Japan
Shin-ya Katsumata*
Affiliation:
National Institute of Informatics, 2-1-2 Chiyoda-ku, Tokyo, Japan
*
Corresponding author: Shin-ya Katsumata; Email: s-katsumata@nii.ac.jp
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Abstract

Several relational program logics have been introduced for integrating reasoning about relational properties of programs and measurement of quantitative difference between computational effects. Toward a general framework for such logics, in this paper, we formalize the concept of quantitative difference between computational effects as divergences on monads, then develop a relational program logic called approximate computational relational logic (acRL for short). It supports generic computational effects and divergences on them. The semantics of the acRL is given by graded strong relational liftings constructed from divergences on monads. We derive two instantiations of the acRL: (1) for the verification of various kinds of differential privacy of higher-order functional probabilistic programs and (2) the other for measuring difference of distributions of cost between higher-order functional probabilistic programs with a cost counting operator.

Keywords

Relational Hoare logicsgraded monadsrelational liftings
Type
Special Issue: Differences and Metrics in Programs Semantics: Advances in Quantitative Relational Reasoning
Information
Mathematical Structures in Computer Science , Volume 33 , Special Issue 4-5: Differences and Metrics in Programs Semantics: Advances in Quantitative Relational Reasoning , April 2023 , pp. 427 - 485
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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