3 research outputs found
Divergences on Monads for Relational Program Logics
Several relational program logics have been introduced for integrating
reasoning about relational properties of programs and measurement of
quantitative difference between computational effects. Towards a general
framework for such logics, in this paper, we formalize quantitative difference
between computational effects as divergence on monad, then develop a relational
program logic acRL that supports generic computational effects and divergences
on them. To give a categorical semantics of acRL supporting divergences, we
give a method to obtain graded strong relational liftings from divergences on
monads. We derive two instantiations of acRL for the verification of 1) various
differential privacy of higher-order functional probabilistic programs and 2)
difference of distribution of costs between higher-order functional programs
with probabilistic choice and cost counting operations.Comment: Preprin