An Assertion-Based Program Logic for Probabilistic Programs

TL;DR

The paper introduces Ellora, an assertion-based logic for probabilistic programs, enhancing expressivity and proving its effectiveness through classical randomized algorithm examples in EasyCrypt.

Contribution

Ellora is a sound, relatively complete assertion-based logic with new proof rules, supporting richer assertions and complex probabilistic reasoning, bridging the gap with expectation-based systems.

Findings

Ellora can verify classical randomized algorithms.

Supports richer assertions and complex probabilistic concepts.

Demonstrates assertion-based logic's potential for probabilistic verification.

Abstract

Research on deductive verification of probabilistic programs has considered expectation-based logics, where pre- and post-conditions are real-valued functions on states, and assertion-based logics, where pre- and post-conditions are boolean predicates on state distributions. Both approaches have developed over nearly four decades, but they have different standings today. Expectation-based systems have managed to formalize many sophisticated case studies, while assertion-based systems today have more limited expressivity and have targeted simpler examples. We present Ellora, a sound and relatively complete assertion-based program logic, and demonstrate its expressivity by verifying several classical examples of randomized algorithms using an implementation in the EasyCrypt proof assistant. Ellora features new proof rules for loops and adversarial code, and supports richer assertions than existing program logics. We also show that Ellora allows convenient reasoning about complex probabilistic concepts by developing a new program logic for probabilistic independence and distribution law, and then smoothly embedding it into Ellora. Our work demonstrates that the assertion-based approach is not fundamentally limited and suggests that some notions are potentially easier to reason about in assertion-based systems.