A Deductive Verification Infrastructure for Probabilistic Programs (Extended Version)

TL;DR

This paper introduces a novel deductive verification framework for probabilistic programs that uses a real-valued logic and an intermediate language, enabling automatic verification of quantitative properties like expectations and probabilities.

Contribution

It develops the first deductive verification infrastructure for expectation-based reasoning in probabilistic programs, extending traditional Boolean-based methods to real-valued logic.

Findings

Supports encoding of various verification techniques

Automatically verifies multiple benchmarks

Establishes a new framework for probabilistic program verification

Abstract

This paper presents a quantitative program verification infrastructure for discrete probabilistic programs. Our infrastructure can be viewed as the probabilistic analogue of Boogie: its central components are an intermediate verification language (IVL) together with a real-valued logic. Our IVL provides a programming-language-style for expressing verification conditions whose validity implies the correctness of a program under investigation. As our focus is on verifying quantitative properties such as bounds on expected outcomes, expected run-times, or termination probabilities, off-the-shelf IVLs based on Boolean first-order logic do not suffice. Instead, a paradigm shift from the standard Boolean to a real-valued domain is required. Our IVL features quantitative generalizations of standard verification constructs such as assume- and assert-statements. Verification conditions are generated by a weakest-precondition-style semantics, based on our real-valued logic. We show that our verification infrastructure supports natural encodings of numerous verification techniques from the literature. With our SMT-based implementation, we automatically verify a variety of benchmarks. To the best of our knowledge, this establishes the first deductive verification infrastructure for expectation-based reasoning about probabilistic programs.