Deductive Verification of Floating-Point Java Programs in KeY

TL;DR

This paper introduces the first support for floating-point reasoning in a Java deductive verification tool, KeY, enabling verification of properties involving floating-point arithmetic and special values.

Contribution

It extends KeY with floating-point decision procedures and axiomatization, allowing for more comprehensive verification of Java programs with floating-point computations.

Findings

Successfully proves absence of floating-point special values in benchmarks

Verifies functional properties of realistic Java programs involving floating-point

Demonstrates the effectiveness of SMT-based decision procedures in verification

Abstract

Deductive verification has been successful in verifying interesting properties of real-world programs. One notable gap is the limited support for floating-point reasoning. This is unfortunate, as floating-point arithmetic is particularly unintuitive to reason about due to rounding as well as the presence of the special values infinity and `Not a Number' (NaN). In this paper, we present the first floating-point support in a deductive verification tool for the Java programming language. Our support in the KeY verifier handles arithmetic via floating-point decision procedures inside SMT solvers and transcendental functions via axiomatization. We evaluate this integration on new benchmarks, and show that this approach is powerful enough to prove the absence of floating-point special values -- often a prerequisite for further reasoning about numerical computations -- as well as certain functional properties for realistic benchmarks.