Combining rule- and SMT-based reasoning for verifying floating-point Java programs in KeY

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 article, we present the first floating-point support in a deductive verification tool for the Java programming language. Our support in the KeY verifier handles floating-point arithmetics, transcendental functions, and potentially rounding-type casts. We achieve this with a combination of delegation to external SMT solvers on the one hand, and KeY-internal, rule-based reasoning on the other hand, exploiting the complementary strengths of both worlds. 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 correct programs—as well as functional properties, for realistic benchmarks.