Validating SMT Solvers for Correctness and Performance via Grammar-Based Enumeration

We introduce ET, a grammar-based enumerator for validating SMT solver correctness and performance. By compiling grammars of the SMT theories to algebraic datatypes, ET leverages the functional enumerator FEAT. ET is highly effective at bug finding and has many complimentary benefits. Despite the extensive and continuous testing of the state-of-the-art SMT solvers Z3 and cvc5, ET found 102 bugs, out of which 84 were confirmed and 40 were fixed. Moreover, ET can be used to understand the evolution of solvers. We derive eight grammars realizing all major SMT theories including the booleans, integers, reals, realints, bit-vectors, arrays, floating points, and strings. Using ET, we test all consecutive releases of the SMT solvers Z3 and CVC4/cvc5 from the last six years (61 versions) on 8 million formulas, and 488 million solver calls. Our results suggest improved correctness in recent versions of both solvers but decreased performance in newer releases of Z3 on small timeouts (since z3-4.8.11) and regressions in early cvc5 releases on larger timeouts. Due to its systematic testing and efficiency, we further advocate ET’s use for continuous integration.