An Abstract Interpretation of DPLL(T)

dpll(t) is a central algorithm for Satisfiability Modulo Theories (smt) solvers. The algorithm combines results of reasoning about the Boolean structure of a formula with reasoning about conjunctions of theory facts to decide satisfiability. This architecture enables modern solvers to combine the performance benefits of propositional satisfiability solvers and conjunctive theory solvers. We characterise dpll(t) as an abstract interpretation algorithm that computes a product of two abstractions. Our characterisation allows a new understanding of dpll(t) as an instance of an abstract procedure to combine reasoning engines beyond propositional solvers and conjunctive theory solvers. In addition, we show theoretically that the split into Boolean and theory reasoning is sometimes unnecessary and demonstrate empirically that it can be detrimental to performance.