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In this paper we relate different formulations of the DPLL(T) procedure. Thefirst formulation is based on a system of rewrite rules, which we denoteDPLL(T). The second formulation is an inference system of, which we denoteLKDPLL(T). The third formulation is the application of a standard proof-searchmechanism in a sequent calculus LKp(T) introduced here. We formalise anencoding from DPLL(T) to LKDPLL(T) that was, to our knowledge, never explicitlygiven and, in the case where DPLL(T) is extended with backjumping and Lemmalearning, never even implicitly given. We also formalise an encoding fromLKDPLL(T) to LKp(T), building on Ivan Gazeau's previous work: we extend hiswork in that we handle the "-modulo-Theory" aspect of SAT-modulo-theory, byextending the sequent calculus to allow calls to a theory solver (seen as ablackbox). We also extend his work in that we handle advanced features of DPLLsuch as backjumping and Lemma learning, etc. Finally, we re fine the approachby starting to formalise quantitative aspects of the simulations: thecomplexity is preserved (number of steps to build complete proofs). Otheraspects remain to be formalised (non-determinism of the search / width ofsearch space).

Two simulations about DPLL(T)