Towards interpolation in an SMT-solver with integrated superposition
نویسندگان
چکیده
Interpolation is a technique for extracting intermediate formulæ from a proof. It has applications in formal verification, where interpolation may enable a program analyser to discover information about intermediate program locations and states. We study interpolation in the theorem proving method DPLL(Γ+T ), which integrates tightly a superposition based prover Γ in a DPLL(T ) based SMT-solver to unite their respective strengths. We show how a first interpolation system for DPLL(Γ+T ) can be obtained from interpolation systems for DPLL, equality sharing and Γ. We describe ongoing work on an interpolation system for Γ, by presenting and proving complete an interpolation system for the ground case, followed by a discussion of ongoing work on an extension to the general case. Thanks to the modular design of DPLL(Γ+T ), its interpolation system can be extended easily beyond the ground case once a general interpolation system for Γ becomes available.
منابع مشابه
Proof Tree Preserving Interpolation
Craig interpolation in SMT is difficult because, e. g., theory combination and integer cuts introduce mixed literals, i. e., literals containing local symbols from both input formulae. In this paper, we present a scheme to compute Craig interpolants in the presence of mixed literals. Contrary to existing approaches, this scheme neither limits the inferences done by the SMT solver, nor does it t...
متن کاملAVATAR: a new Architecture for First-Order Theorem Provers
AVATAR is a new architecture for first-order resolution and superposition theorem provers which tightly integrates the saturation loop with a SAT solver (or an SMT solver) to efficiently implement the clause splitting rule. AVATAR employes the SAT solver to pick splitting branches, thus delegating the propositional essence of the given problem to the dedicated solver. This leads to a combinatio...
متن کاملSMTInterpol: An Interpolating SMT Solver
Craig interpolation is an active research topic and has become a powerful technique in verification. We present SMTInterpol, an interpolating SMT solver for the quantifier-free fragment of the combination of the theory of uninterpreted functions and the theory of linear arithmetic over integers and reals. SMTInterpol is SMTLIB 2 compliant and available under an open source software license (LGP...
متن کاملGröbner Basis Construction Algorithms Based on Theorem Proving Saturation Loops
We present novel Gröbner basis algorithms based on saturation loops used by modern superposition theorem provers. We illustrate the practical value of the algorithms through an experimental implementation within the Z3 SMT solver.
متن کاملSatisfiability Modulo Theories
Satisfiability Modulo Theories (SMT) refers to the problem of determining whether a first-order formula is satisfiable with respect to some logical theory. Solvers based on SMT are used as back-end engines in model checking applications such as bounded, interpolation-based, and predicate abstraction-based model checking. After a brief illustration of these uses, we survey the predominant techni...
متن کامل