Section: New Results

Efficient proof-search techniques in sequent calculus

We have proposed in [11] a sequent calculus which is focussed, polarized, and parameterized by an abstract notion of theory. This new combination of features aims at proposing a framework which is adapted to the simulation in sequent calculus of efficient, general-purpose decision procedures (tableaux methods, satisfiability, ...) that can interact with theory-specific decision procedures (for linear arithmetics, arrays, ...). In particular we propose a tight simulation of the Davis–Putnam–Logemann–Loveland algorithm modulo theory, and show how to simulate some advanced optimizations that are crucial to realistic implementations of SMT solvers.