Theory propagation and reification

SAT Modulo Theories (SMT) is the problem of determining the satisfiability of a formula in which constraints, drawn from a given constraint theory T , are composed with logical connectives. The DPLL(T ) approach to SMT has risen to prominence as a technique for solving these quantifier-free problems. The key idea in DPLL(T ) is to couple unit propagation in the propositional part of the problem with theory propagation in the constraint component. In this paper it is demonstrated how reification provides a natural way for orchestrating this in the setting of logic programming. This allows an elegant implementation of DPLL(T ) solvers in Prolog. The work is motivated by a problem in reverse engineering, that of type recovery from binaries. The solution to this problem requires an SMT solver where the theory is that of rational-tree constraints, a theory not supported in off-the-shelf SMT solvers, but realised as unification in Prolog systems. The approach is also illustrated with SMT solvers for linear constraints and integer difference constraints. The rational-tree solver is benchmarked against a number of type recovery problems, and compared against a lazy-basic SMT solver built on PicoSAT, while the integer difference logic solver is benchmarked against CVC3 and CVC4, both of which are implemented in C++. ∗Corresponding author Email address: [email protected] (Ed Robbins) The PPDP version of the paper, unchanged apart from reformatted in SCP style, is available from http://www.cs.kent.ac.uk/people/staff/amk/ theory-propagation-scp.pdf Preprint submitted to Elsevier April 17, 2014 New material:. The paper includes a number of sections of new material over and above the PPDP version: • A correctness proof of the core algorithm (an extended section 4.3); • An extension of the work to difference logic (new section 7); • Benchmarking difference logic against CVC3 and CVC4 which is reflected in the new structure for the experimental results (new section 8.2) and the discussion (new section 9.2).