Computing with an SMT Solver

Satisfiability modulo theories (SMT) solvers that support quantifier instantiations via matching triggers can be programmed to give practical support for user-defined theories. Care must be taken to avoid so-called matching loops, which may prevent termination of the solver. By design, such avoidance limits the extent to which the SMT solver is able to apply the definitions of user-defined functions. For some inputs to these functions, however, it is instead desireable to allow unadulterated use of the functions; in particular, if it is known that evaluation will terminate. This paper describes the program verifier Dafny’s SMT encoding of recursive user-defined functions. It then describes a novel encoding that, drawing on ideas from offline partial evaluation systems, lets the SMT solver evaluate “safe” function applications while guarding against matching loops for others.