Reduced Functional Consistency of Uninterpreted Functions

A reduction of Equality Logic with Uninterpreted Functions (EUF) to Equality Logic with Ackermann's method suffers from a quadratic growth in the number of functional consistency constraints (constraints of the form x=y→F(x)=F(y)). We propose a framework in which syntactic characteristics of function instances (their signature) is used for guessing which constraints will possibly be needed for the proof. This framework can be either combined in an abstraction-refinement loop, or, in some cases, be used without refinement iterations. The framework is suitable for equivalence verification problems, which is one of the typical uses of Uninterpreted Functions. It enabled us to verify dozens of verification conditions resulting from Translation Validation that we could not prove otherwise.