Relational Decomposition

We introduce relational decomposition, a technique for formally reducing termination-insensitive relational program logics to unary logics, that is program logics for one-execution properties. Generalizing the approach of selfcomposition, we develop a notion of interpolants that decompose along the phrase structure, and relate these interpolants to unary and relational predicate transformers. In contrast to previous formalisms, relational decomposition is applicable across heterogeneous pairs of transition systems. We apply our approach to justify variants of Benton’s Relational Hoare Logic (RHL) for a language with objects, and present novel rules for relating loops that fail to proceed in lockstep. We also outline applications to noninterference and separation logic.