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Hoare-style program logics are a popular and effective technique for softwareverification. Relational program logics are an instance of this approach thatenables reasoning about relationships between the execution of two or moreprograms. Existing relational program logics have focused on verifying that allruns of a collection of programs do not violate a specified relationalbehavior. Several important relational properties, including refinement andnoninterference, do not fit into this category, as they also mandate theexistence of specific desirable executions. This paper presents RHLE, a logicfor verifying these sorts of relational $\forall\exists$ properties. Key to ourapproach is a novel form of function specification that employs a variant ofghost variables to ensure that valid implementations exhibit certain behaviors.We have used a program verifier based on RHLE to verify a diverse set ofrelational $\forall\exists$ properties drawn from the literature.

RHLE: Modular Deductive Verification of Relational $\forall\exists$ Properties