Alignment Completeness for Relational Hoare Logics

Relational Hoare logics (RHL) provide rules for reasoning about relations between programs. Several RHLs include a rule, Sequential-Product, that infers a relational correctness judgment from judgments of ordinary Hoare logic (HL). A variety of other rules have been found useful in practice, but Sequential-Product is relatively complete on its own (with HL). As a more satisfactory way to evaluate RHLs, a notion of alignment completeness for rules is introduced, in terms of the inductive assertion method and product automata. Alignment completeness results are given to account for several different sets of rules. Applying alignment completeness to richer languages and product notions may serve to guide the design of RHLs.