Effectful applicative bisimilarity: Monads, relators, and Howe's method

We study Abramsky's applicative bisimilarity abstractly, in the context of call-by-value λ-calculi with algebraic effects. We first of all endow a computational λ-calculus with a monadic operational semantics. We then show how the theory of relators provides precisely what is needed to generalise applicative bisimilarity to such a calculus, and to single out those monads and relators for which applicative bisimilarity is a congruence, thus a sound methodology for program equivalence. This is done by studying Howe's method in the abstract.