Entangled State Monads

Abstract

We present a monadic treatment of symmetric state-based bidirectional transformations, and show how it arises naturally from the well-known asymmetric lens-based account. We introduce two presentations of a concept we dub the "entangled" state monad, and prove their equivalence. As a step towards a unifying account of bidirectionality in general, we exhibit existing classes of state-based approaches from the literature as instances of our new constructions. This extended abstract reports on work in progress.