You may implement this later: Cofunctors as partial implementations

Abstract

A functor is a familiar model of an implementation, where every operation in a specification is assigned a concrete instantiation at the outset. But some tasks are less eager: we often want to assemble systems while leaving backend choices such as data representations and algorithms for later. We observe that cofunctors admit a direct reading as such partial implementations, which are implementations whose extra argument is a state-dependent family of deferred choices. While cofunctors (also called retrofunctors) are not novel, their conceptual and purposive reading in this manner appears to be.