Lenses and Learners
Abstract
Lenses are a well-established structure for modelling bidirectional trans-
formations, such as the interactions between a database and a view of
it. Lenses may be symmetric or asymmetric, and may be composed,
forming the morphisms of a monoidal category. More recently, the
notion of a learner has been proposed: these provide a compositional
way of modelling supervised learning algorithms, and again form the
morphisms of a monoidal category. In this paper, we show that the
two concepts are tightly linked. We show both that there is a faithful,
identity-on-objects symmetric monoidal functor embedding a category
of asymmetric lenses into the category of learners, and furthermore
there is such a functor embedding the category of learners into a category of symmetric lenses.