  Lenses are a well-established structure for modelling bidirectional
transformations, 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.
