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Lenses are a well-established structure for modelling bidirectionaltransformations, such as the interactions between a database and a view of it.Lenses may be symmetric or asymmetric, and may be composed, forming themorphisms of a monoidal category. More recently, the notion of a learner hasbeen proposed: these provide a compositional way of modelling supervisedlearning algorithms, and again form the morphisms of a monoidal category. Inthis paper, we show that the two concepts are tightly linked. We show both thatthere is a faithful, identity-on-objects symmetric monoidal functor embedding acategory of asymmetric lenses into the category of learners, and furthermorethere is such a functor embedding the category of learners into a category ofsymmetric lenses.

Lenses and Learners