On Structuring Functional Programs with Monoidal Profunctors

ALEXANDRE GARCIA DE OLIVEIRA; MAURO JASKELIOFF; ANA CRISTINA VIEIRA DE MELO

Munich

Workshop; Ninth Workshop on Mathematically Structured Functional Programming; 2022

We study monoidal profunctors as a tool to reason and structure pure functional programs both from a categorical perspective and as a Haskell implementation. From the categorical point of view we approach them as monoids in a certain monoidal category of profunctors. We study properties of this monoidal category and construct and implement the free monoidal profunctor. We study the relationship of the monoidal construction to optics, and introduce a promising generalization of theimplementation which we illustrate by introducing effectful monoidal profunctors.