What you needa know about Yoneda

Profunctor optics are a neat and composable representation of bidirectional data accessors, such as lenses (a "getter" and a "setter", for example onto a field of a record), and their dual, prisms. The profunctor representation exploits higher-order functions and higher-kinded type constructor classes. The relationship with the "getter" and "setter" functions is not at all obvious; it turns out to be a fairly direct application of the Yoneda Lemma, arguably the most important result in category theory. This talk will explain the Yoneda Lemma, with many concrete examples, including profunctor optics.

THIS TALK IN THREE WORDS

Categories 

Functional programming

Lenses

OBJECTIVES

Some insight into the Yoneda Lemma, achieved via profunctor optics

TARGET AUDIENCE

Programmers, especially the categorically-curious

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