Reason Isomorphically!

When are two types the same? In this paper we argue that isomorphism is a more useful notion than equality. We explain a succinct and elegant approach to establishing isomorphisms, with our focus on showing their existence over deriving the witnesses. We use category theory as a framework, but rather than chasing diagrams or arguing with arrows, we present our proofs in a calculational style. In particular, we hope to showcase to the reader why the Yoneda lemma and adjunctions should be in their reasoning toolbox. © 2010 ACM