Erik Hinton (Interactive Developer, The New York Times) talks about the paper The Derivative of a Regular Type Is its Type of One-Hole Contexts by Conor McBride.
Conor poses this question: we call data types "algebraic", so can we "do calculus" on them? It stretches algebraic data types to what should be their breaking point and then demonstrates that it's not a breaking point at all. By considering the paper's set-up and implications, we gain a deeper understanding of types and what they abstract.
In his talk, Erik covers questions like how can we derive a one-hole context from any given type? And what are the one-hole contexts of common types: the list, the binary tree, the ternary tree, and the rose tree?
Read the full paper here.
This talk was given at the Papers We Love meetup at Viggle in NYC.