Get the latest tech news

Baking the Y Combinator from Scratch

It's a pedagogical pet peeve of mine when technical concepts are simply listed in their fully developed state, with little in the way of motivation, derivation, or historical context. This, I think, is like publishing a cookbook filled with beautiful pictures of cakes, but no recipes. My aim with the

A suitable foundational system a) unifies separate areas of mathematics, making it easier to port insights and techniques between them, and b) provides a rock-solid underpinning for concepts that may have been accepted as true without being fully understood. The Curry-Howard Correspondence was a slow-motion realization by Haskell Curry and the logician William Alvin Howard (and a few other mathematicians, at various times) that these two "types" of systems are actually, in a deep and important sense, intertwined! Proof by contradiction is an important and widespread technique, and outlawing it makes it - frankly - pretty difficult to do mathematics (David Hilbert compared it to "prohibiting the boxer the use of his fists.")

Get the Android app