logoalt Hacker News

TimorousBestietoday at 3:02 AM1 replyview on HN

Instead of spending time beating one’s head against Russell and Whitehead, I would advise reading Homotopy Type Theory (aka the HoTT Book). Dependent types are cool and mind-expanding, but higher inductive types are downright mind-altering.

The Little Schemer/Typer could be used as a preparatory text to gear one up for HoTT.

It also has the advantage of being a bit more applicable to functional programming languages, maybe even more so than Mac Lane’s Categories for the Working Mathematician (which I sometimes see suggested to mathematically-inclined Haskell novices).


Replies

js8today at 5:24 AM

I tried to read HoTT. First chapter on type theory is great and pretty easy to follow. The second chapter, I got completely lost. I don't remember why, maybe they fixed it since.

But I find univalence axiom intriguing. I am interested in different approach to types, using triage calculus, which is more "materialist" than "structuralist" - type is given by the structure of the (quoted) term in normal form (unlike lambda calculus, triage calculus makes quoting easy). And I feel like univalence is related to quoting, something like if the two quoted terms are equal under "standard self-interpreter", then they are equal.

show 1 reply