Type Theory quick question

post by Faustus2 · 2017-07-26T19:57:02.877Z · LW · GW · Legacy · 6 comments

Just a quick question, does anybody know or recommend any resources to learn type theory? I do a lot of independent study in my spare time and would be appreciative if anyone has any insight into how to approach this topic from the self-study angle.


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comment by justinpombrio · 2017-07-26T22:31:46.835Z · LW(p) · GW(p)

What is your goal? Type theory is at the intersection of programming languages and logic. If you care about programming languages and type systems, read TAPL:


If you care about type theory purely as a logic, I don't have an obvious recommendation, but could point you at some material.

(Programming Languages researcher)

Replies from: Faustus2, gwillen
comment by Faustus2 · 2017-07-27T19:16:02.283Z · LW(p) · GW(p)

The goal is mainly to understand its relation to proof assistants, I have experience with it before as a purely logical study but i haven't tried to see it in this new context for myself. This book looks excellent though, thank you for your recommendation

Replies from: justinpombrio
comment by justinpombrio · 2017-07-27T22:14:57.041Z · LW(p) · GW(p)

Ah, then you'll want to read about the [https://hal.inria.fr/inria-00076024/document](Calculus of Constructions):

Yeah, TAPL is the book on type systems. I'm not aware of competition.

comment by gwillen · 2017-07-27T01:09:13.205Z · LW(p) · GW(p)

Seconding TAPL, it was the textbook for the type theory course I took in college, it is topnotch.

comment by MrMind · 2017-07-27T12:31:02.347Z · LW(p) · GW(p)

It reeeeeeally depends on your background. You can come at TT from many different directions: logic, programming, category theory, algebraic topology... the good news is that the contemporary view is that those are all facets of the same thing, a sort of generalized Church-Turing thesis.

comment by Manfred · 2017-07-27T00:12:07.177Z · LW(p) · GW(p)

The HoTT book is pretty readable, but I'm not in a position to evaluate its actual goodness.