I spotted this on Twitter [0] and it was timely for me because I've been sorta building my own learning path lately. After learning Haskell a few years ago I got really interested in PLT, type theory, and other higher math (like CT) and also things like formal program verification and automated solvers. So I started trying to decide on a good self-study path (as a guy with a day job who's not going to be starting a Ph.D. anytime soon). I ran across this very helpful Reddit thread [1] and so far I'm thinking of the following path. I'm starting with How to Prove It, because I never did a lot of proof solving in college (and that was >10 yrs ago anyway) and it's a good basis for further work. Then I have two branches.
The first is for abstract algebra and CT, because I find them interesting and they're useful for understanding Haskell, that currently consists of Pinter's A Book of Abstract Algebra, then Conceptual Mathematics by Lawvere and Schanuel, then Awodey's CT book, which is a path straight out of that Reddit thread.
The second is for PLT/type theory, and starts with Software Foundations by Pierce, then Types and Programming Languages by Pierce, then Practical Foundations for Programming Languages by Harper (for completeness, as I have heard pros and cons for both), then maybe moving to Advanced Topics in Types and Programming Languages and such. Mix in some Oregon Programming Language Summer School (OPLSS) [2] videos here and there when they fit. (OPLSS sounds great and I'm glad their videos are online)
Pinter's A Book of Abstract Algebra is one of the best math books I've ever read. It's short, to the point, and doesn't assume you're an idiot. I learned a lot from it and I can't recommend it enough.
The first is for abstract algebra and CT, because I find them interesting and they're useful for understanding Haskell, that currently consists of Pinter's A Book of Abstract Algebra, then Conceptual Mathematics by Lawvere and Schanuel, then Awodey's CT book, which is a path straight out of that Reddit thread.
The second is for PLT/type theory, and starts with Software Foundations by Pierce, then Types and Programming Languages by Pierce, then Practical Foundations for Programming Languages by Harper (for completeness, as I have heard pros and cons for both), then maybe moving to Advanced Topics in Types and Programming Languages and such. Mix in some Oregon Programming Language Summer School (OPLSS) [2] videos here and there when they fit. (OPLSS sounds great and I'm glad their videos are online)
[0] https://twitter.com/manisha72617183/status/61301658769664819...
[1] http://www.reddit.com/r/haskell/comments/29reb7/first_or_sec...
[2] http://www.cs.uoregon.edu/research/summerschool/