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Type Theory and Formal Proof covers metatheory all the way up to calculus of constructions, but I think it is at a fairly introductory level and tbh not that insightful from a mathematical perspective. However, it does give a pretty clear exposition of the type checking rules, and is easily converted to an implementation.

Hi, I'd recommend reading Benjamin Pierce's book "Types and Programming Languages". This is the best introduction to type systems and theory I've encountered:

http://www.amazon.com/Types-Programming-Languages-Benjamin-Pierce/dp/0262162091

Dave

You will want to look into Abadi and Cardelli's excellent A Theory of Objects, which I'm afraid I can't find online.

Agreed. I'm a big fan of Type Theory and Formal Proof: An Introduction by Rob Nederpelt from the perspective of quickly getting up to speed with the the mathematical theory without dwelling too much on programming languages. Very understandable to a wide audience, and fills in the fundamentals of the lambda cube much faster than TAPL does. I think a combination of both is great though.

In the same boat. Roger Hindley (of Hindley-Milner fame) wrote a small book [0] that covers principal type inference (I.e. the HM inference algorithm) for the lambda calculus, some simple (Church-style) typing, and Curry-Howard. Girard also has a book 1. He discovered (in parallel to Reynolds) System F.

Each chapter ends with some historical notes and points to some other papers.

[0]: https://www.amazon.com/Simple-Cambridge-Theoretical-Computer-Science/dp/0521054222