With a type type here and a type type there...

There's an interesting discussion on types and metaclasses over on LtU. The discussion centers around whether types should be thought of as sets of values, or whether types should be thought of as algebras, and what exactly the difference might be between those two positions.

As an afficionado of static typing, I think this kind of discussion is very important, especially when considering designing my own languages. The central concern is what things can or cannot be decided statically. Since most of the language features that I wish for all involve deciding various things statically (e.g. checking that a lookup function will complete in constant time), it's an important discussion.