[Haskell-cafe] ATs vs FDs

[Andrew Coppin]

As I understand it, ATs were invented because FDs are "evil" and must 
never be used ever for any purpose. However, it doesn't seem to be 
possible to use ATs to do the same things that FDs can do.

You can use ATs to write type functions, which take one type and return 
another type. This allows you to express type relationships in a very 
elegant way. However, what it does /not/ seem to allow you to do is 
express one-to-one relationships.

For example, I'd like to be able to say that the next vector up from a 
Vector3 is a Vector4, and the next vector down is a Vector2. And I can 
say that. What I can't say is that the *only* next vector up is a 
Vector4. And thus, all my code is littered with ambiguous type warnings 
because although /currently/ there's only one class instance, somebody 
could come along some day and write another one.

What am I missing?