Lambda the Ultimate

It seems to me that most evaluation strategies are type independent. In other words the evaluation rules are independent of the types yielded by sub-expressions. Is this always the case?

What if we were to write an operational semantics that depended on the type of sub-expressions? Is that a strange thing to do?

For example:


a:fun b:val ::== a(b)
a:val b:fun ::== b(a)


Any help would be much appreciated!