Well, I don't know of any type theory that has that but you could make something up. C^(B^A) = (B^A) -> C = (A -> B) -> C. So you'd get nested higher-order monomorphic functions like if the base is A and the height |B| = 5 then the result of tetration would be (((A -> A) -> A) -> A) -> A. I don't really know what that means though. Maybe an expert Haskeller could recognize a pattern.