{-# LANGUAGE GADTs, EmptyDataDecls, KindSignatures, Rank2Types #-}
data A
data B
-- The data constructors refine the type index
data X :: * -> * where
A :: X A
B :: X B
-- We can't return a different type based on the input string (unless you represent the string as some complex GADT that itself refines the output type), so instead we have a pseudo-existential type represented as a polymorphic function parameter.
-- This basically says, "if you give me a string and a function that can work on X n for all values of n, I'll give you something of the same type as the return value of that function"
op :: String -> (forall n. X n -> r) -> r
op "a" f = f A
op "b" f = f B
If you give a more detailed example of what you need, we might be able to tell you better approaches, though. This rank-2/existential approach is mostly useful for preserving internal (hidden from the end-user) type-level constraints on GADT indices.