As a second addendum, while andolanra's comment is completely true, you can actually do type dispatch in Haskell using the Typeable machinery; however, the type system requires that you mark your types when this occurs.

    what :: Typeable a => a -> a

Here `what` is no longer guaranteed to be `id`. Instead, we can translate it like this

    what :: (a -> TypeRep) -> a -> a

where `TypeRep` is, as it sounds, a representation of the type of a returned dynamically. This means that we can do careful coercions to, say, be `id` unless `a` is `Int` in which case we add `1`.

Suffice to say that the degree of guarantee breaking that this kind of code invites makes Typeable a very specialized library that's almost never recommended without a "unless you really know what you're doing" kind of warning.