In Haskell specifically, arrays really do allow for the more general definition. This makes the library documentation[1] quite a bit more intimidating to newcomers (speaking from personal experience), but saves you the boilerplate and hassle of figuring out the mapping yourself if you're indexing your array by some weird nonsense like `[(False, 'a', 5000, 0)..(True, 'z', 9001, 4)] :: (Bool, Char, Integer, Int8)`.
That is typical in most languages, but Haskell's Data.Array is actually parametric over both the index type and the element type, with the index type required to provide a mapping to contiguous integers. This makes it similar to eg. a hashmap which is parametric over both key and element types, with the key type required to provide hashing.
> Haskell provides indexable arrays, which may be thought of as functions whose domains are isomorphic to contiguous subsets of the integers.
with
> Haskell provides indexable arrays, which are functions on the domain [0, ..., k-1]?
Or is the domain actually anything "isomorphic to contiguous subsets of the integers"?