When to pick 'Natural' over 'Integer' in Haskell?

Question

Not long ago I've discovered Natural data type in base. It's supposed to be taken (as it seems to me) when you intend to use non-negative integer type. But it's not exactly clear why should I prefer Natural to Integer. Both types have arbitrary precision, both have quite optimized runtime representation — Integer representation and Natural representation. But Natural can throw pure exceptions when you subtract natural numbers and this doesn't really add more typesafety to your code. While Integer is more popular across all packages.

So when and why should I use Natural?

Answer 1

I do not see why you want to use Natural or Integer. Why not use Rational instead? It is arbitrary precision, has an optimised runtime representation, and works for naturals, integers, and rationals!

My point is that we should choose a type which makes sense semantically. Lets count the houses on the street with naturals, record our next golf game with integers, and divide a fresh blueberry pie with rationals.