Another way to make the point: when you write 0, which do you mean?

In a pure language like Haskell, 0-ary functions <==> constants

In a non-strict language without side-effects, having a function with no arguments does not make sense. Haskell doesn't even let you do that.

You can write a function that takes a single throw-away argument (eg 0 vs \ () -> 0) and, while the two have some slight differences at runtime, they're so close in practice that you almost never write functions taking a () argument in Haskell. (Which is very different from OCaml!)

Yes, and that becomes more intuitive when you "un-curry" the nested lambdas into a single lamba with twice the number of arguments. The point is that the state of a constant does not depend whatsoever on the state of the (rest of the) world, how much ever of that state piles on.