Comment by KK7NIL

We're talking past each other because we're using different definitions.

If you actually read the article you'll see that the type of arrays and functions they're talking about are not necessarily the types you'll find in your typical programming language (with some exceptions, as others noted) but more in the area of pure math.

The insights one can gain from this pure math definition are still very much useful for real world programming tough (e.g. memoization), you just have to be careful about the slightly different definitions/implementations.