Comment by KK7NIL
18 days ago
Both arrays and (pure) functions are just mappings of inputs to outputs, this is why memoization is possible without any loss of functionality.
Whether storing (arrays) or computing (functions) is faster is a quirk of your hardware and use case.
Memoization is a different way around though. You're turning part of a function into an array and a traditional function is still in charge. It doesn't depend on arrays being functions.
I would also reject the idea that "Arrays are Functions" is equivalent to "Functions are Arrays". They're both true in a sense, but they're not the same statement.
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.
> If you actually read the article
Needless.
> 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.
I agree completely here. But I think that undermines some of the earlier claims. The math definition only serves as inspiration, we're not using the math definition when we memoize. And the important part you need for that inspiration is a lot narrower than full equivalence.
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