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No - An array is a data structure that stores pre-calculated values in memory, whereas a function is executable logic that computes a result only when it is called.
No - An array is a data structure that stores pre-calculated values in memory, whereas a function is executable logic that computes a result only when it is called.
No - An array is a data structure that stores pre-calculated values in memory, whereas a function is executable logic that computes a result only when it is called.
No - An array is a data structure that stores pre-calculated values in memory, whereas a function is executable logic that computes a result only when it is called.
Correct. But indexing into an array is logic that computes a result when it is called.
Is an array a function? From one perspective, the array satisfies the abstract requirements we use to define the word "function." From the other perspective, arrays (contiguous memory) exist and are real things, and functions (programs) exist and are something else.
The matrix multiplication of vectors - or a row and a column vector - which is then just taking the dot product is called an inner product. So for functions the inner product is an integral over where the functions are defined -
= \int f(x) g(x) dx
Likewise you can multiply functions by a "kernel" which is a bit like multiplying a vector by a matrix
= \int \int A(x,y) f(y) g(x) dx dy The fourier transform is a particular kernel
I remember I got a little confused when I was first learning TLA+, because what you normally call "functions" are "operators" [1], and what you'd normally call "maps" or "lists" are called "functions". It was odd to me, because it hadn't really occurred to me before that, given infinite memory (and within a mathematical framework), there's fundamentally not necessarily a difference between a "list" and a "function".…
What about replacing > 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"?
[1] https://hackage.haskell.org/package/array-0.5.8.0/docs/Data-...
Should you?
This is where I'd be more careful. Maybe it makes sense to some of the langs in TFA. But it reminds me of [named]tuples in Python, which are iterable, but when used as tuples, in particular, as heterogeneous arrays¹ to support returning multiple values or a quick and dirty product type (/struct), the ability to iterate is just a problem. Doing so is almost always a bug, because iteration through a such tuple is nigh always nonsensical.
So, can an array also be f(index) -> T? Sure. But does that make sense in enough context, or does it promote more bugs and less clear code is what I'd be thinking hard about before I implemented such a thing.
¹sometimes tuples are used as an immutable homogeneous array, and that case is different; iteration is clearly sane, then