61–70 of 145 posts
Not even in a functional sense because, even though functions are input-output maps we define, the inputs are dimensionally rich, it's nowhere close to equivalent to jerry rig a contiguous input space for that purpose.
No, not in a programming language sense, because arrays are a notation for address offsetting, whereas functions change the execution context of the machine, which is critical to processing performance (think Horner's method). Not even in a functional sense because, even though functions are input-output maps we define, the inputs are dimensionally rich, it's nowhere close to equivalent to jerry rig a contiguous inpu…
Well, that makes arrays a subset of functions. What is still a "yes" to the questions "are arrays functions?"
And yeah, of course the article names Haskell on its second phrase.
Earlier quoted context omitted.
For the downvoters, I think giving examples of what's NOT a function would start an interesting conversation, especially if you don't know how it could possibly be interesting!
Take a parabola and rotate it 90 degrees. The forumula for that is not a function of the x axis: it has two values for all but one point on the curve.
Earlier quoted context omitted.
>Well for example this insight explains Memoization I don't think it does. In fact I don't see (edit: the logcial progression from one idea to the other) at all. Memorization is the natural conclusion of the thought process that begins with the disk/CPU trade off and the idea that "some things are expensive to compute but cheap to store", aka caching.
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.
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.
let v = myObject [ myFunk ];
Whether new keys could be added at runtime or not is a sepearate question.
It should be easy to extend the syntax so that
myObject (anything) === myObject [anything]
Earlier quoted context omitted.
Correct. But indexing into an array is logic that computes a result when it is called.
There are two opposing philosophical viewpoints here. Some view mathematics as a model for understanding the real world. Some see the real world as instantiation of mathematics. 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…
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".…
> 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". You don't even need infinite memory. If your function is over a limited domain like bool or u8 or an enum, very limited memory is enough. However the big difference (in most languages) is that functio…
For some definition of quick. Modern CPUs are usually bottlenecked by memory bandwidth and cache size. So a function that recomputes the value can often be quicker than a look up table, at least outside of microbenchmarks (since in microbenchmarks you won't have to compete with the rest of the code base about cache usage).
Of course this depends heavily of how expensive the function is, but it is worth having in mind that memory is not necessarily quicker than computing again. If you need to go to main memory, you have something on the order of a hundred ns that you could be recomputing the value in instead. Which at 2 GHz would translate to 200 clock cycles. What that means in terms of number of instructions depends on the instruction and number of execution units you can saturated in the CPU, if the CPU can predict and prefetch memory, branch prediction, etc. But RAM is really slow. Even with cache you are talking single digit ns to tens of ns (depending on if it is L1, L2 or L3).
An array is a function that can be mutated at runtime. That’s essentially the main difference.
Earlier quoted context omitted.
For the downvoters, I think giving examples of what's NOT a function would start an interesting conversation, especially if you don't know how it could possibly be interesting!
Closures and fexprs
An fexpr is a function.