Any expression-value can be a function, if you simply define the meaning of applying the the expression-value to another expression-value to be something compatible with your definition of a function.
Are arrays functions?
21–30 of 145 posts
Re: Are arrays functions?
#22Arrays are objects (allocated memory and metadata if you will). The function is what takes the array and an int and returns an item.
In Object Oriented programming, yes, arrays are objects and the functions are a property of another object that can perform instructions on the data of the Array Object. Similarly in Lisp, (a list-oriented language) both functions and arrays are lists. This article however is discussing Haskel, a Functional Language, which means they are both functions.
> Similarly in Lisp, (a list-oriented language) both functions and arrays are lists.
In which Lisp? Try this in Common Lisp and it won't work too well:
(let ((array (make-array 20)))
(car array))
Re: Are arrays functions?
#23It makes obvious sense to consider an array as a function with the index as its input argument and the element its output, i.e. f(x) = A[x]... but this isn't the first time I've encountered this and I still don't see the practical benefit of considering things from this perspective. When I'm writing code and need to reach for an array-like data structure, the conceptual correspondence to a function is not even remote…
Well for example this insight explains Memoization https://en.wikipedia.org/wiki/Memoization If you know that Arrays are Functions or equivalently Functions are Arrays, in some sense, then Memoization is obvious. "Oh, yeah, of course" we should just store the answers not recompute them. This goes both ways, as modern CPUs get faster at arithmetic and yet storage speed doesn't keep up, sometimes rather than use a pre-…
I think this is an after-the-fact connection, rather than an intuitive discovery. I wouldn't explain memoization this way. Memoization doesn't need to specifically use an array, and depending on the argument types, indexing into the array could be very unusual.
Re: Are arrays functions?
#24What 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"?
That is typical in most languages, but Haskell's Data.Array is actually parametric over both the index type and the element type, with the index type required to provide a mapping to contiguous integers. This makes it similar to eg. a hashmap which is parametric over both key and element types, with the key type required to provide hashing.
Re: Are arrays functions?
#25It makes obvious sense to consider an array as a function with the index as its input argument and the element its output, i.e. f(x) = A[x]... but this isn't the first time I've encountered this and I still don't see the practical benefit of considering things from this perspective. When I'm writing code and need to reach for an array-like data structure, the conceptual correspondence to a function is not even remote…
Well for example this insight explains Memoization https://en.wikipedia.org/wiki/Memoization If you know that Arrays are Functions or equivalently Functions are Arrays, in some sense, then Memoization is obvious. "Oh, yeah, of course" we should just store the answers not recompute them. This goes both ways, as modern CPUs get faster at arithmetic and yet storage speed doesn't keep up, sometimes rather than use a pre-…
>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.
Re: Are arrays functions?
#26Earlier quoted context omitted.
Well for example this insight explains Memoization https://en.wikipedia.org/wiki/Memoization If you know that Arrays are Functions or equivalently Functions are Arrays, in some sense, then Memoization is obvious. "Oh, yeah, of course" we should just store the answers not recompute them. This goes both ways, as modern CPUs get faster at arithmetic and yet storage speed doesn't keep up, sometimes rather than use a pre-…
>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.
Re: Are arrays functions?
#27[deleted]
Re: Are arrays functions?
#28In Clojure, vectors literally are functions. You can supply a vector (~= array) or map any place that a single parameter function is expected. So for example:
(map v [4 5 7])
Re: Are arrays functions?
#29IIRC, K rationalizes arrays and dictionaries with functions, e.g. you see arr[x;y] and fun[x;y]. Interestingly, this also highlights the connection between currying and projection, i.e. we can project/curry the above like arr[x] and fun[x].
Re: Are arrays functions?
#30Everything is a function. Next question?
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!
not a downvoter (actually, an upvoter), so grain of salt, but in my experience people cannot stand this framing. my best guess is that they dislike how impractical it is. obviously it's too abstract to be useful for most practical application. but that doesn't make it any less true.
it's a bit like saying "everything is a process", or "everything is a part of the same singular process that has been playing out since observable history". there's some interesting uses you can get out of that framing, but it's not generally applicable in the way that something like "all programs are unable to tell when a process will halt" is.
but if you really want to harvest the downvotes, I haven't found a better lure than "everything, including the foundations of mathematics, is just a story we are telling each other/ourselves." I know it's true and I still hate it, myself. really feels like it's not true. but, obviously, that's just the english major's version of "everything is a function".