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!
I think it depends on what you mean by "is a function". You can think of a constant, `x` as `x_: () -> {x}` (i.e. everything can be indirected). It could be argued that this is "philosophically" "useful" since getting (using) the value of `x`, even as an actual constant, requires at the least loading it as an immediate into the ALU (or whatever execution unit).
Even non-functional relations can be turned into functions (domain has to change). Like a circle, which is not a function of the x-axis, can be parameterized by an angle theta (... `0 <= theta < 2pi`)
For me, a x86 interrupt service routine that services a hardware interrupt[1] doesn't strike me as something I'd consider a function. It shouldn't return a value, and it typically has side effects. So why is it a function?
I mean trivially you could say it's a function from (entire machine state) to (entire machine state), but typically we ignore the trivial solution because it's not 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".
I didn't downvote but I'd be interested to know what the domain is here -- I'm not going to play dumb and be like, 'rocks are not functions', but I'm not sure exactly what class of thing you're asking for examples of.
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!
Waiting for the m word.
In the mathematical sense, all functions are relations, but not all relations are functions.
I think it depends on what you mean by "is a function". You can think of a constant, `x` as `x_: () -> {x}` (i.e. everything can be indirected). It could be argued that this is "philosophically" "useful" since getting (using) the value of `x`, even as an actual constant, requires at the least loading it as an immediate into the ALU (or whatever execution unit).
Even non-functional relations can be turned into functions (domain has to change). Like a circle, which is not a function of the x-axis, can be parameterized by an angle theta (... `0 <= theta < 2pi`)
I think in this context, it is function as in a lambda in LC.
The answer is pretty much, yes, everything can be a function. e.g. A KV Map can be a function "K -> Maybe V"
P.S. If this style of thinking appeals to you, go read Algebra Driven Design! https://leanpub.com/algebra-driven-design
For me, a x86 interrupt service routine that services a hardware interrupt[1] doesn't strike me as something I'd consider a function. It shouldn't return a value, and it typically has side effects. So why is it a function?
I mean trivially you could say it's a function from (entire machine state) to (entire machine state), but typically we ignore the trivial solution because it's not interesting.
[1]: https://alex.dzyoba.com/blog/os-interrupts/
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.
It's still a function of many other things: y, t, angle, ...
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".
I didn't downvote but I'd be interested to know what the domain is here -- I'm not going to play dumb and be like, 'rocks are not functions', but I'm not sure exactly what class of thing you're asking for examples of.
Closures and fexprs
Well a closure is a kind of a record with a function hiding inside it and a record is a function which returns its contents.
An fexpr is a function.