I think you are conflating two things and attacking a strawperson. As someone who is very involved in the functional programming community, I've never heard anyone say that pure functions are "free", and if this has been said it's certainly not the majority perspective. The fact that a function gives you the same result given the same arguments is not meant to be some kind of encouragement to redundantly call a function many times. It's meant to give you a tool to better reason about the program logically. You don't have to worry about _when_ a pure function is called, because it doesn't depend on hidden state that may change over time, and it doesn't change anything about its environment.
In a sense, I think you seem to have been given the _opposite_ idea (not necessarily saying it was your misunderstanding vs. someone else poorly communicating to you); the fact that a function always gives you consistent results means that you never have to invoke it multiple times. In some sense, this viewpoint recognizes the cost of function execution even more than the zeitgeist.
All pure functions are by definition idempotent, and this quality is often celebrated as yet another point of merit. What is the point of highlighting this quality if functional programmers do not expect to over-execute them?
> It's meant to give you a tool to better reason about the program logically. You don't have to worry about _when_ a pure function is called…
If you say you don’t have to worry about when a function is called, the implication is that you don’t have to worry about how many times that function has been called. Functional programmers tend to belittle this sort of reasoning, and yet this sort of reasoning continues to be necessary when evaluating long-running, interactive programs for correctness.
This downplaying of executional reasoning is precisely why even if using pure functions on their own doesn’t encourage overexecution, the systems which functional programmers build typically do. We see this most clearly in discussions of reactivity, the fetishization of spreadsheets as programming model. Discrete events are tranformed into discrete outputs in a many-to-many relationship and yet functional programmers continue to think it’s not important to reason about the code which executed in between, the when and how much, just because it’s a composition of pure functions.
class foo{ enum current_operator;
init() { current_operator = ADD }
evalOp(int a, int b){
if (current_operator == ADD) return a + b;
else if (current_operator == MULTIPLY) return a * b;
}
setOp(enum op){ current_operator = op; }// pure impl
class bar{
evalOp(enum op, int a, int b){
if (op == ADD) return a + b;
else if (op == MULTIPLY) return a * b;
}In the first case, evalOp is not pure since one has no idea on what is the current_operator set as. In the second case it is pure since the operator is part of the input.
Purity refers to reproducibility, as in no matter what else is going on, that function will always behave the same. You can have pure functions in OOP based languages, but in practice devs just default to managing state and having weird behavior depending on outside state of a given function.
As a side note, and since you mention runtime performance cost: if you implement a dummy generic cache layer and you have pure functions you will have an easier time than having stateful impls. In this case, that cache layer must have the ability to introspect into foo, but in bar that cache layer just keeps track of input and that's it.
Pure impl v2:
class foo {
public:
//enum is a keyword, so let's call it _enum
const _enum current_operator;
foo(_enum co) : current_operator(co) { }
// ... evalOp() as in your stateful impl example ...
};
//Example use:
Reduce(foo{ADD}, 1, 2, 3, 4, 5, 6);
There are multiple definitions of idempotence, used even within computer science, and neither of you seem to be aware of the definition used by the other. The common mathematical definition of an idempotent function is that f(f(x)) = f(x) for all x. But in computer science there is another common definition which involves side effects not being repeated (that is, `f(); f();` is the same as `f();`).
where have you ever seen that definition ?!
https://en.wikipedia.org/wiki/Idempotence#Computer_science_m...
I'd be very curious to read someone claiming anything of this sort. One benefit (with respect to the CPU) of pure functions is that they can be cached because you know you'll get the same result for each call (of course, this impacts memory), which you can't guarantee with impure functions. But that's a tradeoff of memory for time. I've never seen anyone claim there's no cost to a pure function.
My example of React.js is the pinnacle of this, all features like hooks, contexts, and concurrent mode only make sense when they estimate the cost of re-executing pure functions to be free, or at least negligible, and yet real-world experience indicates this is definitely not the case.
> One benefit (with respect to the CPU) of pure functions is that they can be cached because you know you'll get the same result for each call (of course, this impacts memory), which you can't guarantee with impure functions. But that's a tradeoff of memory for time.
In my personal experience, I’ve become pretty skeptical of trading memory for execution time. Especially in garbage-collected languages, what you save in execution time you lose in GC pauses, so the end result is you get neither.
[1] The famous quote: "There are only two hard things in Computer Science: cache invalidation and naming things." (attributed to Phil Karlton)
This only applies to GC languages that lack language features support for value types, stack allocation or native heap support.
Only if the input space is very small. If your function takes as input two booleans and a string you know is an ID from a relatively static and small set of IDs, memoization is the way to go. If your function takes in two arbitrary floats, trying to memoize anything will only make your program run slower and leak memory.
Caching the result of common inputs and discarding not-recently-used results can be useful on functions with huge - but nonuniformly distributed - input and output spaces. At the extreme, you might have procedural image or texture generation - perhaps the postprocessing of another image or texture, for example. Impurity is a great way to end up with serious cache invalidation bugs when untracked inputs are changed, and purity a great way to avoid them.
The most important part of that explanation is can. The idea behind certain properties of FP, this being one of the most important ones, is that you are able to describe the results you want (somewhat declarative, moreso than imperative languages, less so than logic programming) and let the "compiler" or the "runtime" determine how that's delivered, without knowing or caring how it's executed. The problem with that is that the "compiler" or the "runtime" has to actually do the optimization, and if it doesn't, you're... executing unoptimized code!
Taking your React example, if it had appropriate heuristics, it could noop a ton of work and devs wouldn't have to even think about optimizing really simple good hygiene patterns. But it doesn't even look at your source code, it has no idea what weird stateful complex mess you're calling into, and it just assumes the worst.
Ultimately, I think reasoning about function effects in such a fine-grained way probably won’t catch on, but it’s a great example of what you can do when you design compiler up. However, the original article, and most in production functional systems, are about attempting to carve out a functional system from imperative parts. The result is like you said, we’re executing unoptimized code.
Strong purity can be checked by having immutable arguments.
P.S. In React for example, in almost all cases the amount of memory dedicated to holding immutable data is typically tiny for modern hardware. So it almost always makes sense to trade memory for faster execution.
Rereading this for the umpteenth time, this is the paragraph which sticks out to me this time around, and a point which I think most people miss, specifically the latter part about “pure” functions consuming CPU and memory.
The reality is that there is no such thing as a “pure” function, insofar as execution of that function costs something. Certain functional programmers corrupted this idea to somehow mean pure functions are free; that these functions can be executed one to infinity times and the result is the same.
For instance, this idea taken to an extreme has resulted in the current situation with React.js, where most React applications pathologically over-execute the “pure” rendering functions which we use to define components, resulting in degraded performance, increased GC pressure, and a lack of understanding of how our code executes.
Just because you can call a pure function many times doesn’t mean you should.