Consider a simple function that adds the first N natural numbers. (e.g. sum(5) = 0 + 1 + 2 + 3 + 4 + 5 = 15
).
Here is a simple JavaScript implementation that uses recursion:
function recsum(x) {
if (x === 0) {
return 0;
} else {
return x + recsum(x - 1);
}
}
If you called recsum(5)
, this is what the JavaScript interpreter would evaluate:
recsum(5)
5 + recsum(4)
5 + (4 + recsum(3))
5 + (4 + (3 + recsum(2)))
5 + (4 + (3 + (2 + recsum(1))))
5 + (4 + (3 + (2 + (1 + recsum(0)))))
5 + (4 + (3 + (2 + (1 + 0))))
5 + (4 + (3 + (2 + 1)))
5 + (4 + (3 + 3))
5 + (4 + 6)
5 + 10
15
Note how every recursive call has to complete before the JavaScript interpreter begins to actually do the work of calculating the sum.
Here's a tail-recursive version of the same function:
function tailrecsum(x, running_total = 0) {
if (x === 0) {
return running_total;
} else {
return tailrecsum(x - 1, running_total + x);
}
}
Here's the sequence of events that would occur if you called tailrecsum(5)
, (which would effectively be tailrecsum(5, 0)
, because of the default second argument).
tailrecsum(5, 0)
tailrecsum(4, 5)
tailrecsum(3, 9)
tailrecsum(2, 12)
tailrecsum(1, 14)
tailrecsum(0, 15)
15
In the tail-recursive case, with each evaluation of the recursive call, the running_total
is updated.
Note: The original answer used examples from Python. These have been changed to JavaScript, since Python interpreters don't support tail call optimization. However, while tail call optimization is part of the ECMAScript 2015 spec, most JavaScript interpreters don't support it.
No, Ruby doesn't perform TCO. However, it also doesn't not perform TCO.
The Ruby Language Specification doesn't say anything about TCO. It doesn't say you have to do it, but it also doesn't say you can't do it. You just can't rely on it.
This is unlike Scheme, where the Language Specification requires that all Implementations must perform TCO. But it is also unlike Python, where Guido van Rossum has made it very clear on multiple occasions (the last time just a couple of days ago) that Python Implementations should not perform TCO.
Yukihiro Matsumoto is sympathetic to TCO, he just doesn't want to force all Implementations to support it. Unfortunately, this means that you cannot rely on TCO, or if you do, your code will no longer be portable to other Ruby Implementations.
So, some Ruby Implementations perform TCO, but most don't. YARV, for example, supports TCO, although (for the moment) you have to explicitly uncomment a line in the source code and recompile the VM, to activate TCO – in future versions it is going to be on by default, after the implementation proves stable. The Parrot Virtual Machine supports TCO natively, therefore Cardinal could quite easily support it, too. The CLR has some support for TCO, which means that IronRuby and Ruby.NET could probably do it. Rubinius could probably do it, too.
But JRuby and XRuby don't support TCO, and they probably won't, unless the JVM itself gains support for TCO. The problem is this: if you want to have a fast implementation, and fast and seamless integration with Java, then you should be stack-compatible with Java and use the JVM's stack as much as possible. You can quite easily implement TCO with trampolines or explicit continuation-passing style, but then you are no longer using the JVM stack, which means that everytime you want to call into Java or call from Java into Ruby, you have to perform some kind of conversion, which is slow. So, XRuby and JRuby chose to go with speed and Java integration over TCO and continuations (which basically have the same problem).
This applies to all implementations of Ruby that want to tightly integrate with some host platform that doesn't support TCO natively. For example, I guess MacRuby is going to have the same problem.
Best Answer
Yes, actually you can take some code and convert every function call—and every return—into a tail call. What you end up with is called continuation-passing style, or CPS.
For example, here's a function containing two recursive calls:
And here's how it would look if you converted this function to continuation-passing style:
The extra argument,
ctn
, is a procedure whichcount-tree-cps
tail-calls instead of returning. (sdcvvc's answer says that you can't do everything in O(1) space, and that is correct; here each continuation is a closure which takes up some memory.)I didn't transform the calls to
car
orcdr
or+
into tail-calls. That could be done as well, but I assume those leaf calls would actually be inlined.Now for the fun part. Chicken Scheme actually does this conversion on all code it compiles. Procedures compiled by Chicken never return. There's a classic paper explaining why Chicken Scheme does this, written in 1994 before Chicken was implemented: CONS should not cons its arguments, Part II: Cheney on the M.T.A.
Surprisingly enough, continuation-passing style is fairly common in JavaScript. You can use it to do long-running computation, avoiding the browser's "slow script" popup. And it's attractive for asynchronous APIs.
jQuery.get
(a simple wrapper around XMLHttpRequest) is clearly in continuation-passing style; the last argument is a function.