# Folding over operator=

Jonathan Müller posted a “Nifty Fold Expression Trick” the other day:

template<class F, class... Ts>
void reverse_for_each(F f, Ts... ts) {
int dummy;
(dummy = ... = (f(ts), 0));
}


For example, reverse_for_each(putchar, 'a', 'b', 'c') prints cba.

However, as I puzzled out each step of the process, I realized that there were several subtleties to this “simple” expression!

## False start #1

Most C++ programmers don’t need to know anything about fold-expressions. But even among those who do know something about them, the “layman’s view” of fold-expressions is basically that (x + ... + E(ts)) expands to (x + E(t0) + E(t1) + E(t2)). If we apply this “layman’s version” of fold-expressions to the above code, we get this instantiation for three char parameters:

// Layman's version -- INCORRECT!
template<>
void reverse_for_each(decltype(puts) *f, char a, char b, char c) {
int dummy;
(dummy = (f(a), 0) = (f(b), 0) = (f(c), 0));
}


But this clearly shouldn’t compile! We know that assignments can be “chained” like this: x = y = z means “assign z to y, then assign y to x.” But (f(a), 0) is an rvalue, not an lvalue.

(f(a), 0) = 42;  // ERROR, can't assign to an rvalue


What went wrong with our layman’s version of fold-expressions?

## False start #2

It turns out that in C++, fold-expressions bring their own associativity with them. The expression (x + ... + E(ts)) is called a binary left fold, and is equivalent to

(((x + E(t0)) + E(t1)) + E(t2))


The expression (E(ts) + ... + x) is called a binary right fold, and is equivalent to

(E(t0) + (E(t1) + (E(t2) + x)))


So Jonathan’s binary left fold over = is actually expanded by the compiler into this:

// Actual expansion -- CORRECT
template<>
void reverse_for_each(decltype(puts) *f, char a, char b, char c) {
int dummy;
(((dummy = (f(a), 0)) = (f(b), 0)) = (f(c), 0));
}


That is, what we have here is not structured like x = y = z; it’s structured like (x = y) = z. First we assign y to x; then we assign z to x.

But wait! If (x = y) = z is basically equivalent to x = y; x = z, then why does Jonathan’s fold-expression seem to evaluate z before y?

## Guaranteed order of evaluation

The final trick here is C++17’s guaranteed order of evaluation. “Order of evaluation” differs from “order of operations” (a.k.a. “precedence”), which of course C++ has always provided. “Order of operations” is about which of * and + is executed first in an expression like f() * g() + h(). “Order of evaluation” is about which of f() and g() is executed first.

In C++17, it is guaranteed that an assignment expression like x = y proceeds in the following order: Evaluate y; then evaluate x; then assign y to x. This ensures that an expression like

a[++i] = b[i];


has defined behavior in C++17: if i is initially 42, then this expression assigns b[42] to a[43]. Certain other operators, notably << and >>, have guaranteed left-to-right order of evaluation. Most operators have no guaranteed order of evaluation: f() * g() might evaluate g() before f(), or vice versa.

So these two C++ constructs produce the same output:

// Example 1
a() = b() = c();

// Example 2
auto& ref = (b() = c());
a() = ref;


But these two constructs produce different output:

// Example 3
(a() = b()) = c();

// Example 4
auto& ref = (a() = b());
ref = c();


Example 3 evaluates c() first; then evaluates (a() = b()); then assigns the result of c() to ref.

Example 4 evaluates (a() = b()) first; then evaluates c() and assigns the result to ref.

So Jonathan’s binary left fold

(dummy = ... = (f(ts), 0));


actually does end up assigning (f(a), 0) to dummy, and then assigning (f(b), 0) to dummy, and then assigning (f(c), 0) to dummy. The assignment operations do happen in that order, because of the associativity implied by a left fold. But because of C++17’s guaranteed right-to-left order of evaluation, the right-hand sides of those assignments are actually evaluated in right-to-left order regardless. In other words:

(((dummy = (f(a), 0)) = (f(b), 0)) = (f(c), 0));


means roughly

auto& refc = (f(c), 0);
auto& refb = (f(b), 0);
auto& refa = (f(a), 0);
(((dummy = refa) = refb) = refc);


## Alternative formulation of reverse_for_each, and a guideline

It seems to me that if you’re doing a “reverse-for-each”, you should prefer to use a right fold expression (Godbolt):

template<class F, class... Ts>
void reverse_for_each(F f, Ts... ts) {
int dummy;
((f(ts), dummy) = ... = 0);
}


This removes the first layer of subtlety in Jonathan’s version, because now we can return to our “layman’s intuition” about fold-expressions:

(E(ts) = ... = x);


is in all respects equivalent to

E(t0) = E(t1) = E(t2) = x;


This seems like a good candidate for a style guideline.

Use left folds only for left-associative operators.
Use binary right folds only for right-associative operators.

Use unary right folds only for right-associative operators, the short-circuiting logical operators, and comma.

For the short-circuiting operators and comma, a unary right fold does exactly the same thing as a unary left fold, but right fold is slightly easier to read (in my opinion).

Unary right fold: (ts || ...)  ==> (t0 || (t1 || t2))

Unary left fold:  (... || ts)  ==> ((t0 || t1) || t2)


Coincidentally, the short-circuiting logical operators and comma are also the only ones that fully support the unary fold syntax even for empty packs. For every other operator, if sizeof...(ts) might be zero, then you must use a binary fold.

Notice that this applies only to the built-in operators || and && and ,! If ts... might overload these operators to do user-defined things, then the difference between a right fold and a left fold is again observable — and I think you should prefer left fold because it matches our “layman’s intuition” about order of evaluation.

Posted 2020-05-07