# Left-folding and right-folding an arbitrary callable

Nerdsnipe: Given an arbitrary binary callable f(x,y), write a function left_fold such that left_fold(f)(a,b,c,...) evaluates to f(f(f(a,b),c),...). Write a function right_fold such that right_fold(f)(a,b,c,...) evaluates to f(a, f(b, f(c, ...))).

That is, we’re looking to define left_fold and right_fold such that

auto leftsub = left_fold(std::minus<>);
auto rightsub = right_fold(std::minus<>);
static_assert(leftsub(1, 2, 3) == (1 - 2) - 3);
static_assert(rightsub(1, 2, 3) == 1 - (2 - 3));


This is easy with “recursive templates,” but in modern C++ we know that “Iteration is better than recursion” (2018-07-23), so let’s try to do it with C++17 fold-expressions. Godbolt:

#define FWD(x) static_cast<decltype(x)>(x)
#define MOVE(x) static_cast<decltype(x)&&>(x)

template<class F, class TRR>
struct Folder {
const F& foo_;
TRR value_;

template<class U>
constexpr auto operator+(Folder<F, U>&& rhs) && -> decltype(auto) {
using R = decltype(foo_(FWD(value_), FWD(rhs.value_)));
return Folder<F, R>{foo_, foo_(FWD(value_), FWD(rhs.value_))};
}
};

template<class F>
constexpr auto left_fold(F foo) {
return [foo = MOVE(foo)](auto&&... args) -> decltype(auto) {
return (... + Folder<F, decltype(args)>{foo, FWD(args)}).value_;
};
}

template<class F>
constexpr auto right_fold(F foo) {
return [foo = MOVE(foo)](auto&&... args) -> decltype(auto) {
return (Folder<F, decltype(args)>{foo, FWD(args)} + ...).value_;
};
}


There are a couple of tricks hiding in here:

• The FWD(x) macro is just a shorter spelling of std::forward<X>(x). I normally use static_cast<X&&>(x), but in this case I have several places where the type X is not easily nameable.

• The MOVE(x) macro is just a shorter spelling of std::move(x), and I’m using it here only to capture foo by move without having to include any standard library headers. I want to capture foo by move, just in case it’s a move-only lambda type.

• All of the uses of -> decltype(auto) are necessary. Try removing them and seeing what goes wrong in folding << over (std::cout, 1, 2, 3).

• We use aggregate initialization for Folder<F, R>{...}, so that the value of foo_(FWD(value_), FWD(rhs.value_)) will be constructed in-place rather than constructing a temporary and then having to move it into place. This allows us to work with non-move-constructible types.

However, if the overall result of the fold is a prvalue of a non-move-constructible type, we fail (Godbolt). I can partially fix left_fold’s issue with non-move-constructible types, but (1) I cannot fix right_fold; (2) I cannot totally fix left_fold; and (3) my change to left_fold causes additional failures in even more pathological cases. (Godbolt.)

template<class F, class TRR>
struct LeftFolder {
const F& foo_;
TRR value_;

template<class U>
constexpr friend auto operator+(U&& lhs, LeftFolder&& rhs) -> decltype(auto) {
return rhs.foo_(FWD(lhs), FWD(rhs.value_));
}
};

template<class F>
constexpr auto left_fold(F foo) {
return [foo = MOVE(foo)](auto&& init, auto&&... args) -> decltype(auto) {
return (FWD(init) + ... + LeftFolder<F, decltype(args)>{foo, FWD(args)});
};
}

Posted 2020-10-12