# Packs of packs

Jason Rice’s interesting (but IMHO too novel) proposal P1221 “Parametric Expressions” is in the pre-Kona mailing. It’s one of these big proposals that claims to solve a whole bunch of perennial problems at once. I bet it would solve maybe half of what it claims, and if you poke a hole in one part, that wouldn’t make the remainder unsalvageable. I’m just going to poke a hole in a hypothetical extension of one part, for the record, so that I don’t have to keep repeating myself on Slack.

P1221 proposes that this should work:

using make_pack(using auto... Is) {
return Is;
}

int arr[] = {
make_pack(1,2,3) ...
};


Here make_pack(1,2,3) calls make_pack and returns not a tuple, but an actual pack of values, back to its caller. (This is superficially similar to some other languages’ “multiple return values,” but it’s not really the same. Packs are still harder to manipulate than actual values, even in P1221’s world.) In standard C++, packs are only ever permitted to appear as parameter packs — or as a special case, lambda-captures. Being able to return a pack from a function would be a big change.

Back in February 2016, something like P1221’s idea of “naked” packs was discussed on the std-proposals list under the title “Improve fundamentals of parameter packs.”. My first message in that thread referred to a previous discussion titled “RFC: Unpacking tuples to value sequences” (January 2016). See also a later discussion of “Variadic decomposition” (October 2016), in which Vicente J. Botet Escribá points to Mike Spertus’s paper P0341 “parameter packs outside of templates” (May 2016). I guess 2016 was a big year for naked packs!

In the January thread, I floated the idea of a core-language syntax t~ where the postfix tilde would mean “take this tuple-like object and explode it into a naked pack of its elements.” That is, I proposed that the P1221 example above ought to be writeable as

int arr[] = {
std::make_tuple(1,2,3)~ ...
};


where make_tuple creates a std::tuple object, ~ explodes it back into a pack, and then ... expands that pack via the usual expression-rewriting rules. Or, vice versa, we could express my postfix-tilde thing in terms of P1221’s primitives (Godbolt):

template<class> struct int_seq_;

template<size_t... Is>
struct int_seq_<std::index_sequence<Is...>> {
static using apply() {
return Is;
}
};

using indices_of(using auto t) {
return int_seq_<
std::make_index_sequence<std::tuple_size_v<decltype(t)>>
>::apply();
}

using postfix_tilde(using auto t) {
return std::get<indices_of(t)>(t);
}

int arr[] = {
postfix_tilde(std::make_tuple(1,2,3)) ...
};


However, this tilde-notation idea runs into trouble with nested pack expansions. Consider:

template<class> struct int_seq_;

template<size_t... Is>
struct int_seq_<std::index_sequence<Is...>> {
static using apply() {
return Is;
}
};

using iota(using auto N) {
return int_seq_<
std::make_index_sequence<N>
>::apply();
}

auto sum = [](auto... ints) {
return (0 + ... + ints);
};

template<size_t N>
constexpr int foo() {
return sum(iota(N) ...);
}


So far so good, right? iota(N) should return a pack, and then we expand that pack with ... and give its elements to sum, which adds them up.

static_assert(foo<2>() == 3);
static_assert(foo<3>() == 6);
static_assert(foo<4>() == 10);


But now we spring the trap. If iota(N) takes a non-pack (N) and produces a pack from it, then iota(Ns) must take a pack and produce from it a… pack of packs?

template<size_t... Ns>
void bar() {
return sum(iota(Ns) ...);  // Uh-oh!
}


Clearly bar<1,2,3>() will not compile as written. But what would we write if we did want to compute, say, sum(iota(1)..., iota(2)..., iota(3)...)?

Or what about this snippet?

template<size_t N>
void baz() {
return sum(iota(iota(N)) ...);  // Uh-oh!
}


This is the same trap as the previous example. baz<3>() should return sum(iota(iota(3)) ...); and we know that iota(3) is a pack containing the integers 0, 1, and 2; so baz<3>() should return the same thing as bar<0,1,2>(). But what is that?

The equivalent in my tuple-exploding tilde notation would be

template<size_t... Is>
constexpr auto iota_helper(std::index_sequence<Is...>) {
return std::make_tuple(Is...);
}
template<size_t N>
constexpr auto iota() {
return iota_helper(std::make_index_sequence<N>());
}

template<size_t N>
constexpr int foo() {
return sum(iota<N>()~ ...);  // Easy peasy
}

static_assert(foo<2>() == 3);
static_assert(foo<3>() == 6);
static_assert(foo<4>() == 10);

template<size_t... Ns>
void bar() {
return sum(iota<Ns>()~ ...);  // Uh-oh! Does ... bind to Ns, or to ~?
}

template<size_t N>
void baz() {
return sum(iota< iota<N>()~ >()~ ...);  // Uh-oh x2!
}


The power of C++11 parameter packs is that they are “vectorized” in only one dimension. There’s a set of primitive operators that can be applied to non-pack values — for example, + — and there’s a completely disjoint set of primitive operators that can be applied to packs — namely, ... and sizeof... (and that’s all). So when the compiler sees Ns + 1, it knows that you aren’t really adding 1 to the pack; what you want to do is crack open the pack and add 1 to each of its elements, producing a new pack. When the compiler sees Ns + Ms, it knows that you aren’t really adding a pack and a pack; what you mean is to crack open each pack and add their corresponding elements, producing a new pack.

And when the compiler sees f(Ns ...), it knows that you don’t really mean to crack open the pack and apply ... to each element (because ... is an operator that applies only to packs). What you must mean is to apply ... to the pack itself, which causes a rewrite of the expression into a comma-separated snippet like elt1, elt2, elt3, and then evaluation of f(elt1, elt2, elt3) can proceed from there.

If C++ were ever to permit “packs of packs,” then Ns ... would become a source of ambiguity. (As we just saw.) In Ns ..., do you mean to apply ... to the pack itself, or do you mean to crack it open and apply ... to each of its elements, which are themselves also packs? Either way, the meaning of the result would not be obvious: you’d end up with an expression rewritten in terms of comma-separated unexpanded packs (whatever that means), or else a pack of snippets like elt1, elt2, elt3 (whatever that means).

Idle thought: Maybe C++17’s fold-expressions and APL’s inner-product notation can produce a baby that makes the whole thing make sense. But I wouldn’t hold my breath for that messiah.

TLDR: If you permit a function to “return a pack,” then you permit the moral equivalent of iota(N). And if you permit that, then you permit the moral equivalent of iota(Ns) / iota(iota(N)). And then you’re in uncharted territory.

Posted 2019-02-11