What does std::includes actually do?

Question

From the standard, std::includes:

Returns: true if [first2, last2) is empty or if every element in the range [first2, last2) is contained in the range [first1, last1). Returns false otherwise.

^{Note: as this is under [alg.set.operations], the ranges must be sorted}

Taking this literally, if we let R1=[first1, last1) and R2=[first2, last2), this is evaluating:

∀a∈R2 a∈R1

However, this is not what is actually being evaluated. For R1={1} and R2={1,1,1}, std::includes(R1, R2) returns false:

#include <algorithm>
#include <iomanip>
#include <iostream>
#include <vector>

int main() {
    std::vector<int> a({1});
    std::vector<int> b({1,1,1});

    // Outputs 'false'
    std::cout << std::boolalpha
        << std::includes(a.begin(), a.end(), b.begin(), b.end()) << '\n';
}

^{Live on Wandbox}

This is surprising. I verified it with both libstdc++ and libc++, but it seems unlikely to me that this would be a bug in the standard library implementation, considering it's part of the algorithms library. If this isn't the algorithm that std::includes is supposed to run, what is?

Answer 1

I posted this in the cpplang slack, and Casey Carter responded:

The description of the algorithm in the standard is defective. The intent is to determine [if] every element in the needle appears in order in the haystack.

[The algorithm it actually performs is:] "Returns true if the intersection of sorted sequences R1 and R2 is equal to R2"

Or, if we ensure we are certain of the meaning of subsequence:

Returns: true if and only if [first2, last2) is a subsequence of [first1, last1)

^{link to Casey Carter's message}