`<numeric>`: reduce/scan algorithms aren't enforcing their Mandates

Reported on r/cpp: https://www.reddit.com/r/cpp/comments/1c0jld0/extended_use_of_stdreduce/

This is an accepts-invalid bug. None of these calls should compile, but we aren't enforcing the Standard's Mandates. For example, WG21-N4971 [reduce]/5 is:

Mandates: All of

• binary_op(init, *first),
• binary_op(*first, init),
• binary_op(init, init), and
• binary_op(*first, *first)

are convertible to T.

C:\Temp>type meow.cpp

#include <functional>
#include <iostream>
#include <iterator>
#include <numeric>
#include <string>
#include <vector>
using namespace std;

void print_strings(const vector<string>& result) {
    for (const auto& elem : result) {
        cout << "\"" << elem << "\", ";
    }
    cout << endl;
}

int main() {
    const vector<int> v{1, 2, 3, 4, 5};
    auto string_plus_int = [](const string& a, int b) { return a + to_string(b); };
    auto square          = [](int x) { return x * x; };

    { // N4971 [reduce]/5
        const auto str = reduce(v.begin(), v.end(), string{}, string_plus_int);
        cout << str << endl;
    }

    { // N4971 [transform.reduce]/3
        const auto str = transform_reduce(v.begin(), v.end(), v.begin(), string{}, string_plus_int, plus<int>{});
        cout << str << endl;
    }

    { // N4971 [transform.reduce]/7
        const auto str = transform_reduce(v.begin(), v.end(), string{}, string_plus_int, square);
        cout << str << endl;
    }

    { // N4971 [exclusive.scan]/3
        vector<string> result;
        (void) exclusive_scan(v.begin(), v.end(), back_inserter(result), string{}, string_plus_int);
        print_strings(result);
    }

    { // N4971 [inclusive.scan]/4
        vector<string> result;
        (void) inclusive_scan(v.begin(), v.end(), back_inserter(result), string_plus_int, string{});
        print_strings(result);
    }

    { // N4971 [transform.exclusive.scan]/1
        vector<string> result;
        (void) transform_exclusive_scan(v.begin(), v.end(), back_inserter(result), string{}, string_plus_int, square);
        print_strings(result);
    }

    { // N4971 [transform.inclusive.scan]/2
        vector<string> result;
        (void) transform_inclusive_scan(v.begin(), v.end(), back_inserter(result), string_plus_int, square, string{});
        print_strings(result);
    }
}

C:\Temp>cl /EHsc /nologo /W4 /std:c++17 /MTd /Od meow.cpp && meow
meow.cpp
12345
246810
1491625
"", "1", "12", "123", "1234",
"1", "12", "123", "1234", "12345",
"", "1", "14", "149", "14916",
"1", "14", "149", "14916", "1491625",

The issue names no repository files or tests; start by locating the numeric algorithm entry points for reduce, transform_reduce, and the four scan variants. Use the provided meow.cpp reproducer and the cited WG21 mandates as the first checks. Done means each listed invalid call is rejected according to its cited mandate, with tests covering the behavior.