Would something like this work for you?
vector<pair<double, double>> v(m1.size());
auto lambda = [](pair<double, tuple<double, double>> p){ return make_pair(p.first, get<0>(p.second)); };
transform(m1.begin(), m1.end(), v.begin(), lambda);
map<double, double> m2(v.begin(), v.end());
Note that we haven't really avoided a loop; we've just made std::transform
do the looping for us. If even indirect looping isn't allowed, what you probably want is a transforming iterator. See http://www.boost.org/doc/libs/1_36_0/libs/iterator/doc/transform_iterator.html