What is the purpose of class template parameter Proj and class template IndirectUnaryPredicate in the ranges TS?

Question

Cpp-reference shows the following function template (among others) from the (experimental) ranges TS:

template< ranges::InputIterator I, ranges::Sentinel<I> S,
   class Proj = ranges::identity,
   ranges::IndirectUnaryPredicate<ranges::projected<I, Proj>> Pred >
bool all_of( I first, S last, Pred pred, Proj proj = Proj{} );

What can the template parameter Proj used for in combination with IndirectUnaryPredicate?

Answer 1

It is a projection. You can use it to "project" the elements of the range before passing them to the predicate. It is useful, for example, when you are going to apply predicate to a complex datatype like std::pair, let's we want to apply predicate to the std::pair::second.

all_of(range_of_std_pairs, pred, &pair_t::second);

checks a range of std::pairs using predicate pred on the pair's second element.