Question

The iota template function was added to the standard library to fill an iterator range with an increasing sequence of values.

  template<typename ForwardIterator, typename Tp>
    void
    iota(ForwardIterator first, ForwardIterator last, Tp value)
    {
      for (; first != last; ++first)
        {
          *first = value;
          ++value;
        }
    }

Most other templates in <numeric> have versions that accept user-specified operators.
Having this:

  template<typename ForwardIterator, typename Tp, typename Operator>
    void
    iota(ForwardIterator first, ForwardIterator last, Tp value, Operator op)
    {
      for (; first != last; ++first)
        {
          *first = value;
          op(value);
        }
    }

would be convenient if you don’t want to (or can’t) overload operator++() for Tp. I would find this version more widely usable than the default operator++() version.
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Answer 1

With lambdas, the second version doesn’t save much, you can just use std::generate.

template<typename ForwardIterator, typename Tp, typename Operator>
void iota(ForwardIterator first, ForwardIterator last, Tp value, Operator op)
{
  std::generate(first, last, [&value,&op](){auto v = value; op(value); return v;});
}

In fact, this makes the existing implementation of std::iota very redundant:

template<typename ForwardIterator, typename Tp>
void iota(ForwardIterator first, ForwardIterator last, Tp value)
{
  std::generate(first, last, [&value](){return value++;});
}