Proposed resolution:

This wording is relative to N4582.

1. Edit [exclusive.scan]/2 as indicated:

   [Drafting note: when i is result, [first, first + (i - result)) is an empty range, so the value to be assigned reduces to GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, init), which is init, so there's no need to special case this.]

   template<class InputIterator, class OutputIterator, class T, class BinaryOperation>
     OutputIterator exclusive_scan(InputIterator first, InputIterator last,
                                   OutputIterator result,
                                   T init, BinaryOperation binary_op);
   

   -2- Effects: Assigns through each iterator i in [result, result + (last - first)) the value of GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, init, *j, ...) for every j in [first, first + (i - result)).

   • init, if i is result, otherwise

   • GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, init, *j, ...) for every j in [first, first + (i - result) - 1).

2. Edit [inclusive.scan]/2 as indicated:

   template<class InputIterator, class OutputIterator, class BinaryOperation>
     OutputIterator inclusive_scan(InputIterator first, InputIterator last,
                                   OutputIterator result,
                                   BinaryOperation binary_op);
   template<class InputIterator, class OutputIterator, class BinaryOperation>
     OutputIterator inclusive_scan(InputIterator first, InputIterator last,
                                   OutputIterator result,
                                   BinaryOperation binary_op, T init);
   

   -2- Effects: Assigns through each iterator i in [result, result + (last - first)) the value of

   • GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, init, *j, ...) for every j in [first, first + (i - result + 1)) if init is provided, or

   • GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, *j, ...) for every j in [first, first + (i - result + 1)) otherwise.

3. Edit [transform.exclusive.scan]/1 as indicated:

   template<class InputIterator, class OutputIterator,
            class UnaryOperation,
            class T, class BinaryOperation>
     OutputIterator transform_exclusive_scan(InputIterator first, InputIterator last,
                                             OutputIterator result,
                                             UnaryOperation unary_op,
                                             T init, BinaryOperation binary_op);
   

   -1- Effects: Assigns through each iterator i in [result, result + (last - first)) the value of GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, init, unary_op(*j), ...) for every j in [first, first + (i - result)).

   • init, if i is result, otherwise

   • GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, init, unary_op(*j), ...) for every j in [first, first + (i - result) - 1).

4. Edit [transform.inclusive.scan]/1 as indicated:

   template<class InputIterator, class OutputIterator,
            class UnaryOperation,
            class BinaryOperation>
     OutputIterator transform_inclusive_scan(InputIterator first, InputIterator last,
                                             OutputIterator result,
                                             UnaryOperation unary_op,
                                             BinaryOperation binary_op);
   template<class InputIterator, class OutputIterator,
            class UnaryOperation,
            class BinaryOperation, class T>
     OutputIterator transform_inclusive_scan(InputIterator first, InputIterator last,
                                             OutputIterator result,
                                             UnaryOperation unary_op,
                                             BinaryOperation binary_op, T init);
   

   -1- Effects: Assigns through each iterator i in [result, result + (last - first)) the value of

   • GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, init, unary_op(*j), ...) for every j in [first, first + (i - result + 1)) if init is provided, or

   • GENERALIZED_NONCOMMUTATIVE_SUM(binary_op, unary_op(*j), ...) for every j in [first, first + (i - result + 1)) otherwise.