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std::ranges::fold_left(3)      C++ Standard Libary     std::ranges::fold_left(3)

NAME
     std::ranges::fold_left - std::ranges::fold_left

Synopsis
	Defined in header <algorithm>
	Call signature
	template< std::input_iterator I, std::sentinel_for<I>
	S, class T,
								      (since
		  /* indirectly-binary-left-foldable */<T, I>	      C++23)
	F >							      (until
								      C++26)
	constexpr auto fold_left( I first, S last, T init, F
	f );
	template< std::input_iterator I, std::sentinel_for<I>
	S,

		  class T = std::iter_value_t<I>,		      (since
		  /* indirectly-binary-left-foldable */<T, I>	      C++26)
	F >

	constexpr auto fold_left( I first, S last, T init, F
	f );						      (1)
	template< ranges::input_range R, class T,

		  /*		  indirectly-binary-left-foldable	      */
     (since C++23)
		      <T,	   ranges::iterator_t<R>>	   F	       >
     (until C++26)

	constexpr auto fold_left( R&& r, T init, F f );
	template< ranges::input_range R, class T =
	ranges::range_value_t<R>,
								  (2)
		  /*		  indirectly-binary-left-foldable	      */
     (since C++26)
		      <T, ranges::iterator_t<R>> F >

	constexpr auto fold_left( R&& r, T init, F f );
	Helper concepts
	template<      class	  F,	  class      T,      class	I      >
     (exposition
	concept   /*  indirectly-binary-left-foldable  */  =  /*	     (3)
     only*)
	see description */;

	Left-folds the elements of given range, that is, returns the  result  of
     evaluation of
	the chain expression:
	f(f(f(f(init, x[1]), x[2]), ...), x[n]), where x[1], x[2], ..., x[n] are
     elements of
	the range.

	Informally,  ranges::fold_left	behaves  like std::accumulate's overload
     that accepts a
	binary predicate.

	The behavior is undefined if [first, last) is not a valid range.

	1) The range is [first, last). Equivalent to return
	ranges::fold_left_with_iter(std::move(first),	last,	std::move(init),
     f).value.
	2)  Same  as  (1),  except  that  uses	r  as  the range, as if by using
     ranges::begin(r) as
	first and ranges::end(r) as last.
	3) Equivalent to:

	Helper concepts
	template< class F, class T, class I, class U >

	concept /*indirectly-binary-left-foldable-impl*/ =
	    std::movable<T> &&
	    std::movable<U> &&
	    std::convertible_to<T, U> &&			     (3A) (expo-
     sition only*)
	    std::invocable<F&, U, std::iter_reference_t<I>> &&
	    std::assignable_from<U&,

		std::invoke_result_t<F&, U,
	std::iter_reference_t<I>>>;
	template< class F, class T, class I >

	concept /*indirectly-binary-left-foldable*/ =
	    std::copy_constructible<F> &&
	    std::indirectly_readable<I> &&
	    std::invocable<F&, T, std::iter_reference_t<I>> &&
	    std::convertible_to<std::invoke_result_t<F&, T,	     (3B) (expo-
     sition only*)
	std::iter_reference_t<I>>,
		std::decay_t<std::invoke_result_t<F&, T,
	std::iter_reference_t<I>>>> &&
	    /*indirectly-binary-left-foldable-impl*/<F, T, I,

		std::decay_t<std::invoke_result_t<F&, T,
	std::iter_reference_t<I>>>>;

	The function-like entities described on this page  are	niebloids,  that
     is:

	  *  Explicit  template  argument lists cannot be specified when calling
     any of them.
	  * None of them are visible to argument-dependent lookup.
	  * When any of them are found by normal unqualified lookup as the  name
     to the left
	    of	the  function-call operator, argument-dependent lookup is inhib-
     ited.

	In practice, they may be implemented as function objects, or  with  spe-
     cial compiler
	extensions.

Parameters
	first, last - the range of elements to fold
	r	    - the range of elements to fold
	init	    - the initial value of the fold
	f	    - the binary function object

Return value
	An  object  of type U that contains the result of left-fold of the given
     range over f,
	where U is equivalent to std::decay_t<std::invoke_result_t<F&, T,
	std::iter_reference_t<I>>>.

	If the range is empty, U(std::move(init)) is returned.

Possible implementations
     struct fold_left_fn {
	 template<std::input_iterator  I,  std::sentinel_for<I>  S,  class  T  =
     std::iter_value_t<I>,
		  /* indirectly-binary-left-foldable */<T, I> F>
	 constexpr auto operator()(I first, S last, T init, F f) const
	 {
	     using U = std::decay_t<std::invoke_result_t<F&, T, std::iter_refer-
     ence_t<I>>>;
	     if (first == last)
		 return U(std::move(init));
	     U accum = std::invoke(f, std::move(init), *first);
	     for (++first; first != last; ++first)
		 accum = std::invoke(f, std::move(accum), *first);
	     return std::move(accum);
	 }

	 template<ranges::input_range R, class T = ranges::range_value_t<R>,
		  /*	indirectly-binary-left-foldable   */<T,   ranges::itera-
     tor_t<R>> F>
	 constexpr auto operator()(R&& r, T init, F f) const
	 {
	     return (*this)(ranges::begin(r),  ranges::end(r),	std::move(init),
     std::ref(f));
	 } };

     inline constexpr fold_left_fn fold_left;

Complexity
	Exactly  ranges::distance(first,  last) applications of the function ob-
     ject f.

Notes
	The following table compares all constrained folding algorithms:

	     Fold function template	  Starts Initial	     Return type
					   from   value
	ranges::fold_left		  left	 init	 U
	ranges::fold_left_first 	  left	 first	 std::optional<U>
						 element
	ranges::fold_right		  right  init	 U
	ranges::fold_right_last 	  right  last	 std::optional<U>
						 element
							 (1)
     ranges::in_value_result<I, U>

	ranges::fold_left_with_iter		left	      init	     (2)
     ranges::in_value_result<BR, U>,

							 where BR is
							 ranges::borrowed_itera-
     tor_t<R>
							 (1)
     ranges::in_value_result<I,
							 std::optional<U>>

	ranges::fold_left_first_with_iter	 left	       first	     (2)
     ranges::in_value_result<BR,
						 element std::optional<U>>

							 where BR is
							 ranges::borrowed_itera-
     tor_t<R>

		  Feature-test macro		Value	  Std		    Fea-
     ture
	__cpp_lib_ranges_fold			202207L (C++23) std::ranges fold
     algorithms
	__cpp_lib_algorithm_default_value_type 202403  (C++26)	List-initializa-
     tion for
							       algorithms (1,2)

Example
     // Run this code

      #include <algorithm>
      #include <complex>
      #include <functional>
      #include <iostream>
      #include <ranges>
      #include <string>
      #include <utility>
      #include <vector>

      int main()
      {
	  namespace ranges = std::ranges;

	  std::vector v{1, 2, 3, 4, 5, 6, 7, 8};

	  int  sum = ranges::fold_left(v.begin(), v.end(), 0, std::plus<int>());
     // (1)
	  std::cout << "sum: " << sum << '\n';

	  int mul = ranges::fold_left(v, 1, std::multiplies<int>()); // (2)
	  std::cout << "mul: " << mul << '\n';

	  // get the product of the std::pair::second of all pairs in  the  vec-
     tor:
	  std::vector<std::pair<char,  float>>	data  {{'A',  2.f},  {'B', 3.f},
     {'C', 3.5f}};
	  float sec = ranges::fold_left
	  (
	      data | ranges::views::values, 2.0f, std::multiplies<>()
	  );
	  std::cout << "sec: " << sec << '\n';

	  // use a program defined function object (lambda-expression):
	  std::string str = ranges::fold_left
	  (
	      v,  "A",	[](std::string	s,  int  x)  {	return	 s   +	 ':'   +
     std::to_string(x); }
	  );
	  std::cout << "str: " << str << '\n';

	  using CD = std::complex<double>;
	  std::vector<CD> nums{{1, 1}, {2, 0}, {3, 0}};
	  #ifdef __cpp_lib_algorithm_default_value_type
	      auto  res = ranges::fold_left(nums, {7, 0}, std::multiplies{}); //
     (2)
	  #else
	      auto res = ranges::fold_left(nums, CD{7,	0},  std::multiplies{});
     // (2)
	  #endif
	  std::cout << "res: " << res << '\n';
      }

Output:
      sum: 36
      mul: 40320
      sec: 42
      str: A:1:2:3:4:5:6:7:8
      res: (42,42)

References
	  * C++23 standard (ISO/IEC 14882:2023):

	  * 27.6.18 Fold [alg.fold]

See also
	ranges::fold_left_first 	   left-folds  a range of elements using
     the first
	(C++23) 			  element as an initial value
					  (niebloid)
	ranges::fold_right		  right-folds a range of elements
	(C++23) 			  (niebloid)
	ranges::fold_right_last 	  right-folds a range of elements  using
     the last
	(C++23) 			  element as an initial value
					  (niebloid)
	ranges::fold_left_with_iter	   left-folds  a  range of elements, and
     returns a pair
	(C++23) 			  (iterator, value)
					  (niebloid)
					  left-folds a range of  elements  using
     the first
	ranges::fold_left_first_with_iter  element  as an initial value, and re-
     turns a pair
	(C++23) 			  (iterator, optional)
					  (niebloid)
	accumulate			  sums up or folds a range of elements
					  (function template)
	reduce				  similar to std::accumulate, except out
     of order
	(C++17) 			  (function template)

http://cppreference.com 	   2024.06.10	       std::ranges::fold_left(3)
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