std::experimental::ranges::StrictTotallyOrdered,(3)

NAME
std::experimental::ranges::StrictTotallyOrdered, - std::experimental::ranges::StrictTotallyOrdered,

Synopsis
   Defined in header <experimental/ranges/concepts>
   template< class T >
   concept bool StrictTotallyOrdered =
       EqualityComparable<T> &&
       requires(const std::remove_reference_t<T>& a,
                const std::remove_reference_t<T>& b) { (1) (ranges TS)
           { a < b } -> Boolean&&;
           { a > b } -> Boolean&&;
           { a <= b } -> Boolean&&;
           { a >= b } -> Boolean&&;
       };
   template< class T, class U >
   concept bool StrictTotallyOrderedWith =
       StrictTotallyOrdered<T> &&
       StrictTotallyOrdered<U> &&
       CommonReference<
           const std::remove_reference_t<T>&,
           const std::remove_reference_t<U>&> &&
       StrictTotallyOrdered<
           ranges::common_reference_t<
               const std::remove_reference_t<T>&,
               const std::remove_reference_t<U>&>> &&
       EqualityComparableWith<T, U> && (2) (ranges TS)
       requires(const std::remove_reference_t<T>& t,
                const std::remove_reference_t<U>& u) {
           { t < u } -> Boolean&&;
           { t > u } -> Boolean&&;
           { t <= u } -> Boolean&&;
           { t >= u } -> Boolean&&;
           { u < t } -> Boolean&&;
           { u > t } -> Boolean&&;
           { u <= t } -> Boolean&&;
           { u >= t } -> Boolean&&;
       };
   1) The concept StrictTotallyOrdered<T> specifies that the comparison operators
   ==,!=,<,>,<=,>= on T yield results consistent with a strict total order on T.
   StrictTotallyOrdered<T> is satisfied only if, given lvalues a, b and c of type const
   std::remove_reference_t<T>:
     * Exactly one of bool(a < b), bool(a > b) and bool(a == b) is true;
     * If bool(a < b) and bool(b < c) are both true, then bool(a < c) is true;
     * bool(a > b) == bool(b < a)
     * bool(a >= b) == !bool(a < b)
     * bool(a <= b) == !bool(b < a)
   2) The concept StrictTotallyOrderedWith<T, U> specifies that the comparison
   operators ==,!=,<,>,<=,>= on (possibly mixed) T and U operands yield results
   consistent with a strict total order. Comparing mixed operands yields results
   equivalent to comparing the operands converted to their common type.
   Formally, StrictTotallyOrderedWith<T, U> is satisfied only if, given any lvalue t of
   type const std::remove_reference_t<T> and any lvalue u of type const
   std::remove_reference_t<U>, and let C be ranges::common_reference_t<const
   std::remove_reference_t<T>&, const std::remove_reference_t<U>&>:
     * bool(t < u) == bool(C(t) < C(u))
     * bool(t > u) == bool(C(t) > C(u))
     * bool(t <= u) == bool(C(t) <= C(u))
     * bool(t >= u) == bool(C(t) >= C(u))
     * bool(u < t) == bool(C(u) < C(t))
     * bool(u > t) == bool(C(u) > C(t))
     * bool(u <= t) == bool(C(u) <= C(t))
     * bool(u >= t) == bool(C(u) >= C(t))
   Equality preservation
   An expression is equality preserving if it results in equal outputs given equal
   inputs.
     * The inputs to an expression consist of its operands.
     * The outputs of an expression consist of its result and all operands modified by
       the expression (if any).
   Every expression required to be equality preserving is further required to be
   stable: two evaluations of such an expression with the same input objects must have
   equal outputs absent any explicit intervening modification of those input objects.
   Unless noted otherwise, every expression used in a requires-expression is required
   to be equality preserving and stable, and the evaluation of the expression may only
   modify its non-constant operands. Operands that are constant must not be modified.
   Implicit expression variations
   A requires-expression that uses an expression that is non-modifying for some
   constant lvalue operand also implicitly requires additional variations of that
   expression that accept a non-constant lvalue or (possibly constant) rvalue for the
   given operand unless such an expression variation is explicitly required with
   differing semantics. These implicit expression variations must meet the same
   semantic requirements of the declared expression. The extent to which an
   implementation validates the syntax of the variations is unspecified.