P2830R10 Standardized Constexpr Type Ordering

Fixes #7954
Fixes cplusplus/papers#1507

Author: AlisdairM

source/support.tex

@@ -842,6 +842,7 @@
   // also in \libheader{utility}, \libheader{tuple}, \libheader{map}, \libheader{unordered_map}
 #define @\defnlibxname{cpp_lib_tuples_by_type}@                    201304L // freestanding, also in \libheader{utility}, \libheader{tuple}
 #define @\defnlibxname{cpp_lib_type_identity}@                     201806L // freestanding, also in \libheader{type_traits}
+#define @\defnlibxname{cpp_lib_type_order}@                        202506L // also in \libheader{compare}
 #define @\defnlibxname{cpp_lib_type_trait_variable_templates}@     201510L // freestanding, also in \libheader{type_traits}
 #define @\defnlibxname{cpp_lib_uncaught_exceptions}@               201411L // freestanding, also in \libheader{exception}
 #define @\defnlibxname{cpp_lib_unordered_map_try_emplace}@         201411L // also in \libheader{unordered_map}
@@ -4765,6 +4766,7 @@
 \indexlibraryglobal{is_geq}%
 \indexlibraryglobal{is_gteq}%
 \indexlibraryglobal{common_comparison_category_t}%
+\indexlibraryglobal{type_order_v}%
 \begin{codeblock}
 // all freestanding
 namespace std {
@@ -4813,6 +4815,13 @@
     inline constexpr @\unspec@ compare_weak_order_fallback = @\unspec@;
     inline constexpr @\unspec@ compare_partial_order_fallback = @\unspec@;
   }
+
+  // \ref{compare.type}, type ordering
+  template<class T, class U>
+    struct type_order;
+
+  template<class T, class U>
+    constexpr strong_ordering type_order_v = type_order<T, U>::value;
 }
 \end{codeblock}
 
@@ -5668,6 +5677,45 @@
 of a template instantiation.
 \end{note}
 
+\rSec2[compare.type]{Type Ordering}
+
+\pnum
+There is an \impldef{total ordering of all types} total ordering of all types.
+For any (possibly incomplete) types \tcode{X} and \tcode{Y},
+the expression \tcode{\exposid{TYPE-ORDER}(X, Y)} is a constant expression\iref{expr.const}
+of type \tcode{strong_ordering}\iref{cmp.strongord}.
+Its value is \tcode{strong_ordering::less} if \tcode{X} precedes \tcode{Y}
+in this implementation-defined total order,
+\tcode{strong_ordering::greater} if \tcode{Y} precedes \tcode{X}, and
+\tcode{strong_ordering::equal} if they are the same type.
+\begin{note}
+\tcode{int}, \tcode{const int} and \tcode{int\&} are different types.
+\end{note}
+\begin{note}
+This ordering need not be consistent with the one induced by \tcode{type_info::before}.
+\end{note}
+\begin{note}
+The ordering of TU-local types from different translation units is not observable,
+because the necessary specialization of \tcode{type_order} is impossible to name.
+\end{note}
+
+\indexlibraryglobal{type_order}%
+\begin{itemdecl}
+template<class T, class U>
+  struct type_order;
+\end{itemdecl}
+
+\begin{itemdescr}
+\pnum
+The name \tcode{type_order} denotes a \oldconcept{BinaryTypeTrait}\iref{meta.rqmts}
+with a base characteristic of
+\tcode{integral_constant<strong_ordering, \exposid{TYPE-ORDER}(X, Y)>}.
+
+\pnum
+\recommended
+The order should be lexicographical on parameter-type-lists and template argument lists.
+\end{itemdescr}
+
 \rSec1[support.coroutine]{Coroutines}
 
 \rSec2[support.coroutine.general]{General}