libstdc++: Do not use 'not' alternative token in <format>

This fixes:
FAIL: 17_intro/headers/c++1998/operator_names.cc  -std=gnu++23 (test for excess errors)
FAIL: 17_intro/headers/c++1998/operator_names.cc  -std=gnu++26 (test for excess errors)

The purpose of 'not defined<format_kind<R>>' is to be ill-formed (as
required by [format.range.fmtkind]) and to give an error that includes
the string "not defined<format_kind<R>>". That was intended to tell you
that format_kind<R> is not defined, just like it says!

But user code can use -fno-operator-names so we can't use 'not' here,
and "! defined" in the diagnostic doesn't seem as user-friendly. It also
raises questions about whether it was intended to be the preprocessor
token 'defined' (it's not) or where 'defined' is defined (it's not).

Replace it with __primary_template_not_defined<format_kind<R>> and a
comment, which seems to give a fairly clear diagnostic with both GCC and
Clang. The diagnostic now looks like:

.../include/c++/15.0.1/format:5165:7: error: use of 'std::format_kind<int>' before deduction of 'auto'
 5165 |       format_kind<_Rg> // you can specialize this for non-const input ranges
      |       ^~~~~~~~~~~~~~~~
.../include/c++/15.0.1/format:5164:35: error: '__primary_template_not_defined' was not declared in this scope
 5164 |     __primary_template_not_defined(
      |     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^
 5165 |       format_kind<_Rg> // you can specialize this for non-const input ranges
      |       ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 5166 |     );
      |     ~

libstdc++-v3/ChangeLog:

	* include/std/format (format_kind): Do not use 'not'
	alternative token to make the primary template ill-formed. Use
	the undeclared identifier __primary_template_not_defined and a
	comment that will appear in diagnostics.
	* testsuite/std/format/ranges/format_kind_neg.cc: New test.

2 files changed, 17 insertions, 1 deletions

diff --git a/libstdc++-v3/include/std/format b/libstdc++-v3/include/std/format
index 2668382..f3fd837 100644
--- a/libstdc++-v3/include/std/format
+++ b/libstdc++-v3/include/std/format
@@ -5160,7 +5160,10 @@ namespace __format
 
   /// @cond undocumented
   template<typename _Rg>
-    constexpr auto format_kind = not defined(format_kind<_Rg>);
+    constexpr auto format_kind =
+    __primary_template_not_defined(
+      format_kind<_Rg> // you can specialize this for non-const input ranges
+    );
 
   template<typename _Tp>
     consteval range_format
diff --git a/libstdc++-v3/testsuite/std/format/ranges/format_kind_neg.cc b/libstdc++-v3/testsuite/std/format/ranges/format_kind_neg.cc
new file mode 100644
index 0000000..bf8619d
--- /dev/null
+++ b/libstdc++-v3/testsuite/std/format/ranges/format_kind_neg.cc
@@ -0,0 +1,13 @@
+// { dg-do compile { target c++23 } }
+
+// C++23 22.14.7.1 [format.range.fmtkind] p1: A program that instantiates
+// the primary template of format_kind is ill-formed.
+
+#include <format>
+
+template<auto> struct Tester { };
+
+Tester<std::format_kind<const int(&)[1]>> t; // { dg-error "here" }
+
+// { dg-error "use of 'std::format_kind" "" { target *-*-* } 0 }
+// { dg-error "primary_template_not_defined" "" { target *-*-* } 0 }