typed exception for private method not found

src/core/Exception.pm

@@ -42,11 +42,15 @@ my class X::AdHoc is Exception {
 my class X::Method::NotFound is Exception {
     has $.method;
     has $.typename;
+    has Bool $.private = False;
     method message() {
-        "No such method '$.method' for invocant of type '$.typename'";
+        $.private
+            ?? "No such private method '$.method' for invocant of type '$.typename'"
+            !! "No such method '$.method' for invocant of type '$.typename'";
     }
 }
 
+
 sub EXCEPTION(|$) {
     my Mu $parrot_ex := nqp::shift(pir::perl6_current_args_rpa__P());
     my Mu $payload   := nqp::atkey($parrot_ex, 'payload');

src/core/Mu.pm

@@ -268,8 +268,11 @@ my class Mu {
         my $meth := $type.HOW.find_private_method($type, $name);
         $meth ??
             $meth($self, |$c) !!
-            die("Private method '$name' not found on type " ~ $type.HOW.name($type))
-
+            X::Method::NotFound.new(
+                    method   => '!' ~ $name,
+                    typename => $type.HOW.name($type),
+                    :private,
+            ).throw;
     }
 
     method dispatch:<.^>(Mu \$self: $name, |$c) is rw is hidden_from_backtrace {