Synthetic function elements don't have a name or enclosing element/library.

pkg/analyzer/test/src/task/strong/front_end_inference_test.dart

 // Copyright (c) 2017, the Dart project authors.  Please see the AUTHORS file
 // for details. All rights reserved. Use of this source code is governed by a
 // BSD-style license that can be found in the LICENSE file.
 
 import 'dart:async';
 import 'dart:convert';
 import 'dart:io';
 
 import 'package:analyzer/dart/ast/ast.dart';
 import 'package:analyzer/dart/ast/visitor.dart';
@@ skipping 101 matching lines @@
   _InstrumentationValueForType(this.type);
 
   @override
   String toString() {
     StringBuffer buffer = new StringBuffer();
     _appendType(buffer, type);
     return buffer.toString();
   }
 
   void _appendElementName(StringBuffer buffer, Element element) {
-    String name = element.name ?? '';
-    if (element.library == null) {
-      // TODO(scheglov) This is wrong - every element must be in a library.
-      buffer.write('<unknown>::$name');
+    // Synthetic FunctionElement(s) don't have a name or enclosing library.
+    if (element.isSynthetic && element is FunctionElement) {
       return;
     }
-    String libraryName = element.library.name;
-    if (libraryName == '') {
-      throw new StateError('The element $name must be in a named library.');
+
+    LibraryElement library = element.library;
+    if (library == null) {
+      throw new StateError('Unexpected element without library: $element');
     }
+    String libraryName = library.name;
+
+    String name = element.name ?? '';
     if (libraryName != 'dart.core' &&
         libraryName != 'dart.async' &&
         libraryName != 'test') {
       buffer.write('$libraryName::$name');
     } else {
       buffer.write('$name');
     }
   }
 
   void _appendList<T>(StringBuffer buffer, String open, String close,
@@ skipping 157 matching lines @@
   void _recordType(int offset, DartType type) {
     _instrumentation.record(
         uri, offset, 'type', new _InstrumentationValueForType(type));
   }
 
   void _recordTypeArguments(int offset, List<DartType> typeArguments) {
     _instrumentation.record(uri, offset, 'typeArgs',
         new _InstrumentationValueForTypeArgs(typeArguments));
   }
 }