Fix type-annotation and add another tests.

lib/compiler/implementation/js_backend/backend.dart

 // Copyright (c) 2012, 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.
 
 typedef void Recompile(Element element);
 
 class ReturnInfo {
   HType returnType;
   List<Element> compiledFunctions;
 
@@ skipping 13 matching lines @@
         compiledFunctions.clear();
       }
       returnType = newType;
       if (recompile != null) {
         compiledFunctions.forEach(recompile);
       }
       compiledFunctions.clear();
     }
   }
 
-  addCompiledFunction(FunctionElement function) =>
-      compiledFunctions.add(function);
+  // Note that lazy initializers are treated like functions (but are not
+  // of type [FunctionElement].
+  addCompiledFunction(Element function) => compiledFunctions.add(function);
 }
 
 class HTypeList {
   final List<HType> types;
 
   HTypeList(int length) : types = new List<HType>(length);
   const HTypeList.withAllUnknown() : types = null;
 
   factory HTypeList.fromInvocation(HInvoke node, HTypeMap types) {
     bool allUnknown = true;
@@ skipping 499 matching lines @@
   }
 
   /**
    * Retrieve the return type of the function [callee]. The type is optimistic
    * in the sense that is is based on the compilation of [callee]. If [callee]
    * is recompiled the return type might change to someting broader. For that
    * reason [caller] is registered for recompilation if this happens. If the
    * function [callee] has not yet been compiled the returned type is [null].
    */
   HType optimisticReturnTypesWithRecompilationOnTypeChange(
-      FunctionElement caller, FunctionElement callee) {
+      Element caller, FunctionElement callee) {
     returnInfo.putIfAbsent(callee, () => new ReturnInfo.unknownType());
     ReturnInfo info = returnInfo[callee];
     if (info.returnType != HType.UNKNOWN && caller != null) {
       info.addCompiledFunction(caller);
     }
     return info.returnType;
   }
 
   SourceString getCheckedModeHelper(DartType type) {
     Element element = type.element;
@@ skipping 27 matching lines @@
           return const SourceString('listSuperTypeCheck');
         }
       } else if (nativeCheck) {
         return const SourceString('callTypeCheck');
       } else {
         return const SourceString('propertyTypeCheck');
       }
     }
   }
 }