Track global keys globally.

Assert that there are no duplicates.
Export GlobalKey from basic.dart, so that people don't have to import widgets.dart just for that.
Fix the "initialFocus" feature which actually didn't work.

packages/flutter/lib/editing/input.dart

@@ -19,7 +19,7 @@ const EdgeDims _kTextfieldPadding = const EdgeDims.symmetric(vertical: 8.0);
 class Input extends StatefulComponent {
 
   Input({
-    Key key,
+    GlobalKey key,
     this.placeholder,
     this.onChanged
   }): super(key: key);

packages/flutter/lib/widgets/basic.dart

@@ -22,7 +22,7 @@ import 'package:sky/widgets/widget.dart';
 export 'package:sky/rendering/box.dart' show BackgroundImage, BoxConstraints, BoxDecoration, Border, BorderSide, EdgeDims;
 export 'package:sky/rendering/flex.dart' show FlexDirection, FlexJustifyContent, FlexAlignItems;
 export 'package:sky/rendering/object.dart' show Point, Offset, Size, Rect, Color, Paint, Path;
-export 'package:sky/widgets/widget.dart' show Key, Widget, Component, StatefulComponent, App, runApp, Listener, ParentDataNode;
+export 'package:sky/widgets/widget.dart' show Key, GlobalKey, Widget, Component, StatefulComponent, App, runApp, Listener, ParentDataNode;
 
 
 // PAINTING NODES

packages/flutter/lib/widgets/focus.dart

@@ -14,11 +14,11 @@ class Focus extends Inherited {
 
   Focus({
     GlobalKey key,
-    GlobalKey initialFocus,
+    this.initialFocus,
     Widget child
   }) : super(key: key, child: child);
 
-  GlobalKey initialFocus;
+  final GlobalKey initialFocus;
 
   GlobalKey _currentlyFocusedKey;
   GlobalKey get currentlyFocusedKey {

packages/flutter/lib/widgets/widget.dart

@@ -140,13 +140,46 @@ abstract class Widget {
       _notifyingMountStatus = false;
       sky.tracing.end("Widget._notifyMountStatusChanged");
     }
+    assert(_debugDuplicateGlobalKeys.isEmpty);
   }
 
+  static final Map<GlobalKey, Widget> _globalKeys = new Map<GlobalKey, Widget>();
+  static final Map<GlobalKey, int> _debugDuplicateGlobalKeys = new Map<GlobalKey, int>();
+
   /// Override this function to learn when this [Widget] enters the widget tree.
-  void didMount() { }
+  void didMount() {
+    if (key is GlobalKey) {
+      assert(() {
+        if (_globalKeys.containsKey(key)) {
+          int oldCount = _debugDuplicateGlobalKeys.putIfAbsent(key, () => 1);
+          assert(oldCount >= 1);
+          _debugDuplicateGlobalKeys[key] = oldCount + 1;
+        }
+        return true;
+      });
+      _globalKeys[key] = this;
+    }
+  }
 
   /// Override this function to learn when this [Widget] leaves the widget tree.
-  void didUnmount() { }
+  void didUnmount() {
+    if (key is GlobalKey) {
+      assert(() {
+        if (_globalKeys.containsKey(key) && _debugDuplicateGlobalKeys.containsKey(key)) {
+          int oldCount = _debugDuplicateGlobalKeys[key];
+          assert(oldCount >= 2);
+          if (oldCount == 2) {
+            _debugDuplicateGlobalKeys.remove(key);
+          } else {
+            _debugDuplicateGlobalKeys[key] = oldCount - 1;
+          }
+        }
+        return true;
+      });
+      if (_globalKeys[key] == this)
+        _globalKeys.remove(key);
+    }
+  }
 
   RenderObject _root;