Split World usage into open, inference, and closed world.

pkg/compiler/lib/src/types/map_type_mask.dart

Index: pkg/compiler/lib/src/types/map_type_mask.dart
diff --git a/pkg/compiler/lib/src/types/map_type_mask.dart b/pkg/compiler/lib/src/types/map_type_mask.dart
index 4645cd7a08b01a0d324f1a73112d68701b8f19f9..57f3c46df533dce0be5d9e9fdb4e4db5fb736d2e 100644
--- a/pkg/compiler/lib/src/types/map_type_mask.dart
+++ b/pkg/compiler/lib/src/types/map_type_mask.dart
@@ -77,7 +77,10 @@ class MapTypeMask extends ForwardingTypeMask {
       return new MapTypeMask(
           newForwardTo, null, null, newKeyType, newValueType);
     } else if (other.isDictionary) {
-      assert(other.keyType == classWorld.compiler.commonMasks.stringType);
+      // TODO(johnniwinther): Find another way to check this invariant that
+      // doesn't need the compiler.
+      assert(
+          other.keyType == classWorld.backend.compiler.commonMasks.stringType);
       TypeMask newKeyType = keyType.union(other.keyType, classWorld);
       TypeMask newValueType =
           other.typeMap.values.fold(keyType, (p, n) => p.union(n, classWorld));