Implement type inference for await expressions in front_end.

pkg/front_end/lib/src/fasta/kernel/kernel_shadow_ast.dart

Index: pkg/front_end/lib/src/fasta/kernel/kernel_shadow_ast.dart
diff --git a/pkg/front_end/lib/src/fasta/kernel/kernel_shadow_ast.dart b/pkg/front_end/lib/src/fasta/kernel/kernel_shadow_ast.dart
index a708c3d066d258e6495ca80fe5fa92bd3a0e94c4..fc6476d6a6edce75691183cfd8dd7f80a504044f 100644
--- a/pkg/front_end/lib/src/fasta/kernel/kernel_shadow_ast.dart
+++ b/pkg/front_end/lib/src/fasta/kernel/kernel_shadow_ast.dart
@@ -110,8 +110,16 @@ class KernelAwaitExpression extends AwaitExpression
   @override
   DartType _inferExpression(
       KernelTypeInferrer inferrer, DartType typeContext, bool typeNeeded) {
-    // TODO(scheglov): implement.
-    return typeNeeded ? const DynamicType() : null;
+    typeNeeded =
+        inferrer.listener.awaitExpressionEnter(this, typeContext) || typeNeeded;
+    if (!inferrer.typeSchemaEnvironment.isEmptyContext(typeContext)) {
+      typeContext = inferrer.wrapFutureOrType(typeContext);
+    }
+    var inferredType =
+        inferrer.inferExpression(operand, typeContext, typeNeeded);
+    inferredType = inferrer.typeSchemaEnvironment.flattenFutures(inferredType);
+    inferrer.listener.awaitExpressionExit(this, inferredType);
+    return inferredType;
   }
 }