Class<X> exceptionType,
      final AsyncClosingFunction<? super X, W> fallback,
      Executor executor) {
    checkNotNull(fallback);
    AsyncFunction<X, W> asyncFunction =
        new AsyncFunction<X, W>() {
          @Override
          public ListenableFuture<W> apply(X exception) throws Exception {
            return closeables.applyAsyncClosingFunction(fallback, exception);
          }