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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:

def with_filter(self, filter):
        '''
        Returns a new service which will process requests with the specified
        filter. Filtering operations can include logging, automatic retrying,
        etc... The filter is a lambda which receives the HTTPRequest and
        another lambda. The filter can perform any pre-processing on the
        request, pass it off to the next lambda, and then perform any
        post-processing on the response.

        :param function(request) filter: A filter function.
        :return: A new service using the specified filter.
        :rtype: a subclass of :class:`StorageClient`
        '''
        res = copy.deepcopy(self)
        old_filter = self._filter

        def new_filter(request):
            return filter(request, old_filter)

        res._filter = new_filter
        return res