A computer is programmed to accept a command for creation of a new aggregation defined by a user to process data incrementally, one tuple at a time. One or more incremental function(s) in a set of instructions written by the user to implement the new aggregation maintain(s) locally any information that is to be passed between successive invocations, to support computing the aggregation for a given set of tuples as a whole. The user writes a set of instructions to perform the aggregation incrementally, including a plus function which is repeatedly invoked, only once, for each addition to a window of a message. The user also writes a minus function to be invoked with the message, to return the value of incremental aggregation over the window after removal of the message. In such embodiments, the computer does not maintain copies of messages in the window for use by aggregation function(s).