Types of Recursive Computable Aggregations

In this paper the relation between aggregation functions, algorithms and computer programs is revisited, extending the concept of recursive aggregation operator by means of the recursive computable aggregation. In particular, two different recursive computable aggregation are distinguished: on the one hand, the hard recursive computable aggregation, which appears when there is a unique recursive function generating the aggregation, and are fully related to associativity; and on the other hand, the soft recursive computable aggregation, which appears when the number of elements to be aggregated is needed. Some illustrative examples are provided.