ABSTRACT. We introduce string data structures as combinatorial descriptions of structured words on totally ordered alphabets. The data can be described by words through a reading map and can be constructed by using an insertion algorithm. The insertion map defines a product on datum. We show that the associativity of this product, the cross section property of the data structure, and the confluence of the rewriting system defined by the insertion map are equivalent properties. We explicit a coherent presentation of the monoid presented by the data structure, made of generators, rewriting rules describing the insertion of letters in words and relations among the insertion algorithms.