Coherence of monoids by insertions
Résumé
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 make 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.
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