A coalgebraic description of web interactions

We introduce a coalgebraic description of static web sites, whereby pages are modeled by their links to other pages together with some extra information. This information can be either related to the contents or to the presentation or to the architecture of the page, etc., and its granularity can vary. This coalgebraic model provides a formal framework for the analysis of the design of single web sites and for the comparison of different sites. We give two alternative coalgebraic accounts of user visits to a web site, as they arise by extracting the information contained in the log file of the web server. The first one is defined in terms of the notion of injective simulation, the latter in terms of an appropriate lax morphism in Rel. These notions provide formal descriptions of user behaviours and can suggest formal tools for the study of the usability of a site.