Models of Computation: A Tribute to Ugo Montanari’s Vision

Abstract

Ugo's research activity in the area of Models of Computation (MoC, for short) has been prominent, influential and broadly scoped. Ugo's trademark is that undefinable ability to understand and distill computational aspects into new models as if you were reading them out of some evident connection between well-know models: only, most often, that connection is really visible only after Ugo shows the way. Like experienced sailors have trusted compasses and sextants to help them find the best routes to harbour, Ugo relies on a bag of favourite tools which he has used along the years to deliver a variety of contributions to the MoC area. To mention just three (in alphabetic order): algebraic techniques, concurrency theory, and unification mechanisms.In this introductory contribution we would like to recall some of the influential MoC models put forward by Ugo which cut across the three approaches. Before doing that, it is worth devoting some space to discuss the three aspects separately. Notably, the use of category theory is a pervasive common trait.Algebraic techniques. By algebraic techniques we refer broadly to the use of universal algebras and initial model semantics; of universal coalgebras and final semantics; and of bialgebras. Many interesting papers witness Ugo's leading role in exploiting algebraic techniques during his entire scientific career. Indeed, his contributions are too many to mention all in the space allocated to this overview; we shall therefore attempt to convey the sense of Ugo's broad-spectrum contribution by recapping only a few key results.Reference [43] is the first paper on final, observational semantics in abstract data types, and the main reference for one of the MoC contributed papers in this volume. It presented several key insights in software specification and development for the first time, like the separation between given sorts and newly specified ones, whereby the given sorts lay the ground to define the observable behaviour for the new sorts. Another key suggestion is that the specification of new data types is often partial -in the sense that it may include "don't care" cases-and that many realisations can exist that exhibit equivalent observable behaviour but are not isomorphic. In fact, [43] shows that the isomorphism classes of observably equivalent algebras conforming to the partial specification form a complete lattice, yielding a so-called loose semantics.Possibly the best known of Ugo's papers, [52] exposes the underlying monoidal structure of the category of Petri net computations. The title itself is revealing: Petri nets are monoids. Besides doing what it says on the tin, this paper opened a long-lasting and fruitful collaboration with José Meseguer, and a research line on the initial semantics of P. Degano et al. (Eds.): Montanari