An Explicit Framework for Interaction Nets

Interaction nets are a graphical formalism inspired by Linear Logic proof-nets often used for studying higher order rewriting e.g. \Beta-reduction. Traditional presentations of interaction nets are based on graph theory and rely on elementary properties of graph theory. We give here a more explicit presentation based on notions borrowed from Girard's Geometry of Interaction: interaction nets are presented as partial permutations and a composition of nets, the gluing, is derived from the execution formula. We then define contexts and reduction as the context closure of rules. We prove strong confluence of the reduction within our framework and show how interaction nets can be viewed as the quotient of some generalized proof-nets

A design model for Open Distributed Processing systems

This paper proposes design concepts that allow the conception, understanding and development of complex technical structures for open distributed systems. The proposed concepts are related to, and partially motivated by, the present work on Open Distributed Processing (ODP). As opposed to the current ODP approach, the concepts are aimed at supporting a design trajectory with several, related abstraction levels. Simple examples are used to illustrate the proposed concepts

Labelled Lambda-calculi with Explicit Copy and Erase

We present two rewriting systems that define labelled explicit substitution lambda-calculi. Our work is motivated by the close correspondence between Levy's labelled lambda-calculus and paths in proof-nets, which played an important role in the understanding of the Geometry of Interaction. The structure of the labels in Levy's labelled lambda-calculus relates to the multiplicative information of paths; the novelty of our work is that we design labelled explicit substitution calculi that also keep track of exponential information present in call-by-value and call-by-name translations of the lambda-calculus into linear logic proof-nets

The uses of process modeling : a framework for understanding modeling formalisms

There is wide-spread recognition of the urgent need to improve software processes in order to improve the performance of software organizations. Process models are essential in achieving understanding and visibility of processes and are important for other uses including the analysis of processes for improvement. It has been increasingly difficult to compare and evaluate the variety of process modeling formalisms that have appeared in recent years without a clear understanding of precisely for what they will be used. The contribution of this paper is to provide an understanding and a fairly comprehensive catalog of the applications of process modeling for which formalisms may be used. The primary mechanism for doing this is a guided tour of the literature on process modeling supplemented by recent industrial experience. In the paper, basic definitions concerning processes, process descriptions and process modeling are reviewed and then uses of process modeling are surveyed under the following headings: communication among process participants, construction of new processes, control of processes, process· analysis, and process support by automation. Comments are offered on paradigms for process modeling formalisms and directions for future work to permit evolution of a discipline of process engineering are given

Abridged Petri Nets

A new graphical framework, Abridged Petri Nets (APNs) is introduced for bottom-up modeling of complex stochastic systems. APNs are similar to Stochastic Petri Nets (SPNs) in as much as they both rely on component-based representation of system state space, in contrast to Markov chains that explicitly model the states of an entire system. In both frameworks, so-called tokens (denoted as small circles) represent individual entities comprising the system; however, SPN graphs contain two distinct types of nodes (called places and transitions) with transitions serving the purpose of routing tokens among places. As a result, a pair of place nodes in SPNs can be linked to each other only via a transient stop, a transition node. In contrast, APN graphs link place nodes directly by arcs (transitions), similar to state space diagrams for Markov chains, and separate transition nodes are not needed. Tokens in APN are distinct and have labels that can assume both discrete values ("colors") and continuous values ("ages"), both of which can change during simulation. Component interactions are modeled in APNs using triggers, which are either inhibitors or enablers (the inhibitors' opposites). Hierarchical construction of APNs rely on using stacks (layers) of submodels with automatically matching color policies. As a result, APNs provide at least the same modeling power as SPNs, but, as demonstrated by means of several examples, the resulting models are often more compact and transparent, therefore facilitating more efficient performance evaluation of complex systems.Comment: 17 figure

Introduction to linear logic and ludics, part II

This paper is the second part of an introduction to linear logic and ludics, both due to Girard. It is devoted to proof nets, in the limited, yet central, framework of multiplicative linear logic and to ludics, which has been recently developped in an aim of further unveiling the fundamental interactive nature of computation and logic. We hope to offer a few computer science insights into this new theory