Reference:
Johan Lilius. On the compositionality and analysis of algebraic highlevel nets. Research Report A16, Helsinki University of Technology, Digital Systems Laboratory, Espoo, Finland, October 1991.
Abstract:
This work discusses three aspects of net theory: compositionality of nets, analysis of nets and highlevel nets. Net theory has often been criticised for the difficulty of giving a compositional semantics to a net. In this work we discuss this problem form a category theoretic point of view. In category theory compositionality is represented by colimits. We show how a highlevel net can be mapped into a lowlevel net that represents its behaviour. This construction is functorial and preserves colimits, giving a compositional semantics for these highlevel nets. Using this semantics we propose some proof rules for compositional reasoning with highlevel nets. Linear logic is a recently discovered logic that has many interesting properties. From a net theoretic point of view its interest lies in the fact that it is able to express resources in an analogous manner to nets. Several interpretations of Petri nets in terms of linear logic exist. In this work we study a model theoretic interpretation where the behaviour of the net gives a model of linear logic. This construction is extended to cover the algebraic highlevel nets defined in this work.
Keywords:
net theory, category theory, algebraic specification,linear logic, Petri nets, highlevel nets, compositionality
Suggested BibTeX entry:
@techreport{HUTTCSA16,
address = {Espoo, Finland},
author = {Johan Lilius},
institution = {Helsinki University of Technology, Digital Systems Laboratory},
month = {October},
number = {A16},
pages = {77},
title = {On the Compositionality and Analysis of Algebraic HighLevel Nets},
type = {Research Report},
year = {1991},
}
