In: Digital Systems Lab. Series A: Research Report No. 16. Helsinki Univ. of Technology, October 1991.
Abstract: This work discusses three aspects of net theory: compositionality of nets, analysis of nets and high-level 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 ahigh-level net can be mapped into a low-level net that represents its behaviour. This construction is funtorial and preserves colimits, giving a compositional semantics for these high-level nets. Using this semantics we propose some proof rules for compositional reasoning with high-level 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 high-level nets defined in this work.