A Calculus for Interaction Nets Based on the Linear Chemical Abstract Machine

Interaction nets are graph rewriting systems which are a generalisation of proof nets for classical linear logic. The linear chemical abstract machine (CHAM) is a term rewriting system which corresponds to classical linear logic, via the Curry-Howard isomorphism. We can obtain a textual calculus for interaction nets which is surprisingly similar to linear CHAM based on the multiplicative fragment of classical linear logic. In this paper we introduce a framework based on the linear CHAM to model interaction net reduction. We obtain a textual calculus for interaction nets that is closer to the graphical representation than previous attempts.