Interaction nets for linear logic

Abstract

This paper presents a system of interaction nets, a graphical paradigm of computation based on net rewriting, for linear logic. The two main features of the encoding are that the system of interaction is a finite one (meaning that there are a finite number of agents and interaction rules), and most importantly, for the multiplicative exponential fragment we obtain for the first time a strong result that nets in normal form correspond to cut-free proofs – thus we can trivially convert a net back into a proof without a complicated read-back algorithm. For the additives, we perform weak cut-elimination (without the additive commutative cut-elimination step), which is the most natural strategy for these connectives since it avoids unnecessary duplication of proofs. For proofs containing additives, our result is that nets in normal form correspond to cut-free proofs modulo additive commutative cuts. This implementation of linear logic is the most faithful and the most efficient of all the extant interaction net encodings of linear logic.