On context semantics and interaction nets

Abstract

Context semantics is a tool inspired by Girard' s geometry of interaction. It has had many applications from study of optimal reduction to proofs of complexity bounds. Yet, context semantics have been defined only on λ-calculus and linear logic. In order to study other languages, in particular languages with more primitives (built-in arithmetic, pattern matching,...) we define a context semantics for a broader framework: interaction nets. These are a well-behaved class of graph rewriting systems. Here, two applications are explored. First, we define a notion of weight, based on context semantics paths, which bounds the length of reduction of nets. Then, we define a denotational semantics for a large class of interaction net systems.