On Context Semantics and Interaction Nets

Matthieu Perrinel (1)

1 LIP - Laboratoire de l'Informatique du Parallélisme

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 $\lambda$-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.

Mots clés: interaction net; context semantics; denotational semantics; implicit computational complexity

Domaines: Logique en informatique [cs.LO]

Matthieu Perrinel. On Context Semantics and Interaction Nets. CSL-LICS, Jul 2014, Austria. pp.10, ⟨10.1145/2603088.2603155⟩. ⟨hal-00992579⟩