Abstract

Interaction nets form a local and strongly confluent model of computation that is per se parallel. We introduce a Curry–Howard correspondence between well-formed interaction nets and a deep-inference deduction system based on linear logic. In particular, linear logic itself is easily expressed in the system and its computational aspects materialise though the correspondence. The system of interaction nets obtained is a typed variant of already well-known sharing graphs. Due to a strong confluence property, strong normalisation for this system follows from weak normalisation. The latter is obtained via an adaptation of Girard’s reducibility method. The approach is modular, readily gives rise to generalisations (e.g. second order, known as polymorphism to the programmer) and could therefore be extended to various systems of interaction nets.

BibTeX

@inproceedings{SGGM-CSL13,
  author    = "St{\'e}phane Gimenez and Georg Moser",
  title     = "The Structure of Interaction",
  booktitle = "Proceedings of the 27th International Workshop on Computer
               Science Logic / 22nd Annual Conference of the EACSL",
  editor    = "Simona Ronchi Della Rocca",
  series    = "Leibniz International Proceedings in Informatics",
  volume    = 23,
  pages     = "316--331",
  year      = 2013,
  doi       = "10.4230/LIPIcs.CSL.2013.316"
}