An Explicit Framework for Interaction Nets

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An Explicit Framework for Interaction Nets
Abstract. Interaction nets are a graphical formalism inspired by Linear Logic proof-nets often used for studying higher order rewriting e.g. β-reduction. Traditional presentations of interaction nets are based on graph theory and rely on elementary properties of graph theory. We give here a more explicit presentation based on notions borrowed from Girard’s Geometry of Interaction: interaction nets are presented as partial permutations and a composition of nets, the gluing, is derived from the execution formula. We then define contexts and reduction as the context closure of rules. We prove strong confluence of the reduction within our framework and show how interaction nets can be viewed as the quotient of some generalized proof-nets.
Marc de Falco
Added 27 May 2010
Updated 27 May 2010
Type Conference
Year 2009
Where RTA
Authors Marc de Falco
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