Abstract
Boxes are a key tool introduced by linear logic proof nets to implement lambda-calculus beta-reduction. In usual graph reduction, on the other hand, there is no need for boxes: the part of a shared graph that may be copied or erased is reconstructed on the fly when needed. Boxes however play a key role in controlling the reductions of nets and in the correspondence between nets and terms with explicit substitutions.
We show that boxes can be represented in a simple and efficient way by adding a jump, i.e. an extra connection, for every explicit sharing position (exponential cut) in the graph, and we characterize our nets by a variant of Lamarche’s correctness criterion for essential nets. The correspondence between explicit substitutions and jumps simplifies the already known correspondence between explicit substitutions and proof net exponential cuts.
Partially supported by the MIUR PRIN grant “CONCERTO” and by the Sapienza S.M.F.N. grant “Applicazione di Strumenti Logici alla Progettazione e Analisi di Sistemi Software”.
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Accattoli, B., Guerrini, S. (2009). Jumping Boxes . In: Grädel, E., Kahle, R. (eds) Computer Science Logic. CSL 2009. Lecture Notes in Computer Science, vol 5771. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04027-6_7
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DOI: https://doi.org/10.1007/978-3-642-04027-6_7
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