Abstract
Starting from Laurent’s work on Polarized Linear Logic, we define a new polarized linear deduction system which handles recursion. This is achieved by extending the cut-rule, in such a way that iteration unrolling is achieved by cut-elimination. The proof nets counterpart of this extension is obtained by allowing oriented cycles, which had no meaning in usual polarized linear logic. We also free proof nets from additional constraints, leading up to a correctness criterion as straightforward as possible (since almost all proof structures are correct). Our system has a sound semantics expressed in traced models.
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Montelatici, R. (2003). Polarized Proof Nets with Cycles and Fixpoints Semantics. In: Hofmann, M. (eds) Typed Lambda Calculi and Applications. TLCA 2003. Lecture Notes in Computer Science, vol 2701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44904-3_18
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DOI: https://doi.org/10.1007/3-540-44904-3_18
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