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Differential interaction nets

Abstract : We introduce interaction nets for a fragment of the differential lambda-calculus and exhibit in this framework a new symmetry between the "of course" and the "why not" modalities of linear logic, which is completely similar to the symmetry between the "tensor" and "par" connectives of linear logic. We use algebraic intuitions for introducing these nets and their reduction rules, and then we develop two correctness criteria (weak typeability and acyclicity) and show that they guarantee strong normalization. Finally, we outline the correspondence between this interaction nets formalism and the resource lambda-calculus.
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https://hal.archives-ouvertes.fr/hal-00150274
Contributor : Thomas Ehrhard Connect in order to contact the contributor
Submitted on : Tuesday, May 29, 2007 - 11:41:49 PM
Last modification on : Monday, March 29, 2021 - 3:24:02 PM

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Thomas Ehrhard, Laurent Regnier. Differential interaction nets. Theoretical Computer Science, Elsevier, 2006, 364 (2), pp.166-195. ⟨10.1016/j.tcs.2006.08.003⟩. ⟨hal-00150274⟩

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