Theoretical Computer Science
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Strong Normalization of Explicit Substitutions via Cut Elimination in Proof Nets
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Proof nets and explicit substitutions
Mathematical Structures in Computer Science
Mathematical Structures in Computer Science
Theoretical Computer Science - Logic, language, information and computation
Interpreting a finitary pi-calculus in differential interaction nets
CONCUR'07 Proceedings of the 18th international conference on Concurrency Theory
Strong normalization property for second order linear logic
Theoretical Computer Science
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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We study the confluence of Ehrhard and Regnier's differential nets with exponential promotion, in a pure setting. Confluence fails with promotion and codereliction in absence of associativity of (co)contractions. We thus introduce it as a necessary equivalence, together with other optional ones. We then prove that pure differential nets are Church-Rosser modulo such equivalences. This result generalizes to linear logic regular proof nets, where the same notion of equivalence was already studied in the literature, but only with respect to the problem of normalization in a typed setting. Our proof uses a result of finiteness of developments, which in this setting is given by strong normalization when blocking a suitable notion of "new" cuts.