Understanding untyped $\overline{\lambda}\mu\widetilde{\mu}$ calculus

Abstract : We prove the confluence of $\overline{\lambda}\mu\widetilde{\mu}_T$ and $\overline{\lambda}\mu\widetilde{\mu}_Q$, two well-behaved subcalculi of the $\overline{\lambda}\mu\widetilde{\mu}$ calculus, closed under call-by-value and call-by-name reduction, respectively. Moreover, we give the interpretation of $\overline{\lambda}\mu\widetilde{\mu}_T$ in the category of negated domains, and the interpretation of $\overline{\lambda}\mu\widetilde{\mu}_Q$ in the Kleisli category. To the best of our knowledge this is the first interpretation of $\overline{\lambda}\mu\widetilde{\mu}$ calculus,
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Pierre Lescanne, Silvia Likavec. Understanding untyped $\overline{\lambda}\mu\widetilde{\mu}$ calculus. [Research Report] LIP RR-2004-50, Laboratoire de l'informatique du parallélisme. 2004, 2+15p. ⟨hal-02101786⟩

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