Abstract
The \(\lambda\mu\widetilde{\mu}\)-calculus is a variant of the λ-calculus with significant differences, including non-confluence and a Curry-Howard isomorphism with the classical sequent calculus.
We present an encoding of the \(\lambda\mu\widetilde{\mu}\)-calculus into the π-calculus. We establish the operational correctness of the encoding, and then we extract from it an abstract machine for the \(\lambda\mu\widetilde{\mu}\)-calculus. We prove that there is a tight relationship between such a machine and Curien and Herbelin’s abstract machine for the \(\lambda\mu\widetilde{\mu}\)-calculus. The π-calculus image of the (typed) \(\lambda\mu\widetilde{\mu}\)-calculus is a nontrivial set of terminating processes.
Cimini’s work is supported by the project ”New Developments in Operational Semantics” (nr. 080039021) of the Icelandic Research Fund.; Sangiorgi’s by the EU projects Sensoria and Hats.
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Cimini, M., Coen, C.S., Sangiorgi, D. (2010). Functions as Processes: Termination and the \(\lambda\mu\widetilde{\mu}\)-Calculus. In: Wirsing, M., Hofmann, M., Rauschmayer, A. (eds) Trustworthly Global Computing. TGC 2010. Lecture Notes in Computer Science, vol 6084. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15640-3_5
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DOI: https://doi.org/10.1007/978-3-642-15640-3_5
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