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2010•Unpublished venueRequires access

Functions as processes: termination and the λµµ-calculus

Matteo Cimini, Claudio Sacerdoti Coen, Davide Sangiorgi

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Abstract

Abstract. The ¯λµ˜µ-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 ¯λµ˜µ-calculus into the π-calculus. We establish the machine for the ¯λµ˜µ-calculus. We prove that there is a tight relationship between such a machine and Curien and Herbelin’s abstract machine for the ¯λµ˜µ-calculus. The π-calculus image of the (typed) ¯λµ˜µ-calculus is a nontrivial set of terminating processes. 1

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What this paper is about

Abstract. The ¯λµ˜µ-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 ¯λµ˜µ-calculus into the π-calculus. We establish the machine for the ¯λµ˜µ-calculus. We prove that there is a tight relationship between such a machine and Curien and Herbelin’s abstract machine for the ¯λµ˜µ-calculus. The π-calculus image of the (typed) ¯λµ˜µ-calculus is a nontrivial set of terminating processes. 1

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Available abstract

Abstract. The ¯λµ˜µ-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 ¯λµ˜µ-calculus into the π-calculus. We establish the machine for the ¯λµ˜µ-calculus. We prove that there is a tight relationship between such a machine and Curien and Herbelin’s abstract machine for the ¯λµ˜µ-calculus. The π-calculus image of the (typed) ¯λµ˜µ-calculus is a nontrivial set of terminating processes. 1

Key concepts: Calculus (dental), Cut-elimination theorem, Natural deduction, Sequent calculus, Correctness, Proof calculus, Time-scale calculus, Mathematics

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