Functions as processes: termination and the λµµ-calculus

The λµµ-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 λµµ-calculus into the π-calculus. We establish the operational correctness of the encoding, and then we extract from it an abstract machine for the λµµ-calculus. We prove that there is a tight relationship between such a machine and Curien and Herbelin's abstract machine for the λµµ-calculus. The π-calculus image of the (typed) λµµ-calculus is a nontrivial set of terminating processes.

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