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**1 - 1**of**1**### The call-by-value lambda-calculus, the SECD machine, and the pi-calculus

, 2000

"... We present an encoding of the call-by-value lambda-calculus into the pi-calculus, alternative to the well-known Milner's encodings. We show that our encoding is barbed congruent (under typed contexts) to Milner's "light" encoding, and that it takes two pi-steps to mimic a beta-re ..."

Abstract
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We present an encoding of the call-by-value lambda-calculus into the pi-calculus, alternative to the well-known Milner's encodings. We show that our encoding is barbed congruent (under typed contexts) to Milner's "light" encoding, and that it takes two pi-steps to mimic a beta-reduction for normalizing terms. We describe a translation of Plotkin's SECD machine into the pi-calculus, and show that there is an operational correspondence between a SECD machine and its encoding. Equipped with a notion of state-based machine and two kinds of correspondences between them, we compare the encodings of the call-by-value lambdacalculus and the SECD machine into the pi-calculus. Contents 1 Introduction 2 2 The correspondences 4 2.1 Machines and correspondences . . . . . . . . . . . . . . . . . . . 4 2.2 Some properties of convergences . . . . . . . . . . . . . . . . . . 5 2.3 Summary of the correspondences . . . . . . . . . . . . . . . . . . 6 3 The call-by-value #-calculus 8 4 The SECD machin...