The call-by-value $\lambda$-calculus, the SECD machine, and the $\pi$-calculus

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 a state-based machine and two kinds of correspondences between them, we compare the encodings of the call-by-value $\lambda$-calculus and the SECD machine into the $\pi$-calculu