Fully Abstract Encodings of $\lambda$-Calculus in HOcore through Abstract Machines

Abstract

We present fully abstract encodings of the call-by-name and call-by-value $\lambda$-calculus into HOcore, a minimal higher-order process calculus with no name restriction. We consider several equivalences on the $\lambda$-calculus side -- normal-form bisimilarity, applicative bisimilarity, and contextual equivalence -- that we internalize into abstract machines in order to prove full abstraction of the encodings. We also demonstrate that this technique scales to the $\lambda \mu$-calculus, i.e., a standard extension of the $\lambda$-calculus with control operators.

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