Fully Abstract Encodings of λ-Calculus in HOcore through Abstract Machines

05/13/2022

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by   Małgorzata Biernacka, et al.

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We present fully abstract encodings of the call-by-name and call-by-value λ-calculus into HOcore, a minimal higher-order process calculus with no name restriction. We consider several equivalences on the λ-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 λμ-calculus, i.e., a standard extension of the λ-calculus with control operators.