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Relational Parametricity and Control

Masahito Hasegawa
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Abstract

We study the equational theory of Parigot's second-order λμ-calculus in connection with a call-by-name continuation-passing style (CPS) translation into a fragment of the second-order λ-calculus. It is observed that the relational parametricity on the target calculus induces a natural notion of equivalence on the λμ-terms. On the other hand, the unconstrained relational parametricity on the λμ-calculus turns out to be inconsistent with this CPS semantics. Following these facts, we propose to formulate the relational parametricity on the λμ-calculus in a constrained way, which might be called ``focal parametricity''.

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Masahito Hasegawa. 2006-06-15. Relational Parametricity and Control. https://doi.org/10.2168/lmcs-2(3%3A3)2006

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