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arXiv · 1103.0510

Logical Step-Indexed Logical Relations

Derek Dreyer·Amal Ahmed·Lars Birkedal
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Abstract

Appel and McAllester's "step-indexed" logical relations have proven to be a simple and effective technique for reasoning about programs in languages with semantically interesting types, such as general recursive types and general reference types. However, proofs using step-indexed models typically involve tedious, error-prone, and proof-obscuring step-index arithmetic, so it is important to develop clean, high-level, equational proof principles that avoid mention of step indices. In this paper, we show how to reason about binary step-indexed logical relations in an abstract and elegant way. Specifically, we define a logic LSLR, which is inspired by Plotkin and Abadi's logic for parametricity, but also supports recursively defined relations by means of the modal "later" operator from Appel, Melli\`es, Richards, and Vouillon's "very modal model" paper. We encode in LSLR a logical relation for reasoning relationally about programs in call-by-value System F extended with general recursive types. Using this logical relation, we derive a set of useful rules with which we can prove contextual equivalence and approximation results without counting steps.

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BibTeXRIS

Derek Dreyer, Amal Ahmed, Lars Birkedal. 2011-03-02. Logical Step-Indexed Logical Relations. https://doi.org/10.2168/lmcs-7(2%3A16)2011

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