Papers › Proving Soundness of Extensional Normal-Form Bisimilarities
Proving Soundness of Extensional Normal-Form Bisimilarities
Dariusz Biernacki, Serguei Lenglet, Piotr Polesiuk
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Normal-form bisimilarity is a simple, easy-to-use behavioral equivalence that relates terms in λ-calculi by decomposing their normal forms into bisimilar subterms. Moreover, it typically allows for powerful up-to techniques, such as bisimulation up to context, which simplify bisimulation proofs even further. However, proving soundness of these relations becomes complicated in the presence of η-expansion and usually relies on ad hoc proof methods which depend on the language. In this paper we propose a more systematic proof method to show that an extensional normal-form bisimilarity along with its corresponding up to context technique are sound. We illustrate our technique with three calculi: the call-by-value λ-calculus, the call-by-value λ-calculus with the delimited-control operators shift and reset, and the call-by-value λ-calculus with the abortive control operators call/cc and abort. In the first two cases, there was previously no sound up to context technique validating the η-law, whereas no theory of normal-form bisimulations for a calculus with call/cc and abort has been presented before. Our results have been fully formalized in the Coq proof assistant.
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