Proving Soundness of Extensional Normal-Form Bisimilarities

Proving Soundness of Extensional Normal-Form Bisimilarities

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Normal-form bisimilarity is a simple, easy-to-use behavioral equivalence that relates terms in $lambda$-calculi by decomposing their normal forms into bisimilar subterms.Moreover, bovi-shield gold fp 5 l5 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 $eta$-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 $lambda$-calculus, the call-by-value $lambda$-calculus with the delimited-control operators shift and reset, and the call-by-value $lambda$-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 $eta$-law, whereas no theory of normal-form bisimulations for a calculus with call/cc silver lining herbs kidney support and abort has been presented before.

Our results have been fully formalized in the Coq proof assistant.