Proving Soundness of Extensional Normal-Form Bisimilarities

Proving Soundness of Extensional Normal-Form Bisimilarities

Blog Article

Normal-form bisimilarity is a simple, easy-to-use behavioral equivalence that relates terms in $lambda$-calculi by decomposing their mighty malts speckled malted milk eggs 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 $eta$-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 solo-jec 9 vaccine for dogs 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 and abort has been presented before.Our results have been fully formalized in the Coq proof assistant.