## Biernacki, Dariusz and Lenglet, Serguei and Polesiuk, Piotr - Proving Soundness of Extensional Normal-Form Bisimilarities

lmcs:4041 - Logical Methods in Computer Science, March 29, 2019, Volume 15, Issue 1 - https://doi.org/10.23638/LMCS-15(1:31)2019
Proving Soundness of Extensional Normal-Form Bisimilarities

Authors: Biernacki, Dariusz and Lenglet, Serguei and Polesiuk, Piotr

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, 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 and abort has been presented before. Our results have been fully formalized in the Coq proof assistant.

Volume: Volume 15, Issue 1
Published on: March 29, 2019
Submitted on: November 2, 2017
Keywords: Computer Science - Logic in Computer Science,Computer Science - Programming Languages