An Equational Theory for Weak Bisimulation via Generalized Parameterized Coinduction
Coinductive reasoning about infinitary structures such as streams is widely applicable. However, practical frameworks for developing coinductive proofs and finding reasoning principles that help structure such proofs remain a challenge, especially in the context of machine-checked formalization.
This paper gives a novel presentation of an equational theory for reasoning about structures up to weak bisimulation. The theory is both compositional, making it suitable for defining general-purpose lemmas, and also incremental, meaning that the bisimulation can be created interactively. To prove the theory’s soundness, this paper also introduces generalized parametric coinduction, which addresses expressivity problems of earlier works and provides a practical framework for coinductive reasoning. The paper presents the resulting equational theory for streams, but the technique applies to other structures too.
All of the results in this paper have been proved in Coq, and the generalized parametric coinduction framework is available as a Coq library.
Conference DayMon 20 JanDisplayed time zone: Saskatchewan, Central America change
14:00 - 15:05
|An Equational Theory for Weak Bisimulation via Generalized Parameterized Coinduction|
Yannick ZakowskiUniversity of Pennsylvania, Paul HeUniversity of Pennsylvania, Chung-Kil HurSeoul National University, Steve ZdancewicUniversity of PennsylvaniaDOI Pre-print Media Attached File Attached
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Qingxiang WangUniversity of Innsbruck, Chad BrownCzech Technical University in Prague, Cezary KaliszykUniversity of Innsbruck, Josef UrbanCzech Technical University in PragueDOI Pre-print
|REPLICA: REPL Instrumentation for Coq Analysis|
Talia RingerUniversity of Washington, Alex Sanchez-SternUniversity of California, San Diego, Dan GrossmanUniversity of Washington, Sorin LernerUniversity of California, San DiegoDOI Pre-print Media Attached