Regarding hyper-properties: I assume they only work on immutable data values, otherwise it would be hard to manage historical objects so that they can be part of any of the predicates.
I'm working on a similar project that you may find interesting: https://odipar.github.io/manikin/. I may want to include hyper-properties in future releases.
edit: found this on hyperproperties: https://lamport.azurewebsites.net/pubs/hyper2.pdf