What is a hyper property?

Question

I am reading the paper Foundations and tools for the static analysis of Ethereum contracts, by Grischenko et al. Sometimes the authors speak about hyper properties (e.g. Section 5). What exactly is a hyper property in this context?

Answer 1

A trace is a (finite or infinite) sequence of program steps. (Some works only consider finite traces, or only infinite ones.)

A property is a set of traces. E.g. all those traces where variable $x$ is never negative.

A hyperproperty is a set of sets of traces. E.g. the sets of traces $T$ where each trace in $T$ is finite.

Some complex security goals can not be described as a property. Non-interference, for instance, can not be checked on a single trace, but only on the set of all the possible traces a given system can generate during execution.