Dependency Analysis for Hybrid Programs

Formally verifying the correctness of programs in a program logic provides strong static guarantees about the program’s runtime behaviour. Unlike static analysis techniques, proving such correctness properties typically requires some form of user interaction, e.g. the user might need to manually state appropriate loop invariants. In the context of dL, this problem is somewhat exacerbated because one has to reason about both discrete loop invariants, and continuous differential invariants for hybrid programs. In this paper, we first explore a version of dependency analysis that we have designed and implemented for hybrid programs in KeYmaera X. We claim that such an analysis is non-trivial in the non-deterministic setting of dL, and we point out the subtleties in our definition. We then make use of dependency analysis in two application areas: finding differential invariants, and generating a variable order for quantifier elimination.