Toward Structured Proofs for Dynamic Logics

Abstract: We present Kaisar, a structured interactive proof language for differential dynamic logic (dL), for safety-critical cyber-physical systems (CPS). The defining feature of Kaisar is nominal terms, which simplify CPS proofs by making the frequently needed historical references to past program states first-class. To support nominals, we extend the notion of structured proof with a first-class notion of structured symbolic execution of CPS models. We implement Kaisar in the theorem prover KeYmaera X and reproduce an example on the safe operation of a parachute and a case study on ground robot control. We show how nominals simplify common CPS reasoning tasks when combined with other features of structured proof. We develop an extensive metatheory for Kaisar. In addition to soundness and completeness, we show a formal specification for Kaisar's nominals and relate Kaisar to a nominal variant of dL.