Compositional Proofs in Differential Dynamic Logic dL

Modularity and composability are essential properties to facilitate and scale the design of cyber-physical systems from the specification of hybrid, discrete and continuous, components. Modularity is essential to break down a system model into comprehensible and manageable component specifications. Composability is essential to design a system from component models while preserving their verified properties, expressed as assume-guarantee contracts. In this paper, we address the specification of hybrid system using Platzer's differential dynamic logic (dL). Our contribution is threefold: (1) We define a new composition operator in dL and prove that it is associative and commutative (AC). Prior notions of composition in dL were not associative. (2) We provide a theorem which characterizes necessary conditions to automate the proof that composed components satisfy the composition of their individual contracts, enabling modular and compositional verification. (3) We case-study our AC composition operator by considering the modular and detailed specification of a cruise controller in KeYmaeraX, the latest implementation of dL, to demonstrate the proof automation capability of our contribution and exemplify a compositional design methodology.