Declarative semantics of the hybrid constraint language HydLa

Hybrid systems are dynamical systems with continuous evolution of states and discrete evolution of states and governing equations. We have worked on the design and implementation of HydLa, a constraint-based modeling language for hybrid systems, with a view to the proper handling of uncertanties and the integration of simulation and verification. HydLa's constraint hierarchies facilitate the description of constraints with adequate strength, but its semantical foundations are not obvious due to the interaction of various language constructs. This paper gives the declarative semantics of HydLa and discusses its properties and consequences by means of examples.