Verification of unit and dimensional consistencies in polychronous specifications

Cyber physical systems are characterized by continuous interaction between digital control systems and physical systems. To design critical control software that is to be used in control systems, a modeldriven correct-by-construction approach is preferable. Modeling languages based on synchronous model of time – such as Simulink, State Chart, Esterel, Lustre etc., are often used for sequential software synthesis and languages with a polychronous timing model such as Signal, MRICDF (Multi-Rate Instantaneous Channel-connected Data Flow) etc., are often used for concurrent software synthesis. The interfaces of such software to the real world are through digital signals that are often sampled quantities of physical entities – such as velocity, acceleration, pressure etc. Standard type systems available in programming or modeling languages assign traditional data types such as float, real etc., to these signals. Modelers might mistakenly connect two signals with the same traditional data types but representing different physical entities leading to critical bugs in the synthesized software. Early detection of such mistakes require enhanced type system and type checking algorithms. In this work, we attempt to extend the type system of the polychronous modeling language MRICDF and propose type inference techniques that consider the physical dimensions and units of the signals along with the data types. We also propose an SMT (Satisfiability Modulo Theories) based verification approach that verifies type consistency and provides invariants under which the type consistency is upheld.