A Higher-Order Duration Calculus and Its Completeness

This paper studies how to describe the real-time behaviour of programs using Duration Calculus. Since program variables are interpreted as functions over time in real-time programming, and it is inevitable to introduce quantifications over program variables in order to describe local variable declaration and declare local channel and so on, therefore, to establish a higher-order duration calculus (HDC) is necessary. We firstly establish HDC, then show some real-time properties of programs in terms of HDC, and lastly, prove that HDC is complete on abstract domains under the assumption that all program variables vary finitely in the paper.