Run-Time Analysis of Temporal Constrained Objects

The programming paradigm of constrained objects is a declarative variant of the object-oriented paradigm wherein objects define the structure of a system and declarative constraints (rather than imperative methods) define its behavior. Constrained objects have many uses in the engineering domain and computation in this paradigm is essentially constraint solving. This paper is concerned with an extension of constrained objects called temporal constrained objects, which are especially appropriate for modeling dynamical systems. The main extensions are series variables and metric temporal operators to declaratively specify time-varying behavior. The language TCOB exemplifies this paradigm and the execution of TCOB programs consists of constraint solving within a time-based simulation framework. One of the challenges in TCOB is identifying errors owing both to the complexity of programs and the underlying constraint solving methods. We address this problem by extracting a run-time trace of the execution of a TCOB program and providing an analysis of the cause of error. The run-time trace also serves as a basis, in many cases, for constructing a finite-state machine which in turn can be used for 'model-checking' properties of the system. The paper also presents abstraction techniques for dealing with simulations that result in large state spaces.