Modeling Systems in CLP with Coinductive Tabling

We present a methodology for the modelling of complex program behavior in CLP. The first part of this paper is an informal description about how to represent a system in CLP. At its basic level, this representation captures the precise trace semantics of concurrent programs, or even high-level specifications, in the form of a predicate transformer. Based on traces, the method can also capture properties of the underlying runtime system such as the scheduler and the microarchitecture, so as to provide a foundation for reasoning about resources such as time and space. The second part of this paper presents a formal and compositional proof method for reasoning about safety properties of the underlying system. The idea is that a safety property is simply a CLP goal, and is proof established by executing the goal by a CLP interpreter. However, a traditional CLP interpreter does not suffice. We thus introduce a technique of coinductive tabling to CLP. Essentially, this extends CLP so that it can inductively use proof obligations that are assumed but not yet proven, and it can generate new proof obligations assertions dynamically.