Computing Termination Conditions of Iterative Programs

It is common to use invariant assertions to analyze functional properties of loops (such as partial correctness) and to use variant functions to analyze operational properties of loops (such as termination). In this paper, we explore an orthogonal approach, based on invariant relations, which enables us to reason about functional properties as well as termination in a uniform manner; also, our definition of termination encompasses not only the property that the loop executes a finite number of iterations, but also the property that every single iteration of the loop executes without raising an exception and/or causing an abort. We present a general theorem that provides a necessary condition of termination (in the sense of having a finite number of iterations, and in the sense of avoiding aborts), and discuss under what circumstances the given condition can be deemed sufficient, in addition to being provably necessary.