Approximate Fixed Points in Abstract Interpretation

Much of the earlier development of abstract interpretation, and its application to imperative programming languages, has concerned techniques for finding fixed points in large (often infinite) lattices. The standard approach in the abstract interpretation of functional languages has been to work with small, finite lattices and this supposedly circumvents the need for such techniques. However, practical experience has shown that, in the presence of higher order functions, the lattices soon become too large (although still finite) for the fixed-point finding problem to be tractable. This paper develops some approximation techniques which were first proposed by Hunt and shows how these techniques relate to the earlier use of widening and narrowing operations by the Cousots.