An inductive approach to finding fixpoints in abstract interpretation

A new method for finding fixpoints in abstract interpretation, based on the technique of computational induction, is presented. This technique has the advantage that it allows elements of the fixpoint to be computed separately without restricting the size of abstract domains which can be handled. Since abstract interpretation typically only requires one or two elements of the fixpoint in order to test some property of a program, it is expected that in the general case this method will perform better than any of the other methods. The well known technique of strictness analysis is used to introduce abstract interpretation. Other techniques for finding fixpoints are briefly reviewed. It is first shown how to apply the method based on computational induction to strictness analysis, then the more general case is considered. Dealing with nested function applications and mutual recursion is demonstrated. Analyses involving higher-order functions are discussed briefly, and the overall correctness of the approach is examined. An example of an analysis featuring non-flat domains is presented.<>