Automatic Modular Abstractions for Template Numerical Constraints

The authors propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and containing linear assignments and tests. Given the specification of an abstract domain, and a program block, the method automatically outputs an implementation of the corresponding abstract transformer. It is thus a form of program transformation. In addition to loop-free code, the same method also applies for obtaining least fixed points as functions of the precondition, which permits the analysis of loops and recursive functions.