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We propose a method for automatically generating abstract transformers forstatic analysis by abstract interpretation. The method focuses on linearconstraints on programs operating on rational, real or floating-point variablesand containing linear assignments and tests. In addition to loop-free code, thesame method also applies for obtaining least fixed points as functions of theprecondition, which permits the analysis of loops and recursive functions. Ouralgorithms are based on new quantifier elimination and symbolic manipulationtechniques. Given the specification of an abstract domain, and a program block,our method automatically outputs an implementation of the correspondingabstract transformer. It is thus a form of program transformation. Themotivation of our work is data-flow synchronous programming languages, used forbuilding control-command embedded systems, but it also applies to imperativeand functional programming.

Automatic Modular Abstractions for Linear Constraints