Automatic modular abstractions for template numerical constraints

TL;DR

This paper introduces a novel method for automatically generating abstract transformers for static analysis of programs with linear constraints, applicable to loops, recursive functions, and various programming paradigms.

Contribution

It presents new quantifier elimination and symbolic manipulation techniques to automatically produce abstract transformers from domain specifications and program blocks.

Findings

Automatically generates abstract transformers for linear constraints.

Applies to loop-free code, loops, and recursive functions.

Utilizes new quantifier elimination techniques.

Abstract

We 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. 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. Our algorithms are based on new quantifier elimination and symbolic manipulation techniques. Given the specification of an abstract domain, and a program block, our method automatically outputs an implementation of the corresponding abstract transformer. It is thus a form of program transformation. The motivation of our work is data-flow synchronous programming languages, used for building control-command embedded systems, but it also applies to imperative and functional programming.