Automatic Modular Abstractions for Linear Constraints

TL;DR

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

Contribution

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

Findings

Automates the creation of abstract transformers for linear constraints.

Handles loops and recursive functions through fixed point computation.

Applicable to multiple programming paradigms including data-flow, imperative, and functional.

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.