Automating Abstract Interpretation of Abstract Machines

TL;DR

This paper introduces a systematic and automatable method for creating efficient, correct, and analyzable abstract interpreters from traditional interpreters using Abstracting Abstract Machines, improving static analysis for scripting languages.

Contribution

It presents a novel systematic approach to derive abstract interpreters from interpreters, including a meta-language and proof techniques for correctness, with significant performance improvements.

Findings

Abstract interpreters can be generated systematically from interpreters.

Mathematical modifications lead to 1000x faster analysis.

Proof techniques ensure correctness of abstract models.

Abstract

Static program analysis is a valuable tool for any programming language that people write programs in. The prevalence of scripting languages in the world suggests programming language interpreters are relatively easy to write. Users of these languages lament their inability to analyze their code, therefore programming language analyzers are not easy to write. This thesis investigates a systematic method of creating abstract interpreters from traditional interpreters, called Abstracting Abstract Machines. Abstract interpreters are difficult to develop due to technical, theoretical, and pragmatic problems. Technical problems include engineering data structures and algorithms. I show that modest and simple changes to the mathematical presentation of abstract machines result in 1000 times better running time - just seconds for moderately sized programs. In the theoretical realm, abstraction can make correctness difficult to ascertain. I provide proof techniques for proving the correctness of regular, pushdown, and stack-inspecting pushdown models of abstract computation by leaving computational power to an external factor: allocation. Even if we don't trust the proof, we can run models concretely against test suites to better trust them. In the pragmatic realm, I show that the systematic process of abstracting abstract machines is automatable. I develop a meta-language for expressing abstract machines similar to other semantics engineering languages. The language's special feature is that it provides an interface to abstract allocation. The semantics guarantees that if allocation is finite, then the semantics is a sound and computable approximation of the concrete semantics.