A Systematic Approach to Abstract Interpretation of Program Transformations

Keidel, Sven; Erdweg, Sebastian

doi:10.1007/978-3-030-39322-9_7

Cited by 2 publications

(1 citation statement)

References 23 publications

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“…Recently, Keidel and Erdweg [34] have developed a framework, Sturdy, that allows modularly constructing abstract interpreters for program transformations. Sturdy separates the concerns of interpreting a program transformation language from the choice of abstract domains.…”

Section: Related Workmentioning

confidence: 99%

Verification of Program Transformations with Inductive Refinement Types

Al-Sibahi

Jensen

Dimovski

et al. 2021

ACM Trans. Softw. Eng. Methodol.

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High-level transformation languages like Rascal include expressive features for manipulating large abstract syntax trees: first-class traversals, expressive pattern matching, backtracking, and generalized iterators. We present the design and implementation of an abstract interpretation tool, Rabit, for verifying inductive type and shape properties for transformations written in such languages. We describe how to perform abstract interpretation based on operational semantics, specifically focusing on the challenges arising when analyzing the expressive traversals and pattern matching. Finally, we evaluate Rabit on a series of transformations (normalization, desugaring, refactoring, code generators, type inference, etc.) showing that we can effectively verify stated properties.

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Section: Related Workmentioning

confidence: 99%

Verification of Program Transformations with Inductive Refinement Types

Al-Sibahi

Jensen

Dimovski

et al. 2021

ACM Trans. Softw. Eng. Methodol.

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Combinator-Based Fixpoint Algorithms for Big-Step Abstract Interpreters

Keidel,

Erdweg,

Hombücher

2023

Proc. ACM Program. Lang.

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Big-step abstract interpreters are an approach to build static analyzers based on big-step interpretation. While big-step interpretation provides a number of benefits for the definition of an analysis, it also requires particularly complicated fixpoint algorithms because the analysis definition is a recursive function whose termination is uncertain. This is in contrast to other analysis approaches, such as small-step reduction, abstract machines, or graph reachability, where the analysis essentially forms a finite transition system between widened analysis states. We show how to systematically develop sophisticated fixpoint algorithms for big-step abstract interpreters and how to ensure their soundness. Our approach is based on small and reusable fixpoint combinators that can be composed to yield fixpoint algorithms. For example, these combinators describe the order in which the program is analyzed, how deep recursive functions are unfolded and loops unrolled, or they record auxiliary data such as a (context-sensitive) call graph. Importantly, each combinator can be developed separately, reused across analyses, and can be verified sound independently. Consequently, analysis developers can freely compose combinators to obtain sound fixpoint algorithms that work best for their use case. We provide a formal metatheory that guarantees a fixpoint algorithm is sound if its composed from sound combinators only. We experimentally validate our combinator-based approach by describing sophisticated fixpoint algorithms for analyses of Stratego, Scheme, and WebAssembly.

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A Systematic Approach to Abstract Interpretation of Program Transformations

Cited by 2 publications

References 23 publications

Verification of Program Transformations with Inductive Refinement Types

Verification of Program Transformations with Inductive Refinement Types

Combinator-Based Fixpoint Algorithms for Big-Step Abstract Interpreters

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