Abstract interpretation is a technique for developing static analyses. Yet, proving abstract interpreters sound is challenging for interesting analyses, because of the high proof complexity and proof effort . To reduce complexity and effort, we propose a framework for abstract interpreters that makes their soundness proof compositional. Key to our approach is to capture the similarities between concrete and abstract interpreters in a single shared interpreter, parameterized over an arrow-based interface. In our framework, a soundness proof is reduced to proving reusable soundness lemmas over the concrete and abstract instances of this interface; the soundness of the overall interpreters follows from a generic theorem. To further reduce proof effort, we explore the relationship between soundness and parametricity. Parametricity not only provides us with useful guidelines for how to design non-leaky interfaces for shared interpreters, but also provides us soundness of shared pure functions as free theorems . We implemented our framework in Haskell and developed a k -CFA analysis for PCF and a tree-shape analysis for Stratego. We were able to prove both analyses sound compositionally with manageable complexity and effort, compared to a conventional soundness proof.

@article{paperbot272,
  title = {Compositional soundness proofs of abstract interpreters},
  author = {Sven Keidel and Casper Bach Poulsen and Sebastian Erdweg},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {2},
  number = {ICFP},
  year = {2018},
  doi = {10.1145/3236767}
}