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Generalized Program Sketching by Abstract Interpretation and Logical Abduction

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Static Analysis (SAS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14284))

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Abstract

This paper presents a new approach for synthesizing missing parts from imperative programs by using abstract interpretation and logical abduction. Given a partial program with missing arbitrary expressions, our approach synthesizes concrete expressions that are strong enough to prove the assertions in the given program. Furthermore, the synthesized elements by our approach are the simplest and the weakest among all possible that guarantee the validity of assertions. In particular, we use a combination of forward and backward numerical analyses based on abstract interpretation to generate constraints that are solved by using the logical abduction technique.

We have implemented our approach in a prototype synthesis tool for C programs, and we show that the proposed approach is able to successfully synthesize arithmetic and boolean expressions for various C programs.

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Notes

  1. 1.

    This condition guarantees that the assertion is valid for any non-deterministic choice [2, 3]. If we have used an over-approximating backward analysis, it would infer the necessary condition \((\texttt {z+3>y})\) that may lead to the assertion satisfaction for some non-deterministic choices of [2, 3] (e.g., the execution where the non-deterministic choice [2, 3] returns 3).

  2. 2.

    A solution is simplest if it contains the fewest number of variables.

  3. 3.

    Concretization-based abstraction is a relaxation of the known Galois connection, which uses only a concretization function \(\gamma _{\mathbb {D}}\) (e.g. Polyhedra domain).

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Authors and Affiliations

  1. Mother Teresa University, st. Mirche Acev nr. 4, 1000, Skopje, North Macedonia

    Aleksandar S. Dimovski

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  1. Aleksandar S. Dimovski
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Correspondence to Aleksandar S. Dimovski .

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  1. U. Politécnica de Madrid (UPM) and IMDEA Software Institute, Pozuelo de Alarcón, Madrid, Spain

    Manuel V. Hermenegildo

  2. U. Politécnica de Madrid (UPM) and IMDEA Software Institute, Pozuelo de Alarcon, Spain

    José F. Morales

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Dimovski, A.S. (2023). Generalized Program Sketching by Abstract Interpretation and Logical Abduction. In: Hermenegildo, M.V., Morales, J.F. (eds) Static Analysis. SAS 2023. Lecture Notes in Computer Science, vol 14284. Springer, Cham. https://doi.org/10.1007/978-3-031-44245-2_11

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  • DOI: https://doi.org/10.1007/978-3-031-44245-2_11

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