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Automation for proof engineering: Machine-checked proofs at scale

Authors

Daniel Matichuk

Data61, CSIRO, Australia
UNSW, Australia

Abstract

Formal proofs, interactively developed and machine-checked, are a means to achieve the highest level of assurance in the correctness of software. In larger verification projects, with multi-year timelines and hundreds of thousands of lines of proof text, the emerging discipline of proof engineering plays a critical role in minimizing both the cost and effort of developing formal proofs. The work presented in this thesis targets the scalability challenges present in such projects. In a systematic analysis of several large software verification projects in the interactive proof assistant Isabelle, we demonstrate that in these projects, as the size of a formal specification increases, the required effort for its corresponding proof grows quadratically. Proof engineering encompasses both authoring proofs, and developing the necessary infrastructure to make those proofs tractable, scalable and robust against specification changes. Proof automation plays a key role here. However, in the context of Isabelle, many advanced features, such as developing custom automated reasoning procedures, are outside the standard repertoire of the majority of proof authors. To address this problem, we present Eisbach: an extension to Isabelle's formal proof document language Isar. Eisbach allows proof authors to write automated reasoning procedures, known as proof methods, at the familiar level of abstraction provided by Isar. Additionally, Eisbach is extensible through specialized methods that act as general language constructs, providing high-level access to advanced features of Isabelle, such as subgoal matching. We show how Eisbach provides a framework for extending Isar with more automation than was previously possible, by allowing proof methods to be treated as first-class language elements. Today, Eisbach is already used in many Isabelle proof developments. We further demonstrate its effectiveness by implementing several language extensions, together with a collection of proof methods for performing program refinement proofs. By applying these to proofs from the L4.verified project, the one of the largest formal proof projects in history, we show that effective use of Eisbach results in a reduction in the overall proof size and required effort for a given specification.

BibTeX Entry

  @phdthesis{Matichuk:phd,
    school           = {UNSW},
    title            = {Automation for Proof Engineering: Machine-Checked Proofs At Scale},
    author           = {Daniel Matichuk},
    month            = july,
    note             = {Available from publications page at \url{http://ts.data61.csiro.au/}},
    year             = {2018},
    typ              = {{PhD} thesis},
    address          = {Sydney, Australia}
  }

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