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The aim of static analysis is to infer invariants about programs that are precise enough to establish semantic properties, such as the absence of run-time errors. Broadly speaking, there are two major branches of static analysis for imperative programs. Pointer and shape analyses focus on inferring properties of pointers, dynamically-allocated memory, and recursive data structures, while numeric analyses seek to derive invariants on numeric values. Although simultaneous inference of shape-numeric invariants is often needed, this case is especially challenging and is not particularly well explored. Notably, simultaneous shape-numeric inference raises complex issues in the design of the static analyzer itself. In this paper, we study the construction of such shape-numeric, static analyzers. We set up an abstract interpretation framework that allows us to reason about simultaneous shape-numeric properties by combining shape and numeric abstractions into a modular, expressive abstract domain. Such a modular structure is highly desirable to make its formalization and implementation easier to do and get correct. To achieve this, we choose a concrete semantics that can be abstracted step-by-step, while preserving a high level of expressiveness. The structure of abstract operations (i.e., transfer, join, and comparison) follows the structure of this semantics. The advantage of this construction is to divide the analyzer in modules and functors that implement abstractions of distinct features.

Abstract   Astrée was the first static analyzer able to prove automatically the total absence of runtime errors of actual industrial programs of hundreds of thousand lines. What makes Astrée such an innovative tool is its scalability, while retaining the required precision, when it is used to analyze a specific class of programs: that of reactive control-command software. In this paper, we discuss the important choice of algorithms and data-structures we made to achieve this goal. However, what really made this task possible was the ability to also take semantic decisions, without compromising soundness, thanks to the abstract interpretation framework. We discuss the way the precision of the semantics was tuned in Astrée in order to scale up, the differences with some more academic approaches and some of the dead-ends we explored. In particular, we show a development process which was not specific to the particular usage Astrée was built for, hoping that it might prove helpful in building other scalable static analyzers. [ABSTRACT FROM AUTHOR]