Real-world data structures are often enhanced with additional pointers capturing alternative paths through a basic inductive skeleton (e.g., back pointers, head pointers). From the static analysis point of view, we must obtain several interlocking shape invariants. At the same time, it is well understood in abstract interpretation design that supporting a separation of concerns is critically important to designing powerful static analyses. Such a separation of concerns is often obtained via a reduced product on a case-by-case basis. In this paper, we lift this idea to abstract domains for shape analyses, introducing a domain combination operator for memory abstractions. As an example, we present simultaneous separating shape graphs, a product construction that combines instances of separation logic-based shape domains. The key enabler for this construction is a static analysis on inductive data structure definitions to derive relations between the skeleton and the alternative paths. From the engineering standpoint, this construction allows each component to reason independently about different aspects of the data structure invariant and then separately exchange information via a reduction operator. From the usability standpoint, we enable describing a data structure invariant in terms of several inductive definitions that hold simultaneously.

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Abstract. The breadth and depth of heap properties that can be inferred by the union of today's shape analyses is quite astounding. Yet, achieving scalability while supporting a wide range of complex data structures in a generic way remains a long-standing challenge. In this paper, we propose a way to side-step this issue by defining a generic abstract domain combinator for combining memory abstractions on disjoint regions. In essence, our abstract domain construction is to the separating conjunction in separation logic as the reduced product construction is to classical, non-separating conjunction. This approach eases the design of the analysis as memory abstract domains can be re-used by applying our separating conjunction domain combinator. And more importantly, this combinator enables an analysis designer to easily create a combined domain that applies computationally-expensive abstract domains only where it is required.

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