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International School on Formal Methods for the Design of Computer, Communication and Software Systems

SFM 2015: Formal Methods for Multicore Programming pp 179–210Cite as

Refined Ownership:

Fine-Grained Controlled Internal Sharing

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9104))

Abstract

Ownership type systems give a strong notion of separation between aggregates. Objects belonging to different owners cannot be aliased, and thus a mutating operation internal to one object is guaranteed to be invisible to another. This naturally facilitates reasoning about correctness on a local scale, but also proves beneficial for coarse-grained parallelism as noninterference between statements touching differentobjects is easily established. For fine-grained parallelism, ownership types fall short as owner-based disjointness only allows separation of the innards of different aggregates, which is very coarse-grained. Concretely: ownership types can reason about the disjointness of two different data structures, but cannot reason about the internal structure or disjointness within the data structure, without resorting to static and overly constraining measures. For similar reasons, ownership fails to determine internal disjointness of external pointers to objects that share a common owner.

In this paper, we introduce the novel notion of refined ownership which overcomes these limitations by allowing precise local reasoning about a group of objects even though they belong to the same external owner. Using refined ownership, we can statically check determinism of parallel operations on tree-shaped substructures of a data structure, including operations on values external to the structure, without imposing any non-local alias restrictions.

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Notes

  1. 1.

    We would like to note that there’s risk of confusion as to which tree is focused on when focusing on an owner that is used multiple times in a type. The solution is simple and just requires that the programmer is explicit about which parameter is meant, however we leave this out in the examples and the formalism because it does not add to the story.

  2. 2.

    The formalism notably uses explicit destructive reads and unique pointers for simplicity, but these can be inferred in the actual language implementation. See however anecdotal evidence by Gordon et al. [20] that programmers appreciate explicit operations on uniques.

  3. 3.

    This is called the movement bound and investigated further in [11]. It is required for soundness of ownership transfer, but otherwise of little relevance for refined ownership.

  4. 4.

    In addition to disjoint effects, two async blocks in the same finish must not update the same variable—a trivial compile-time analysis.

  5. 5.

    The tree rooted in last in Fig. 7 notably stops immediately after its first object. To create trees which overlap in “interesting ways,” e.g., a doubly-linked lists additional machinery is needed, e.g., a “splitting operator” that allows introduction of multiple aliases to a value which are bound to different trees. We do not yet have a convincing simple extension for this, and refer to future work.

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Authors and Affiliations

  1. Uppsala University, Uppsala, Sweden

    Elias Castegren, Johan Östlund & Tobias Wrigstad

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  1. Elias Castegren
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  2. Johan Östlund
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  3. Tobias Wrigstad
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Correspondence to Johan Östlund .

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  1. Università di Urbino "Carlo Bo", Urbino, Italy

    Marco Bernardo

  2. University of Oslo, Oslo, Norway

    Einar Broch Johnsen

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Castegren, E., Östlund, J., Wrigstad, T. (2015). Refined Ownership:. In: Bernardo, M., Johnsen, E. (eds) Formal Methods for Multicore Programming. SFM 2015. Lecture Notes in Computer Science(), vol 9104. Springer, Cham. https://doi.org/10.1007/978-3-319-18941-3_5

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  • DOI: https://doi.org/10.1007/978-3-319-18941-3_5

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