Matthew J. Parkinson ; Alexander J. Summers - The Relationship Between Separation Logic and Implicit Dynamic Frames

lmcs:802 - Logical Methods in Computer Science, July 31, 2012, Volume 8, Issue 3 -
The Relationship Between Separation Logic and Implicit Dynamic FramesArticle

Authors: Matthew J. Parkinson ; Alexander J. Summers

    Separation logic is a concise method for specifying programs that manipulate dynamically allocated storage. Partially inspired by separation logic, Implicit Dynamic Frames has recently been proposed, aiming at first-order tool support. In this paper, we precisely connect the semantics of these two logics. We define a logic whose syntax subsumes both that of a standard separation logic, and that of implicit dynamic frames as sub-syntaxes. We define a total heap semantics for our logic, and, for the separation logic subsyntax, prove it equivalent the standard partial heaps model. In order to define a semantics which works uniformly for both subsyntaxes, we define the novel concept of a minimal state extension, which provides a different (but equivalent) definition of the semantics of separation logic implication and magic wand connectives, while also giving a suitable semantics for these connectives in implicit dynamic frames. We show that our resulting semantics agrees with the existing definition of weakest pre-condition semantics for the implicit dynamic frames fragment. Finally, we show that we can encode the separation logic fragment of our logic into the implicit dynamic frames fragment, preserving semantics. For the connectives typically supported by tools, this shows that separation logic can be faithfully encoded in a first-order automatic verification tool (Chalice).

    Volume: Volume 8, Issue 3
    Published on: July 31, 2012
    Imported on: October 20, 2011
    Keywords: Computer Science - Programming Languages,Computer Science - Logic in Computer Science,F.3.1

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