The Relationship between Separation Logic and Implicit Dynamic Frames

Separation logic is a concise method for specifying programs that manipulatedynamically allocated storage. Partially inspired by separation logic, Implicit DynamicFrames 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 syntaxsubsumes both that of a standard separation logic, and that of implicit dynamic framesas sub-syntaxes. We define a total heap semantics for our logic, and, for the separationlogic subsyntax, prove it equivalent the standard partial heaps model. In order to definea semantics which works uniformly for both subsyntaxes, we define the novel concept ofa minimal state extension, which provides a different (but equivalent) definition of thesemantics of separation logic implication and magic wand connectives, while also givinga suitable semantics for these connectives in implicit dynamic frames. We show that ourresulting semantics agrees with the existing definition of weakest pre-condition semanticsfor the implicit dynamic frames fragment. Finally, we show that we can encode the sep-aration logic fragment of our logic into the implicit dynamic frames fragment, preservingsemantics. For the connectives typically supported by tools, this shows that separationlogic can be faithfully encoded in a first-order automatic verification tool (Chalice).