Graphical models of separation logic

In this paper, we present a trace semantics based on graphs: nodes represent the events of a program’s execution, and edges represent dependencies among the events. The style is reminiscent of partially ordered models [Pra84, Win86], though we do not generally require properties like transitivity or acyclicity. Concurrency and sequentiality are defined using variations on separating conjunctions: whereas the conjunction in the original separation logic partitions addresses in a heap [ORY01, Rey02], the conjunctions here partition events in a trace. The model has pleasant algebraic properties, which are shown with surprisingly simple proofs. We present a number of theorems about the generic model, including the soundness of the laws of Hoare logic [Hoa69] and the Jones rely/guarantee calculus [Jon81]. No particular languages or applications are studied in the paper; we leave this to future work.