Memory Management: An Abstract Formulation of Incremental Tracing

We present an abstract model of computer memory, in the form of directed, labeled graphs with simple transitions corresponding to valid memory operations. We also introduce a refinement of this basic model of memory that incorporates features of memory management. After giving some examples of how this refined model captures various incremental tracing algorithms, we investigate properties of the two representations and show that they are behaviorally equivalent. The proofs have been formally verified in the proof assistant Coq.