A Certified Decision Procedure for Sophisticated Fractional Permissions

We develop a certified decision procedure for reasoning about systems of equations over the “tree share” fractional permission model of Dockins et al. Fractional permissions are used to track and reason about shared ownership of resources between multiple parties, e.g. in a concurrent program. We show how to extend the theory over systems of equations of tree shares to handle both positive and negative clauses using a new proof technique we dub “separate, cut and glue”. In addition to being certified, our new procedure enjoys better performance than previous work and incorporates a better treatment nonzero variables.