A Certified Decision Procedure for Tree Shares

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 can reason about shared ownership of resources, e.g. in a concurrent program. We imported our certified procedure into the HIP/SLEEK verification system and found bugs in both the previous, uncertified, decision procedure and HIP/SLEEK itself. In addition to being certified, our new procedure improves previous work by correctly handling negative clauses and enjoys better performance.