Priority Inheritance Protocol Proved Correct

In real-time systems with threads, resource locking and priority scheduling, one faces the problem of Priority Inversion. This problem can make the behaviour of threads unpredictable and the resulting bugs can be hard to find. The Priority Inheritance Protocol is one solution implemented in many systems for solving this problem, but the correctness of this solution has never been formally verified in a theorem prover. As already pointed out in the literature, the original informal investigation of the Property Inheritance Protocol presents a correctness “proof” for an incorrect algorithm. In this paper we fix the problem of this proof by making all notions precise and implementing a variant of a solution proposed earlier. Our formalisation in Isabelle/HOL uncovers facts not mentioned in the literature, but also shows how to efficiently implement this protocol. Earlier correct implementations were criticised as too inefficient. Our formalisation is based on Paulson’s inductive approach to verifying protocols.