Tasks in modular proofs of concurrent algorithms

Abstract

Proving the correctness of distributed or concurrent algorithms is a complex process. Errors in the reasoning are hard to find, calling for computer-checked proof systems like Coq or TLA+. To use these tools, sequential specifications of base objects are required to build modular proofs by composition. Unfortunately, many concurrent objects lack a sequential specification. This article describes a method to transform any task, a specification of a concurrent one-shot distributed problem, into a sequential specification involving two calls, set and get. This enables designers to compose proofs, facilitating modular computer-checked proofs of algorithms built using tasks and sequential objects as building blocks. Moir & Anderson implementation of renaming using splitters, wait-free concurrent objects, is an algorithm designed by composition, but it is not modular. Using our transformation, a modular description of the algorithm is given in TLA+ and mechanically verified using the TLA+ Proof System. As far as we know, this is the first time this algorithm is mechanically verified.