  Synchronisation classes are an important building block for shared memory
concurrent programs. Thus to reason about such programs, it is important to be
able to verify the implementation of these synchronisation classes, considering
atomic operations as the synchronisation primitives on which the
implementations are built. For synchronisation classes controlling exclusive
access to a shared resource, such as locks, a technique has been proposed to
reason about their behaviour. This paper proposes a technique to verify
implementations of both exclusive access and shared-reading synchronisers. We
use permission-based Separation Logic to describe the behaviour of the main
atomic operations, and the basis for our technique is formed by a specification
for class AtomicInteger, which is commonly used to implement synchronisation
classes in java.util.concurrent. To demonstrate the applicability of our
approach, we mechanically verify the implementation of various synchronisation
classes like Semaphore, CountDownLatch and Lock.
