  Linearisability has become the standard correctness criterion for concurrent
data structures, ensuring that every history of invocations and responses of
concurrent operations has a matching sequential history. Existing proofs of
linearisability require one to identify so-called linearisation points within
the operations under consideration, which are atomic statements whose execution
causes the effect of an operation to be felt. However, identification of
linearisation points is a non-trivial task, requiring a high degree of
expertise. For sophisticated algorithms such as Heller et al's lazy set, it
even is possible for an operation to be linearised by the concurrent execution
of a statement outside the operation being verified. This paper proposes an
alternative method for verifying linearisability that does not require
identification of linearisation points. Instead, using an interval-based logic,
we show that every behaviour of each concrete operation over any interval is a
possible behaviour of a corresponding abstraction that executes with
coarse-grained atomicity. This approach is applied to Heller et al's lazy set
to show that verification of linearisability is possible without having to
consider linearisation points within the program code.
