  Linearizability is a commonly accepted notion of correctness for libraries of
concurrent algorithms. Unfortunately, it assumes a complete isolation between a
library and its client, with interactions limited to passing values of a given
data type. This is inappropriate for common programming languages, where
libraries and their clients can communicate via the heap, transferring the
ownership of data structures, and can even run in a shared address space
without any memory protection. In this paper, we present the first definition
of linearizability that lifts this limitation and establish an Abstraction
Theorem: while proving a property of a client of a concurrent library, we can
soundly replace the library by its abstract implementation related to the
original one by our generalisation of linearizability. This allows abstracting
from the details of the library implementation while reasoning about the
client. We also prove that linearizability with ownership transfer can be
derived from the classical one if the library does not access some of data
structures transferred to it by the client.
