Control abstraction is the process by which programmers define new
control constructs, specifying a statement ordering separately from an
implementation of that ordering.  We argue that control abstraction can
and should play a central role in parallel programming.  Control
abstraction can be used to build new control constructs for the
expression of parallelism.  A control construct can have several
implementations, representing the varying degrees of parallelism to be
exploited on different architectures.  Control abstraction also reduces
the need for explicit synchronization, since it admits a precise
specification of control flow.  Using several examples, we illustrate
these benefits of control abstraction.  We also show that we can
efficiently implement a parallel programming language based on control
abstraction.  We conclude that the enormous benefits and reasonable
costs of control abstraction argue for its inclusion in explicitly
parallel programming languages.