We describe a compilation system for the concurrent programming language Program Composition Notation (PCN). This notation provides a single-assignment programming model that permits concurrent-programming concerns such as decomposition, communication, synchronization, mapping, granularity, and load balancing to be addressed separately in a design. PCN is also extensible with programmer-defined operators , allowing common abstractions to be encapsulated and reused in different contexts. The compilation system incorporates a concurrent-transformation system that allows abstractions to be defined through concurrent source-to-source transformations; these convert programmer-defined operators into a core notation. Run-time techniques allow the core notation to be compiled into a simple concurrent abstract machine which can be implemented in a portable fashion using a run-time library. The abstract machine provides a uniform treatment of single-assignment and mutable data structures, allowing data sharing between concurrent and sequential program segments and permitting integration of sequential C and Fortran code into concurrent programs. This compilation system forms part of a program development toolkit that operates on a wide variety of networked workstations, multicomputers, and shared-memory multiprocessors. The toolkit has been used both to develop substantial applications and to teach introductory concurrent-programming classes, including a freshman course at Caltech.