Abstract In data-parallel programming, operations are performed simultaneously on all elements of large data structures. Backus′s FP functional language promotes this view. FP provides a large set of data rearrangement primitives, and a useful set of functional combining forms that are applied to entire data structures. We describe an FP compiler that generates programs capable of exploiting data-parallelism. The FP compiler deduces the type and shape of objects through type inference, and generates efficient parallel implementations of combining forms. In addition, the compiler determines the effects of data rearrangement functions at compile-time, thereby avoiding creation of large intermediate data structures, and reducing interprocessor communication overhead. FP and its compiler are formally specified, reducing ambiguity concerning constructs of the language and results of the compiler. Performance and speed-ups achieved from our compilation and optimization techniques are demonstrated with timings from a prototype implementation on the Connection Machine CM-2.