This report describes Nesl, a strongly-typed, applicative, data-parallel language. Nesl is intended to be used as a portable interface for programming a variety of parallel and vector supercomputers, and as a basis for teaching parallel algorithms. Parallelism is supplied through a simple set of data-parallel constructs based on vectors, including a mechanism for applying any function over the elements of a vector in parallel, and a broad set of parallel functions that manipulate vectors. Nesl fully supports nested vectors and nested parallelism---the ability to take a parallel function and then apply it over multiple instances in parallel. Nested parallelism is important for implementing algorithms with complex and dynamically changing data structures, such as required in many graph or sparse matrix algorithms. Nesl also provides a mechanism for calculating the asymptotic running time for a program on various parallel machine models, including the parallel random access machine (PRAM...