Array Structures and Data-Parallel Algorithms

We integrate the semantics of higher-order functional programs with a notion of explicit static processes as used in BSP and PRAM algorithms. The result is the construction of a cartesian closed category (CCC), a model for typed functional languages. Concrete data structures (CDS) yield many useful CCC and Brookes and Geva have generalised (gCDS) and used them as domains of a CCC whose arrows are asynchronous but deterministic parallel algorithms. We specialise their construction to explicit static processes by showing that data-parallel algorithms (distributed Brookes-Geva algorithms) between array structures (distributed gCDS) are themselves array structures. This model brings notions of data locality, synchronisation and higher-order functions in a uniied denotational framework.