A Calculus for Exploiting Data Parallelism on Recursively De ned Data ( Preliminary Report ) ?

Array based data parallel programming can be generalized in two ways to make it an appropriate paradigm for parallel processing of general recursively de ned data. The rst is the introduction of a parallel evaluation mechanism for dynamically allocated recursively dened data. It achieves the e ect of applying the same function to all the subterms of a given datum in parallel. The second is a new notion of recursion, which we call parallel recursion, for parallel evaluation of recursively de ned data. In contrast with ordinary recursion, which only uses the nal results of the recursive calls of its immediate subterms, the new recursion repeatedly transforms a recursive datum represented by a system of equations to another recursive datum by applying the same function to each of the equation simultaneously, until the nal result is obtained. This mechanism exploits more parallelism and achieves signi cant speedup compared to the conventional parallel evaluation of recursive functions. Based on these observations, we propose a typed lambda calculus for data parallel programming and give an operational semantics that integrates the parallel evaluation mechanism and the new form of recursion in the semantic core of a typed lambda calculus. We also describe an implementation method for massively parallel multicomputers, which makes it possible to execute parallel recursion in the expected performance.