PELCR: Parallel environment for optimal lambda-calculus reduction

: In this article we present the implementation of an environment supporting Levy's optimal reduction for the X-calculus on parallel (or distributed) computing systems. In a similar approach to Lamping's, we base our work on a graph reduction technique, known as directed virtual reduction, which is actually a restriction of Danos-Regnier virtual reduction. The environment, which we refer to as PELCR (parallel environment for optimal lambdacalculus reduction), relies on a strategy for directed virtual reduction, namely half combustion. While developing PELCR we adopted both a message aggregation technique, allowing reduction of the communication overhead, and a fair policy for distributing dynamically originated load among processors. We also present an experimental study demonstrating the ability of PELCR to definitely exploit the parallelism intrinsic to lambda-terms while performing the reduction. We show how PELCR allows achieving up to 70-80% of the ideal speedup on last generation multiprocessor computing systems. As a last note, the software modules have been developed with. the C language and using a standard interface for message passing, that is, MPI, thus making PELCR itself a highly portable software package.