A parallel implementation for optimal lambda-calculus reduction

In this paper we present a parallel implementation of Lévy's optimal reduction for the λ-calculus [11]. In a similar approach to Lamping's one in [10], we base our work on a graph reduction technique known as directed virtual reduction [3] which is actually a restriction of Danos-Regnier virtual reduction [4]. The parallel implementation relies on a strategy for directed virtual reduction, namely half combustion, which we introduce in this paper. We embed in the implementation both a message aggregation technique, allowing a reduction of the communication overhead, and a fair policy for distributing dynamically originated load among processors. The aggregation technique is mandatory as the granularity of the computation is fine. Through this technique we obtain a linear speedup close to 80% of the ideal one on a shared memory multiprocessor. This result points out the viability of parallel implementations for optimal reduction.