Speculative parallel graph reduction for lambda calculus

Yong-Hack Lee, Suh-Hyun Cheon
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Abstract

In a parallel graph reduction system, speculative evaluation can increase parallelism but waste machine resources by evaluating an expression which may eventually be discarded. When a speculative task reduces a lambda expression to WHNF (weak head normal form), substitution can lead to unbounded growth of the graph size and require a copy operation. This speculative task may be unnecessary. In that case the performance is affected by the overheads to terminate all tasks to be propagated from a speculative task and to refresh the memory cells to be allocated for the copy operation. We propose a lambda form called DSF (deferred substitution form) in which substitution is deferred until a mandatory task evaluates the substitution. In a speculative task to the DSF, since there is no substitution, it cannot grow the graph size and require a copy operation. Therefore the overhead can be decreased when a expression reduced to the DSF is eventually unnecessary. In addition we propose an evaluation model for the DSF to increase the parallelism.
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λ演算的推测并行图约简
在并行图约简系统中,推测性求值可以增加并行性,但由于求值的表达式最终可能被丢弃,从而浪费了机器资源。当推测任务将lambda表达式缩减为WHNF(弱头范式)时,替换可能导致图大小无限增长,并需要复制操作。这种推测的任务可能是不必要的。在这种情况下,终止从推测任务传播的所有任务和刷新为复制操作分配的内存单元的开销会影响性能。我们提出了一种称为DSF(延迟替换形式)的lambda形式,其中替换被延迟到强制任务评估替换。在对DSF的推测任务中,由于没有替换,它不能增加图的大小并需要复制操作。因此,当最终不需要简化为DSF的表达式时,可以减少开销。此外,我们还提出了DSF的评估模型,以提高并行性。
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