Speculative parallel graph reduction for lambda calculus

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.