Speculative parallel graph reduction of lambda calculus to deferred substitution form

In a parallel graph reduction system, speculative evaluation can increase parallelism but waste machine resources by evaluating 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 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 copy operation. We propose a lambda form called DSF (Deferred Substitution Form) which substitution is deferred until a mandatory task will evaluate substitution. In a speculative task to DSF, since there is no substitution. It cannot grow the graph size and require copy operation. Therefore the overhead can be decreased when a expression reduced to DSF is eventually unnecessary. In addition we propose an evaluation model for DSF to increase the parallelism