Interpretation versus Demand Propagation Wadler [1987] uses abstract interpretation over a four-point domain for reasoning about strictness on lists. The four points correspond to undefined list (represented by value 0), infinite lists and lists with some tail undefined (value 1), lists with at least one head undefined (value 2), and all lists (value 3). Burn's work [Burn 1987] on evaluation transformers also uses abstract interpretation on the above-mentioned domain for strictness analysis. He defines four evaluators that correspond to the four points mentioned above in the sense that the ith evaluator will fail to produce an answer when given a list with the abstract value i \Gamma 1.

Equals is a system for parallel evaluation of lazy functional programs implemented on a Sequent Symmetry. A preliminary implementation of equals [4] was used to establish the validity of Normal Form (NF) demand propagation and memory reclamation via reference counting. However, that implementation did not exploit vertical parallelism, where the arguments to a function can be evaluated in parallel with the function itself. The overheads of vertical parallelism can be as high as the overheads in systems that do not propagate NF demand. Hence careful integration of vertical parallelism with horizontal parallelism (parallelism among the arguments to a function) is needed to fully benefit from NF-demand propagation. In this paper we describe schemes to harness vertical parallelism within the context of the current equals system. We identify the aspects of the runtime system (task management) that affect the overall efficiency of the combined system. We also provide preliminary performance figures indicating the effectiveness of the selected schemes.