An operational semantics for parallel lazy evaluation

Abstract

We present an operational semantics for parallel lazy evaluation that accurately models the parallel behaviour of the non-strict parallel functional language GpH. Parallelism is modelled synchronously, that is, single reductions are carried out separately then combined before proceeding to the next set of reductions. Consequently the semantics has two levels, with transition rules for individual threads at one level and combining rules at the other. Each parallel thread is modelled by a binding labelled with an indication of its activity status. To the best of our knowledge this is the first semantics that models such thread states. A set of labelled bindings corresponds to a heap and is used to model sharing.The semantics is set at a higher level of abstraction than an abstract machine and is therefore more manageable for proofs about programs rather than implementations. At the same time, it is sufficiently low level to allow us to reason about programs in terms of parallelism (i.e. the number of processors used) as well as work and run-time with different numbers of processors.The framework used by the semantics is sufficiently flexible and general that it can easily be adapted to express other evaluation models such as sequential call-by-need, speculative evaluation, non-deterministic choice and others.

The adequacy of Launchbury's natural semantics for lazy evaluation

“…We have provided two ways to fix the problem: One by adding a stack to the operational semantics, and one by changing the denotation of heaps. Both variants have precursors in the literature: The extended heaps of [SGHHOM10] resemble the heapstack-pairs of our semantics, while Baker-Finch et al [BKT00] and Nakata [Nak10] use right-sided updates in their denotational heap semantics.…”

“…An interesting case is the work by Baker-Finch et al on parallel call-by-need: While an earlier report [BFKHT99] uses Launchbury's definitions unmodified and states the flawed 'Theorem' 2, the following publication at ICFP [BKT00] uses an update-based denotational semantics, unfortunately without motivating that change.…”

Parallel functional programming in Eden

“…However, this view completely neglects parallelism and ignores issues like process creation and communication. In the following we define an operational semantics in the style of Baker-Finch et al (2000) which is based on Launchbury's natural semantics for lazy evaluation (Launchbury, 1993). The semantics handles process creation and communication and is precise about expression scheduling and evaluation order.…”