An approach to fair applicative multiprogramming

Abstract

This paper presents a brief formal semantics of constructors for ordered sequences (cons) and for unordered multisets (frons) followed by a detailed operational semantics for both. A multiset is a generalization of a list structure which lacks order a priori; its order is determined by the a posteriori migration of computationally convergent elements to the front. The introductory material includes an example which demonstrates that a multiset of yet-unconverged values and a timing primitive may be used to implement the scheduler for an operating system in an applicative style. The operational semantics, given in PASCAL-like code, is described in two detailed steps: first a uniprocessor implementation of the cons/frons constructors and the first/rest probes, followed by an extension to a multiprocessor implementation. The center of either implementation is the EUREKA structure transformation, which brings convergent elements to the fore while preserving order of shared structures. The multiprocessor version is designed to run on an arbitrary number of processors with only one semaphore but makes heavy use of the sting memory store primitive. Stinging is a conditional store operation which is carried out independently of its dispatching processor so that shared nodes may be somewhat altered without interfering with other processors. An appendix presents the extension of this code to a ‚fair“ implementation of multisets.