A Simulation of Demand-Driven Dataflow: Translation from Lucid into MDC Language

Message Driven Computation (MIX) is a model of computation with which we haw been eqerimenting at the Illinois Institute of Technology. It is our h i r e to prove the viability of MDC in practice for the expression of parallel algorithms and the implementation of ficnctional and datajlbw programming hguuges. In the following pages we &cuss our implementation of the Lucid programming language in ME. The discussion will present a subset of Lucid which illustrates the principles ofLuci4 Message Driven Computing, and the translation into and the interpretation of ahtaflow graphs. 1.0 Message Driven Computing Message Driven Computing (MDC) is a model of parallel and distributed computation developed at the Illinois Institute of Technology by Thomas Christopher [Christopher 19891. Central to MDC is the notion of a computational event. Computational events are executions of functions which map input messages into output messages. All message passing between locations in MDC is achieved unidirectionally and asynchronously. A computational event occurs at a location when a pattern of messages accumulates at the location. Locations are named by computable tuples of information. When two or more computational events OCCUT at a location, mutual exclusion between the computational events is guaranteed. MDC has been implemented on a variety of machines: the Encore Multimax, the BBN Butterfly, and the NCUBE. 2.0 Lucid Lucid is a family of functional dataflow languages defined and designed by Wadge and Ashcroft Wadge and Ashcroft 19851. Inherent to the definition of any particular Lucid language are sequences, Lucid operators, pointwise infix and prefix numeric operatow user functions (filters), and list operators (optional). 2.1 Terminology of Lucid A sequence in Lucid is def ied to be an infinite series of values ordered (or tagged) by time. The sequence is the basic tenet of Lucid programming. Some examples of sequences are constants, definitions, and the results of function calls. A constant sequence is a sequence whose value at every time is the same. A definition of a sequence provides a programmer the facility to have variables which change over time but not to have variables whme history of updates is destroyed. A definition implies that Lucid is a single-assignment language (a tenet of pure dataflow and functional languages). A function maps one or more input sequences into an output sequence. In the literature, functions are often alluded to as filters. Sequenoes are operated on by Lucid operators, pointwise operators, and functions. A Lucid operator is a function which maps one or two input streams onto an output stream whose values are usually values in the history of the input streams. 2.2 Selected Lucid Operators Defmed