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Towards a theory of parallel algorithms on concrete data structures
 In Semantics for Concurrency, Leicester
, 1990
"... The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of DARPA or the U.S. government. Building on Kahn and Plotkin’s theory of concrete data structures and sequential functions, ..."
Abstract

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The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of DARPA or the U.S. government. Building on Kahn and Plotkin’s theory of concrete data structures and sequential functions, Berry and Curien defined an intensional model of sequential algorithms between concrete data structures. In this paper we report on an attempt to develop a similar intensional model of concurrent computation. We present a notion of parallel algorithm between concrete data structures, together with suitable application and currying operations. We define an intensional strictness ordering on parallel algorithms, with respect to which application is well behaved (at first order types). We define the inputoutput function computed by a parallel algorithm, and we show that every parallel algorithm computes a continuous function. Thus, a parallel algorithm may be viewed as a continuous function together with a parallel computation strategy. In contrast, a Berry