Dijkstra's famous thesis "goto considered harmful", which paved the way for structured programming, was formally substantiated by the result of Böhm and Jacopini on the Turing universality of the three well-known basic programming constructs. We argue for a similar ideal in parallel programming — "send-receive considered harmful" — i.e. abandoning explicit send-receive statements between processors and expressing programs using a restricted set of parallel constructs. We deal with recursive patterns of parallelism, represented formally as morphisms in a suitable calculus. The aim of this paper is to study the expressive power of two morphisms – catamorphisms and anamorphisms. For a restricted program calculus based on these morphisms, we constructively prove two formal results, whose pragmatic message is: (1) A programming language based on catamorphisms is computationally equivalent to the class of primitive recursive functions; (2) A programming language based on both catamorphisms and anamorphisms is equivalent to the class of partial recursive functions and is therefore Turing-universal. We present a case study on numerical integration, demonstrating the expressive power of ana- and catamorphisms for parallel programming.
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