Calculational design of special purpose parallel algorithms

This paper adopts a transformational programming approach for deriving massively parallel algorithms from functional specifications. It gives a brief description of a framework for relating key higher order functions such as map, reduce, and scan with communicating processes with different configurations. The parallelisation of many interesting functional algorithms can then be systematically synthesized by combining “off the shelf” parallel implementations of instances of these higher order functions. Efficiency in the final message-passing algorithms is achieved by exploiting data parallelism, for generating the intermediate results in parallel; and functional parallelism, for processing intermediate results in stages such that the output of one stage is simultaneously input to the next one. This approach is illustrated through a case study for testing whether all the elements of a given list are distinct. Bird-Meertens formalism is used to concisely carry out algebraic transformations