Shortcut fusion is a well-known optimization technique for functional programs. Its aim is to transform multi-pass algorithms into single pass ones, achieving deforestation of the intermediate structures that multi-pass algorithms need to construct. Shortcut fusion has already been extended in several ways. It can be applied to monadic programs, maintaining the global effects, and also to obtain circular and higher-order programs. The techniques proposed so far, however, only consider programs denned as the composition of a single producer with a single consumer. In this paper, we analyse shortcut fusion laws to deal with programs consisting of an arbitrary number of function compositions.
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