We propose a classification for a set of linearly recursive functions, which can be expressed as instances of a skeleton for parallel linear recursion, and present new parallel implementations for them. This set includes well known higher-order functions, like Broadcast, Reduction and Scan, which we call basic components. Many compositions of these basic components are also linearly recursive functions; we present transformation rules from compositions of up to three basic components to instances of our skeleton. The advantage of this approach is that these instances have better parallel implementations than the compositions of the individual implementations of the corresponding basic components.
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