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Computing Downwards Accumulations on Trees Quickly
, 1995
"... Downwards passes on binary trees are essentially functions which pass information down a tree, from the root towards the leaves. Under certain conditions, a downwards pass is both `efficient' (computable in a functional style in parallel time proportional to the depth of the tree) and `manipula ..."
Abstract

Cited by 9 (3 self)
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Downwards passes on binary trees are essentially functions which pass information down a tree, from the root towards the leaves. Under certain conditions, a downwards pass is both `efficient' (computable in a functional style in parallel time proportional to the depth of the tree) and `manipulable' (enjoying a number of distributivity properties useful in program construction); we call a downwards pass satisfying these conditions a downwards accumulation. In this paper, we show that these conditions do in fact yield a stronger conclusion: the accumulation can be computed in parallel time proportional to the logarithm of the depth of the tree, on a Crew Pram machine.
An InitialAlgebra Approach to Directed Acyclic Graphs
, 1995
"... The initialalgebra approach to modelling datatypes consists of giving constructors for building larger objects of that type from smaller ones, and laws identifying different ways of constructing the same object. The recursive decomposition of objects of the datatype leads directly to a recursive ..."
Abstract

Cited by 6 (0 self)
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The initialalgebra approach to modelling datatypes consists of giving constructors for building larger objects of that type from smaller ones, and laws identifying different ways of constructing the same object. The recursive decomposition of objects of the datatype leads directly to a recursive pattern of computation on those objects, which is very helpful for both functional and parallel programming. We show how to model a particular kind of directed acyclic graph using this initialalgebra approach.