Results 1 
3 of
3
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 `manipulable' ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
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.
Deriving Tidy Drawings of Trees
, 1995
"... The treedrawing problem is to produce a `tidy' mapping of elements of a tree to points in the plane. In this paper, we derive an efficient algorithm for producing tidy drawings of trees. The specification, the starting point for the derivations, consists of a collection of intuitively appealing cri ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
The treedrawing problem is to produce a `tidy' mapping of elements of a tree to points in the plane. In this paper, we derive an efficient algorithm for producing tidy drawings of trees. The specification, the starting point for the derivations, consists of a collection of intuitively appealing criteria satisfied by tidy drawings. The derivation shows constructively that these criteria completely determine the drawing. Indeed, the criteria completely determine a simple but inefficient algorithm for drawing a tree, which can be transformed into an efficient algorithm using just standard techniques and a small number of inventive steps. The algorithm consists of an upwards accumulation followed by a downwards accumulation on the tree, and is further evidence of the utility of these two higherorder tree operations.
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 di#erentways of constructing the same object. The recursive decomposition of objects of the datatype leads directly to a recursiv ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
. The initialalgebra approach to modelling datatypes consists of giving constructors for building larger objects of that type from smaller ones, and laws identifying di#erentways of constructing the same object. The recursive decomposition of objects of the datatype leads directly to a recursive pattern of computation on those objects, whichisvery helpful for both functional and parallel programming. We showhow to model a particular kind of directed acyclic graph using this initialalgebra approach. Keywords. Graphs, data types, catamorphisms, initial algebras, BirdMeertens Formalism, program derivation. 1 Introduction It is now widely recognized that the traditional adhoc approaches to program construction do not yield reliable software; a more systematic and formal approach is required. One such approach consists of program veri#cationproving after the fact that a given program satis#es its formal speci#cation. This approach turns out to be di#cult to implement, not lea...