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Functional Pearls

Deriving tidy drawings of trees

Part of: JFP Research Articles

Published online by Cambridge University Press:  07 November 2008

Jeremy Gibbons
Jeremy Gibbons
Affiliation:
Department of Computer Science, University of Auckland, Private Bag 92019, Auckland, New Zealand. Email jeremy@cs. auckland. ac.nz
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Abstract

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The tree-drawing problem is to produce a ‘tidy’ mapping from 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 higher-order tree operations.

Keywords

Derivationtreesupwards and downwards accumulationsdrawing.
Type
Articles
Information
Journal of Functional Programming , Volume 6 , Issue 3 , May 1996 , pp. 535 - 562
Copyright
Copyright © Cambridge University Press 1996

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