This article describes the application of functional programming techniques to a problem previously studied by imperative programmers, that of drawing general trees automatically. We first consider the nature of the problem and the ideas behind its solution (due to Radack), independent of programming language implementation. We then describe a Standard ML program which reflects the structure of the abstract solution much better than an imperative language implementation. We conclude with an informal discussion on the correctness of the implementation and some changes which improve the algorithm's worst-case time complexity. 1 The problem and its solution The problem is this: given a labelled tree, assign to each node a position on the page to give an aesthetically pleasing rendering of the tree. We assume that nodes at the same depth are positioned on the same horizontal line on the page, so the problem reduces to finding a position horizontally for each node. But what do we mean by "...

The tree-drawing 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 higher-order tree operations.

This article describes the application of functional programming techniques to a problem previously studied by imperative programmers, that of drawing general trees automatically. We first consider the nature of the problem and the ideas behind its solution (due to Radack), independent of programming language implementation. We then describe a Standard ML program which reflects the structure of the abstract solution much better than an imperative language implementation. We conclude with an informal discussion on the correctness of the implementation and some changes which improve the algorithm’s worst-case time complexity. 1 The problem and its solution The problem is this: given a labelled tree, assign to each node a position on the page to give an aesthetically pleasing rendering of the tree. We assume that nodes at the same depth are positioned on the same horizontal line on the page, so the problem reduces to finding a position horizontally for each node. But what do we mean by “aesthetically pleasing”? The various papers on the subject (Radack, 1988;