# Deriving Tidy Drawings of Trees

*Jeremy Gibbons*

### Abstract

The \em 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 \em criteria\/ satisfied by tidy drawings. The derivation shows constructively that these criteria completely determine the drawing. Indeed, there is essentially only one reasonable drawing algorithm satisfying the criteria; its development is almost mechanical. \par The algorithm consists of an \em upwards accumulation\/ followed by a \em downwards accumulation\/ on the tree, and is further evidence of the utility of these two higher-order tree operations.