PLAND2D — Towards a Two-Dimensional Programming Language

Abstract

A program in a two-dimensional language is expressed in some diagrammatic, pictorial form, whereas a program in a “normal” language consists of a one-dimensional (linear) string of characters. To put it briefly, in the former case a program is “drawn”, whilst in the latter case it is “written”. A two-dimensional notation has been used or seems to be worthwhile at least in the following areas:

• 1. Mathematical expressions are much more readable, if their sub- and superscripts, fractional lines, summation and integration signs with lower and upper bounds, etc. can be written in their usual two-dimensional, not in a somehow linearized form. Due to its non-numeric nature PLAN2D does not deal with such features.

• 2. The most common use of a two-dimensional notation is the representation of control structures, especially with flow charts.⁺⁾ But there are still other possibilities for exploiting the two dimensions for describing the flow of control in algorithms. Besides the features used in PLAN2D, e.g. parallelism and synchronisation in non-sequential algorithms might be well expressed diagrammatically. No major effort in this direction is known to the authors.

• 3. Description and manipulation of linked data structures are the main concern of PLAN2D. There is a motivation for that, as simple as convincing: when dealing with linked data structures most programmers develop their algorithms with the aid of diagrams. In /Kn 68/, p. 256 Knuth recommends:“... it is helpful to draw ”before and after“ diagrams and to compare them to see which links need to be changed.” But if these diagrams are so closely related to the problem, why translating them into the linear notation of some programming language instead of using them as programs directly understandable to the computer? So, the basic feature of PLAN2D consists of “before and after” diagrams which are merged into one diagram describing the desired manipulations of links and other entities. Matching the “before” diagram with the data structure is required, i.e. pattern matching is — besides the two-dimensional notation — the most important feature of PLAN2D.

One picture is worth more than ten thousand words.