Leon S. Levy

The Towers of Hanoi problem

In the Towers of Hanoi Problem there are three pegs A, B and C, and n (n 3 1) disks of different diameters. The disks are placed on peg A in order of decreasing diameter with the smallest disk on top. The object is to move all the disks from peg A to one of the other two pegs by moving one disk at a time. Only the top disk may be moved from any peg, and this must never be placed upon a disk of smaller diameter. There is a simple recursive solution to this problem, which is used by many texts as an example of recursive programming. However, there is an equally simple iterative program that is tr otivated by the following observations. Consider the pegs to be in a ring so that, moving clockwise, the pegs are A, B, C, A, B, . . . . Given any configuration of the disks, there are at most three possible moves: the smallest disk ran be moved to either of two pegs, and the second smallest of the topmost disks may be moved onto the other peg that does not contain the smallest disk. Now, two consecutive moves of the smallest disk may be combined into one move, and two consecutive moves of the other movable disk will cancel each other. Therefore one should consider an algorithm that alternately moves the smallest disk and makes the other possible’ move. If, for simplicity, we assume that the smallest disk should move in only one direction, say clockwise, then we are led to the algorithm

A metaprogramming method and its economic justification

Metaprogramming, defined as creating application programs by writing programs that produce programs, is presented as the basis of a method for reducing software costs and improving software quality. The method starts with a rapid prototyping phase in which selected representative parts of the application are prototyped; this is followed by a tooling up phase, during which the metaprogramming occurs. The final phase is the production of the application programs using the software tools and techniques of the metaprogramming phase. The author summarizes the experience of two projects that support the assertion that metaprogramming is an efficient way to produce programs, since these projects used metaprogramming in their development. An economic theory which justifies this approach is outlined. It is shown how to do a cost/benefit analysis of the method.

A walk through AWK

This tutorial on AWK is intended for readers who have a general familiarity with UNIX*, and who have at least a rudimentary knowledge of programming in some procedural language.AWK is an interpretive programming language, which makes it useful for prototyping. Primary applications of AWK are information retrieval, report writing, and data manipulation.AWK is often used as a special purpose information processing language - many of whose capabilities are easily accessible to non-programmers. We present it as a programming language - with added capabilities - particularly useful for rapid prototyping.

Local constraints in programming languages part I: syntax☆

Abstract The method of local constraints attempts to describe context-free languages in an apparently context-sensitive form which helps to retain the intuitive insights about the grammatical structure. This form of description, while apparently context-sensitive is, in fact, context-free and allows a program derivation structure to be represented as a tree with additional constraints, thus allowing for the possibility of a correctness proof in the form of Knuthian semantics. These semantic aspects will be discussed in a sequel to this paper (Part II: Semantics). Several detailed examples are given to motivate the use of local constraints grammars including some examples from the syntax of ALGOL 60. A parsing algorithm has been described; its purpose is to show that the computation of local constraints is quite reasonable. Transformation rules for transferring a context-free grammar into a local constraints grammar have been described and some heuristic approaches for the inverse transformation have been presented.

PHRASE STRUCTURE TREES BEAR MORE FRUIT THAN YOU WOULD HAVE THOUGHT

In this paper we will present several results concerning phrase structure trees. These results show that phrase structure trees, when viewed in certain ways, have much more descriptive power than one would have thought. We have given a brief account of local constraints on structural descriptions and an intuitive proof of a theorem about local constraints. We have compared the local constraints approach to some aspects of Gazdars framework and that of Peters and Ritchie and of Karttunen. We have also presented some results on skeletons (phrase structure trees without labels) which show that phrase structure trees, even when deprived of the labels, retain in a certain sense all the structural information. This result has implications for grammatical inference procedures.

The Cartesian Programmer and the Hacker

The literature of programming contains a rich variety of approaches to programming. In this chapter I explain two fictitious but representative notions of programming as being rooted in deeper philosophic and psychological factors. I also consider briefly the consequences of such an analysis.