On Program Design

Abstract

Chapter 1 introduced the concept of designing programs by the method of stepwise refinement. In essence, we try to decompose a problem into a simple series of subproblems. Given a problem P, we try to discover a set of smaller problems P₁, P₂, P₃, …, such that solving first P₁, then P₂ and so on will be a solution to the original P. This approach is then applied to each of the subproblems P₁, P₂, P₃, …, producing a set of sub-subproblems whose solutions taken together are a solution to P₁. We continue this process until the problems are sufficiently small to be capable of solution directly. It is the continual outside-in analysis of the problem which develops the solution to the problem. This analysis and thus the structure of the solution can be usefully represented and guided by a development tree as shown in figure 5.1.