Discovering Algorithms with Matrix Code

TL;DR

This paper introduces Matrix Code, a program format that facilitates algorithm discovery by transforming specifications into executable code through a step-by-step matrix growth process, exemplified by generating prime numbers.

Contribution

It presents a novel program format, Matrix Code, enabling a structured discovery process from specification to code, grounded in Floyd-Hoare verification principles.

Findings

Matrix Code supports stepwise algorithm development.

The method is demonstrated with a Java prime number generator.

The approach bridges specification and implementation effectively.

Abstract

In first-year programming courses it is often difficult to show students how an algorithm can be discovered. In this paper we present a program format that supports the development from specification to code in small and obvious steps; that is, a discovery process. The format, called Matrix Code, can be interpreted as a proof according to the Floyd-Hoare program verification method. The process consists of expressing the specification of a function body as an initial code matrix and then growing the matrix by adding rows and columns until the completed matrix is translated in a routine fashion to compilable code. As worked example we develop a Java program that generates the table of the first N prime numbers.