Limitations of SML in computational category theory

Abstract

The main theme of this paper is to provide a basic introduction to the notion of category theory in computer science. It will include primer sections or chapters on category theory and functional programming. The category theory tutorial will discuss the basic concepts of the definition a category, and categorical limits, including the special limits (products and equalizers). Next, we have the functional programming (FP) tutorial: it contains a description of functional languages. This chapter also contains a brief history of FP. The tutorial is then further refined into description of the functional language ML and providing a basic reference of useful functions and syntax of ML. These primers and tutorials gives the necessary insight for the final illustration of a categorical proof encoded in the programming language of SML/NJ (standard meta-language of New Jersey). The illustration makes use of the constructions and definitions from the tutorial chapters, and provides a sense of cohesion to the material.