Categorical Ideas As Expressed in the Programming Language Charity

Within the past ten years, category theory has become§an import avenue of research in computer science. §This book explores some categorical ideas introduced§by B. Jacobs and J. Rutten in "A tutorial on§(co)algebras and (co)induction" [EATCS Bulletin,§62(222-259):3-13, 1997]. From foundational sets and§functions, we gradually build up to definitions of§functors and diagrams. Then, we define algebras and§coalgebras and prove some properties used in the next§section, where we show by examples how the§categorical ideas are implemented in the programming§language Charity. Exercises are sprinkled throughout§the first chapter to reinforce understanding. The§prerequisites for this book are basic intuitions and§notational knowledge for sets and functions; no§understanding of Charity is assumed. As such, this§work should be useful to anyone interested in§category theory that finds programming to be a useful§tool in understanding abstract ideas. In addition,§as an introductory work, this book should prepare the§reader for more advanced literature in the field.