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.

Autorentext
Anseok Joo, B.A. Mathematics, Reed College

Klappentext
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.