Isomorphism -- Mathematics of Programming

2021/03

This book introduces the mathematics behind computer programming.

Contents

The book can be downloaded in both English (EN) and Chinese (中文).

• Preface
• Chapter 1, Natural numbers. Peano Axiom, list and folding;
• Chapter 2, Recursion. Euclidean algorithm, Lambda calculus, and Y-combinator;
• Chapter 3, Symmetry. Group, Ring, and Field. Galois Theory;
• Chapter 4, Category theory and type system;
• Chapter 5, Deforest. Build-fold fusion law, optimization, and algorithm deduction;
• Chapter 6, Infinity. Set theory, Infinity and stream;
• Chapter 7, Logic paradox, Gödel's incompleteness theorems, and Turing halting problem.
• Answers to the exercise.

Install

To build the book in PDF format from the sources, you need the following software pre-installed.

• TeXLive, The book is built with XeLaTeX, a Unicode friendly version of TeX;

Install TeXLive

In Debian/Ubuntu like Linux environment, do NOT install the TeXLive through apt-get. Go to TeXLive official site to download the setup script.

$ wget http://mirror.ctan.org/systems/texlive/tlnet/install-tl.zip
$ unzip install-tl.zip
$ cd install-tl
$ sudo ./install-tl -gui text -repository http://mirror.ctan.org/systems/texlive/tlnet

In Windows, TeXLive provide a gui based installer, in Mac OS X, there's a MacTeX.

Customize font (Optional)

If the host system fonts are available, e.g. under VM. they could be imported as the following example:

$ sudo mkdir /usr/share/fonts/host-system
$ sudo cp /Host-System/Fonts/{FontName, fontname}* /usr/share/fonts/host-system/
$ fc-cache

Others

You need the GNU make tool, in Debian/Ubuntu like Linux, it can be installed through the apt-get command:

$ sudo apt-get install build-essential

In Windows, you can install the MSYS for it. In Mac OS X, please install the developer tool from this command line:

$ xcode-select --install

Build the PDF book

enter the folder contains the book TeX manuscript, run

$ make

This will generate unplugged-en.pdf and unplugged-zh-cn.pdf. If you only need the Chinese version for example, you can run make cn instead.

--

LIU Xinyu

[email protected]

``Cogito ergo sum''