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Awesome Open Source

Isomorphism -- Mathematics of Programming


This book introduces the mathematics behind computer programming.


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.


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
$ unzip
$ cd install-tl
$ sudo ./install-tl -gui text -repository

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


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''

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