Make it into a book, and did some updates

Makefile

@@ -0,0 +1,7 @@
+all:
+	lhs2TeX -o main.tex main.lhs
+	pdflatex --interaction=nonstopmode main.tex
+#	bibtex main
+	pdflatex --interaction=nonstopmode main.tex
+#	pdflatex --interaction=nonstopmode main.tex
+	rm main.tex main.aux main.bbl main.blg main.log main.out main.ptb main.toc

bib.bib

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+@article{BerniePopeFix,
+   author = {Bernie Pope},
+   title = {Getting a Fix from the Right Fold},
+   journal = {The Monad.Reader},
+   volume = {6},
+   pages = {5--15}
+}
+
+@ARTICLE{Hutton93atutorial,
+    author = {Graham Hutton},
+    title = {A Tutorial on the Universality and Expressiveness of Fold},
+    journal = {Journal of Functional Programming},
+    year = {1993},
+    volume = {9},
+    pages = {355--372}
+}
+
+@INPROCEEDINGS{Meijer91functionalprogramming,
+    author = {Erik Meijer and Maarten Fokkinga and Ross Paterson},
+    title = {Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire},
+    booktitle = {},
+    year = {1991},
+    pages = {124--144},
+    publisher = {Springer-Verlag}
+}
+
+@article{BrentYorgeyType,
+   author = {Brent Yorgey},
+   title = {The Typeclassopedia},
+   journal = {The Monad.Reader},
+   volume = {13},
+   year = {2009},
+   pages = {17--68}
+}
+
+@unpublished{PopePreludeTour,
+   author = {B. Pope},
+   title = {A Tour of the {H}askell {P}relude},
+   year = {1999},
+}
+
+@unpublished{McDiarmidMuller2011,
+   author = {Colin McDiarmid, Tobias M\"{u}ller},
+   title = {The number of disk graphs},
+   year = {2011},
+}
+
+@INPROCEEDINGS{Bird03arithmeticcoding,
+    author = {Richard Bird and Jeremy Gibbons},
+    title = {Arithmetic Coding with Folds and Unfolds},
+    booktitle = {Advanced Functional Programming, 4th International Summer School},
+    year = {2003},
+    publisher = {Springer-Verlag}
+}
+
+@INPROCEEDINGS{Wadler89theoremsfor,
+    author = {Philip Wadler},
+    title = {Theorems for free!},
+    booktitle = {FUNCTIONAL PROGRAMMING LANGUAGES AND COMPUTER ARCHITECTURE},
+    year = {1989},
+    pages = {347--359},
+    publisher = {ACM Press}
+}
+
+@book{goodman2004handbook,
+  title={Handbook of discrete and computational geometry},
+  author={Goodman, J.E. and O'Rourke, J.},
+  isbn={9781584883012},
+  lccn={2004040662},
+  series={CRC Press series on discrete mathematics and its applications},
+  url={http://books.google.com/books?id=QS6vnl8WlnQC},
+  year={2004},
+  publisher={Chapman \& Hall/CRC}
+}
+@ARTICLE{Erwig_probabilisticfunctional,
+    author = {Martin Erwig and Steve Kollmansberger},
+    title = {Probabilistic Functional Programming in Haskell},
+    journal = {Journal of Functional Programming},
+    year = {},
+    volume = {2005},
+    pages = {2006}
+}
+@ARTICLE{Mcbride_applicativeprogramming,
+    author = {Conor Mcbride and Ross Paterson},
+    title = {Applicative programming with effects},
+    journal = {Journal of Functional Programming},
+    year = {},
+    volume = {18},
+    pages = {2007}
+}
+@book{koautomata,
+	title={Problem Solving in Automata, Languages, and Complexity},
+	author={Ding-Zhu Du and Ker-I Ko},
+	isbn={9780471439608},
+	year={2001},
+	publisher={John Wiley \& Sons}
+}
+@book{putnamandbeyond,
+	title={Putnam and Beyond},
+	author={R\u{a}zvan Gelca and Titu Andreescu},
+	isbn={9780387257655},
+	year={2007},
+	publisher={Springer}
+}
+@book{algostring,
+	title={Algorithms on Strings, Trees and Sequences: Computer Science and
+		Computational Biology},
+	author={Dan Gusfield},
+	isbn={9780521585194},
+	year={1997},
+	publisher={Cambridge University Press}
+}

main.lhs

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+\documentclass[oneside]{book}
+%include polycode.fmt
+%include greek.fmt
+%include lambda.fmt
+%include exists.fmt
+%include style.fmt
+\usepackage{enumerate}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{amsfonts}
+\usepackage{amsthm}
+\usepackage{latexsym}
+\usepackage{mathrsfs}
+\usepackage[usenames,dvipsnames]{color}
+\usepackage{mathrsfs}
+%\usepackage[x11names, rgb]{xcolor}
+\usepackage[utf8]{inputenc}
+\usepackage{tikz}
+\usepackage{multicol}
+\usepackage{hyperref}
+\usepackage{cite}
+\usepackage{stmaryrd}
+\setlength{\topmargin}{-0.5in} \setlength{\textwidth}{6.5in}
+\setlength{\oddsidemargin}{0.0in} \setlength{\textheight}{9.1in}
+
+
+\newlength{\pagewidth}
+\setlength{\pagewidth}{6.5in} %\pagestyle{empty}
+\pagenumbering{arabic}
+\newcommand{\R}{\mathbb{R}}
+\newcommand{\N}{\mathbb{N}}
+\newcommand{\B}{\mathfrak{B}}
+\newcommand{\Z}{\mathbb{Z}}
+\newcommand{\lcm}{\mathop{\mathrm{lcm}}}
+\newcommand{\sgn}{\mathop{\mathrm{sgn}}}
+\newcommand{\topics}[1]{[\textcolor{CornflowerBlue}{\emph{#1}}]\\}
+
+\newcommand{\catamorphism}[1]{\llparenthesis #1 \rrparenthesis}
+\newcommand{\hylomorphism}[1]{[|#1 |]}
+\newcommand{\anamorphism}[1]{[(#1 ])}
+\newcommand{\paramorphism}[1]{#1}
+
+\theoremstyle{plain}
+\newtheorem{theorem}{Theorem}[section]
+\newtheorem{lemma}[theorem]{Lemma}
+\newtheorem{proposition}[theorem]{Proposition}
+\newtheorem{corollary}[theorem]{Corollary}
+
+\theoremstyle{definition}
+\newtheorem{problem}{Problem}[section]
+\newtheorem{definition}{Definition}[section]
+\newtheorem{conjecture}{Conjecture}[section]
+\newtheorem{example}{Example}[section]
+
+\theoremstyle{remark}
+\newtheorem*{remark}{Remark}
+\newtheorem*{note}{Note}
+
+%opening
+
+\title{Cookbook}
+\date{Last update: \today}
+\begin{document}
+\maketitle
+\setcounter{tocdepth}{1}
+\tableofcontents
+\chapter{Algebraic Algorithms}
+\section{Exponentiation by squaring}
+
+\begin{problem}
+~\newline
+\noindent \emph{Input}:
+
+Given the operator $\cdot$, element $a$ and positive integer $n$. Where $a$ is
+an element of a semigroup under $\cdot$.
+
+\noindent \emph{Output}:
+
+Find $a^n$, where $a^n = a\cdot a^{n-1}$.
+\end{problem}
+
+The general method to solve the problem is exponentiation by squaring. It is
+originally used for integer exponentiation, but any associate operator can be
+used in it's place. Here is a theorem stated in algebraic flavor.
+
+\begin{theorem}
+For any semigroup $(S,\cdot)$, $x\in S$ and $n\in \N$, $x^n$ can be computed 
+with $O(\log n)$ applications of $\cdot$.
+\end{theorem}
+
+\begin{proof}
+Express $n$ as binary $c_kc_{k-1}\ldots c_0$, where $c_i\in \{0,1\}$. We
+make sure $0\cdot a$ is the treated as the identity, and $1\cdot a = a$ for
+all $a$. The following observations are crucial.
+\begin{align*}
+a^n &= c_0a^{2^0}\cdot c_1a^{2^1}\cdot \ldots \cdot c_ka^{2^k}\\
+a^{2^{i+1}} &= a^{2^i}\cdot a^{2^i}
+\end{align*}
+
+The code that compute $a^n$ from the above two equalities.
+
+\begin{code}
+import Data.Digits
+exponentiationBySquaring :: Integral a => (b -> b -> b) -> b -> a -> b
+exponentiationBySquaring op a n = foldr1 op $ [y | (x,y) <- (zip binary twoPow), x/=0]
+  where twoPow = a:zipWith op twoPow twoPow
+        binary = digitsRev 2 n
+\end{code}
+
+One can analyize the number of times the operator is used. The |twoPow| is the
+infinite list $[a,a^2,\ldots,a^{2^i},\ldots$. It takes $k$ operations to
+generate the first $k+1$ elements. At most $k$ additional operations are
+required to combine the result with the operator. Therefore the operator is
+used $O(\log n)$ times.
+\end{proof}
+
+This result can of course be extended to monoid and groups, so it work for all
+non-negative and integer exponents, respectively.
+
+\section{Linear homogeneous recurrence relations with constant coefficients}
+
+\begin{definition}[Linear homogeneous recurrence relations with constant
+coefficients]
+A linear homogeneous recurrence relations in ring $R$ with constant coefficients of order
+$k$ is a sequence with the following recursive relation
+\[
+a_n = \sum_{i=1}^k c_ia_{n-i}
+\],
+where $c_i$ are constants.
+
+We use linear recurrence relation to abbreviate.
+\end{definition}
+
+The most common example is the Fibonacci sequence. $F_0=0, F_1=1$ and $F_n =
+F_{n-1}+F_{n-2}$ in the ring $\Z$. The Fibonacci sequence have a simple implementation. 
+|fibs = 0 : 1 : zipWith (+) fibs (tail fibs)|. We want to generalize it.
+
+\subsection{Lazy sequence}
+\begin{problem}
+\emph{Input}: 
+\begin{enumerate}
+\item A list of coefficients $[c_1,c_2,\ldots,c_n]$ of a linear recurrence relation.
+\item A list of base cases $[a_0,a_1,\ldots,a_{n-1}]$ of a linear recurrence relation.
+\end{enumerate}
+
+\emph{Output}:
+The sequence of values of the linear recurrence relation as a infinite list $[a_0,a_1,\ldots$.
+\end{problem}
+
+Here is a specific implementation where we are working in the ring $\Z$.
+\begin{code}
+import Data.List
+linearRecurrence :: Integral a => [a] -> [a] -> [a]
+
+linearRecurrence coef base = a
+  where a = base ++ map (sum . (zipWith (*) coef)) (map (take n) (tails a))
+        n = (length coef)
+\end{code}
+
+One can generalize it easily to any ring. 
+
+Having a infinite list allows simple manipulations. However, finding the nth
+element in the sequence cost $O(nk)$ time. It becomes unreasonable if a person
+only need to know the $n$th element.
+
+\subsection{Determine $n$th element in the index}
+If $n$ is very large, a more common technique would be solve for $a_n$ using
+matrix multiplication.
+
+\subsection{Linear Recurrence in Finite Ring}
+Linear recurrence is perodic in finite rings. Therefore one might want to
+produce only the periodic part of the ring. [INSERT MORE ON THIS SUBJECT]
+
+\chapter{Combinatorial Algorithms}
+\section{Integer Partitions}
+To find all possible partition of a integer, we proceed with a simple
+recursive formula.
+
+Let $p(n,k)$ be the list of ways to partition integer $n$ using integers less
+or equal to $k$. $p(n,n)$ is the solution to our problem. It is implemented as
+$part$ in the code.
+\begin{code}
+integerPartitions :: Integral a => a -> [a]
+integerPartitions n = part n n
+  where part 0 _ = [[]]
+        part n k = [(i:is) | i<-[1..min k n], is <- part (n-i) i]
+\end{code}
+\bibliography{bib}
+\bibliographystyle{plain}
+\end{document}

main.toc

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+\contentsline {chapter}{\numberline {1}Algebraic Algorithms}{2}{chapter.1}
+\contentsline {section}{\numberline {1.1}Exponentiation by squaring}{2}{section.1.1}
+\contentsline {section}{\numberline {1.2}Linear homogeneous recurrence relations with constant coefficients}{2}{section.1.2}
+\contentsline {subsection}{\numberline {1.2.1}Lazy sequence}{3}{subsection.1.2.1}
+\contentsline {subsection}{\numberline {1.2.2}Determine $n$th element in the index}{3}{subsection.1.2.2}
+\contentsline {subsection}{\numberline {1.2.3}Linear Recurrence in Finite Ring}{3}{subsection.1.2.3}
+\contentsline {chapter}{\numberline {2}Combinatorial Algorithms}{4}{chapter.2}
+\contentsline {section}{\numberline {2.1}Integer Partitions}{4}{section.2.1}

style.fmt

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+%format `elem` = "$\in$"