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preamble.tex
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\usepackage{polyglossia}
\setmainlanguage[variant=usmax]{english}
\setotherlanguage{spanish}
\usepackage{amsmath}
\usepackage{amsthm}
\let\equation\gather
\let\endequation\endgather
\usepackage{enumitem}
\usepackage{epigraph}
\setlength{\epigraphrule}{0pt}
\setlength{\epigraphwidth}{0.55\textwidth}
\usepackage{fancyhdr}
\pagestyle{fancy}
\renewcommand{\chaptermark}[1]{
\ifnum\value{chapter}>0
\markboth{\thechapter.\ #1}{}
\else
\markboth{#1}{}
\fi
}
\fancyhead{}
\fancyhead[ER]{\textsl{\nouppercase{\leftmark}}}
\fancyhead[OL]{\textsl{\nouppercase{\rightmark}}}
\fancyhead[LE,RO]{\thepage}
\fancyfoot{}
\renewcommand{\headrulewidth}{0pt}
\renewcommand{\footrulewidth}{0pt}
\newcommand{\clearemptydoublepage}{\clearpage{\pagestyle{empty}\cleardoublepage}}
\usepackage{fontspec}
\usepackage{subcaption}
\usepackage{unicode-math}
\setmathfont{latinmodern-math.otf}
\setmathfont[range={\llparenthesis,\rrparenthesis}]{xits-math.otf}
\setmonofont
[ BoldFont = DejaVuSansMono-Bold.ttf,
ItalicFont = DejaVuSansMono-Oblique.ttf,
BoldItalicFont = DejaVuSansMono-BoldOblique.ttf,
Scale = MatchLowercase,
]
{DejaVuSansMono.ttf}
\usepackage{xltxtra}
\usepackage{xunicode}
\usepackage{xspace}
\usepackage{tikz}
\tikzset{node distance=2.5cm,auto}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% biblatex
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[style=authoryear,backref=true]{biblatex}
\usepackage[english=american]{csquotes}
\SetCiteCommand{\parencite}
\DeclareFieldFormat[article]{title}{#1}
\DeclareFieldFormat[inbook]{title}{#1}
\DeclareFieldFormat[inproceedings]{title}{#1}
\DeclareFieldFormat[thesis]{title}{#1}
\renewcommand{\subtitlepunct}{\ifterm{}{\addcolon}\addspace}
\addbibresource{cain.bib}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% hyperref
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{hyperref}
\hypersetup{colorlinks=true}
\hypersetup{linktocpage=true}
\definecolor{citecolor}{rgb}{0,0.7,0}
\definecolor{linkcolor}{rgb}{0.7,0,0}
\definecolor{urlcolor}{rgb}{0,0,0.7}
\hypersetup{citecolor=citecolor}
\hypersetup{linkcolor=linkcolor}
\hypersetup{urlcolor=urlcolor}
\ifcolor
\else
\hypersetup{hidelinks}
\fi
\hypersetup{pdftitle={Category Theory Applied to Functional Programming}}
\hypersetup{pdfauthor={Juan Pedro Villa Isaza}}
\hypersetup{pdfkeywords={category theory, functional programming}}
\hypersetup{pdfsubject={Systems Engineering undergraduate project}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Verbatim
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newfontfamily\dejavu{DejaVuSansMono.ttf}
\usepackage{fancyvrb}
\usepackage{relsize}
\DefineVerbatimEnvironment
{codeagda}
{Verbatim}
{frame=lines}
\DefineVerbatimEnvironment
{codehaskell}
{Verbatim}
{frame=lines}
\DefineVerbatimEnvironment
{code}
{Verbatim}
{frame=lines}
\newcommand{\textagda}[1]{\texttt{#1}}
\newcommand{\texthaskell}[1]{\texttt{#1}}
\newcommand{\module}[1]{\textsf{#1}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Steps
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newlist{steps}{enumerate}{1}
\setlist[steps]{label=\arabic*.,ref=\arabic*,itemsep=0pt}
\newcommand{\case}[1]{\noindent{Case {#1}:}}
\newcommand{\caseh}[1]{\case{\texthaskell{#1}}}
\newcommand{\step}[1]{\item[]{#1}}
\newcommand{\steph}[1]{\step{\texthaskell{#1}}}
\newcommand{\stepm}[1]{\step{\ensuremath{#1}}}
\newcommand{\by}[1]{(by {#1})}
\newcommand{\bydef}[1]{(by definition of {#1})}
\newcommand{\bydefh}[1]{\bydef{\texthaskell{#1}}}
\newcommand{\bydefs}[1]{(by definitions of {#1})}
\newcommand{\bydefsh}[2]{\bydefs{\texthaskell{#1} and \texthaskell{#2}}}
\newcommand{\byih}[1]{(by inductive hypothesis)}
\newcommand{\eq}{\ensuremath{=}}
\newcommand{\eqh}{\texthaskell{=}}
\newcommand{\eqby}[1]{\item[]\quad\eq\quad\by{#1}}
\newcommand{\eqbyh}[1]{\item[]\quad\eqh\quad\by{#1}}
\newcommand{\eqbydef}[1]{\item[]\quad\eq\quad\bydef{#1}}
\newcommand{\eqbydefh}[1]{\item[]\quad\eqh\quad\bydefh{#1}}
\newcommand{\eqbydefsh}[2]{\item[]\quad\eqh\quad\bydefsh{#1}{#2}}
\newcommand{\eqbyih}{\item[]\quad\eq\quad\byih{}}
\newcommand{\eqbyihh}[1]{\item[]\quad\eqh\quad\byih{\texthaskell{#1}}}
\newcommand{\eqtext}[1]{\item[]\quad\eq\quad({#1})}
\newcommand{\eqbynothing}{\item[]\quad\eq\quad}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Theorems
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\theoremstyle{definition}
\newtheorem{definition}{Definition}[chapter]
\newtheorem{example}{Example}[section]
\newtheorem{convention}{Convention}
\newtheorem{remark}{Remark}[chapter]
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}[chapter]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Lemma}
\theoremstyle{remark}
\newtheorem*{terminology}{Terminology}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Commands and operators
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Categories
\DeclareMathOperator{\obj}{O}
\DeclareMathOperator{\mor}{M}
\DeclareMathOperator{\dom}{dom}
\DeclareMathOperator{\cod}{cod}
\DeclareMathOperator{\id}{id}
\newcommand{\idO}[1]{\natO{\id}{#1}}
\newcommand{\comp}{\ensuremath{\mathrel{\circ}}}
\newcommand{\pmoc}{\ensuremath{\mathrel{;}}}
\newcommand{\cat}[1]{\ensuremath{\mathcal{#1}}}
\newcommand{\catO}[1]{\ensuremath{\cat{#1}_{\obj}}}
\newcommand{\catM}[1]{\ensuremath{\cat{#1}_{\mor}}}
\newcommand{\catbf}[1]{\ensuremath{\mathbf{#1}}\xspace}
\newcommand{\alg}{\catbf{Alg}}
\newcommand{\falg}[1]{\func{#1}\text{-}\alg}
\newcommand{\hask}{\catbf{Hask}}
\newcommand{\set}{\catbf{Set}}
\newcommand{\agda}{\catbf{Agda}}
%% Functors
\newcommand{\func}[1]{\ensuremath{\mathsf{#1}}}
\newcommand{\funcO}[1]{\ensuremath{\func{#1}_{\obj}}}
\newcommand{\funcM}[1]{\ensuremath{\func{#1}_{\mor}}}
%% Natural transformations
\newcommand{\nat}[1]{\ensuremath{#1}}
\newcommand{\natO}[2]{\ensuremath{\nat{#1}_{#2}}}
%% Monads
\newcommand{\underscore}{\ensuremath{\underline{~}}}
\newcommand{\mon}[1]{\func{#1}}
\newcommand{\monM}[2]{\ensuremath{#2^*}}
%% Algebras
\DeclareMathOperator{\inmo}{in}
\newcommand{\cata}[1]{\ensuremath{\llparenthesis#1\rrparenthesis}}
\DeclareMathOperator{\zero}{zero}
\DeclareMathOperator{\suc}{succ}
\newcommand{\listof}[1]{\text{List}(#1)}
\DeclareMathOperator{\nil}{nil}
\DeclareMathOperator{\cons}{cons}
\DeclareMathOperator{\fold}{fold}
\DeclareMathOperator{\foldr}{foldr}
\DeclareMathOperator{\add}{add}
\DeclareMathOperator{\mul}{mult}
\DeclareMathOperator{\length}{length}
\DeclareMathOperator{\append}{append}
\DeclareMathOperator{\map}{map}
%% \newcommand{\term}[1]{#1}