\documentclass[10pt,a4paper]{article}

% Packages
\usepackage{fancyhdr}           % For header and footer
\usepackage{multicol}           % Allows multicols in tables
\usepackage{tabularx}           % Intelligent column widths
\usepackage{tabulary}           % Used in header and footer
\usepackage{hhline}             % Border under tables
\usepackage{graphicx}           % For images
\usepackage{xcolor}             % For hex colours
%\usepackage[utf8x]{inputenc}    % For unicode character support
\usepackage[T1]{fontenc}        % Without this we get weird character replacements
\usepackage{colortbl}           % For coloured tables
\usepackage{setspace}           % For line height
\usepackage{lastpage}           % Needed for total page number
\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{kvp\_}
\pdfinfo{
  /Title (comp302.pdf)
  /Creator (Cheatography)
  /Author (kvp\_)
  /Subject (COMP302 Cheat Sheet)
}

% Lengths and widths
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\renewcommand{\headrulewidth}{0pt} % Remove header line
\renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit
% This two commands together give roughly
% the right line height in the tables
\renewcommand{\arraystretch}{1.3}
\onehalfspacing

% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
\newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols
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\newcommand{\tn}{\tabularnewline} % Required as custom column type in use

% Font and Colours
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\definecolor{FootBackground}{HTML}{666666}
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\renewcommand{\familydefault}{\sfdefault}
\color{TextColor}

% Header and Footer
\pagestyle{fancy}
\fancyhead{} % Set header to blank
\fancyfoot{} % Set footer to blank
\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
    }
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{COMP302 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{kvp\_} via \textcolor{DarkBackground}{\uline{cheatography.com/20610/cs/3336/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}kvp\_ \\
  \uline{cheatography.com/kvp} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 20th February, 2015.\\
   Updated 13th May, 2016.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{x{5.52 cm} x{2.48 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{SML Syntax}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{8.4cm}}{{\bf{String}}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
`\#"str"` & character \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
`String.sub : string * int -\textgreater{} char` & n-th character \tn 
% Row Count 4 (+ 2)
% Row 3
\SetRowColor{white}
`chr` & ascii to character \tn 
% Row Count 6 (+ 2)
% Row 4
\SetRowColor{LightBackground}
`ord : char -\textgreater{} int` & character to ascii \tn 
% Row Count 8 (+ 2)
% Row 5
\SetRowColor{white}
`\textasciicircum{}` & concatenate \tn 
% Row Count 9 (+ 1)
% Row 6
\SetRowColor{LightBackground}
`String.tokens : (char -\textgreater{} bool) -\textgreater{} string -\textgreater{} string list` & tokenize a string \tn 
% Row Count 12 (+ 3)
% Row 7
\SetRowColor{white}
`String.explode : string -\textgreater{} char list` & also implode \tn 
% Row Count 14 (+ 2)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{8.4cm}}{{\bf{List}}} \tn 
% Row Count 15 (+ 1)
% Row 9
\SetRowColor{white}
`@ : 'a list @ 'a list` & \seqsplit{concatenation} \tn 
% Row Count 17 (+ 2)
% Row 10
\SetRowColor{LightBackground}
`List.partition : ('a -\textgreater{} bool) -\textgreater{} 'a list -\textgreater{} 'a list * 'a list` & quicksort \tn 
% Row Count 20 (+ 3)
% Row 11
\SetRowColor{white}
`List.rev : 'a list -\textgreater{} 'a list` & reverse \tn 
% Row Count 22 (+ 2)
% Row 12
\SetRowColor{LightBackground}
`List.exists : ('a -\textgreater{} bool) -\textgreater{} 'a list -\textgreater{} bool` & true for any \tn 
% Row Count 24 (+ 2)
% Row 13
\SetRowColor{white}
`List.all : ('a -\textgreater{} bool) -\textgreater{} 'a list -\textgreater{} bool` & true for all \tn 
% Row Count 26 (+ 2)
% Row 14
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{8.4cm}}{`String.concatWith : string -\textgreater{} string list -\textgreater{} string`} \tn 
% Row Count 28 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Referential Transparency}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Replace any expression with another expression of "equal" value does not affect the value of the expression% Row Count 3 (+ 3)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Equivalence}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Two programs are equivalent iff \newline % Row Count 1 (+ 1)
1. They both evaluate to the same value, or \newline % Row Count 2 (+ 1)
2. They both raise the same exception, or \newline % Row Count 3 (+ 1)
3. They both enter an infinite loop \newline % Row Count 4 (+ 1)
Properties \newline % Row Count 5 (+ 1)
1. Equivalence is an equivalence relation \newline % Row Count 6 (+ 1)
2. Equivalence is a congruence (one program can be substituted for another) \newline % Row Count 8 (+ 2)
3. If e |-\textgreater{} e' then e is equivalent to e'% Row Count 9 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Valuable \& Total}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Expression {\bf{e}} is valuable iff there is some value {\bf{v}} s.t. {\bf{e}} == {\bf{v}} \newline % Row Count 2 (+ 2)
- If {\bf{e}} = ({\bf{e1}},{\bf{e2}})  \newline % Row Count 3 (+ 1)
- If {\bf{e}} = {\bf{e1}}+{\bf{e2}} \newline % Row Count 4 (+ 1)
- If {\bf{e}} = {\bf{e1}} :: {\bf{e2}} \newline % Row Count 5 (+ 1)
then e is valuable iff e1 is valuable and e2 is valuable \newline % Row Count 7 (+ 2)
A function {\bf{f}} : A -\textgreater{} B is total iff for all values {\bf{v}} : A,{\bf{ f(v)}} is valuable% Row Count 9 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Currying}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{=== Non-curried === \newline fun pow (x, y) : int {\emph{ int -\textgreater{} int = \newline     case y of` \newline         0 =\textgreater{} 1` \newline     | ~ \_ =\textgreater{} x }} pow(x, y-1) \newline === Curried === \newline fun pow x : int -\textgreater{} int -\textgreater{} int = \newline     fn (y) =\textgreater{} case y of \newline                   0 =\textgreater{} 1 \newline               | ~ \_ =\textgreater{} x {\emph{ pow(x, y-1) \newline fun pow x y = \newline     case y of \newline         0 =\textgreater{} 1 \newline     | ~ \_ =\textgreater{} x }} pow(x, y-1) \newline === Currying and Uncurrying === \newline curry : (('a * 'b) -\textgreater{} 'c) -\textgreater{} ('a -\textgreater{} 'b -\textgreater{} 'c)) \newline fun curry f x y = f (x,y) \newline fun uncurry f (x,y) = f x y \newline uncurry : ('a -\textgreater{} 'b -\textgreater{} 'c) -\textgreater{} (('a 'b) -\textgreater{} 'c)} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Composition}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{`fun compose (f, g) = fn x =\textgreater{} f(g x)` \newline % Row Count 1 (+ 1)
Using infix operator \newline % Row Count 2 (+ 1)
`val sqrt\_of\_abs = Math.sqrt o Real.fromInt o abs` \newline % Row Count 4 (+ 2)
Pipelining and infix pipeline operator \newline % Row Count 5 (+ 1)
`fun pipeline (f, g) = g f \newline % Row Count 6 (+ 1)
`infix !\textgreater{}` \newline % Row Count 7 (+ 1)
`fun x !\textgreater{} f = f x` \newline % Row Count 8 (+ 1)
`fun sqrt\_of\_abs i =i !\textgreater{} Real.fromInt !\textgreater{} Math.sqrt` \newline % Row Count 10 (+ 2)
`datatype 'a list = Nil | :: of 'a * 'a list`% Row Count 12 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Mergesort}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{fun split (lst : int list) : int list * int list = \newline     case lst of \newline         {[}{]} =\textgreater{} ({[}{]}, {[}{]}) \newline     | ~ {[}x{]} =\textgreater{} ({[}x{]}, {[}{]}) \newline     | ~ x::y::xs =\textgreater{} let val (pile1, pile2) = split xs \newline                     in (x::pile1, y::pile2) \newline                     end \newline fun merge(lst1 : int list, lst2 : int list) : int list = \newline     case (lst1, lst2) of \newline         ({[}{]}, lst2) =\textgreater{} lst2 \newline     | ~ (lst1, {[}{]}) =\textgreater{} lst1 \newline     | ~ (x::xs, y::ys) =\textgreater{} \newline             (case x \textless{} y of \newline                 true =\textgreater{} x::merge(xs,lst2) \newline             | ~ false =\textgreater{} y::merge(lst1, ys) \newline fun mergesort (lst : int list) : int list = \newline     case lst of \newline         {[}{]} =\textgreater{} {[}{]} \newline     | ~ {[}x{]} =\textgreater{} {[}x{]} \newline     | \_ =\textgreater{} let val (pile1, pile2) = split lst \newline            in merge(mergesort pile1, mergesort pile2) \newline            end} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Generalized math functions}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{fun sum (f, a, b, inc) :  \newline     if (a \textgreater{} b) then 0 \newline     else (f a) + sum(f, inc(a), b, inc) \newline  \newline fun piOver8 = sum(fn x =\textgreater{} 1.0 / (x{\emph{(x+2.0)), a, b, fn x =\textgreater{} x + 4.0) \newline  \newline fun integral (f, a, b, dx) = \newline     dx }} sum(f, a+dx/2.0, b, fn x =\textgreater{} x+dx) \newline  \newline fun series (operator, f, lo, hi, inc, identity) = \newline     if (lo \textgreater{} hi) then identity \newline     else operator((f lo), series (operator, f, inc(lo), hi, inc, identity)) \newline  \newline fun sumSeries (f, a, b, inc) = series (op +, f, a, b, inc, 0) \newline fun prodSeries(f, a, b, inc) = series(op *, f, a, b, inc, 1)} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Data types}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{User defined types \newline % Row Count 1 (+ 1)
`datatype tree  = Empty | Node of tree * int * tree` \newline % Row Count 3 (+ 2)
`datatype 'a option = NONE | SOME of 'a` \newline % Row Count 4 (+ 1)
Type synonym \newline % Row Count 5 (+ 1)
`type intPairList = (int * int) list`% Row Count 6 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Map}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{map : ('a -\textgreater{} 'b) * 'a list -\textgreater{} b' list \newline fun map (f lst) = \newline     case lst of \newline         {[}{]} =\textgreater{} {[}{]} \newline     | ~ h::tail =\textgreater{} (f h)::(map f tail)} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Fold}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{fun foldl(f, acc, lst) = \newline     case lst of \newline         {[}{]} =\textgreater{} acc \newline     | ~ h::t =\textgreater{} foldl(f, f(h, acc), t) (*tail recursive*) \newline fun foldr(f, acc, lst) = \newline     case lst of \newline         {[}{]} =\textgreater{} acc \newline     | ~ h::t =\textgreater{} f(h, foldr(f, acc, t)) (*not tail recursive*)} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Associativity}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{`'a -\textgreater{} 'b -\textgreater{} 'c = 'a -\textgreater{} ('b -\textgreater{} 'c)` \newline % Row Count 1 (+ 1)
`f a1 a2 = (f a1) a2`% Row Count 2 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Filter}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{filter : ('a -\textgreater{} bool) * 'a list -\textgreater{} 'a list \newline fun filter (p : 'a -\textgreater{} bool, lst : 'a list) = \newline     case lst of \newline         {[}{]} =\textgreater{} {[}{]} \newline     | ~ x::xs =\textgreater{} if p x then x::(filter p xs) \newline                  else filter p xs} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}