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  /Title (haskell-patterns.pdf)
  /Creator (Cheatography)
  /Author (logcat)
  /Subject (Haskell patterns Cheat Sheet)
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\noindent
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    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Haskell patterns Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{logcat} via \textcolor{DarkBackground}{\uline{cheatography.com/27075/cs/12218/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}logcat \\
  \uline{cheatography.com/logcat} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 5th July, 2017.\\
   Updated 5th July, 2017.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
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% www.emerson.emory.edu/services/latex/latex_169.html
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
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\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Composition and application}}  \tn
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`(.) :: (b -\textgreater{} c) -\textgreater{} (a -\textgreater{} b) -\textgreater{}~a~-\textgreater{}~c` & function composition \tn 
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% Row 1
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`(\$) :: (a -\textgreater{} b) -\textgreater{} a -\textgreater{} b` & application operator, has low, right-associative binding precedence, for example \seqsplit{`f \$ g \$ h x  =  f (g (h x))`} \tn 
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
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\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Monoid}}  \tn
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\mymulticolumn{2}{x{17.67cm}}{typeclass where empty/append are defined} \tn 
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\seqsplit{`mempty  :: Monoid} a =\textgreater{} a` & identity of mappend (mappend mempty x = x) \tn 
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`mappend :: Monoid a =\textgreater{} a -\textgreater{} a -\textgreater{} a` & append two monoids (associative: brackets does not matter)\{\{nl\}\}`mappend x (mappend y z) = mappend (mappend x y) z` \tn 
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% Row 3
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`\textless{}\textgreater{}      :: Monoid m =\textgreater{} m -\textgreater{} m -\textgreater{} m` & infix synonym for mappend (`"he" \textless{}\textgreater{} "llo"`) \tn 
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`mconcat :: {[}a{]} -\textgreater{} a` & fold list using mappend and mempty \tn 
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
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\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Functor}}  \tn
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\mymulticolumn{2}{x{17.67cm}}{typeclass where `fmap` (`map`/`\textless{}\$\textgreater{}`) is defined} \tn 
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should satisfy laws & `fmap id  ==  id`\{\{nl\}\}`fmap (f . g)  ==  fmap f . fmap g` \tn 
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`fmap :: Functor f =\textgreater{} (a -\textgreater{} b) -\textgreater{} f a -\textgreater{} f b` & map function over functor\{\{nl\}\}`fmap (+1) (Just 3)` is `Just 4` \tn 
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`\textless{}\$\textgreater{}  :: Functor f =\textgreater{} (a -\textgreater{} b) -\textgreater{} f a -\textgreater{} f b` & function mapped over functor\{\{nl\}\}infix synonym for `fmap`\{\{nl\}\}`(+1) \textless{}\$\textgreater{} (Just 3)` is `Just 4` \tn 
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
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\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Applicative}}  \tn
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typeclass where `pure`/`\textless{}*\textgreater{}` are defined\{\{nl\}\}have `Functor` as super class & \{\{nl\}\}every instance of `Applicative` must have instance of `Functor`\{\{nl\}\}so `fmap` (`map`/`\textless{}\$\textgreater{}`) can be used \tn 
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`pure :: Applicative f =\textgreater{} a -\textgreater{} f a` & create an instance of Applicative\{\{nl\}\}`pure 3 :: {[}Int{]} ` is `{[}3{]}`\{\{nl\}\}`pure 3 :: Maybe Int` is `Just 3`\{\{nl\}\}`pure (+3) :: Maybe (Int -\textgreater{} Int)` is `Just` a function from Int to Int\{\{nl\}\}`pure (+3) :: {[}Int -\textgreater{} Int{]}` is list of function\{\{nl\}\}`pure 1 :: IO Int` is how it is printed in ghci \tn 
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`(\textless{}*\textgreater{}) :: Applicative f =\textgreater{} f (a -\textgreater{} b) -\textgreater{} f a -\textgreater{} f b` & sequential application / apply\{\{nl\}\}`Just (+1) \textless{}*\textgreater{} Just 1 :: Maybe Int` is `Just 2`\{\{nl\}\}`{[}(+1), (+2){]} \textless{}*\textgreater{} {[}0{]} :: {[}Int{]}` is `{[}1, 2{]}` \tn 
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
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\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Monad}}  \tn
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typeclass\{\{nl\}\}have `Applicative` as super class & \{\{nl\}\}every instance of `Monad` must have instance of `Applicative` and `Functor`\{\{nl\}\}so `fmap` (`map`/`\textless{}\$\textgreater{}`) and `\textless{}*\textgreater{}`/`pure` can be used \tn 
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`return :: Monad m =\textgreater{} a -\textgreater{} m a` & is `pure` \tn 
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`(\textgreater{}\textgreater{}) :: Monad m =\textgreater{} m a -\textgreater{} m b -\textgreater{} m b` & sequentially compose two monads, first is usually\{\{nl\}\}`Just 2 \textgreater{}\textgreater{} Just 3` is `Just 3`\{\{nl\}\}`Nothing \textgreater{}\textgreater{} Just 3` is `Nothing`\{\{nl\}\}`{[}9, 9{]} \textgreater{}\textgreater{} {[}0, 0, 0{]}` is `{[}0,0,0,0,0,0{]}` \tn 
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`(\textgreater{}\textgreater{}=) :: Monad m =\textgreater{} m a -\textgreater{} (a -\textgreater{} m b) -\textgreater{} m b` & bind, sequentially compose two monads, value of first passed as argument to the second\{\{nl\}\}`Just 3 \textgreater{}\textgreater{}= \textbackslash{}x -\textgreater{} Just (x + 1)` is `Just 4`\{\{nl\}\}`Nothing \textgreater{}\textgreater{}= \textbackslash{}x -\textgreater{} Just (x + 1)` is `Nothing`\{\{nl\}\}`{[}0, 0{]} \textgreater{}\textgreater{}= \textbackslash{}x -\textgreater{} {[}x + 1{]}` is `{[}1, 1{]}`\{\{nl\}\}`{[}0, 0{]} \textgreater{}\textgreater{}= \textbackslash{}x -\textgreater{} {[}x + 1, 2{]}` is `{[}1,2,1,2{]}`\{\{nl\}\}`{[}{]} \textgreater{}\textgreater{}= \textbackslash{}x -\textgreater{} {[}x + 1{]}` is `{[}{]}` \tn 
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