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% Document Info
\author{cawinkelmann}
\pdfinfo{
  /Title (haskell-typeclasses.pdf)
  /Creator (Cheatography)
  /Author (cawinkelmann)
  /Subject (Haskell Typeclasses Cheat Sheet)
}

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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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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Haskell Typeclasses Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{cawinkelmann} via \textcolor{DarkBackground}{\uline{cheatography.com/91540/cs/20520/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}cawinkelmann \\
  \uline{cheatography.com/cawinkelmann} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 14th September, 2019.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\mymulticolumn{1}{x{17.67cm}}{\bf\textcolor{white}{Functor Definitions}}  \tn
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\mymulticolumn{1}{x{17.67cm}}{class Functor f where \newline   fmap :: (a -\textgreater{} b) -\textgreater{} f a -\textgreater{} f b \newline   (\textless{}\$) :: a -\textgreater{} f b -\textgreater{} f a \newline   (\textless{}\$) = fmap . const \newline  \newline {\emph{ -{}- Example Instances }} \newline  \newline instance Functor ((-\textgreater{}) r) where \newline   fmap = (.) \newline  \newline instance Functor {[}a{]} where \newline   fmap = map \newline  \newline instance Functor Maybe where \newline   fmap \_ Nothing = Nothing \newline   fmap f (Just a) = Just (f a) \newline  \newline instance Functor IO where \newline   fmap f x = x \textgreater{}\textgreater{}= (pure . f)} \tn 
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\mymulticolumn{1}{x{17.67cm}}{{\bf{Functor Laws:}} \newline  \newline {\emph{ Functors must preserve identity morphisms }} \newline `fmap id = id` \newline {\emph{ Functors preserve composition of morphisms }} \newline `fmap (f . g) = fmap f . fmap g`}  \tn 
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\mymulticolumn{1}{x{17.67cm}}{class Functor f =\textgreater{} Applicative f where \newline     \{-\# MINIMAL pure, ((\textless{}{\emph{\textgreater{}) | liftA2) \#-\} \newline     pure :: a -\textgreater{} f a \newline     (\textless{}}}\textgreater{}) :: f (a -\textgreater{} b) -\textgreater{} f a -\textgreater{} f b \newline     (\textless{}{\emph{\textgreater{}) = liftA2 id \newline     liftA2 :: (a -\textgreater{} b -\textgreater{} c) -\textgreater{} f a -\textgreater{} f b -\textgreater{} f c \newline     liftA2 f x = (\textless{}}}\textgreater{}) (fmap f x) \newline     ({\emph{\textgreater{}) :: f a -\textgreater{} f b -\textgreater{} f b \newline     a1 }}\textgreater{} a2 = (id \textless{}\$ a1) \textless{}{\emph{\textgreater{} a2 \newline     (\textless{}}}) :: f a -\textgreater{} f b -\textgreater{} f a \newline     (\textless{}{\emph{) = liftA2 const \newline  \newline }} -{}- Example instances {\emph{ \newline  \newline instance Applicative Maybe where \newline     pure = Just \newline  \newline     Just f  \textless{}}}\textgreater{} m       = fmap f m \newline     Nothing \textless{}{\emph{\textgreater{} \_m      = Nothing \newline  \newline     liftA2 f (Just x) (Just y) = Just (f x y) \newline     liftA2 \_ \_ \_ = Nothing \newline  \newline     Just \_m1 }}\textgreater{} m2      = m2 \newline     Nothing  {\emph{\textgreater{} \_m2     = Nothing \newline  \newline instance Applicative IO where \newline     \{-\# INLINE pure \#-\} \newline     \{-\# INLINE (}}\textgreater{}) \#-\} \newline     \{-\# INLINE liftA2 \#-\} \newline     pure  = returnIO \newline     ({\emph{\textgreater{})  = thenIO \newline     (\textless{}}}\textgreater{}) = ap \newline     liftA2 = liftM2} \tn 
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