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styling
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3 changed files with 136 additions and 25 deletions
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@ -4,3 +4,9 @@ hd (x : _) = x
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main :: IO ()
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main = print (hd []::[String])
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reverse :: [a] -> [a]
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reverse l = rev l []
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where
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rev [] a = a
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rev (x:xs) a = rev xs (x:a)
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@ -140,6 +140,95 @@ Leon Vatthauer%\inst{1}
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\usepackage{MnSymbol} % for \squaredots
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\usepackage{listings}
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\lstset{mathescape}
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\usepackage{xcolor}
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\definecolor{codegray}{rgb}{0.5,0.5,0.5}
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\definecolor{string}{HTML}{79731B}
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\definecolor{keyword}{HTML}{447A59}
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\definecolor{background}{HTML}{E6E6E6}
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\definecolor{error}{HTML}{9B0511}
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\definecolor{agda-name}{HTML}{3b31f9}
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\definecolor{agda-keyword}{HTML}{fc970a}
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\definecolor{agda-constructor}{HTML}{08aa20}
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\lstdefinestyle{mystyle}{
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backgroundcolor=\color{background},
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% commentstyle=\color{codegreen},
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% keywordstyle=\color{keyword},
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numberstyle=\tiny\color{codegray},
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stringstyle=\color{string},
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basicstyle=\ttfamily\small,
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breakatwhitespace=false,
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breaklines=true,
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captionpos=b,
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keepspaces=true,
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numbers=left,
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numbersep=5pt,
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showspaces=false,
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showstringspaces=false,
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showtabs=false,
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tabsize=2
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}
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\lstdefinelanguage{myhaskell}{
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keywords=[1]{
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where
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},
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keywordstyle=[1]\color{agda-keyword},
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keywords=[2]{
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error
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},
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keywordstyle=[2]\color{error},
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keywords=[3]{
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head, reverse, rev
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},
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keywordstyle=[3]\color{agda-name},
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morestring=[b]"
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}
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\lstdefinelanguage{myagda}{
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keywords=[1]{
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data, where
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},
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keywordstyle=[1]\color{agda-keyword},
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keywords=[2]{
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Delay, Set, foldl, Colist, reverse, reverseAcc, run_for_steps, run, for, steps, fin-colist, inf-colist, never, head, List, Maybe
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},
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keywordstyle=[2]\color{agda-name},
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keywords=[3]{
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now, later, zero, suc, just, nothing, nil, cons
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},
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keywordstyle=[3]\color{agda-constructor}
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}
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\lstset{style=mystyle}
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\usepackage{lmodern}
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\usepackage{tikz}
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\usetikzlibrary{shapes.callouts}
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\usepackage{xparse}
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\tikzset{
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invisible/.style={opacity=0,text opacity=0},
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visible on/.style={alt=#1{}{invisible}},
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alt/.code args={<#1>#2#3}{%
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\alt<#1>{\pgfkeysalso{#2}}{\pgfkeysalso{#3}} % \pgfkeysalso doesn't change the path
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},
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}
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\NewDocumentCommand{\mycallout}{r<> O{opacity=0.8,text opacity=1} m m}{%
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\tikz[remember picture, overlay]\node[align=left, fill=red!50, text width=15cm,
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#2,visible on=<#1>, rounded corners,
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draw,rectangle]
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at (#3) {#4};
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}
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\newcommand{\tikzmark}[1]{\tikz[overlay,remember picture,baseline=-0.5ex] \node (#1) {};}
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\begin{document}
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% Title page
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\begin{frame}[t,titleimage]{-}
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@ -1,72 +1,88 @@
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\begin{frame}[t, fragile]{Partiality in Haskell}{}
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Haskell allows users to define arbitrary partial functions, some can be spotted easily by their definition:
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\begin{lstlisting}[language=haskell]
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\begin{itemize}[<+->]
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\item Haskell allows users to define arbitrary partial functions, some can be spotted easily by their definition:
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\vskip 1cm
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\begin{lstlisting}[language=myhaskell, linewidth=12cm]
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head :: [a] -> a
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head [] = error "empty list"
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head (x:xs) = x
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\end{lstlisting}
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% TODO right of this add error bubble that shows what happens for `head []`
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others might be more subtle:
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\begin{lstlisting}[language=haskell]
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\mycallout<3->{21, 1.5}{
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ghci> head []\\
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*** Exception: empty list\\
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CallStack (from HasCallStack):\\
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error, called at example.hs:2:9 in main:Main
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}
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\item
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others might be more subtle:
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\vskip 1cm
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\begin{lstlisting}[language=myhaskell, linewidth=12cm]
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reverse l = rev l []
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where
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rev [] a = a
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rev (x:xs) a = rev xs (x:a)
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\end{lstlisting}
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\mycallout<4->{21, 2}{
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ghci> ones = 1 : ones\\
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ghci> reverse ones\\
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...
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}
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\end{itemize}
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% TODO right of this add error bubble that shows `reverse ones`
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\end{frame}
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\begin{frame}[t, fragile]{Partiality in Agda}{The Maybe Monad}
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In Agda every function has to be total and terminating, so how do we model partial functions?
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\begin{lstlisting}
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\begin{itemize}[<+->]
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\item Simple errors can be modelled with the maybe monad
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\begin{lstlisting}[linewidth=14cm, language=myagda]
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data Maybe (A : Set) : Set where
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just : A $\rightarrow$ Maybe A
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nothing : Maybe A
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\end{lstlisting}
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for head we can then do:
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for head we can then do:
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\begin{lstlisting}
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\begin{lstlisting}[linewidth=14cm, language=myagda]
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head : $\forall$ A $\rightarrow$ List A $\rightarrow$ Maybe A
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head nil = nothing
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head (cons x xs) = just x
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\end{lstlisting}
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But what about \lstinline|reverse|?
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\item What about \lstinline|reverse|?
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\end{itemize}
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\end{frame}
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\begin{frame}[t, fragile]{Partiality in Agda}{Capretta's Delay Monad}
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Capretta's Delay Monad is a coinductive data type whose inhabitants can be viewed as suspended computations.
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\begin{lstlisting}
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\begin{itemize}[<+->]
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\item Capretta's Delay Monad is a \textbf{coinductive} data type whose inhabitants can be viewed as suspended computations.
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\begin{lstlisting}[linewidth=20cm, language=myagda]
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data Delay (A : Set) : Set where
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now : A $\rightarrow$ Delay A
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later : $\infty$ (Delay A) $\rightarrow$ Delay A
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\end{lstlisting}
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\lstinline|now| lifts a computation, while \lstinline|later| delays it by one time unit.
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The delay datatype contains a constant for non-termination:
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\begin{lstlisting}
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\item The delay datatype contains a constant for non-termination:
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\begin{lstlisting}[linewidth=20cm, language=myagda]
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never : Delay A
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never = later ($\sharp$ never)
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\end{lstlisting}
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\item and we can define a function for \textit{running} a computation (for some amount of steps):
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and we can define a function for \textit{running} a computation (for some amount of steps):
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\begin{lstlisting}
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\begin{lstlisting}[linewidth=20cm, language=myagda]
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run_for_steps : Delay A $\rightarrow$ $\mathbb{N}$ $\rightarrow$ Delay A
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run now x for n steps = now x
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run later x for zero steps = later x
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run later x for suc n steps = run $\flat$ x for n steps
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\end{lstlisting}
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\end{itemize}
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\end{frame}
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\begin{frame}[t, fragile]{Partiality in Agda}{Reversing (possibly infinite) lists}
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\begin{lstlisting}
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\begin{frame}[c, fragile]{Partiality in Agda}{Reversing (possibly infinite) lists}
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\centering
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\begin{lstlisting}[language=myagda]
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foldl : $\forall$ {A B : Set} $\rightarrow$ (A $\rightarrow$ B $\rightarrow$ A) $\rightarrow$ A $\rightarrow$ Colist B $\rightarrow$ Delay A
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foldl c n [] = now n
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foldl c n (x $\squaredots$ xs) = later ($\sharp$ foldl c (c n x) ($\flat$ xs))
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reverse {A} = reverseAcc []
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where
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reverseAcc : Colist A $\rightarrow$ Colist A $\rightarrow$ Delay (Colist A)
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reverseAcc = foldl ($\lambda$ xs x $\rightarrow$ x $\squaredots$ ($\sharp$ xs)) -- 'flip _$\squaredots$_' with extra steps
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reverseAcc = foldl ($\lambda$ xs x $\rightarrow$ x $\squaredots$ ($\sharp$ xs))
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\end{lstlisting}
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\end{frame}
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