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\author{Daniel Hillerström}
\title{Foundations for Programming and Implementing Effect Handlers}
\institute{The University of Edinburgh, Scotland UK}
\subtitle{PhD viva}
\date{August 13, 2021}

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\begin{document}

%
% Title slide
%
\begin{frame}
  \maketitle
\end{frame}

% Dissertation overview
\begin{frame}
  \frametitle{My dissertation at glance}
\end{frame}

\begin{frame}
  \frametitle{Calculi for deep, shallow, and parameterised handlers}

  The calculi capture key aspects of the implementation of effect
  handlers in Links.

  \begin{itemize}
    \item $\HCalc$ ordinary deep handlers (fold).
    \item $\SCalc$ shallow handlers (case-split).
    \item $\HPCalc$ parameterised deep handlers (fold+state).
  \end{itemize}

  The actual implementation is the union of the three calculi.
\end{frame}

% UNIX
\begin{frame}
  \frametitle{Effect handlers as composable operating systems}

  An interpretation of \citeauthor{RitchieT74}'s
  UNIX~\cite{RitchieT74} in terms of effect handlers.\\[2em]

  \[
    \bl
    \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\textbf{Basic idea}
      \ba[m]{@{\qquad}r@{~}c@{~}l}
        \text{\emph{system call}} &\approx& \text{\emph{operation invocation}}\\
        \text{\emph{system call implementation}} &\approx& \text{\emph{operation interpretation}}
      \ea
    \el
  \]\hfill\\[2em]

  \textbf{Key point} Legacy code is modularly retrofitted with functionality.
\end{frame}

% CPS translation
\begin{frame}
  \frametitle{CPS transforms for effect handlers}

  A higher-order CPS transform for effect handlers with generalised
  continuations.\\[1em]

  \textbf{Generalised continuation} Structured representation of
  delimited continuations.\\[0.5em]

  \[
    \Scale[1.8]{\kappa = \overline{(\sigma, (\hret,\hops))}}
  \]\\[1em]

  \textbf{Key point} Separate the \emph{doing} layer ($\sigma$) from the \emph{being} layer ($H$).
\end{frame}

% Abstract machine
\begin{frame}
  \frametitle{Abstract machine semantics for effect handlers}

  Plugging generalised continuations into \citeauthor{FelleisenF86}'s
  CEK machine~\cite{FelleisenF86} yields a runtime for effect
  handlers.\\[2em]

  \[
    \Scale[2]{\cek{C \mid E \mid K = \overline{((H,E), \sigma)}}}
  \]

\end{frame}

% Interdefinability of handlers
\begin{frame}
  \frametitle{Interdefinability of effect handlers}

  Deep, shallow, and parameterised handlers are interdefinable
  w.r.t. to typability-preserving macro-expressiveness.

  \begin{itemize}
    \item Deep as shallow, $\mathcal{D}\llbracket - \rrbracket$, image is lightweight.
    \item Shallow as deep, $\mathcal{S}\llbracket - \rrbracket$, image is computationally expensive.
    \item Parameterised as deep, $\mathcal{P}\llbracket - \rrbracket$,
      image uses explicit state-passing.
  \end{itemize}
\end{frame}

% Asymptotic speed up with first-class control
\begin{frame}
  \frametitle{Asymptotic speed up with effect handlers}

  Effect handlers can make some programs faster!

  \[
    \Count_n : ((\Nat_n \to \Bool) \to \Bool) \to \Nat
  \]\\[1em]
  %
  Using type-respecting expressiveness
  \begin{itemize}
  \item There \textbf{exists} an implementation of $\Count_n \in \HPCF$ with
    effect handlers such that the runtime for every $n$-standard predicate $P$ is
    $\Count_n~P = \BigO(2^n)$.
  \item Forall implementations of $\Count_n \in \BPCF$ the runtime for every $n$-standard predicate $P$ is $\Count_n~P = \Omega(n2^n)$
  \end{itemize}
\end{frame}

% Background
\begin{frame}
  \frametitle{Continuations literature review}
\end{frame}

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% References
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\begin{frame}%[allowframebreaks]
  \frametitle{References}
  \nocite{*}
  \bibliographystyle{plainnat}
  \bibliography{\jobname}
\end{frame}
\end{document}