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Daniel Hillerström 5 years ago
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thesis.tex

@ -129,14 +129,17 @@
%% Acknowledgements %% Acknowledgements
\begin{acknowledgements} \begin{acknowledgements}
Firstly, I want to thank Sam Lindley for his guidance, advice, and Firstly, I want to thank Sam Lindley for his guidance, advice, and
encouragement throughout my studies. He has been ardent supervisor,
and he has always been generous with his time. I am fortunate to
have been supervised by him.
My work has been supported by \href{https://www.epsrc.ac.uk/}{EPSRC}
grant \href{http://pervasiveparallelism.inf.ed.ac.uk}{EP/L01503X/1}
(EPSRC Centre for Doctoral Training in Pervasive Parallelism) and by
ERC Consolidator Grant Skye (grant number 682315).
encouragement throughout my studies. He has been enthusiastic
supervisor, and he has always been generous with his time. I am
fortunate to have been supervised by him.
Throughout my studies I have received funding from the
\href{https://www.ed.ac.uk/informatics}{School of Informatics} at
The University of Edinburgh, as well as an
\href{https://www.epsrc.ac.uk/}{EPSRC} grant
\href{http://pervasiveparallelism.inf.ed.ac.uk}{EP/L01503X/1} (EPSRC
Centre for Doctoral Training in Pervasive Parallelism), and by ERC
Consolidator Grant Skye (grant number 682315).
List of people to thank List of people to thank
\begin{itemize} \begin{itemize}
@ -3385,7 +3388,7 @@ deconstructions also gets bigger. The continuation representation
needs more structure. While it is seductive to program with lists, it needs more structure. While it is seductive to program with lists, it
quickly gets unwieldy. quickly gets unwieldy.
\subsection{Simultaneous CPS transform for deep and shallow handlers}
\subsection{Effect handlers via generalised continuations}
\label{sec:cps-deep-shallow} \label{sec:cps-deep-shallow}
\begin{figure} \begin{figure}
% %
@ -3393,31 +3396,31 @@ quickly gets unwieldy.
% %
\begin{equations} \begin{equations}
\cps{-} &:& \ValCat \to \UValCat\\ \cps{-} &:& \ValCat \to \UValCat\\
% \cps{x} &\defas& x\\
\cps{x} &\defas& x\\
\cps{\lambda x.M} &\defas& \dlam x\,\dhk.\Let\;(\dk \dcons \dhk') = \dhk\;\In\;\cps{M} \sapp (\reflect\dk \scons \reflect \dhk') \\ \cps{\lambda x.M} &\defas& \dlam x\,\dhk.\Let\;(\dk \dcons \dhk') = \dhk\;\In\;\cps{M} \sapp (\reflect\dk \scons \reflect \dhk') \\
\cps{\Lambda \alpha.M} &\defas& \dlam \Unit\,\dhk.\Let\;(\dk \dcons \dhk') = \dhk\;\In\;\cps{M} \sapp (\reflect\dk \scons \reflect \dhk') \\ \cps{\Lambda \alpha.M} &\defas& \dlam \Unit\,\dhk.\Let\;(\dk \dcons \dhk') = \dhk\;\In\;\cps{M} \sapp (\reflect\dk \scons \reflect \dhk') \\
\cps{\Rec\,g\,x.M} &\defas& \Rec\,g\,x\,\dhk.\Let\;(\dk \dcons \dhk') = \dhk\;\In\;\cps{M} \sapp (\reflect\dk \scons \reflect \dhk') \\ \cps{\Rec\,g\,x.M} &\defas& \Rec\,g\,x\,\dhk.\Let\;(\dk \dcons \dhk') = \dhk\;\In\;\cps{M} \sapp (\reflect\dk \scons \reflect \dhk') \\
% \multicolumn{3}{c}{
% \cps{\Record{}} \defas \Record{}
% \qquad
% \cps{\Record{\ell = \!\!V; W}} \defas \Record{\ell = \!\cps{V}; \cps{W}}
% \qquad
% \cps{\ell\,V} \defas \ell\,\cps{V}
% }
\multicolumn{3}{c}{
\cps{\Record{}} \defas \Record{}
\qquad
\cps{\Record{\ell = \!\!V; W}} \defas \Record{\ell = \!\cps{V}; \cps{W}}
\qquad
\cps{\ell\,V} \defas \ell\,\cps{V}
}
\end{equations} \end{equations}
% %
\textbf{Computations} \textbf{Computations}
% %
\begin{equations} \begin{equations}
\cps{-} &:& \CompCat \to \SValCat^\ast \to \UCompCat\\ \cps{-} &:& \CompCat \to \SValCat^\ast \to \UCompCat\\
% \cps{V\,W} &\defas& \slam \shk.\cps{V} \dapp \cps{W} \dapp \reify \shk \\
% \cps{V\,T} &\defas& \slam \shk.\cps{V} \dapp \Record{} \dapp \reify \shk \\
% \cps{\Let\; \Record{\ell=x;y} = V \; \In \; N} &\defas& \slam \shk.\Let\; \Record{\ell=x;y} = \cps{V} \; \In \; \cps{N} \sapp \shk \\
% \cps{\Case~V~\{\ell~x \mapsto M; y \mapsto N\}} &\defas&
% \slam \shk.\Case~\cps{V}~\{\ell~x \mapsto \cps{M} \sapp \shk; y \mapsto \cps{N} \sapp \shk\} \\
% \cps{\Absurd~V} &\defas& \slam \shk.\Absurd~\cps{V} \\
% \end{equations}
% \begin{equations}
\cps{V\,W} &\defas& \slam \shk.\cps{V} \dapp \cps{W} \dapp \reify \shk \\
\cps{V\,T} &\defas& \slam \shk.\cps{V} \dapp \Record{} \dapp \reify \shk \\
\cps{\Let\; \Record{\ell=x;y} = V \; \In \; N} &\defas& \slam \shk.\Let\; \Record{\ell=x;y} = \cps{V} \; \In \; \cps{N} \sapp \shk \\
\cps{\Case~V~\{\ell~x \mapsto M; y \mapsto N\}} &\defas&
\slam \shk.\Case~\cps{V}~\{\ell~x \mapsto \cps{M} \sapp \shk; y \mapsto \cps{N} \sapp \shk\} \\
\cps{\Absurd~V} &\defas& \slam \shk.\Absurd~\cps{V} \\
\end{equations}
\begin{equations}
\cps{\Return\,V} &\defas& \slam \shk.\kapp\;(\reify \shk)\;\cps{V} \\ \cps{\Return\,V} &\defas& \slam \shk.\kapp\;(\reify \shk)\;\cps{V} \\
\cps{\Let~x \revto M~\In~N} &\defas& \cps{\Let~x \revto M~\In~N} &\defas&
\bl\slam \sRecord{\shf, \sRecord{\svhret, \svhops}} \scons \shk. \bl\slam \sRecord{\shf, \sRecord{\svhret, \svhops}} \scons \shk.

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