Classification of control operators [WIP].

macros.tex

@@ -425,10 +425,13 @@
 \newcommand{\Cupto}{\keyw{cupto}}
 \newcommand{\Callcc}{\keyw{callcc}}
 \newcommand{\Throw}{\keyw{throw}}
+\newcommand{\Continue}{\keyw{continue}}
 \newcommand{\Catch}{\keyw{catch}}
 \newcommand{\Catchcont}{\keyw{catchcont}}
-\newcommand{\shift}{\keyw{shift}}
-\newcommand{\reset}{\keyw{reset}}
 \newcommand{\Control}{\keyw{control}}
 \newcommand{\Prompt}{\keyw{prompt}}
-\newcommand{\Escape}{\keyw{escape}}
+\newcommand{\Escape}{\keyw{escape}}
+\newcommand{\shift}{\ensuremath{\mathcal{S}}}
+\newcommand{\reset}[1]{\ensuremath{\langle #1 \rangle}}
+
+\newcommand{\cont}{\keyw{cont}}

thesis.bib

@@ -1065,7 +1065,7 @@
 
 # Scheme
 @techreport{SussmanS75,
-  author = {Gerald J. Sussman and Guy L. Steele Jr.},
+  author = {Gerald J. Sussman and Guy L. Steele},
   institution = {{MIT}},
   month = {December},
   number = {AI Memo No. 349},
@@ -1391,6 +1391,19 @@
   year      = {1991}
 }
 
+# Spawn
+@article{HiebDA94,
+  author    = {Robert Hieb and
+               R. Kent Dybvig and
+               Claude W. Anderson III},
+  title     = {Subcontinuations},
+  journal   = {{LISP} Symb. Comput.},
+  volume    = {7},
+  number    = {1},
+  pages     = {83--110},
+  year      = {1994}
+}
+
 # Comparison of (some) delimited control operators
 @misc{Shan04,
   author    = {Chung{-}chieh Shan},
@@ -1553,6 +1566,17 @@
 }
 
 # Catchcont
+@inproceedings{Longley09,
+  author    = {John Longley},
+  title     = {Some Programming Languages Suggested by Game Models (Extended Abstract)},
+  booktitle = {{MFPS}},
+  series    = {Electronic Notes in Theoretical Computer Science},
+  volume    = {249},
+  pages     = {117--134},
+  publisher = {Elsevier},
+  year      = {2009}
+}
+
 @misc{LongleyW08,
   author    = {John Longley and Nicholas Wolverson},
   title     = {Eriskay: a programming language based on game semantics},
@@ -1760,4 +1784,12 @@
   pages     = {158--168},
   publisher = {{ACM} Press},
   year      = {1988}
+}
+
+# Racket
+@misc{Flatt20,
+  author = {Matthew Flatt and {PLT}},
+  title  = {The {R}acket Reference (version 7.9)},
+  month  = nov,
+  year   = 2020
 }

thesis.tex

@@ -647,10 +647,65 @@ Downward and upward use of continuations.
 Describe how effect handlers fit amongst shift/reset, prompt/control,
 callcc, J, catchcont, etc.
 
+\begin{table}
+  \centering
+  \begin{tabular}{| l | l | l | l |}
+    \hline
+    \multicolumn{1}{| l |}{\textbf{Name}} & \multicolumn{1}{l |}{\textbf{Extent}} & \multicolumn{1}{l |}{\textbf{Behaviour}} & \multicolumn{1}{l |}{\textbf{Canonical reference}}\\
+    \hline
+    call/cc  & Undelimited & Abortive & \citet{AbelsonHAKBOBPCRFRHSHW85} \\
+    \hline
+    call/cc* & Undelimited & Composable & \citet{Flatt20} \\
+    \hline
+    catch               & Delimited & Abortive & \citet{SussmanS75} \\
+    \hline
+    catchcont           & Delimited & Composable & \citet{Longley09}\\
+    \hline
+    cupto               & Delimited & Composable & \citet{GunterRR95}\\
+    \hline
+    control/prompt      & Delimited & Composable & \citet{Felleisen88}\\
+    \hline
+    effect handlers     & Delimited & Composable & \citet{PlotkinP09,PlotkinP13} \\
+    \hline
+    escape              & Delimited & Abortive & \citet{Reynolds98a}\\
+    \hline
+    fcontrol            & Delimited & Composable & \citet{Sitaram93} \\
+    \hline
+    shift/reset         & Delimited & Composable & \citet{DanvyF90}\\
+    \hline
+    spawn               & Delimited & Composable & \citet{HiebDA94}\\
+    \hline
+    splitter            & Delimited & Abortive, composable & \citet{QueinnecS91}\\
+    \hline
+  \end{tabular}
+  \caption{Classification of first-class sequential control operators.}\label{tbl:classify-ctrl}
+\end{table}
+
 \subsection{Abortive operators}
 
+\paragraph{Sussman and Steele's catch}
+
+\paragraph{Reynolds' escape}
+
 \subsection{Undelimited operators}
+
+\paragraph{Landin's J operator}
+
+\paragraph{Call-with-current-continuation}
+%
+\begin{reductions}
+  \slab{Capture} &  \EC[\Callcc~k.M] &\reducesto& \EC[M[\cont_{\EC}/k]]\\
+  \slab{Invoke}  &  \EC[\Throw~\cont_{\EC'}~V]  &\reducesto& \EC'[V]
+\end{reductions}
+%
+
+\paragraph{Call-with-composable-continuation}
 call-with-composable-continuation (MzScheme 360, November 2006).
+%
+\begin{reductions}
+  \slab{Capture} &  \EC[\Callcc^\ast~k.M] &\reducesto& \EC[M[\cont_{\EC}/k]]\\
+  \slab{Invoke}  &  \EC[\Continue~\cont_{\EC'}~V]  &\reducesto& \EC[\EC'[V]]
+\end{reductions}
 
 \subsection{Delimited operators}
 Delimited control: Control delimiters form the basis for delimited
@@ -671,6 +726,68 @@ Comparison of various delimited control
 operators~\cite{Shan04}. Simulation of delimited control using
 undelimited control~\cite{Filinski94}
 
+%\paragraph{Felleisen's F and prompt}
+
+\paragraph{Control/prompt}
+
+\paragraph{Cupto}
+
+\paragraph{Effect handlers}
+%
+\begin{reductions}
+  \slab{Value}    & \Handle\; V \;\With\;H   &\reducesto& M[V/x], \text{ where } \{\Return\;x \mapsto M\} \in H\\
+  \slab{Capture}  & \Handle\;\EC[\Do\;\ell~V] \;\With\; H &\reducesto& M[V/p,\cont_{\Record{\EC;H}}/k],\\
+  \multicolumn{4}{l}{\hfill\bl\text{where $\ell$ is not handled in $\EC$}\\\text{and }\{\ell~p~k \mapsto M\} \in H\el}\\
+  \slab{Invoke}   & \Continue~\cont_{\Record{\EC;H}}~V &\reducesto& \Handle\;\EC[V]\;\With\;H\\
+\end{reductions}
+%
+\begin{reductions}
+  \slab{Capture}  & \Handle\;\EC[\Do\;\ell~V] \;\With\; H &\reducesto& M[V/p,\cont_{\EC}/k],\\
+  \multicolumn{4}{l}{\hfill\bl\text{where $\ell$ is not handled in $\EC$}\\\text{and }\{\ell~p~k \mapsto M\} \in H\el}\\
+  \slab{Invoke}   & \Continue~\cont_{\EC}~V &\reducesto& \EC[V]\\
+\end{reductions}
+%
+
+\paragraph{Sitaram's fcontrol}
+
+\paragraph{Longley's catch-with-continue}
+%
+\begin{mathpar}
+  \inferrule*
+    {\typ{\Gamma, f : A \to B}{M : C \times D} \\ \Ground\;C}
+    {\typ{\Gamma}{\Catchcont\;f.~M : C \times ((A \to B) \to D) + (A \times (B \to (A \to B) \to C \times D))}}
+\end{mathpar}
+%
+\begin{reductions}
+  \slab{Value} &
+     \Catchcont \; f . \Record{V;W} &\reducesto& \Inl\; \Record{V;\lambda\,f. W}\\
+  \slab{Capture} &
+     \Catchcont \; f .~\EC[\,f\,V]   &\reducesto& \Inr\; \Record{V; \cont_{\Record{\EC;f}}}\\
+  \slab{Invoke} & \Continue~\cont_{\Record{\EC;\,f}}~x &\reducesto& \lambda\, f.\EC[x]
+\end{reductions}
+
+\paragraph{Shift/reset}
+%
+\begin{reductions}
+  \slab{Value}    & \reset{V}               &\reducesto& V\\
+  \slab{Capture}  & \reset{\EC[\shift\,k.M]} &\reducesto& \reset{M[\cont_{\reset{\EC}}/k]}\\
+  % \slab{Invoke}   & \reset{\EC[\Continue~\cont_{\reset{\EC'}}~V]} &\reducesto& \reset{\EC[\reset{\EC'[V]}]}\\
+  \slab{Invoke}   & \Continue~\cont_{\reset{\EC}}~V &\reducesto& \reset{\EC[V]}\\
+\end{reductions}
+%
+
+%
+\begin{reductions}
+  % \slab{Value}    & \reset{V}               &\reducesto& V\\
+  \slab{Capture}  & \reset{\EC[\shift\,k.M]} &\reducesto& M[\cont_{\reset{\EC}}/k]\\
+  % \slab{Invoke}   & \Continue~\cont_{\reset{\EC}}~V &\reducesto& \reset{\EC[V]}\\
+\end{reductions}
+%
+
+\paragraph{Splitter}
+
+\paragraph{Spawn/controller}
+
 \section{Second-Class control operators}
 Coroutines, async/await, generators/iterators, amb.