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@ -679,7 +679,7 @@ non-exhaustive list of first-class control operators. |
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\hline |
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\multicolumn{1}{| l |}{\textbf{Name}} & \multicolumn{1}{l |}{\textbf{Extent}} & \multicolumn{1}{l |}{\textbf{Continuation behaviour}} & \multicolumn{1}{l |}{\textbf{Canonical reference}}\\ |
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\hline |
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\FelleisenC & Undelimited & Abortive & \citet{FelleisenF86} \\ |
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C & Undelimited & Abortive & \citet{FelleisenF86} \\ |
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\hline |
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call/cc & Undelimited & Abortive & \citet{AbelsonHAKBOBPCRFRHSHW85} \\ |
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\hline |
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@ -697,7 +697,7 @@ non-exhaustive list of first-class control operators. |
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\hline |
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escape & Undelimited & Abortive & \citet{Reynolds98a}\\ |
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\hline |
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\FelleisenF & Undelimited & Composable & \citet{FelleisenFDM87}\\ |
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F & Undelimited & Composable & \citet{FelleisenFDM87}\\ |
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\hline |
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fcontrol & Delimited & Composable & \citet{Sitaram93} \\ |
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\hline |
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@ -837,7 +837,24 @@ As an aside it is worth to mention that \citet{CartwrightF92} used a |
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variation of $\Catch$ to show that control operators enable programs |
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to observe the order of evaluation. |
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\paragraph{Call-with-current-continuation} |
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\paragraph{Call-with-current-continuation} In 1982 the Scheme |
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implementors observed that they could dispense of the special syntax |
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for $\Catch$ in favour of a higher-order function that would apply its |
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argument to the current continuation, and thus callcc was born (callcc |
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is short for |
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call-with-current-continuation)~\cite{AbelsonHAKBOBPCRFRHSHW85}. |
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% |
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Unlike the previous operators, callcc augments the syntactic |
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categories of values. |
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% |
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\[ |
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V,W \in \ValCat ::= \cdots \mid \Callcc |
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\] |
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% |
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The value $\Callcc$ is essentially a hard-wired function name. The |
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typing rule for $\Callcc$ makes it clear that it is a particular |
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higher-order function. |
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% |
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\begin{mathpar} |
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\inferrule* |
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@ -849,11 +866,22 @@ to observe the order of evaluation. |
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{\typ{\Gamma}{\Continue~W~V : \Zero}} |
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\end{mathpar} |
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% |
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An invocation of $\Callcc$ returns a value of type $A$. This value can |
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be produced in one of two ways, either the function argument returns |
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normally or it applies the provided continuation object to a value |
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that then becomes the result of $\Callcc$-application. |
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% |
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\begin{reductions} |
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\slab{Capture} & \EC[\Callcc~V] &\reducesto& \EC[V~\cont_{\EC}]\\ |
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\slab{Resume} & \EC[\Continue~\cont_{\EC'}~V] &\reducesto& \EC'[V] |
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\end{reductions} |
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% |
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From the dynamic semantics it is evident that $\Callcc$ is a |
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syntax-free alternative to $\Catch$, i.e. |
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% |
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\[ |
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\sembr{\Catch~k.M} = \Callcc\,(\lambda k.M) |
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\] |
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\paragraph{Call-with-composable-continuation} |
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call-with-composable-continuation (MzScheme 360, November 2006). |
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@ -1014,8 +1042,8 @@ annotate the evaluation contexts for ordinary applications. |
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\slab{Resume} & \EC[\Continue~\cont_{\Record{\EC';W}}\,V] &\reducesto& \EC'[W\,V] |
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\end{reductions} |
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% |
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$\slab{Capture}$ rule only applies if the application of $\J$ takes |
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place in annotated evaluation context. The continuation object |
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The $\slab{Capture}$ rule only applies if the application of $\J$ |
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takes place in annotated evaluation context. The continuation object |
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produced by a $\J$ application encompasses the caller's continuation |
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$\EC_\lambda$ and the value argument $W$. |
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% |
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@ -1055,6 +1083,8 @@ undelimited control~\cite{Filinski94} |
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\paragraph{Control/prompt} |
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% |
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The operator control is a rebranding of Felleisen's F operator. |
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% |
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\begin{reductions} |
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\slab{Value} & |
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\Prompt~V &\reducesto& V\\ |
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@ -1123,9 +1153,9 @@ undelimited control~\cite{Filinski94} |
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% |
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\begin{reductions} |
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\slab{Value} & \reset{V} &\reducesto& V\\ |
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\slab{Capture} & \reset{\EC[\shift\,k.M]} &\reducesto& \reset{M[\cont_{\reset{\EC}}/k]}, \text { where $\EC$ contains no $\reset{-}$}\\ |
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\slab{Capture} & \reset{\EC[\shift\,k.M]} &\reducesto& \reset{M[\cont_{\EC}/k]}, \text { where $\EC$ contains no $\reset{-}$}\\ |
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% \slab{Resume} & \reset{\EC[\Continue~\cont_{\reset{\EC'}}~V]} &\reducesto& \reset{\EC[\reset{\EC'[V]}]}\\ |
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\slab{Resume} & \Continue~\cont_{\reset{\EC}}~V &\reducesto& \reset{\EC[V]}\\ |
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\slab{Resume} & \Continue~\cont_{\EC}~V &\reducesto& \reset{\EC[V]}\\ |
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\end{reductions} |
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% |
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@ -1139,9 +1169,9 @@ undelimited control~\cite{Filinski94} |
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\paragraph{Splitter} |
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\begin{reductions} |
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\slab{Throw} & \splitter~f~g.\EC[\,f~V] &\reducesto& V~\Unit\\ |
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\slab{Throw} & \splitter~throw~callpc.\EC[\,throw~V] &\reducesto& V~\Unit\\ |
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\slab{Capture} & |
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\splitter~f~g.\EC[g~V] &\reducesto& V~\cont_{\EC} \\ |
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\splitter~throw~callpc.\EC[callpc~V] &\reducesto& V~\cont_{\EC} \\ |
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\slab{Resume} & \Continue~\cont_{\EC}~V &\reducesto& \EC[V] |
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\end{reductions} |
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