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Remove static semantics paragraphs from escape and catch.

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Daniel Hillerström
2020-12-01 23:23:50 +00:00
parent ab36a78a50
commit bebb40ce9f
1 changed files with 34 additions and 29 deletions
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63
thesis.tex
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@@ -817,28 +817,34 @@ available for use within $N$. \citeauthor{Reynolds98a} recognised the
power of this idiom and noted that it could be used to implement
coroutines and backtracking~\cite{Reynolds98a}.
%
In our simply-typed setting it is not possible for the continuation to
propagate outside its binding $\Escape$-expression as it would require
the addition of either recursive types or some other escape hatch like
\citeauthor{Reynolds98a} did not develop the static semantics for
$\Escape$, however, it is worth noting that this idiom require
recursive types to type check. Even in a language without recursive
types, the continuation may propagate outside its binding
$\Escape$-expression if the language provides an escape hatch such as
mutable reference cells.
%
% In our simply-typed setting it is not possible for the continuation to
% propagate outside its binding $\Escape$-expression as it would require
% the addition of either recursive types or some other escape hatch like
% mutable reference cells.
% %
The typing of $\Escape$ and $\Continue$ reflects that the captured
continuation is abortive.
%
\begin{mathpar}
\inferrule*
{\typ{\Gamma,k : \Cont\,\Record{A;\Zero}}{M : A}}
{\typ{\Gamma}{\Escape\;k\;\In\;M : A}}
% The typing of $\Escape$ and $\Continue$ reflects that the captured
% continuation is abortive.
% %
% \begin{mathpar}
% \inferrule*
% {\typ{\Gamma,k : \Cont\,\Record{A;\Zero}}{M : A}}
% {\typ{\Gamma}{\Escape\;k\;\In\;M : A}}
% \inferrule*
% {\typ{\Gamma}{V : A} \\ \typ{\Gamma}{W : \Cont\,\Record{A;\Zero}}}
% {\typ{\Gamma}{\Continue~W~V : \Zero}}
\end{mathpar}
%
The return type of the continuation object can be taken as a telltale
sign that an invocation of this object never returns, since there are
no inhabitants of the empty type.
% % \inferrule*
% % {\typ{\Gamma}{V : A} \\ \typ{\Gamma}{W : \Cont\,\Record{A;\Zero}}}
% % {\typ{\Gamma}{\Continue~W~V : \Zero}}
% \end{mathpar}
% %
% The return type of the continuation object can be taken as a telltale
% sign that an invocation of this object never returns, since there are
% no inhabitants of the empty type.
%
An invocation of the continuation discards the invocation context and
plugs the argument into the captured context.
@@ -869,18 +875,17 @@ with access to the current continuation. Thus it is same as
M,N ::= \cdots \mid \Catch~k.M
\]
%
Although, their syntax differ, their static and dynamic semantics are
the same.
Although, their syntax differ, their dynamic semantics are the same.
%
\begin{mathpar}
\inferrule*
{\typ{\Gamma,k : \Cont\,\Record{A;\Zero}}{M : A}}
{\typ{\Gamma}{\Catch~k.M : A}}
% \begin{mathpar}
% \inferrule*
% {\typ{\Gamma,k : \Cont\,\Record{A;\Zero}}{M : A}}
% {\typ{\Gamma}{\Catch~k.M : A}}
% \inferrule*
% {\typ{\Gamma}{V : A} \\ \typ{\Gamma}{W : \Cont\,\Record{A;B}}}
% {\typ{\Gamma}{\Continue~W~V : B}}
\end{mathpar}
% % \inferrule*
% % {\typ{\Gamma}{V : A} \\ \typ{\Gamma}{W : \Cont\,\Record{A;B}}}
% % {\typ{\Gamma}{\Continue~W~V : B}}
% \end{mathpar}
%
\begin{reductions}
\slab{Capture} & \EC[\Catch~k.M] &\reducesto& \EC[M[\qq{\cont_{\EC}}/k]]\\