dhil/phd-dissertation
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Daniel Hillerström
2021-04-10 18:47:49 +01:00
parent 4c480a4b6e
commit 817676f8e8
1 changed files with 6 additions and 6 deletions
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thesis.tex
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@@ -11887,7 +11887,7 @@ For all shallow handlers $H$, the following context is administrative
&\Let\; z \revto
\Handle\; \EC'[\Do\;\ell\;V]\;\With\;\sdtrans{H}\;\In\;
\Let\;\Record{f;\_} = z\;\In\;f\,\Unit\\
\reducesto& \reason{\semlab{Op} using assumption $\ell \notin \EC'$}\\
\reducesto& \reason{\semlab{Op} using assumption $\ell \notin \BL(\EC')$}\\
&\bl \Let\; z \revto
\bl
\Let\;r\revto
@@ -11963,7 +11963,7 @@ $N'$ such that $N' \approxa \sdtrans{N}$ and $M' \reducesto^+ N'$.
\lambda\Unit.\Let\;x \revto \Do\;\ell~\sdtrans{V}\;\In\;r~x;\\
\lambda\Unit.\sdtrans{N_\ell}}[\lambda x.
\bl
\Let\;z \revto (\lambda y.\Handle\;\sdtrans{E}[\Return\;y]\;\With\;\sdtrans{H})~x\;\In\\
\Let\;z \revto (\lambda y.\Handle\;\sdtrans{\EC}[\Return\;y]\;\With\;\sdtrans{H})~x\;\In\\
\Let\;\Record{f;g} = z\;\In\;f\,\Unit/r,\sdtrans{V}/p]\;\In\; g\,\Unit
\el
\el\\
@@ -11971,13 +11971,13 @@ $N'$ such that $N' \approxa \sdtrans{N}$ and $M' \reducesto^+ N'$.
\reducesto^+ &\reason{\semlab{Split}, \semlab{App}}\\
&\sdtrans{N_\ell}[\lambda x.
\bl
\Let\;z \revto (\lambda y.\Handle\;\sdtrans{E}[\Return\;y]\;\With\;\sdtrans{H})~x\;\In\\
\Let\;z \revto (\lambda y.\Handle\;\sdtrans{\EC}[\Return\;y]\;\With\;\sdtrans{H})~x\;\In\\
\Let\;\Record{f;g} = z\;\In\;f\,\Unit/r,\sdtrans{V}/p]
\el\\
=& \reason{by Lemma~\ref{lem:sdtrans-subst}}\\
&\sdtrans{N_\ell[\lambda x.
\bl
\Let\;z \revto (\lambda y.\Handle\;E[\Return\;y]\;\With\;H)~x\;\In\\
\Let\;z \revto (\lambda y.\Handle\;\EC[\Return\;y]\;\With\;H)~x\;\In\\
\Let\;\Record{f;g} = z\;\In\;f\,\Unit/r,V/p]}
\el
\end{derivation}
@@ -11996,7 +11996,7 @@ $N'$ such that $N' \approxa \sdtrans{N}$ and $M' \reducesto^+ N'$.
%
\[
(\bl
\lambda x.\Let\;z \revto (\lambda y.\Handle\;\sdtrans{E}[\Return\;y]\;\With\;\sdtrans{H})~x\;\In\\
\lambda x.\Let\;z \revto (\lambda y.\Handle\;\sdtrans{\EC}[\Return\;y]\;\With\;\sdtrans{H})~x\;\In\\
\Let\;\Record{f;g} = z \;\In\;f\,\Unit)~W \approxa (\lambda y.\sdtrans{\EC}[\Return\;y])~W.
\el
\]
@@ -12005,7 +12005,7 @@ $N'$ such that $N' \approxa \sdtrans{N}$ and $M' \reducesto^+ N'$.
applications of \semlab{App} on the left hand side yield the term
%
\[
\Let\;z \revto \Handle\;\sdtrans{E}[\Return\;W]\;\With\;\sdtrans{H}\;\In\;\Let\;\Record{f;g} = z \;\In\;f\,\Unit.
\Let\;z \revto \Handle\;\sdtrans{\EC}[\Return\;W]\;\With\;\sdtrans{H}\;\In\;\Let\;\Record{f;g} = z \;\In\;f\,\Unit.
\]
%
Define