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koizel
phdNotes
Commits
917ee033
Commit
917ee033
authored
2 years ago
by
ghondet
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Diagram for proof irrelevance
parent
e98ca1cc
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phdSlides@v1
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phd_slides/main.tex
+19
-28
19 additions, 28 deletions
phd_slides/main.tex
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28 deletions
phd_slides/main.tex
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19
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28
View file @
917ee033
...
...
@@ -492,34 +492,25 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
% \end{thebibliography}
\end{frame}
\begin{frame}
\frametitle
{
Proof irrelevance in
\lpmr
}
\onslide
<+->
\begin{columns}
\begin{column}
{
0.5
\textwidth
}
\begin{exampleblock}
{}
Assume
\begin{itemize}
\item
\(
z
_
1
=
\tapp
{
\epair
,
0
, h
_
1
}
:
\tapp
*
{
\El
,
\tapp
{
\epsub
,
\N
, P
}}\)
,
\item
\(
z
_
2
=
\tapp
{
\epair
,
0
, h
_
2
}
:
\tapp
*
{
\El
,
\tapp
{
\epsub
,
\N
, P
}}\)
\end{itemize}
\end{exampleblock}
\end{column}
\begin{column}
{
0.5
\textwidth
}
\onslide
<+->
If
\(
h
_
1
\ne
h
_
2
\)
, then
\(
\alert
{
z
_
1
\ne
z
_
2
}\)
\end{column}
\end{columns}
\onslide
<+->
\vfill
\begin{block}
{
Embedding proof irrelevance
}
\begin{center}
\(
\tapp
*
{
\epair
,
0
, h
_
1
}
\onslide
<
+-
>
{
\rw
\tapp
*
{
\epair
*
,
0
}
\wr
}
\tapp
*
{
\epair
,
0
, h
_
2
}
\)
\end{center}
\end{block}
\begin{frame}
{
Proof irrelevance in
\lpmr
}
\begin{center}
\begin{tikzpicture}
[node distance = 2cm and 4cm]
\node
(pcert-left)
{\(
\tapp
*
{
\tpair
, v, g
}\)}
;
\node
[right = of pcert-left] (pcert-right)
{\(
\tapp
*
{
\tpair
, v, h
}\)}
;
\node
[below = of pcert-left] (lpcert-left)
{\(
\tapp
*
{
\epair
,
[
v
]
,
[
g
]
}\)}
;
\node
[below = of pcert-right] (lpcert-right)
{\(
\tapp
*
{
\epair
,
[
v
]
,
[
h
]
}\)}
;
\draw
[->] (pcert-left) -- (lpcert-left);
\draw
[->] (pcert-right) -- (lpcert-right);
\onslide
<2->
\draw
[<->, double] (pcert-left) -- (pcert-right);
\onslide
<3->
\node
[below = of lpcert-left] (lpcert-left-virt)
{}
;
\node
[below = of lpcert-right] (lpcert-right-virt)
{}
;
\path
(lpcert-left-virt) -- (lpcert-right-virt) node[midway] (lpcert-pair-p)
{\(
\tapp
*
{
\epair
*
, v
}\)}
;
\draw
[->] (lpcert-left) -- (lpcert-pair-p);
\draw
[->] (lpcert-right) -- (lpcert-pair-p);
\end{tikzpicture}
\end{center}
\end{frame}
\begin{frame}
{
Preservation of typing
}
...
...
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