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koizel
phdNotes
Commits
26f126cb
Commit
26f126cb
authored
2 years ago
by
ghondet
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ee111778
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phd_slides/main.tex
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102
View file @
26f126cb
...
...
@@ -49,8 +49,8 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
\usepackage
{
expl3
}
\usepackage
{
xspace
}
\newcommand\lpmr
{\
(
\lambda\Pi
\)
{
/R
}
\xspace
}
\newcommand\
dk
{
\text
{
Dk
}}
\newcommand\lpmr
{
\
ensuremath
{
\lambda\Pi
}
{
/R
}
\xspace
}
\newcommand\
lpTag
{
\ensuremath
{
\lambda\Pi
}}
\newcommand\tr
[1]
{
\left\llbracket
#1
\right\rrbracket
}
\newcommand\trA
[1]
{
\left
| #1
\right
|
}
\newcommand\trB
[1]
{
\left\Vert
#1
\right\Vert
}
...
...
@@ -186,6 +186,7 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
\item
Function reduction
\hfill
\(
\tapp
{
(
\tabst
{
x
}
x
)
,
0
}
=
0
\)
\item
Arbitrary reductions
\hfill
\(
\tapp
*
{
\func
{
fst
}
,
\tapp
{
\func
{
pair
}
, x, y
}}
=
x
\)
\end{itemize}
\onslide
<+->
\begin{block}
{
Implementations
}
\begin{description}
[<+->]
\item
[Dedukti]
concrete syntax for
\lpmr
, parser + type checker
...
...
@@ -195,7 +196,7 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
\end{frame}
\begin{frame}
{
Embedding a system
\(
\mathcal
{
S
}\)
in
\lpmr
}
Sound (and complete)
translation
\(
[-]
\)
from
\(
\mathcal
{
S
}\)
to
\lpmr
.
Sound (and complete)
embedding
\(
[-]
\)
from
\(
\mathcal
{
S
}\)
to
\lpmr
.
\vfill
\setcounter
{
beamerpauses
}{
2
}
...
...
@@ -211,96 +212,56 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
% \begin{center} \verb+U = {z : complex | EXISTS (n: nat): z ** n = 1}+\end{center}
% \verb+e: U+ \hspace{2em} ``\(e \in \mathbb{C}\) and \(\exists n, e^n = 1\)''
% \end{block}
\begin{block}
{}
\[
\{
n
\in
\mathbf
{
N
}
\mid
0
< n
\}
\]
\(
\tcheck
{}{
1
}{
\{
n :
\mathbf
{
N
}
\mid
0
< n
\}
}\)
means `
\(
1
\in
\mathbf
{
N
}\)
and
\(
0
<
1
\)
', but also
\\
\(
\tcheck
{}{
1
}{
\mathbf
{
N
}}\)
\end{block}
\[
\tpsub
{
n
}{
\mathbf
{
N
}}{
0
< n
}
\]
\vfill
\onslide
<+->
\begin{itemize}
[<+->]
\item
Expressive type-system
\item
Concise and `intuitive' language
\end{itemize}
\vfill
\onslide
<+->
\[
\tcheck
{
\Gamma
}{
1
}{
\tpsub
{
n
}{
\mathbf
{
N
}}{
0
< n
}}
;
\hspace
{
4
em
}
\tcheck
{
\Gamma
}{
1
}{
\mathbf
{
N
}}
\]
\vfill
\
pause
\
onslide
<+->
\begin{block}
{
PVS
}
\begin{itemize}
\begin{itemize}
[<+->]
\item
Specification language + type checker + (semi) automated theorem prover
\item
Used by Rockwell-Collins, Fujitsu, Stanford, NASA
\&
c.
\end{itemize}
\end{block}
\end{frame}
\begin{frame}
{
Introduction
}
\begin{center}
\begin{tikzpicture}
\scriptsize
\node
(PVS)
{
\textcolor
{
emph2
}{
PVS
}}
;
\node
[below right = 1.1cm of PVS]
(Lp-PVS-subt)
{\(
\mathrm
{
\textcolor
{
emph
1
}{
Lp
}
[
\textcolor
{
emph
2
}{
PVS
}
]
_{
<
}}\)}
;
\node
[right = 1.1cm of Lp-PVS-subt]
(Lp-PVS-meta)
{\(
\mathrm
{
\textcolor
{
emph
1
}{
Lp
}
[
\textcolor
{
emph
2
}{
PVS
}
]
_{
?
}}\)}
;
\node
[above = 0.4cm of Lp-PVS-meta]
(provers)
{
Why3,
\(
\lambda
\)
Prolog,
\emoji
{
writing-hand
}
}
;
\node
[right = 1.1cm of Lp-PVS-meta]
(Lp-PVS)
{\(
\mathrm
{
\textcolor
{
emph
1
}{
Lp
}
[
\textcolor
{
emph
2
}{
PVS
}
]
}\)}
;
\node
[right = 1.6cm of Lp-PVS]
(Ok)
{
\emoji
{
check-mark
}
}
;
\draw
[ultra thick,draw=ocre,fill=ocre,fill opacity=0.1]
(Lp-PVS-meta) ellipse (3.8cm and 1.2cm);
\node
[below = 0.9cm of Lp-PVS-meta]
{
\textcolor
{
emph1
}{
Lambdapi
}}
;
\path
(provers.south) edge[bend right=20] (Lp-PVS.west);
\path
(PVS.south) edge[bend right=30,->] (Lp-PVS-subt.west)
(Lp-PVS-subt) edge[->] (Lp-PVS-meta)
(Lp-PVS-meta) edge[->] (Lp-PVS)
(Lp-PVS) edge[->] (Ok)
;
\node
[below = of Ok, xshift = -0.6cm]
(Dk-PVS)
{
\textcolor
{
emph1
}{
Dk
}
[
\textcolor
{
emph2
}{
PVS
}
]
}
;
\node
[right = of Dk-PVS]
(sttfa)
{\(
\mathrm
{
STT
}_
\forall
\)}
;
\node
[below = of sttfa]
(provers)
{
Coq, Lean, Matita,
\dots
}
;
\path
(Lp-PVS.south) edge[bend right=40,->] (Dk-PVS.west)
(Dk-PVS) edge[->] (sttfa)
(sttfa.south) edge[->] (provers);
\path
(Dk-PVS) edge[bend left=20,->] (Ok);
\node
[right = 0.3cm of Dk-PVS]
(Dk-centre)
{}
;
\draw
[ultra thick, draw = fuschia, fill = fuschia, fill opacity = 0.1]
(Dk-centre) ellipse (2cm and 0.8cm);
\node
[below=of Dk-centre,yshift=0.3cm]
{
\textcolor
{
emph1
}{
Dedukti
}}
;
\end{tikzpicture}
\end{center}
\end{frame}
\begin{frame}
{
Outline
}
\tableofcontents
\end{frame}
\section
{
Explicit predicate subtyping
}
\begin{frame}
\tableofcontents
[currentsection]
\end{frame}
\begin{frame}
{
Simple type theory and predicate subtyping
}
\[
t ::
=
x
\mid
c
\mid
\tapp
*
{
t, t
}
\mid
\tabst
{
x
}
[
t
]
t
\mid
\tprod
[
x
]
{
t
}
t
\mid
\tprod
{
t
}
t
\onslide
<
3
-
>
{
\mid
\tpsub
{
x
}{
t
}{
t
}
\mid
\tapp
{
\tfst
, t
}}
\onslide
<
3
-
>
{
\mid
\tpsub
{
x
}{
t
}{
t
}
\mid
\tapp
{
\tpair
, t, t
}
\mid
\tapp
{
\tfst
, t
}}
\]
\onslide
<2->
{
\begin{empheq}
{
equation*
}
\forall
_{
\iota
}
x, P
\simeq
\tprod
[x]
{
\iota
}
P
\hspace
{
4em
}
P
\Rightarrow
Q
\simeq
\tprod
[x]
{
P
}
Q
\end{empheq}
\begin{center}
\begin{tabular}
{
ll
}
STT
&
\(
\lambda
\)
HOL
\\
\toprule
\(
\forall
_{
\iota
}
x, P
\)
&
\(
\tprod
[
x
]
{
\iota
}
P
\)
\\
\(
P
\Rightarrow
Q
\)
&
\(
\tprod
[
x
]
{
P
}
Q
\)
\end{tabular}
\end{center}
}
\onslide
<4->
{
\[
\tcheck
{
\mathit
{
isPos
}
:
\tprod
[
n
]
{
\math
it
{
nat
}}
\tapp
{
\mathit
{
Pos
}
,
(
n
+
1
)
}}
\tcheck
[
system
=
e
]
{
\mathit
{
isPos
}
:
\tprod
[
n
]
{
\math
bf
{
N
}}
\tapp
{
\mathit
{
Pos
}
,
(
n
+
1
)
}}
{
\tapp
{
\tpair
,
1
,
{
\tapp
{
\mathit
{
isPos
}
,
0
}}}}
{
\tpsub
{
n
}{
\math
it
{
nat
}}{
\tapp
*
{
\mathit
{
Pos
}
, n
}}}
{
\tpsub
{
n
}{
\math
bf
{
N
}}{
\tapp
*
{
\mathit
{
Pos
}
, n
}}}
\]
}
\setcounter
{
beamerpauses
}{
5
}
...
...
@@ -326,7 +287,7 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
\end{thebibliography}
\end{frame}
\begin{frame}
{
E
nco
ding PVS-Cert in
Dedukti
}
\begin{frame}
{
E
mbed
ding PVS-Cert in
\lpmr
}
\begin{block}
{}
\(
\Set
:
\sType
\)
\\
\(
\El
:
\Set
\to
\sType
\)
\\
...
...
@@ -345,7 +306,7 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
\end{frame}
\begin{frame}
[fragile]
\frametitle
{
Principles of e
nco
dings in
Dedukti
}
\frametitle
{
Principles of e
mbed
dings in
\lpmr
}
\note
{
\begin{itemize}
\item
Technique used to encode CoC (say CoC because it is more widely known than PTSs) (in Cousineau article);
...
...
@@ -355,9 +316,12 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
\end{itemize}
}
\begin{tikzpicture}
[
term/.style=
{
draw,ellipse,fill=white
}
,
type/.style=
{
draw=fuschia,ellipse,fill=white
}
]
[ term/.style=
{
draw,ellipse,fill=white
}
, type/.style=
{
draw=fuschia,ellipse,fill=white
}
, pvsBoxes/.style =
{
draw = black, fill = ocre!5!white
}
, pvsBigBox/.style =
{
pvsBoxes, rounded corners = 8pt
}
, lpmrBoxes/.style =
{
fill = light-blue!5!white, draw = black
}
, lpmrBigBox/.style =
{
lpmrBoxes, rounded corners = 8pt
}
]
\node
(rect-sysa-sw) at (0, 0)
{}
;
\node
(rect-sysa-nw) [above =
\boxheight
of rect-sysa-sw]
{}
;
...
...
@@ -367,13 +331,11 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
\node
(rect-sysb-nw) [above =
\boxheight
of rect-sysb-sw]
{}
;
\node
(rect-sysb-ne) [above right =
\boxheight
and
\boxwidth
of rect-sysb-sw]
{}
;
\filldraw
[fill=light-blue!5!white, draw=black, rounded corners=8pt]
(rect-sysa-sw) rectangle (rect-sysa-ne);
\node
[draw,fill=light-blue!5!white] at (rect-sysa-nw.south)
{
Dedukti
}
;
\filldraw
[lpmrBigBox] (rect-sysa-sw) rectangle (rect-sysa-ne);
\node
[lpmrBoxes] at (rect-sysa-nw.south)
{
\lpmr
}
;
\filldraw
[fill=ocre!5!white, draw=black, rounded corners=8pt]
(rect-sysb-sw) rectangle (rect-sysb-ne);
\node
[draw,fill=ocre!5!white] at (rect-sysb-nw.south)
{
PVS
}
;
\filldraw
[pvsBigBox] (rect-sysb-sw) rectangle (rect-sysb-ne);
\node
[pvsBoxes] at (rect-sysb-nw.south)
{
PVS
}
;
\pause
...
...
@@ -446,7 +408,7 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
\end{column}
\begin{column}
{
0.5
\textwidth
}
\onslide
<+->
If
\(
h
_
1
\ne
h
_
2
\)
, then
\(
z
_
1
\ne
z
_
2
\)
If
\(
h
_
1
\ne
h
_
2
\)
, then
\(
\alert
{
z
_
1
\ne
z
_
2
}
\)
\end{column}
\end{columns}
...
...
@@ -464,11 +426,11 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
If
\(
\tcheck
[
system
=
e
]
{
\Gamma
}{
t
}{
T
}\)
,
\\
\vfill
\pause
then
\(
\tcheck
[
system
=
\
dk
]
{
[
\Gamma
]
}{
[
t
]
}{
\tapp
*
{
\El
,
[
T
]
}}\)
.
then
\(
\tcheck
[
system
=
\
lpTag
]
{
[
\Gamma
]
}{
[
t
]
}{
\tapp
*
{
\El
,
[
T
]
}}\)
.
\end{frame}
\begin{frame}
{
Preservation of typing
}
\framesubtitle
{
Preservation of
C
omputation
}
\framesubtitle
{
Preservation of
c
omputation
}
\newcommand\pieq
{
\ensuremath
{
\mathrel
{
\leftrightarrow
^
*
_{
\text
{
pi
}}}}}
\newcommand\pieqS
{
\ensuremath
{
\mathrel
{
\leftrightarrow
_{
\text
{
pi
}}}}}
...
...
@@ -514,26 +476,53 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
\begin{frame}
{
Completeness
}
\begin{block}
{
Statement
}
If
\(
\tcheck
{
\Gamma
}{
e
_
0
}{
\tapp
*
{
\Prf
,
[
P
]
}}\)
\\
If
\(
\tcheck
[
system
=
\lpTag
]
{
\Gamma
}{
e
_
0
}{
\tapp
*
{
\Prf
,
[
P
]
}}\)
\\
then
\(
\tcheck
[
system
=
e
]
{
\Delta
}{
e
_
1
}{
P
}\)
\end{block}
\pause
\vfill
\begin{exampleblock}
{
Proof approaches
}
\begin{itemize}
[<+->]
\item
t
ermination + (Cousineau
\&
Dowek, 2007)
\item
T
ermination
(of embedding)
+ (Cousineau
\&
Dowek, 2007)
\item
(Assaf, 2015)
\item
d
eep embeddings (Felicissimo, 2022)
\item
D
eep embeddings (Felicissimo, 2022)
\end{itemize}
\end{exampleblock}
\end{frame}
\begin{frame}
{
Example
}
\(
\func
{
stack
}
:
\Set
\)
\\
\(
\func
{
empty
}
:
\tapp
*
{
\El
,
\func
{
stack
}}\)
\\
\(
\func
{
isNonEmpty
}
\coloneqq
\tabst
{
s
}
s
\ne
\func
{
empty
}\)
\\
\(
\func
{
nonEmpty
}
\coloneqq
\tapp
*
{
\epsub
,
\func
{
stack
}
,
\func
{
isNonEmpty
}}\)
\\
\(
\func
{
push
}
:
\tapp
*
{
\El
,
(
\mathbf
{
N
}
\earr
\func
{
stack
}
\earr
\func
{
nonEmpty
}
)
}\)
\\
\(
\func
{
pop
}
:
\tapp
*
{
\El
,
(
\func
{
nonEmpty
}
\earr
\func
{
stack
}
)
}\)
\\
\(
\func
{
top
}
:
\tapp
*
{
\El
,
(
\func
{
nonEmpty
}
\earr
\mathbf
{
N
}
)
}\)
\\
\begin{exampleblock}
{}
\(
\func
{
pushTopPop
}
:
\Prf
\)
\\
\hspace
{
2ex
}\(
\eall\,
\func
{
stack
}
\,
(
\lambda
s,
\tapp
{
\func
{
isNonEmpty
}
, s
}
\eimp
\)
\\
\hspace
{
2ex
}\(
\tapp
*
{
\efst
,
\tapp
{
\func
{
push
}
,
\tapp
{
\func
{
top
}
,
\tapp
{
\epair
, s, ?
}}
,
\tapp
{
\func
{
pop
}
,
\tapp
{
\epair
, s, ?
}}}}
=
s
)
\)
\end{exampleblock}
\end{frame}
\section
{
Implicit predicate subtyping
}
\begin{frame}
\tableofcontents
[currentsection]
\end{frame}
\begin{frame}
{
Implicitness
}
\begin{exampleblock}
{}
\(
\tapp
*
{
\efst
,
\tapp
{
\func
{
push
}
,
\tapp
{
\func
{
top
}
,
\tapp
{
\epair
, s,
{
?
_
1
}}}
,
\tapp
{
\func
{
pop
}
,
\tapp
{
\epair
, s,
{
?
_
2
}}}}}
=
s
\)
\end{exampleblock}
\vfill
\pause
\begin{block}
{}
\(
\tapp
*
{
\func
{
push
}
,
\tapp
{
\func
{
top
}
, s
}
,
\tapp
{
\func
{
pop
}
, s
}}
=
s
\)
\end{block}
\end{frame}
\begin{frame}
{
Baked-in subtyping
}
\[
\begin
{
prooftree
}
...
...
@@ -630,13 +619,13 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
\end{columns}
\end{frame}
\begin{frame}
{
Going online (feat.
\
rewriting, cont'd)
}
\begin{frame}
{
Going on
line (feat.
\
rewriting, cont'd)
}
\begin{center}
\(
\inferrule
{
\tcheck
[
dir
=
infer,system
=
\
dk
]
{
\Gamma
}{
t
}{
T
}
\\
T
\simeq
U
\tcheck
[
dir
=
infer,system
=
\
lpTag
]
{
\Gamma
}{
t
}{
T
}
\\
T
\simeq
U
}{
\tcheck
[
dir
=
check, system
=
\
dk
]
{
\Gamma
}{
t
}{
U
}
\tcheck
[
dir
=
check, system
=
\
lpTag
]
{
\Gamma
}{
t
}{
U
}
}
\)
\\
\vfill
...
...
@@ -645,9 +634,9 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
\vfill
\(
\inferrule
{
\tcheck
[
dir
=
infer, system
=
\
dk
]
{
\Gamma
}{
t
}{
T
}
\\
\tapp
{
\kappa
, T, U
}
\rw
f
\\
\tcheck
[
dir
=
check, system
=
\
dk
]
{
\Gamma
}{
\tapp
{
f, t
}}{
U
}
}{
\tcheck
[
dir
=
check, system
=
\
dk
]
{
\Gamma
}{
t
}{
U
}
}
\tcheck
[
dir
=
infer, system
=
\
lpTag
]
{
\Gamma
}{
t
}{
T
}
\\
\tapp
{
\kappa
, T, U
}
\rw
f
\\
\tcheck
[
dir
=
check, system
=
\
lpTag
]
{
\Gamma
}{
\tapp
{
f, t
}}{
U
}
}{
\tcheck
[
dir
=
check, system
=
\
lpTag
]
{
\Gamma
}{
t
}{
U
}
}
\)
\pause
\note
{
No need for the premise
\(
\kappa
\not\in
f
\)
here because
\(
\kappa
\)
is not typeable anyway
}
...
...
@@ -673,8 +662,8 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
\begin{frame}
{
Typing preservation
}
If
\(
\tcheck
[
system
=
i
]
{
\Gamma
}{
e
}{
T
}\)
, then
\begin{itemize}
\item
\(
\tcheck
[
dir
=
check, r
=
\hat
{
T
}
, system
=
\
dk
]
{
[
\Gamma
]
}{
[
T
]
}{
\Set
}\)
\item
\(
\tcheck
[
dir
=
check, r
=
\hat
{
t
}
, system
=
\
dk
]
{
[
\Gamma
]
}{
[
t
]
}{
\tapp
*
{
\El
,
\hat
{
T
}}}\)
.
\item
\(
\tcheck
[
dir
=
check, r
=
\hat
{
T
}
, system
=
\
lpTag
]
{
[
\Gamma
]
}{
[
T
]
}{
\Set
}\)
\item
\(
\tcheck
[
dir
=
check, r
=
\hat
{
t
}
, system
=
\
lpTag
]
{
[
\Gamma
]
}{
[
t
]
}{
\tapp
*
{
\El
,
\hat
{
T
}}}\)
.
\end{itemize}
\vfill
...
...
@@ -693,6 +682,10 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
\begin{frame}
{
Completing the equational theory
}
% Show why surjective pairing is needed, potentially extrapolate to
% confluence of coercion system
\(
\tcheck
[
dir
=
infer, r
=
{
\tapp
{
(
\tabst
{
x
}
[
A
]
\tapp
{
f,
\tapp
{
\epair
, x,
{
?
_
0
}}}
)
,
\tapp
{
\efst
,
1
}}}
]
{
1
:
\tapp
{
\epsub
,
\mathbf
{
N
}
,
(
<
0
)
}
,
\mathit
{
prec
}
:
\tprod
{
\tapp
{
\epsub
,
\mathbf
{
N
}
,
(
<
0
)
}}
\mathbf
{
N
}}
{
\tapp
{
(
\tabst
{
x
}
[
\mathbf
{
N
}
]
\tapp
{
f, x
}
)
,
1
}}
{
\mathbf
{
N
}}\)
\end{frame}
\section
{
Results: translation of PVS into Dedukti
}
...
...
@@ -751,6 +744,52 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
\end{block}
\end{frame}
\begin{frame}
{
Introduction
}
\begin{center}
\begin{tikzpicture}
\scriptsize
\node
(PVS)
{
\textcolor
{
emph2
}{
PVS
}}
;
\node
[below right = 1.1cm of PVS]
(Lp-PVS-subt)
{\(
\mathrm
{
\textcolor
{
emph
1
}{
Lp
}
[
\textcolor
{
emph
2
}{
PVS
}
]
_{
<
}}\)}
;
\node
[right = 1.1cm of Lp-PVS-subt]
(Lp-PVS-meta)
{\(
\mathrm
{
\textcolor
{
emph
1
}{
Lp
}
[
\textcolor
{
emph
2
}{
PVS
}
]
_{
?
}}\)}
;
\node
[above = 0.4cm of Lp-PVS-meta]
(provers)
{
Why3,
\(
\lambda
\)
Prolog,
\emoji
{
writing-hand
}
}
;
\node
[right = 1.1cm of Lp-PVS-meta]
(Lp-PVS)
{\(
\mathrm
{
\textcolor
{
emph
1
}{
Lp
}
[
\textcolor
{
emph
2
}{
PVS
}
]
}\)}
;
\node
[right = 1.6cm of Lp-PVS]
(Ok)
{
\emoji
{
check-mark
}
}
;
\draw
[ultra thick,draw=ocre,fill=ocre,fill opacity=0.1]
(Lp-PVS-meta) ellipse (3.8cm and 1.2cm);
\node
[below = 0.9cm of Lp-PVS-meta]
{
\textcolor
{
emph1
}{
Lambdapi
}}
;
\path
(provers.south) edge[bend right=20] (Lp-PVS.west);
\path
(PVS.south) edge[bend right=30,->] (Lp-PVS-subt.west)
(Lp-PVS-subt) edge[->] (Lp-PVS-meta)
(Lp-PVS-meta) edge[->] (Lp-PVS)
(Lp-PVS) edge[->] (Ok)
;
\node
[below = of Ok, xshift = -0.6cm]
(Dk-PVS)
{
\textcolor
{
emph1
}{
Dk
}
[
\textcolor
{
emph2
}{
PVS
}
]
}
;
\node
[right = of Dk-PVS]
(sttfa)
{\(
\mathrm
{
STT
}_
\forall
\)}
;
\node
[below = of sttfa]
(provers)
{
Coq, Lean, Matita,
\dots
}
;
\path
(Lp-PVS.south) edge[bend right=40,->] (Dk-PVS.west)
(Dk-PVS) edge[->] (sttfa)
(sttfa.south) edge[->] (provers);
\path
(Dk-PVS) edge[bend left=20,->] (Ok);
\node
[right = 0.3cm of Dk-PVS]
(Dk-centre)
{}
;
\draw
[ultra thick, draw = fuschia, fill = fuschia, fill opacity = 0.1]
(Dk-centre) ellipse (2cm and 0.8cm);
\node
[below=of Dk-centre,yshift=0.3cm]
{
\textcolor
{
emph1
}{
Dedukti
}}
;
\end{tikzpicture}
\end{center}
\end{frame}
\begin{frame}
{
Translation of Prelude
}
\begin{table}
\caption
{
Amount of translated entities.
}
...
...
@@ -790,7 +829,7 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
\end{frame}
\begin{frame}
{
On proof representations
}
\begin{block}
{
Certificates --
Dedukti
}
\begin{block}
{
Certificates --
\lpmr
}
\setcounter
{
beamerpauses
}{
2
}
\begin{description}
[<+->]
\item
[Data]
terms
...
...
@@ -912,15 +951,13 @@ fit, calc, decorations.pathmorphing, decorations.shapes, matrix}
\end{frame}
\begin{frame}
{
Perspectives
}
\begin{block}
{
Proof export
}
\begin{itemize}
\item
[\emoji{check-mark}]
\(
\text
{
PVS
-
Cert
}
\to
\text
{
Dedukti
}\)
\hfill
personoj
\item
[\emoji{check-mark}]
\(
\frac
{
Q
}{
P
}
\mapsto
\frac
{
\dots
}{
Q
\Rightarrow
P
}\)
\hfill
personoj
\item
[\emoji{check-mark}]
\(
\phi
:
\text
{
PVS
-
Cert
}
\to
\text
{
STT
}\)
\hfill
F.~Gilbert
\item
[\emoji{check-mark}]
ATP in Dedukti (FOL only)
\hfill
Y.~El~Haddad
\item
[\emoji{thinking}]
\(
\psi
:
\text
{
STT
}
\to
\text
{
PVS
-
Cert
}\)
\end{itemize}
\end{block}
\begin{itemize}
[<+->]
\item
[\emoji{check-mark}]
\(
\text
{
PVS
-
Cert
}
\to
\text
{
Dedukti
}\)
\hfill
personoj
\item
[\emoji{check-mark}]
\(
\frac
{
Q
}{
P
}
\mapsto
\frac
{
\dots
}{
Q
\Rightarrow
P
}\)
\hfill
personoj
\item
[\emoji{check-mark}]
\(
\phi
:
\text
{
PVS
-
Cert
}
\to
\text
{
STT
}\)
\hfill
F.~Gilbert
\item
[\emoji{check-mark}]
ATP in Dedukti (FOL only)
\hfill
Y.~El~Haddad
\item
[\emoji{thinking}]
\(
\psi
:
\text
{
STT
}
\to
\text
{
PVS
-
Cert
}\)
\end{itemize}
\end{frame}
\section*
{
Conclusion
}
...
...
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