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fe66881e
Commit
fe66881e
authored
Aug 23, 2016
by
Ralf Jung
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docs: fix V being about any CMRA; fix V's timeless axiom
parent
62299a95
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2
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docs/logic.tex
docs/logic.tex
+2
-2
docs/model.tex
docs/model.tex
+2
-2
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docs/logic.tex
View file @
fe66881e
...
...
@@ -270,7 +270,7 @@ In writing $\vctx, x:\type$, we presuppose that $x$ is not already declared in $
\infer
{
\vctx
\proves
\wtt
{
\melt
}{
\textlog
{
M
}}}
{
\vctx
\proves
\wtt
{
\ownGGhost
{
\melt
}}{
\Prop
}}
\and
\infer
{
\vctx
\proves
\wtt
{
\melt
}{
\t
extlog
{
M
}
}}
\infer
{
\vctx
\proves
\wtt
{
\melt
}{
\t
ype
}
\and
\text
{$
\type
$
is a CMRA
}}
{
\vctx
\proves
\wtt
{
\mval
(
\melt
)
}{
\Prop
}}
\and
\infer
{
\vctx
\proves
\wtt
{
\state
}{
\textlog
{
State
}}}
...
...
@@ -464,7 +464,7 @@ A type $\type$ being \emph{inhabited} means that $ \proves \wtt{\term}{\type}$ i
{
\timeless
{
\ownGGhost\melt
}}
\infer
{
\text
{$
\melt
$
is a
discrete COFE element
}}
{
\text
{$
\melt
$
is a
n element of a discrete CMRA
}}
{
\timeless
{
\mval
(
\melt
)
}}
\infer
{}
...
...
docs/model.tex
View file @
fe66881e
...
...
@@ -40,8 +40,8 @@ We introduce an additional logical connective $\ownM\melt$, which will later be
\Lam
\melt
.
\setComp
{
n
}{
\begin{aligned}
\All
m,
\meltB
.
&
m
\leq
n
\land
\melt\mtimes\meltB
\in
\mval
_
m
\Ra
{}
\\
&
m
\in
\Sem
{
\vctx
\proves
\prop
:
\Prop
}_
\gamma
(
\meltB
)
\Ra
{}
\\
&
m
\in
\Sem
{
\vctx
\proves
\propB
:
\Prop
}_
\gamma
(
\melt\mtimes\meltB
)
\end{aligned}
}
\\
\Sem
{
\vctx
\proves
\ownM
{
\melt
}
:
\Prop
}_
\gamma
&
\eqdef
\Lam\meltB
.
\setComp
{
n
}{
\
melt
\mincl
[n]
\meltB
}
\\
\Sem
{
\vctx
\proves
\mval
(
\melt
) :
\Prop
}_
\gamma
&
\eqdef
\Lam\any
.
\setComp
{
n
}{
\
melt
\in
\mval
_
n
}
\\
\Sem
{
\vctx
\proves
\ownM
{
\melt
}
:
\Prop
}_
\gamma
&
\eqdef
\Lam\meltB
.
\setComp
{
n
}{
\
Sem
{
\vctx
\proves
\melt
:
\textlog
{
M
}}
\mincl
[n]
\meltB
}
\\
\Sem
{
\vctx
\proves
\mval
(
\melt
) :
\Prop
}_
\gamma
&
\eqdef
\Lam\any
.
\setComp
{
n
}{
\
Sem
{
\vctx
\proves
\melt
:
\type
}
\in
\mval
_
n
}
\\
\end{align*}
For every definition, we have to show all the side-conditions: The maps have to be non-expansive and monotone.
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