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Jonas Kastberg
iris
Commits
8775b908
Commit
8775b908
authored
Nov 23, 2017
by
Dan Frumin
Browse files
Fix some typos in Section 9.2 in the docs.
parent
d7f8ff30
Changes
1
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Inline
Side-by-side
docs/derived.tex
View file @
8775b908
...
...
@@ -82,7 +82,7 @@ The two core assertions are: $\BoxSlice\namesp\prop\sname$, saying that there is
\inferH
{
Slice-delete-empty
}
{
f(
\sname
) =
\BoxEmp
}
{
\BoxSlice\namesp\propB\sname
\proves
\lateropt
b
\ABox\namesp\prop
{
f
}
\vs
[\namesp]
\Exists
\prop
'.
\lateropt
b(
\later
(
\prop
=
\prop
' *
\propB
) *
\ABox\namesp
{
\prop
'
}{
\mapinsert\
g
name\bot
{
f
}}
)
}
{
\BoxSlice\namesp\propB\sname
\proves
\lateropt
b
\ABox\namesp\prop
{
f
}
\vs
[\namesp]
\Exists
\prop
'.
\lateropt
b(
\later
(
\prop
=
\prop
' *
\propB
) *
\ABox\namesp
{
\prop
'
}{
\mapinsert\
s
name\bot
{
f
}}
)
}
\inferH
{
Slice-fill
}
{
f(
\sname
) =
\BoxEmp
}
...
...
@@ -117,10 +117,10 @@ We need a CMRA as follows:
Now we can define the assertions:
\begin{align*}
\SliceInv
(
\sname
,
\prop
)
\eqdef
{}&
\Exists
b.
\ownGhost\sname
{
(
\authfull
b,
\munit
)
}
* (b =
1
\Ra
\prop
)
\\
\SliceInv
(
\sname
,
\prop
)
\eqdef
{}&
\Exists
b.
\ownGhost\sname
{
(
\authfull
b,
\munit
)
}
*
(
(b =
\BoxFull
)
\Ra
\prop
)
\\
\BoxSlice\namesp\prop\sname
\eqdef
{}&
\ownGhost\sname
{
(
\munit
,
\prop
)
}
*
\knowInv\namesp
{
\SliceInv
(
\sname
,
\prop
)
}
\\
\ABox\namesp\prop
{
f
}
\eqdef
{}&
\Exists
\propB
:
\nat
\to
\Prop
.
\later\left
(
\prop
=
\Sep
_{
\sname
\in
\dom
(f)
}
\propB
(
\sname
)
\right
) *
{}
\\
&
\Sep
_{
\sname
\in
\dom
(f)
}
\Exists
\gname
.
\ownGhost\sname
{
(
\authfrag
f(
\sname
),
\propB
(
\sname
))
}
*
\knowInv\namesp
{
\SliceInv
(
\sname
,
\propB
(
\sname
))
}
&
\Sep
_{
\sname
\in
\dom
(f)
}
\ownGhost\sname
{
(
\authfrag
f(
\sname
),
\propB
(
\sname
))
}
*
\knowInv\namesp
{
\SliceInv
(
\sname
,
\propB
(
\sname
))
}
\end{align*}
\endgroup
% Model paragraph
...
...
@@ -136,7 +136,7 @@ Here are some derived rules:
\inferH
{
Slice-split
}
{
f(
\sname
) = s
}
{
\kern
-4ex
\BoxSlice\namesp
{
\propB
_
1 *
\propB
_
2
}
\sname
\proves
\lateropt
b
\ABox\namesp\prop
{
f
}
\vs
[\namesp]
\Exists
\sname
_
1
\notin
\dom
(f),
\sname
_
2
\notin
\dom
(f).
\sname
_
1
\neq
\sname
_
1
\land
{}
\\\kern
5ex
\always\BoxSlice\namesp
{
\propB
_
1
}{
\sname
_
1
}
*
\always\BoxSlice\namesp
{
\propB
_
2
}{
\sname
_
2
}
*
\lateropt
b
\ABox\namesp\prop
{
\mapinsert
{
\sname
_
2
}{
s
}{
\mapinsert
{
\sname
_
1
}{
s
}{
\mapinsert\sname\bot
{
f
}}}}}
{
\kern
-4ex
\BoxSlice\namesp
{
\propB
_
1 *
\propB
_
2
}
\sname
\proves
\lateropt
b
\ABox\namesp\prop
{
f
}
\vs
[\namesp]
\Exists
\sname
_
1
\notin
\dom
(f),
\sname
_
2
\notin
\dom
(f).
\sname
_
1
\neq
\sname
_
2
\land
{}
\\\kern
5ex
\always\BoxSlice\namesp
{
\propB
_
1
}{
\sname
_
1
}
*
\always\BoxSlice\namesp
{
\propB
_
2
}{
\sname
_
2
}
*
\lateropt
b
\ABox\namesp\prop
{
\mapinsert
{
\sname
_
2
}{
s
}{
\mapinsert
{
\sname
_
1
}{
s
}{
\mapinsert\sname\bot
{
f
}}}}}
\inferH
{
Slice-merge
}
{
\sname
_
1
\neq
\sname
_
2
\and
f(
\sname
_
1) = f(
\sname
_
2) = s
}
...
...
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