Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
I
Iris
Project overview
Project overview
Details
Activity
Releases
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Issues
116
Issues
116
List
Boards
Labels
Service Desk
Milestones
Merge Requests
20
Merge Requests
20
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Operations
Operations
Incidents
Environments
Analytics
Analytics
CI / CD
Repository
Value Stream
Wiki
Wiki
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
Iris
Iris
Commits
9e98ff8b
Commit
9e98ff8b
authored
Mar 08, 2016
by
Ralf Jung
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
docs: describe the unit of a CMRA and how the logic demands one
parent
fa0ed70a
Pipeline
#286
passed with stage
Changes
4
Pipelines
1
Hide whitespace changes
Inline
Side-by-side
Showing
4 changed files
with
19 additions
and
6 deletions
+19
-6
docs/algebra.tex
docs/algebra.tex
+11
-1
docs/iris.sty
docs/iris.sty
+1
-0
docs/logic.tex
docs/logic.tex
+6
-4
docs/setup.tex
docs/setup.tex
+1
-1
No files found.
docs/algebra.tex
View file @
9e98ff8b
...
...
@@ -112,6 +112,16 @@ This operation is needed to prove that $\later$ commutes with existential quanti
\end{mathpar}
(This assumes that the type
$
\type
$
is non-empty.)
\begin{defn}
An element
$
\munit
$
of a CMRA
$
\monoid
$
is called the
\emph
{
unit
}
of
$
\monoid
$
if it satisfies the following conditions:
\begin{enumerate}
[itemsep=0pt]
\item
$
\munit
$
is valid:
\\
$
\All
n,
\munit
\in
\mval
_
n
$
\item
$
\munit
$
is left-identity of the operation:
\\
$
\All
\melt
\in
M.
\munit
\mtimes
\melt
=
\melt
$
\item
$
\munit
$
is discrete
\end{enumerate}
\end{defn}
\begin{defn}
It is possible to do a
\emph
{
frame-preserving update
}
from
$
\melt
\in
\monoid
$
to
$
\meltsB
\subseteq
\monoid
$
, written
$
\melt
\mupd
\meltsB
$
, if
\[
\All
n,
\melt
_
f.
\melt
\mtimes
\melt
_
f
\in
\mval
_
n
\Ra
\Exists
\meltB
\in
\meltsB
.
\meltB
\mtimes
\melt
_
f
\in
\mval
_
n
\]
...
...
@@ -124,7 +134,7 @@ Note that for RAs, this and the RA-based definition of a frame-preserving update
\begin{defn}
A function
$
f : M
\to
N
$
between two CMRAs is
\emph
{
monotone
}
if it satisfies the following conditions:
\begin{enumerate}
\begin{enumerate}
[itemsep=0pt]
\item
$
f
$
is non-expansive
\item
$
f
$
preserves validity:
\\
$
\All
n, x
\in
M. x
\in
\mval
_
n
\Ra
f
(
x
)
\in
\mval
_
n
$
...
...
docs/iris.sty
View file @
9e98ff8b
...
...
@@ -129,6 +129,7 @@
\newcommand
{
\mcar
}
[1]
{
|#1|
}
\newcommand
{
\mcarp
}
[1]
{
\mcar
{
#1
}^{
+
}}
\newcommand
{
\munit
}{
\varepsilon
}
\newcommand
{
\mcore
}
[1]
{
\lfloor
#1
\rfloor
}
\newcommand
{
\mtimes
}{
\mathbin
{
\cdot
}}
\newcommand
{
\mdiv
}{
\mathbin
{
\div
}}
...
...
docs/logic.tex
View file @
9e98ff8b
...
...
@@ -26,7 +26,7 @@ It does not matter whether they fork off an arbitrary expression.
\begin{defn}
[Context]
A function
$
\lctx
:
\textdom
{
Expr
}
\to
\textdom
{
Expr
}$
is a
\emph
{
context
}
if the following conditions are satisfied:
\begin{enumerate}
\begin{enumerate}
[itemsep=0pt]
\item
$
\lctx
$
does not turn non-values into values:
\\
$
\All\expr
.
\toval
(
\expr
)
=
\bot
\Ra
\toval
(
\lctx
(
\expr
))
=
\bot
$
\item
One can perform reductions below
$
\lctx
$
:
\\
...
...
@@ -64,8 +64,7 @@ For any language $\Lang$, we define the corresponding thread-pool semantics.
To instantiate Iris, you need to define the following parameters:
\begin{itemize}
\item
A language
$
\Lang
$
\item
A locally contractive functor
$
\iFunc
:
\COFEs
\to
\CMRAs
$
defining the ghost state
\ralf
{$
\iFunc
$
also needs to have a single-unit.
}
\item
A locally contractive functor
$
\iFunc
:
\COFEs
\to
\CMRAs
$
defining the ghost state, such that for all COFEs
$
A
$
, the CMRA
$
\iFunc
(
A
)
$
has a unit
\end{itemize}
\noindent
...
...
@@ -107,6 +106,7 @@ Iris syntax is built up from a signature $\Sig$ and a countably infinite set $\t
\pi
_
i
\;
\term
\mid
\Lam
\var
:
\type
.
\term
\mid
\term
(
\term
)
\mid
\munit
\mid
\mcore\term
\mid
\term
\mtimes
\term
\mid
\\
&
...
...
@@ -213,6 +213,8 @@ In writing $\vctx, x:\type$, we presuppose that $x$ is not already declared in $
{
\vctx
\proves
\wtt
{
\term
}{
\type
\to
\type
'
}
\and
\wtt
{
\termB
}{
\type
}}
{
\vctx
\proves
\wtt
{
\term
(
\termB
)
}{
\type
'
}}
%%% monoids
\and
\infer
{}{
\vctx
\proves
\wtt\munit
{
\textlog
{
M
}}}
\and
\infer
{
\vctx
\proves
\wtt\melt
{
\textlog
{
M
}}}{
\vctx
\proves
\wtt
{
\mcore\melt
}{
\textlog
{
M
}}}
\and
...
...
@@ -416,7 +418,7 @@ This is entirely standard.
\begin{mathpar}
\begin{array}
{
rMcMl
}
\ownGGhost
{
\melt
}
*
\ownGGhost
{
\meltB
}
&
\Lra
&
\ownGGhost
{
\melt
\mtimes
\meltB
}
\\
%
\TRUE &\Ra& \ownGGhost{\munit}\\
\TRUE
&
\Ra
&
\ownGGhost
{
\munit
}
\\
\ownGGhost
{
\melt
}
&
\Ra
&
\melt
\in
\mval
% * \ownGGhost{\melt}
\end{array}
\and
...
...
docs/setup.tex
View file @
9e98ff8b
...
...
@@ -22,7 +22,7 @@
\usepackage
{
xcolor
}
% for print version
\usepackage
{
graphicx
}
\usepackage
{
enumitem
}
\usepackage
{
semantic
}
\usepackage
{
csquotes
}
...
...
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment