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
107
Issues
107
List
Boards
Labels
Service Desk
Milestones
Merge Requests
16
Merge Requests
16
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Operations
Operations
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
9ba4ad2b
Commit
9ba4ad2b
authored
Aug 04, 2016
by
Ralf Jung
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
fix some typos in the docs
parent
ef669d81
Changes
2
Hide whitespace changes
Inline
Side-by-side
Showing
2 changed files
with
3 additions
and
3 deletions
+3
-3
docs/algebra.tex
docs/algebra.tex
+2
-2
docs/logic.tex
docs/logic.tex
+1
-1
No files found.
docs/algebra.tex
View file @
9ba4ad2b
...
...
@@ -35,7 +35,7 @@ In order to solve the recursive domain equation in \Sref{sec:model} it is also e
A function
$
f :
\cofe
\to
\cofeB
$
between two COFEs is
\emph
{
non-expansive
}
(written
$
f :
\cofe
\nfn
\cofeB
$
) if
\[
\All
n, x
\in
\cofe
, y
\in
\cofe
. x
\nequiv
{
n
}
y
\Ra
f
(
x
)
\nequiv
{
n
}
f
(
y
)
\]
It is
\emph
{
contractive
}
if
\[
\All
n, x
\in
\cofe
, y
\in
\cofe
.
(
\All
m < n. x
\nequiv
{
m
}
y
)
\Ra
f
(
x
)
\nequiv
{
n
}
f
(
x
)
\]
\[
\All
n, x
\in
\cofe
, y
\in
\cofe
.
(
\All
m < n. x
\nequiv
{
m
}
y
)
\Ra
f
(
x
)
\nequiv
{
n
}
f
(
y
)
\]
\end{defn}
Intuitively, applying a non-expansive function to some data will not suddenly introduce differences between seemingly equal data.
Elements that cannot be distinguished by programs within
$
n
$
steps remain indistinguishable after applying
$
f
$
.
...
...
@@ -211,7 +211,7 @@ Furthermore, discrete CMRAs can be turned into RAs by ignoring their COFE struct
\end{defn}
Note that every object/arrow in
$
\CMRAs
$
is also an object/arrow of
$
\COFEs
$
.
The notion of a locally non-expansive (or contractive) bifunctor naturally generalizes to bifunctors between these categories.
\ralf
{
Discuss how we probably have a commuting square of functors between Set, RA, CMRA, COFE.
}
%TODO: Discuss how we probably have a commuting square of functors between Set, RA, CMRA, COFE.
%%% Local Variables:
%%% mode: latex
...
...
docs/logic.tex
View file @
9ba4ad2b
...
...
@@ -135,7 +135,7 @@ Recursive predicates must be \emph{guarded}: in $\MU \var. \term$, the variable
Note that
$
\always
$
and
$
\later
$
bind more tightly than
$
*
$
,
$
\wand
$
,
$
\land
$
,
$
\lor
$
, and
$
\Ra
$
.
We will write
$
\pvs
[
\term
]
\prop
$
for
$
\pvs
[
\term
][
\term
]
\prop
$
.
If we omit the mask, then it is
$
\top
$
for weakest precondition
$
\wpre\expr
{
\Ret\var
.
\prop
}$
and
$
\emptyset
$
for primitive view shifts
$
\pvs
\prop
$
.
\ralf
{$
\top
$
is not a term in the logic. Neither is any of the operations on masks that we use in the rules for weakestpre.
}
%FIXME $\top$ is not a term in the logic. Neither is any of the operations on masks that we use in the rules for weakestpre.
Some propositions are
\emph
{
timeless
}
, which intuitively means that step-indexing does not affect them.
This is a
\emph
{
meta-level
}
assertion about propositions, defined as follows:
...
...
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