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
iriscoq
Project overview
Project overview
Details
Activity
Releases
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Issues
0
Issues
0
List
Boards
Labels
Service Desk
Milestones
Merge Requests
0
Merge Requests
0
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Operations
Operations
Incidents
Environments
Analytics
Analytics
CI / CD
Repository
Value Stream
Wiki
Wiki
Snippets
Snippets
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
Marianna Rapoport
iriscoq
Commits
d4aa9dd9
Commit
d4aa9dd9
authored
Dec 08, 2017
by
Ralf Jung
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
on unique representatives
parent
1df177bd
Changes
2
Hide whitespace changes
Inline
Sidebyside
Showing
2 changed files
with
22 additions
and
4 deletions
+22
4
docs/constructions.tex
docs/constructions.tex
+17
0
theories/base_logic/upred.v
theories/base_logic/upred.v
+5
4
No files found.
docs/constructions.tex
View file @
d4aa9dd9
...
...
@@ 31,6 +31,23 @@ You can think of uniform predicates as monotone, stepindexed predicates over a
$
\UPred
()
$
is a locally nonexpansive functor from
$
\CMRAs
$
to
$
\COFEs
$
.
It is worth noting that the above quotient admits canonical
representatives. More precisely, one can show that every
equivalence class contains exactly one element
$
P
_
0
$
such that:
\[
\All
n,
\melt
.
(
\mval
(
\melt
)
\nincl
{
n
}
P
_
0
(
\melt
))
\Ra
n
\in
P
_
0
(
\melt
)
\tagH
{
UPred

canonical
}
\]
Intuitively, this says that
$
P
_
0
$
trivially holds whenever the resource is invalid.
Starting from any element
$
P
$
, one can find this canonical
representative by choosing
$
P
_
0
(
\melt
)
:
=
\setComp
{
n
}{
n
\in
\mval
(
\melt
)
\Ra
n
\in
P
(
\melt
)
}$
.
Hence, as an alternative definition of
$
\UPred
$
, we could use the set
of canonical representatives. This alternative definition would
save us from using a quotient. However, the definitions of the various
connectives would get more complicated, because we have to make sure
they all verify
\ruleref
{
UPredcanonical
}
, which sometimes requires some adjustments. We
would moreover need to prove one more property for every logical
connective.
\clearpage
\section
{
RA and CMRA constructions
}
...
...
theories/base_logic/upred.v
View file @
d4aa9dd9
...
...
@@ 24,10 +24,11 @@ Set Default Proof Using "Type".
It is worth noting that this equivalence relation admits canonical
representatives. More precisely, one can show that every
equivalence class contains exactly one element P0 such that:
∀ x, (✓ x → P(x)) → P(x) (2)
(Again, this assertion has to be understood in sProp). Starting
from an element P of a given class, one can build this canonical
representative by chosing:
∀ x, (✓ x → P0(x)) → P0(x) (2)
(Again, this assertion has to be understood in sProp). Intuitively,
this says that P0 trivially holds whenever the resource is invalid.
Starting from any element P, one can find this canonical
representative by choosing:
P0(x) := ✓ x → P(x) (3)
Hence, as an alternative definition of uPred, we could use the set
...
...
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