Skip to content
Projects
Groups
Snippets
Help
Loading...
Help
Support
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
I
Iris
Project
Project
Details
Activity
Releases
Cycle Analytics
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Charts
Issues
74
Issues
74
List
Boards
Labels
Milestones
Merge Requests
9
Merge Requests
9
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Charts
Wiki
Wiki
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Charts
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
Iris
Iris
Commits
3f9e2ea5
Commit
3f9e2ea5
authored
Aug 12, 2019
by
Rodolphe Lepigre
Committed by
Robbert
Aug 12, 2019
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Add some trivial but useful heaplang libraries.
parent
6c620a09
Changes
3
Hide whitespace changes
Inline
Sidebyside
Showing
3 changed files
with
72 additions
and
0 deletions
+72
0
_CoqProject
_CoqProject
+2
0
arith.v
theories/heap_lang/lib/arith.v
+43
0
diverge.v
theories/heap_lang/lib/diverge.v
+27
0
No files found.
_CoqProject
View file @
3f9e2ea5
...
...
@@ 116,6 +116,8 @@ theories/heap_lang/lib/clairvoyant_coin.v
theories/heap_lang/lib/counter.v
theories/heap_lang/lib/atomic_heap.v
theories/heap_lang/lib/increment.v
theories/heap_lang/lib/diverge.v
theories/heap_lang/lib/arith.v
theories/proofmode/base.v
theories/proofmode/tokens.v
theories/proofmode/coq_tactics.v
...
...
theories/heap_lang/lib/arith.v
0 → 100644
View file @
3f9e2ea5
From
iris
.
program_logic
Require
Export
weakestpre
.
From
iris
.
heap_lang
Require
Export
lang
.
From
iris
.
proofmode
Require
Import
tactics
.
From
iris
.
heap_lang
Require
Import
proofmode
notation
.
Set
Default
Proof
Using
"Type"
.
(** A library defining binary [minimum] and [maximum] functions, together with
their expected specs. These operations come up often when working manipulating
array indices (checking for bounds). *)
Definition
minimum
:
val
:=
λ
:
"m"
"n"
,
if
:
"m"
<
"n"
then
"m"
else
"n"
.
Definition
maximum
:
val
:=
λ
:
"m"
"n"
,
if
:
"m"
<
"n"
then
"n"
else
"m"
.
Lemma
minimum_spec
`
{!
heapG
Σ
}
s
E
(
Φ
:
val
→
iProp
Σ
)
(
m
n
:
Z
)
:
▷
Φ
#(
m
`
min
`
n
)

∗
WP
minimum
#
m
#
n
@
s
;
E
{{
Φ
}}.
Proof
.
iIntros
"HΦ"
.
wp_lam
.
wp_pures
.
case_bool_decide
;
wp_pures
.

rewrite
Z
.
min_l
;
[
done

by
lia
].

rewrite
Z
.
min_r
;
[
done

by
lia
].
Qed
.
Lemma
minimum_spec_nat
`
{!
heapG
Σ
}
s
E
(
Φ
:
val
→
iProp
Σ
)
(
m
n
:
nat
)
:
▷
Φ
#(
m
`
min
`
n
)%
nat

∗
WP
minimum
#
m
#
n
@
s
;
E
{{
Φ
}}.
Proof
.
iIntros
"HΦ"
.
iApply
minimum_spec
.
by
rewrite
Nat2Z
.
inj_min
.
Qed
.
Lemma
maximum_spec
`
{!
heapG
Σ
}
s
E
(
Φ
:
val
→
iProp
Σ
)
(
m
n
:
Z
)
:
▷
Φ
#(
m
`
max
`
n
)

∗
WP
maximum
#
m
#
n
@
s
;
E
{{
Φ
}}.
Proof
.
iIntros
"HΦ"
.
wp_lam
.
wp_pures
.
case_bool_decide
;
wp_pures
.

rewrite
Z
.
max_r
;
[
done

by
lia
].

rewrite
Z
.
max_l
;
[
done

by
lia
].
Qed
.
Lemma
maximum_spec_nat
`
{!
heapG
Σ
}
s
E
(
Φ
:
val
→
iProp
Σ
)
(
m
n
:
nat
)
:
▷
Φ
#(
m
`
max
`
n
)%
nat

∗
WP
maximum
#
m
#
n
@
s
;
E
{{
Φ
}}.
Proof
.
iIntros
"HΦ"
.
iApply
maximum_spec
.
by
rewrite
Nat2Z
.
inj_max
.
Qed
.
theories/heap_lang/lib/diverge.v
0 → 100644
View file @
3f9e2ea5
From
iris
.
program_logic
Require
Export
weakestpre
.
From
iris
.
heap_lang
Require
Export
lang
.
From
iris
.
proofmode
Require
Import
tactics
.
From
iris
.
heap_lang
Require
Import
proofmode
notation
.
Set
Default
Proof
Using
"Type"
.
(** This library provides a [diverge] function that goes into an infinite loop
when provided with an (arbitrary) argument value. This function can be used to
let the program diverge in corner cases that one wants to omit in proofs. This
mechanism should be used with care and communicated clearly, obviously.
Note that this mechanism only works when establishing partial correctness with
the ordinary version of weakest preconditions, and not when establishing total
correctness using the total version of weakest preconditions.
A typical application for [diverge] is insertion functions for data structures
having a fixed capacity. In such cases, we can choose divergence instead of an
explicit error handling when the full capacity has already been reached. *)
Definition
diverge
:
val
:=
rec
:
"diverge"
"v"
:=
"diverge"
"v"
.
Lemma
wp_diverge
`
{!
heapG
Σ
}
s
E
(
Φ
:
val
→
iProp
Σ
)
(
v
:
val
)
:
WP
diverge
v
@
s
;
E
{{
Φ
}}%
I
.
Proof
.
iL
ö
b
as
"IH"
.
wp_lam
.
iApply
"IH"
.
Qed
.
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