Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
What's new
10
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
Open sidebar
Rodolphe Lepigre
Iris
Commits
beebaa6e
Commit
beebaa6e
authored
Apr 13, 2017
by
Robbert Krebbers
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Reorganize proofmode tests.
parent
2821e99e
Changes
1
Hide whitespace changes
Inline
Side-by-side
Showing
1 changed file
with
38 additions
and
41 deletions
+38
-41
theories/tests/proofmode.v
theories/tests/proofmode.v
+38
-41
No files found.
theories/tests/proofmode.v
View file @
beebaa6e
...
...
@@ -4,8 +4,9 @@ Set Default Proof Using "Type".
Section
tests
.
Context
{
M
:
ucmraT
}.
Lemma
demo_0
(
P
Q
:
uPred
M
)
:
□
(
P
∨
Q
)
-
∗
(
∀
x
,
⌜
x
=
0
⌝
∨
⌜
x
=
1
⌝
)
→
(
Q
∨
P
).
Implicit
Types
P
Q
R
:
uPred
M
.
Lemma
demo_0
P
Q
:
□
(
P
∨
Q
)
-
∗
(
∀
x
,
⌜
x
=
0
⌝
∨
⌜
x
=
1
⌝
)
→
(
Q
∨
P
).
Proof
.
iIntros
"#H #H2"
.
(* should remove the disjunction "H" *)
...
...
@@ -39,7 +40,7 @@ Proof.
-
done
.
Qed
.
Lemma
demo_2
(
P1
P2
P3
P4
Q
:
uPred
M
)
(
P5
:
nat
→
uPredC
M
)
:
Lemma
demo_2
P1
P2
P3
P4
Q
(
P5
:
nat
→
uPredC
M
)
:
P2
∗
(
P3
∗
Q
)
∗
True
∗
P1
∗
P2
∗
(
P4
∗
(
∃
x
:
nat
,
P5
x
∨
P3
))
∗
True
-
∗
P1
-
∗
(
True
∗
True
)
-
∗
(((
P2
∧
False
∨
P2
∧
⌜
0
=
0
⌝
)
∗
P3
)
∗
Q
∗
P1
∗
True
)
∧
...
...
@@ -57,17 +58,17 @@ Proof.
*
iSplitL
"HQ"
.
iAssumption
.
by
iSplitL
"H1"
.
Qed
.
Lemma
demo_3
(
P1
P2
P3
:
uPred
M
)
:
Lemma
demo_3
P1
P2
P3
:
P1
∗
P2
∗
P3
-
∗
▷
P1
∗
▷
(
P2
∗
∃
x
,
(
P3
∧
⌜
x
=
0
⌝
)
∨
P3
).
Proof
.
iIntros
"($ & $ & H)"
.
iFrame
"H"
.
iNext
.
by
iExists
0
.
Qed
.
Definition
foo
(
P
:
uPred
M
)
:
=
(
P
→
P
)%
I
.
Definition
bar
:
uPred
M
:
=
(
∀
P
,
foo
P
)%
I
.
Lemma
demo_4
:
True
-
∗
bar
.
Lemma
test_unfold_constants
:
True
-
∗
bar
.
Proof
.
iIntros
.
iIntros
(
P
)
"HP //"
.
Qed
.
Lemma
demo_5
(
x
y
:
M
)
(
P
:
uPred
M
)
:
Lemma
test_iRewrite
(
x
y
:
M
)
P
:
(
∀
z
,
P
→
z
≡
y
)
-
∗
(
P
-
∗
(
x
,
x
)
≡
(
y
,
x
)).
Proof
.
iIntros
"H1 H2"
.
...
...
@@ -76,7 +77,7 @@ Proof.
done
.
Qed
.
Lemma
demo_6
(
P
Q
:
uPred
M
)
:
Lemma
test_fast_iIntros
P
Q
:
(
∀
x
y
z
:
nat
,
⌜
x
=
plus
0
x
⌝
→
⌜
y
=
0
⌝
→
⌜
z
=
0
⌝
→
P
→
□
Q
→
foo
(
x
≡
x
))%
I
.
Proof
.
...
...
@@ -85,29 +86,14 @@ Proof.
iIntros
"# _ //"
.
Qed
.
Lemma
demo_7
(
P
Q1
Q2
:
uPred
M
)
:
P
∗
(
Q1
∧
Q2
)
-
∗
P
∗
Q1
.
Lemma
test_iDestruct_spatial_and
P
Q1
Q2
:
P
∗
(
Q1
∧
Q2
)
-
∗
P
∗
Q1
.
Proof
.
iIntros
"[H1 [H2 _]]"
.
by
iFrame
.
Qed
.
Section
iris
.
Context
`
{
invG
Σ
}.
Implicit
Types
E
:
coPset
.
Implicit
Types
P
Q
:
iProp
Σ
.
Lemma
demo_8
N
E
P
Q
R
:
↑
N
⊆
E
→
(
True
-
∗
P
-
∗
inv
N
Q
-
∗
True
-
∗
R
)
-
∗
P
-
∗
▷
Q
={
E
}=
∗
R
.
Proof
.
iIntros
(?)
"H HP HQ"
.
iApply
(
"H"
with
"[% //] [$] [> HQ] [> //]"
).
by
iApply
inv_alloc
.
Qed
.
End
iris
.
Lemma
demo_9
(
x
y
z
:
M
)
:
Lemma
test_iFrame_pure
(
x
y
z
:
M
)
:
✓
x
→
⌜
y
≡
z
⌝
-
∗
(
✓
x
∧
✓
x
∧
y
≡
z
:
uPred
M
).
Proof
.
iIntros
(
Hv
)
"Hxy"
.
by
iFrame
(
Hv
Hv
)
"Hxy"
.
Qed
.
Lemma
demo_10
(
P
Q
:
uPred
M
)
:
P
-
∗
Q
-
∗
True
.
Lemma
test_iAssert_persistent
P
Q
:
P
-
∗
Q
-
∗
True
.
Proof
.
iIntros
"HP HQ"
.
iAssert
True
%
I
as
"#_"
.
{
by
iClear
"HP HQ"
.
}
...
...
@@ -117,44 +103,43 @@ Proof.
done
.
Qed
.
Lemma
demo_11
(
P
Q
R
:
uPred
M
)
:
Lemma
test_iSpecialize_auto_frame
P
Q
R
:
(
P
-
∗
True
-
∗
True
-
∗
Q
-
∗
R
)
-
∗
P
-
∗
Q
-
∗
R
.
Proof
.
iIntros
"H HP HQ"
.
by
iApply
(
"H"
with
"[$]"
).
Qed
.
(* Check coercions *)
Lemma
demo_12
(
P
:
Z
→
uPred
M
)
:
(
∀
x
,
P
x
)
-
∗
∃
x
,
P
x
.
Lemma
test_iExist_coercion
(
P
:
Z
→
uPred
M
)
:
(
∀
x
,
P
x
)
-
∗
∃
x
,
P
x
.
Proof
.
iIntros
"HP"
.
iExists
(
0
:
nat
).
iApply
(
"HP"
$!
(
0
:
nat
)).
Qed
.
Lemma
demo_13
(
P
:
uPred
M
)
:
(|==>
False
)
-
∗
|==>
P
.
Lemma
test_iAssert_modality
P
:
(|==>
False
)
-
∗
|==>
P
.
Proof
.
iIntros
.
iAssert
False
%
I
with
"[> - //]"
as
%[].
Qed
.
Lemma
demo_14
(
P
:
uPred
M
)
:
False
-
∗
P
.
Lemma
test_iAssumption_False
P
:
False
-
∗
P
.
Proof
.
iIntros
"H"
.
done
.
Qed
.
(* Check instantiation and dependent types *)
Lemma
demo_15
(
P
:
∀
n
,
vec
nat
n
→
uPred
M
)
:
Lemma
test_iSpecialize_dependent_type
(
P
:
∀
n
,
vec
nat
n
→
uPred
M
)
:
(
∀
n
v
,
P
n
v
)
-
∗
∃
n
v
,
P
n
v
.
Proof
.
iIntros
"H"
.
iExists
_
,
[#
10
].
iSpecialize
(
"H"
$!
_
[#
10
]).
done
.
Qed
.
Lemma
demo_16
(
P
Q
R
:
uPred
M
)
`
{!
PersistentP
R
}
:
Lemma
test_eauto_iFramE
P
Q
R
`
{!
PersistentP
R
}
:
P
-
∗
Q
-
∗
R
-
∗
R
∗
Q
∗
P
∗
R
∨
False
.
Proof
.
eauto
with
iFrame
.
Qed
.
Lemma
demo_17
(
P
Q
R
:
uPred
M
)
`
{!
PersistentP
R
}
:
Lemma
test_iCombine_persistent
P
Q
R
`
{!
PersistentP
R
}
:
P
-
∗
Q
-
∗
R
-
∗
R
∗
Q
∗
P
∗
R
∨
False
.
Proof
.
iIntros
"HP HQ #HR"
.
iCombine
"HR HQ HP HR"
as
"H"
.
auto
.
Qed
.
Lemma
test_iNext_evar
(
P
:
uPred
M
)
:
P
-
∗
True
.
Lemma
test_iNext_evar
P
:
P
-
∗
True
.
Proof
.
iIntros
"HP"
.
iAssert
(
▷
_
-
∗
▷
P
)%
I
as
"?"
;
last
done
.
iIntros
"?"
.
iNext
.
iAssumption
.
Qed
.
Lemma
test_iNext_sep1
(
P
Q
:
uPred
M
)
Lemma
test_iNext_sep1
P
Q
(
R1
:
=
(
P
∗
Q
)%
I
)
(
R2
:
=
(
▷
P
∗
▷
Q
)%
I
)
:
(
▷
P
∗
▷
Q
)
∗
R1
∗
R2
-
∗
▷
(
P
∗
Q
)
∗
▷
R1
∗
R2
.
Proof
.
...
...
@@ -162,21 +147,33 @@ Proof.
rewrite
{
1
2
}(
lock
R1
).
(* check whether R1 has not been unfolded *)
done
.
Qed
.
Lemma
test_iNext_sep2
(
P
Q
:
uPred
M
)
:
▷
P
∗
▷
Q
-
∗
▷
(
P
∗
Q
).
Lemma
test_iNext_sep2
P
Q
:
▷
P
∗
▷
Q
-
∗
▷
(
P
∗
Q
).
Proof
.
iIntros
"H"
.
iNext
.
iExact
"H"
.
(* Check that the laters are all gone. *)
Qed
.
Lemma
test_
f
rame_persistent
(
P
Q
:
uPred
M
)
:
Lemma
test_
iF
rame_persistent
(
P
Q
:
uPred
M
)
:
□
P
-
∗
Q
-
∗
□
(
P
∗
P
)
∗
(
P
∧
Q
∨
Q
).
Proof
.
iIntros
"#HP"
.
iFrame
"HP"
.
iIntros
"$"
.
Qed
.
Lemma
test_split_box
(
P
Q
:
uPred
M
)
:
□
P
-
∗
□
(
P
∗
P
).
Lemma
test_iSplit_always
P
Q
:
□
P
-
∗
□
(
P
∗
P
).
Proof
.
iIntros
"#?"
.
by
iSplit
.
Qed
.
Lemma
test_
s
pecialize_persistent
(
P
Q
:
uPred
M
)
:
Lemma
test_
iS
pecialize_persistent
P
Q
:
□
P
-
∗
(
□
P
-
∗
Q
)
-
∗
Q
.
Proof
.
iIntros
"#HP HPQ"
.
by
iSpecialize
(
"HPQ"
with
"HP"
).
Qed
.
End
tests
.
Section
more_tests
.
Context
`
{
invG
Σ
}.
Implicit
Types
P
Q
R
:
iProp
Σ
.
Lemma
test_masks
N
E
P
Q
R
:
↑
N
⊆
E
→
(
True
-
∗
P
-
∗
inv
N
Q
-
∗
True
-
∗
R
)
-
∗
P
-
∗
▷
Q
={
E
}=
∗
R
.
Proof
.
iIntros
(?)
"H HP HQ"
.
iApply
(
"H"
with
"[% //] [$] [> HQ] [> //]"
).
by
iApply
inv_alloc
.
Qed
.
End
more_tests
.
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