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
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
Rice Wine
Iris
Commits
9a2e4b47
Commit
9a2e4b47
authored
Jan 27, 2016
by
Ralf Jung
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
prove the very first Coq-verified iris Hoare Triple :)
parent
782a0cd5
Changes
2
Hide whitespace changes
Inline
Side-by-side
Showing
2 changed files
with
72 additions
and
24 deletions
+72
-24
barrier/lifting.v
barrier/lifting.v
+32
-15
barrier/tests.v
barrier/tests.v
+40
-9
No files found.
barrier/lifting.v
View file @
9a2e4b47
Require
Import
prelude
.
gmap
iris
.
lifting
.
Require
Export
barrier
.
parameter
.
Require
Export
iris
.
weakestpre
barrier
.
parameter
.
Import
uPred
.
(* TODO RJ: Figure out a way to to always use our Σ. *)
...
...
@@ -43,19 +43,20 @@ Qed.
(* TODO RJ: Figure out some better way to make the
postcondition a predicate over a *location* *)
Lemma
wp_alloc
E
σ
v
:
ownP
(
Σ
:
=
Σ
)
σ
⊑
wp
(
Σ
:
=
Σ
)
E
(
Alloc
(
v2e
v
))
Lemma
wp_alloc
E
σ
e
v
:
e2v
e
=
Some
v
→
ownP
(
Σ
:
=
Σ
)
σ
⊑
wp
(
Σ
:
=
Σ
)
E
(
Alloc
e
)
(
λ
v'
,
∃
l
,
■
(
v'
=
LocV
l
∧
σ
!!
l
=
None
)
∧
ownP
(
Σ
:
=
Σ
)
(<[
l
:
=
v
]>
σ
)).
Proof
.
(* RJ FIXME (also for most other lemmas in this file): rewrite would be nicer... *)
etransitivity
;
last
eapply
wp_lift_step
with
(
σ
1
:
=
σ
)
intros
Hvl
.
etransitivity
;
last
eapply
wp_lift_step
with
(
σ
1
:
=
σ
)
(
φ
:
=
λ
e'
σ
'
,
∃
l
,
e'
=
Loc
l
∧
σ
'
=
<[
l
:
=
v
]>
σ
∧
σ
!!
l
=
None
)
;
last
first
.
-
intros
e2
σ
2
ef
Hstep
.
inversion_clear
Hstep
.
split
;
first
done
.
rewrite
v2v
in
Hv
.
inversion_clear
Hv
.
rewrite
Hv
in
Hvl
.
inversion_clear
Hvl
.
eexists
;
split_ands
;
done
.
-
set
(
l
:
=
fresh
$
dom
(
gset
loc
)
σ
).
exists
(
Loc
l
),
((<[
l
:
=
v
]>)
σ
),
None
.
eapply
AllocS
;
first
by
rewrite
v2v
.
exists
(
Loc
l
),
((<[
l
:
=
v
]>)
σ
),
None
.
eapply
AllocS
;
first
done
.
apply
(
not_elem_of_dom
(
D
:
=
gset
loc
)).
apply
is_fresh
.
-
reflexivity
.
-
reflexivity
.
...
...
@@ -79,7 +80,7 @@ Proof.
(
φ
:
=
λ
e'
σ
'
,
e'
=
v2e
v
∧
σ
'
=
σ
)
;
last
first
.
-
intros
e2
σ
2
ef
Hstep
.
move
:
Hl
.
inversion_clear
Hstep
=>{
σ
}.
rewrite
Hlookup
.
case
=>->.
done
.
-
do
3
eexists
.
e
apply
LoadS
;
eassumption
.
-
do
3
eexists
.
e
constructor
;
eassumption
.
-
reflexivity
.
-
reflexivity
.
-
rewrite
-
pvs_intro
.
rewrite
-{
1
}[
ownP
σ
](@
right_id
_
_
_
_
uPred
.
sep_True
).
...
...
@@ -92,16 +93,17 @@ Proof.
+
done
.
Qed
.
Lemma
wp_store
E
σ
l
v
v'
:
Lemma
wp_store
E
σ
l
e
v
v'
:
e2v
e
=
Some
v
→
σ
!!
l
=
Some
v'
→
ownP
(
Σ
:
=
Σ
)
σ
⊑
wp
(
Σ
:
=
Σ
)
E
(
Store
(
Loc
l
)
(
v2e
v
)
)
(
λ
v'
,
■
(
v'
=
Lit
VUnit
)
∧
ownP
(
Σ
:
=
Σ
)
(<[
l
:
=
v
]>
σ
)).
ownP
(
Σ
:
=
Σ
)
σ
⊑
wp
(
Σ
:
=
Σ
)
E
(
Store
(
Loc
l
)
e
)
(
λ
v'
,
■
(
v'
=
Lit
UnitV
)
∧
ownP
(
Σ
:
=
Σ
)
(<[
l
:
=
v
]>
σ
)).
Proof
.
intros
Hl
.
etransitivity
;
last
eapply
wp_lift_step
with
(
σ
1
:
=
σ
)
intros
H
vl
H
l
.
etransitivity
;
last
eapply
wp_lift_step
with
(
σ
1
:
=
σ
)
(
φ
:
=
λ
e'
σ
'
,
e'
=
LitUnit
∧
σ
'
=
<[
l
:
=
v
]>
σ
)
;
last
first
.
-
intros
e2
σ
2
ef
Hstep
.
move
:
Hl
.
inversion_clear
Hstep
=>{
σ
2
}.
rewrite
v2v
in
Hv
.
inversion_clear
Hv
.
done
.
-
do
3
eexists
.
eapply
StoreS
;
last
(
eexists
;
eassumption
).
by
rewrite
v2v
.
rewrite
Hvl
in
Hv
.
inversion_clear
Hv
.
done
.
-
do
3
eexists
.
eapply
StoreS
;
last
(
eexists
;
eassumption
).
eassumption
.
-
reflexivity
.
-
reflexivity
.
-
rewrite
-
pvs_intro
.
rewrite
-{
1
}[
ownP
σ
](@
right_id
_
_
_
_
uPred
.
sep_True
).
...
...
@@ -117,7 +119,7 @@ Qed.
(** Base axioms for core primitives of the language: Stateless reductions *)
Lemma
wp_fork
E
e
:
▷
wp
(
Σ
:
=
Σ
)
coPset_all
e
(
λ
_
,
True
)
⊑
wp
(
Σ
:
=
Σ
)
E
(
Fork
e
)
(
λ
_
,
True
).
▷
wp
(
Σ
:
=
Σ
)
coPset_all
e
(
λ
_
,
True
)
⊑
wp
(
Σ
:
=
Σ
)
E
(
Fork
e
)
(
λ
v
,
■
(
v
=
LitUnitV
)
).
Proof
.
etransitivity
;
last
eapply
wp_lift_pure_step
with
(
φ
:
=
λ
e'
ef
,
e'
=
LitUnit
∧
ef
=
Some
e
)
;
...
...
@@ -136,7 +138,8 @@ Proof.
transitivity
(
True
★
wp
coPset_all
e
(
λ
_
:
ival
Σ
,
True
))%
I
;
first
by
rewrite
left_id
.
apply
sep_mono
;
last
reflexivity
.
rewrite
-
wp_value'
;
reflexivity
.
rewrite
-
wp_value'
;
last
reflexivity
.
by
apply
const_intro
.
Qed
.
Lemma
wp_lift_pure_step
E
(
φ
:
expr
→
Prop
)
Q
e1
:
...
...
@@ -185,3 +188,17 @@ Proof.
by
asimpl
.
Qed
.
Lemma
wp_plus
n1
n2
E
P
Q
:
P
⊑
Q
(
LitNatV
(
n1
+
n2
))
→
▷
P
⊑
wp
(
Σ
:
=
Σ
)
E
(
Plus
(
LitNat
n1
)
(
LitNat
n2
))
Q
.
Proof
.
intros
HP
.
etransitivity
;
last
eapply
wp_lift_pure_step
with
(
φ
:
=
λ
e'
,
e'
=
LitNat
(
n1
+
n2
))
;
last
first
.
-
intros
?
?
?
?
Hstep
.
inversion_clear
Hstep
;
done
.
-
intros
?.
do
3
eexists
.
econstructor
.
-
reflexivity
.
-
apply
later_mono
,
forall_intro
=>
e2
.
apply
impl_intro_l
.
apply
const_elim_l
=>->.
rewrite
-
wp_value'
;
last
reflexivity
;
done
.
Qed
.
barrier/tests.v
View file @
9a2e4b47
(** This file is essentially a bunch of testcases. *)
Require
Import
modures
.
base
.
Require
Import
barrier
.
parameter
.
Require
Import
modures
.
logic
.
Require
Import
barrier
.
lifting
.
Import
uPred
.
Module
LangTests
.
Definition
add
:
=
Op2
plus
(
Lit
21
)
(
Lit
21
).
Goal
∀
σ
,
prim_step
add
σ
(
Lit
42
)
σ
None
.
Definition
add
:
=
Plus
(
LitNat
21
)
(
LitNat
21
).
Goal
∀
σ
,
prim_step
add
σ
(
LitNat
42
)
σ
None
.
Proof
.
apply
Op2S
.
constructor
.
Qed
.
Definition
rec
:
=
Rec
(
App
(
Var
0
)
(
Var
1
)).
(* fix f x => f x *)
Definition
rec_app
:
=
App
rec
(
Lit
0
).
Definition
rec_app
:
=
App
rec
(
Lit
Nat
0
).
Goal
∀
σ
,
prim_step
rec_app
σ
rec_app
σ
None
.
Proof
.
move
=>?.
eapply
BetaS
.
reflexivity
.
Qed
.
Definition
lam
:
=
Lam
(
Op2
plus
(
Var
0
)
(
Li
t
21
)).
Goal
∀
σ
,
prim_step
(
App
lam
(
Lit
21
))
σ
add
σ
None
.
Definition
lam
:
=
Lam
(
Plus
(
Var
0
)
(
LitNa
t
21
)).
Goal
∀
σ
,
prim_step
(
App
lam
(
Lit
Nat
21
))
σ
add
σ
None
.
Proof
.
move
=>?.
eapply
BetaS
.
reflexivity
.
Qed
.
...
...
@@ -28,3 +28,34 @@ End LangTests.
Module
ParamTests
.
Print
Assumptions
Σ
.
End
ParamTests
.
Module
LiftingTests
.
(* TODO RJ: Some syntactic sugar for language expressions would be nice. *)
Definition
e3
:
=
Load
(
Var
0
).
Definition
e2
:
=
Seq
(
Store
(
Var
0
)
(
Plus
(
Load
(
Var
0
))
(
LitNat
1
)))
e3
.
Definition
e
:
=
Let
(
Alloc
(
LitNat
1
))
e2
.
Goal
∀
σ
E
,
(
ownP
(
Σ
:
=
Σ
)
σ
)
⊑
(
wp
(
Σ
:
=
Σ
)
E
e
(
λ
v
,
■
(
v
=
LitNatV
2
))).
Proof
.
move
=>
σ
E
.
rewrite
/
e
.
rewrite
-(
wp_bind
_
_
(
LetCtx
EmptyCtx
e2
)).
rewrite
-
wp_mono
.
{
eapply
wp_alloc
;
done
.
}
move
=>
v
;
apply
exist_elim
=>
l
.
apply
const_elim_l
;
move
=>[->
_
]
{
v
}.
rewrite
(
later_intro
(
ownP
_
))
;
apply
wp_lam
.
asimpl
.
rewrite
-(
wp_bind
_
_
(
SeqCtx
(
StoreRCtx
(
LocV
_
)
(
PlusLCtx
EmptyCtx
_
))
(
Load
(
Loc
_
)))).
rewrite
-
wp_mono
.
{
eapply
wp_load
.
apply
:
lookup_insert
.
}
(* RJ TODO: figure out why apply and eapply fail. *)
move
=>
v
;
apply
const_elim_l
;
move
=>->
{
v
}.
rewrite
-(
wp_bind
_
_
(
SeqCtx
(
StoreRCtx
(
LocV
_
)
EmptyCtx
)
(
Load
(
Loc
_
)))).
rewrite
(
later_intro
(
ownP
_
))
;
apply
wp_plus
.
rewrite
-(
wp_bind
_
_
(
SeqCtx
EmptyCtx
(
Load
(
Loc
_
)))).
rewrite
-
wp_mono
.
{
eapply
wp_store
;
first
reflexivity
.
apply
:
lookup_insert
.
}
move
=>
v
;
apply
const_elim_l
;
move
=>->
{
v
}.
rewrite
(
later_intro
(
ownP
_
))
;
apply
wp_lam
.
asimpl
.
rewrite
-
wp_mono
.
{
eapply
wp_load
.
apply
:
lookup_insert
.
}
move
=>
v
;
apply
const_elim_l
;
move
=>->
{
v
}.
by
apply
const_intro
.
Qed
.
End
LiftingTests
.
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