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
F
Fairis
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
Iris
Fairis
Commits
66a6ce6c
Commit
66a6ce6c
authored
Mar 05, 2016
by
Ralf Jung
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
start proving spawn-join
parent
69fea45d
Changes
3
Hide whitespace changes
Inline
Side-by-side
Showing
3 changed files
with
104 additions
and
1 deletion
+104
-1
_CoqProject
_CoqProject
+1
-0
heap_lang/lang.v
heap_lang/lang.v
+15
-1
heap_lang/spawn.v
heap_lang/spawn.v
+88
-0
No files found.
_CoqProject
View file @
66a6ce6c
...
...
@@ -81,6 +81,7 @@ heap_lang/lifting.v
heap_lang/derived.v
heap_lang/heap.v
heap_lang/notation.v
heap_lang/spawn.v
heap_lang/tests.v
heap_lang/substitution.v
barrier/barrier.v
...
...
heap_lang/lang.v
View file @
66a6ce6c
...
...
@@ -417,6 +417,17 @@ Proof.
apply
wsubst_closed
,
not_elem_of_nil
.
Qed
.
(
**
to_val
propagation
.
TODO:
automatically
appliy
in
wp_tactics
?
*
)
Lemma
to_val_InjL
e
v
:
to_val
e
=
Some
v
→
to_val
(
InjL
e
)
=
Some
(
InjLV
v
).
Proof
.
move
=>
H
.
simpl
.
by
rewrite
H
.
Qed
.
Lemma
to_val_InjR
e
v
:
to_val
e
=
Some
v
→
to_val
(
InjR
e
)
=
Some
(
InjRV
v
).
Proof
.
move
=>
H
.
simpl
.
by
rewrite
H
.
Qed
.
Lemma
to_val_Pair
e1
e2
v1
v2
:
to_val
e1
=
Some
v1
→
to_val
e2
=
Some
v2
→
to_val
(
Pair
e1
e2
)
=
Some
(
PairV
v1
v2
).
Proof
.
move
=>
H1
H2
.
simpl
.
by
rewrite
H1
H2
.
Qed
.
(
**
Basic
properties
about
the
language
*
)
Lemma
to_of_val
v
:
to_val
(
of_val
v
)
=
Some
v
.
Proof
.
by
induction
v
;
simplify_option_eq
.
Qed
.
...
...
@@ -525,7 +536,7 @@ Lemma alloc_fresh e v σ :
to_val
e
=
Some
v
→
head_step
(
Alloc
e
)
σ
(
Loc
l
)
(
<
[
l
:=
v
]
>
σ
)
None
.
Proof
.
by
intros
;
apply
AllocS
,
(
not_elem_of_dom
(
D
:=
gset
_
)),
is_fresh
.
Qed
.
(
**
Equality
stuff
*
)
(
**
Equality
and
other
typeclass
stuff
*
)
Instance
base_lit_dec_eq
(
l1
l2
:
base_lit
)
:
Decision
(
l1
=
l2
).
Proof
.
solve_decision
.
Defined
.
Instance
un_op_dec_eq
(
op1
op2
:
un_op
)
:
Decision
(
op1
=
op2
).
...
...
@@ -567,6 +578,9 @@ Instance val_dec_eq (v1 v2 : val) : Decision (v1 = v2).
Proof
.
refine
(
cast_if
(
decide
(
of_val
v1
=
of_val
v2
)));
abstract
naive_solver
.
Defined
.
Instance
expr_inhabited
X
:
Inhabited
(
expr
X
)
:=
populate
(
Lit
LitUnit
).
Instance
val_inhabited
:
Inhabited
val
:=
populate
(
LitV
LitUnit
).
End
heap_lang
.
(
**
Language
*
)
...
...
heap_lang/spawn.v
0 → 100644
View file @
66a6ce6c
From
program_logic
Require
Export
global_functor
.
From
heap_lang
Require
Export
heap
.
From
heap_lang
Require
Import
wp_tactics
notation
.
Import
uPred
.
Definition
spawn
:
val
:=
λ
:
"f"
,
let
:
"c"
:=
ref
(
InjL
#
0
)
in
Fork
(
'
"c"
<-
InjR
(
'
"f"
#()))
;;
'
"c"
.
Definition
join
:
val
:=
rec:
"join"
"c"
:=
match
:
!
'
"c"
with
InjR
"x"
=>
'
"x"
|
InjL
<>
=>
'
"join"
'
"c"
end
.
(
**
The
monoids
we
need
.
*
)
(
*
Not
bundling
heapG
,
as
it
may
be
shared
with
other
users
.
*
)
Class
spawnG
Σ
:=
SpawnG
{
spawn_tokG
:>
inG
heap_lang
Σ
(
exclR
unitC
);
}
.
Definition
spawnGF
:
rFunctors
:=
[
constRF
(
exclR
unitC
)].
Instance
inGF_spawnG
`
{
inGF
heap_lang
Σ
(
constRF
(
exclR
unitC
))
}
:
spawnG
Σ
.
Proof
.
split
.
apply
:
inGF_inG
.
Qed
.
(
**
Now
we
come
to
the
Iris
part
of
the
proof
.
*
)
Section
proof
.
Context
{
Σ
:
rFunctorG
}
`
{!
heapG
Σ
,
!
spawnG
Σ
}
.
Context
(
heapN
N
:
namespace
).
Local
Notation
iProp
:=
(
iPropG
heap_lang
Σ
).
Definition
spawn_inv
(
γ
:
gname
)
(
l
:
loc
)
(
Ψ
:
val
→
iProp
)
:
iProp
:=
(
∃
lv
,
l
↦
lv
★
(
lv
=
InjLV
#
0
∨
∃
v
,
lv
=
InjRV
v
★
(
Ψ
v
∨
own
γ
(
Excl
()))))
%
I
.
Definition
join_handle
(
l
:
loc
)
(
Ψ
:
val
→
iProp
)
:
iProp
:=
(
■
(
heapN
⊥
N
)
★
∃
γ
,
heap_ctx
heapN
★
own
γ
(
Excl
())
★
inv
N
(
spawn_inv
γ
l
Ψ
))
%
I
.
Global
Instance
spawn_inv_ne
n
γ
l
:
Proper
(
pointwise_relation
val
(
dist
n
)
==>
dist
n
)
(
spawn_inv
γ
l
).
Proof
.
solve_proper
.
Qed
.
Global
Instance
join_handle_ne
n
l
:
Proper
(
pointwise_relation
val
(
dist
n
)
==>
dist
n
)
(
join_handle
l
).
Proof
.
solve_proper
.
Qed
.
(
**
The
main
proofs
.
*
)
Lemma
spawn_spec
(
Ψ
:
val
→
iProp
)
(
f
:
val
)
(
Φ
:
val
→
iProp
)
:
heapN
⊥
N
→
(
heap_ctx
heapN
★
#
>
f
#()
{{
Ψ
}}
★
∀
l
,
join_handle
l
Ψ
-
★
Φ
(
%
l
))
⊑
#
>
spawn
f
{{
Φ
}}
.
Proof
.
intros
Hdisj
.
rewrite
/
spawn
.
wp_let
.
(
ewp
eapply
wp_alloc
);
eauto
with
I
.
strip_later
.
apply
forall_intro
=>
l
.
apply
wand_intro_l
.
wp_let
.
rewrite
(
forall_elim
l
).
eapply
sep_elim_True_l
.
{
eapply
(
own_alloc
(
Excl
())).
done
.
}
rewrite
!
pvs_frame_r
.
eapply
wp_strip_pvs
.
rewrite
!
sep_exist_r
.
apply
exist_elim
=>
γ
.
(
*
TODO
:
Figure
out
a
better
way
to
say
"I want to establish ▷ spawn_inv"
.
*
)
trans
(
heap_ctx
heapN
★
#
>
f
#()
{{
Ψ
}}
★
(
join_handle
l
Ψ
-
★
Φ
(
%
l
)
%
V
)
★
own
γ
(
Excl
())
★
▷
(
spawn_inv
γ
l
Ψ
))
%
I
.
{
ecancel
[
#
>
f
#()
{{
_
}}
;
_
-
★
_
;
heap_ctx
_
;
own
_
_
]
%
I
.
rewrite
-
later_intro
/
spawn_inv
-
(
exist_intro
(
InjLV
#
0
)).
cancel
[
l
↦
InjLV
#
0
]
%
I
.
apply
or_intro_l
'
.
by
rewrite
const_equiv
.
}
rewrite
(
inv_alloc
N
)
// !pvs_frame_l. eapply wp_strip_pvs.
ewp
eapply
wp_fork
.
rewrite
[
heap_ctx
_
]
always_sep_dup
[
inv
_
_
]
always_sep_dup
.
rewrite
!
assoc
[(
_
★
(
own
_
_
))
%
I
]
comm
!
assoc
[(
_
★
(
inv
_
_
))
%
I
]
comm
.
rewrite
!
assoc
[(
_
★
(
_
-
★
_
))
%
I
]
comm
.
rewrite
-!
assoc
3
!
assoc
.
apply
sep_mono
.
-
wp_seq
.
rewrite
-!
assoc
.
eapply
wand_apply_l
;
[
done
..
|
].
rewrite
/
join_handle
.
rewrite
const_equiv
// left_id -(exist_intro γ).
solve_sep_entails
.
-
wp_focus
(
f
_
).
rewrite
wp_frame_r
wp_frame_l
.
apply
wp_mono
=>
v
.
eapply
(
inv_fsa
(
wp_fsa
_
))
with
(
N0
:=
N
);
simpl
;
(
*
TODO
:
Collect
these
in
some
Hint
DB
?
Or
add
to
an
existing
one
?
*
)
eauto
using
to_val_InjR
,
to_val_InjL
,
to_of_val
with
I
ndisj
.
apply
wand_intro_l
.
rewrite
/
spawn_inv
{
1
}
later_exist
!
sep_exist_r
.
apply
exist_elim
=>
vl
.
rewrite
later_sep
.
eapply
wp_store
;
eauto
using
to_val_InjR
,
to_val_InjL
,
to_of_val
with
I
ndisj
.
cancel
[
▷
(
l
↦
vl
)]
%
I
.
strip_later
.
apply
wand_intro_l
.
rewrite
right_id
-
later_intro
-{
2
}
[(
∃
_
,
_
↦
_
★
_
)
%
I
](
exist_intro
(
InjRV
v
)).
ecancel
[
l
↦
_
]
%
I
.
apply
or_intro_r
'
.
rewrite
sep_elim_r
sep_elim_r
sep_elim_l
.
rewrite
-
(
exist_intro
v
).
rewrite
const_equiv
// left_id. apply or_intro_l.
Qed
.
Lemma
join_spec
(
Ψ
:
val
→
iProp
)
l
(
Φ
:
val
→
iProp
)
:
(
join_handle
l
Ψ
★
∀
v
,
Ψ
v
-
★
Φ
(
%
l
))
⊑
#
>
join
(
%
l
)
{{
Φ
}}
.
Proof
.
Abort
.
End
proof
.
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