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PierreMarie Pédrot
Iris
Commits
ae510d09
Commit
ae510d09
authored
Sep 21, 2017
by
Robbert Krebbers
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Hacky way of dealing with `iSpecialize ("H" !$ x)` where `x` contains TC holes.
parent
48448482
Changes
3
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3 changed files
with
31 additions
and
10 deletions
+31
10
theories/heap_lang/lib/barrier/proof.v
theories/heap_lang/lib/barrier/proof.v
+4
3
theories/proofmode/tactics.v
theories/proofmode/tactics.v
+20
7
theories/tests/proofmode.v
theories/tests/proofmode.v
+7
0
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theories/heap_lang/lib/barrier/proof.v
View file @
ae510d09
...
@@ 138,7 +138,7 @@ Proof.
...
@@ 138,7 +138,7 @@ Proof.
iMod
(
sts_openS
(
barrier_inv
l
P
)
_
_
γ
with
"[Hγ]"
)
iMod
(
sts_openS
(
barrier_inv
l
P
)
_
_
γ
with
"[Hγ]"
)
as
([
p
I
])
"(% & [Hl Hr] & Hclose)"
;
eauto
.
as
([
p
I
])
"(% & [Hl Hr] & Hclose)"
;
eauto
.
wp_load
.
destruct
p
.
wp_load
.
destruct
p
.

iMod
(
"Hclose"
$!
(
State
Low
I
)
with
"[Hl Hr]"
)
as
"Hγ"
.

iMod
(
"Hclose"
$!
(
State
Low
I
)
{[
Change
i
]}
with
"[Hl Hr]"
)
as
"Hγ"
.
{
iSplit
;
first
done
.
rewrite
/
barrier_inv
/=.
by
iFrame
.
}
{
iSplit
;
first
done
.
rewrite
/
barrier_inv
/=.
by
iFrame
.
}
iAssert
(
sts_ownS
γ
(
i_states
i
)
{[
Change
i
]})%
I
with
"[> Hγ]"
as
"Hγ"
.
iAssert
(
sts_ownS
γ
(
i_states
i
)
{[
Change
i
]})%
I
with
"[> Hγ]"
as
"Hγ"
.
{
iApply
(
sts_own_weaken
with
"Hγ"
)
;
eauto
using
i_states_closed
.
}
{
iApply
(
sts_own_weaken
with
"Hγ"
)
;
eauto
using
i_states_closed
.
}
...
@@ 150,7 +150,7 @@ Proof.
...
@@ 150,7 +150,7 @@ Proof.
iDestruct
(
big_opS_delete
_
_
i
with
"Hsp"
)
as
"[#HΨi Hsp]"
;
first
done
.
iDestruct
(
big_opS_delete
_
_
i
with
"Hsp"
)
as
"[#HΨi Hsp]"
;
first
done
.
iAssert
(
▷
Ψ
i
∗
▷
[
∗
set
]
j
∈
I
∖
{[
i
]},
Ψ
j
)%
I
with
"[HΨ]"
as
"[HΨ HΨ']"
.
iAssert
(
▷
Ψ
i
∗
▷
[
∗
set
]
j
∈
I
∖
{[
i
]},
Ψ
j
)%
I
with
"[HΨ]"
as
"[HΨ HΨ']"
.
{
iNext
.
iApply
(
big_opS_delete
_
_
i
)
;
first
done
.
by
iApply
"HΨ"
.
}
{
iNext
.
iApply
(
big_opS_delete
_
_
i
)
;
first
done
.
by
iApply
"HΨ"
.
}
iMod
(
"Hclose"
$!
(
State
High
(
I
∖
{[
i
]}))
(
∅
:
set
token
)
with
"[HΨ' Hl Hsp]"
).
iMod
(
"Hclose"
$!
(
State
High
(
I
∖
{[
i
]}))
∅
with
"[HΨ' Hl Hsp]"
).
{
iSplit
;
[
iPureIntro
;
by
eauto
using
wait_step
].
{
iSplit
;
[
iPureIntro
;
by
eauto
using
wait_step
].
rewrite
/
barrier_inv
/=.
iNext
.
iFrame
"Hl"
.
iExists
Ψ
;
iFrame
.
auto
.
}
rewrite
/
barrier_inv
/=.
iNext
.
iFrame
"Hl"
.
iExists
Ψ
;
iFrame
.
auto
.
}
iPoseProof
(
saved_prop_agree
with
"HQ HΨi"
)
as
"#Heq"
.
iPoseProof
(
saved_prop_agree
with
"HQ HΨi"
)
as
"#Heq"
.
...
@@ 169,7 +169,8 @@ Proof.
...
@@ 169,7 +169,8 @@ Proof.
iMod
(
saved_prop_alloc_strong
(
R2
:
∙
%
CF
(
iProp
Σ
))
(
I
∪
{[
i1
]}))
iMod
(
saved_prop_alloc_strong
(
R2
:
∙
%
CF
(
iProp
Σ
))
(
I
∪
{[
i1
]}))
as
(
i2
)
"[Hi2' #Hi2]"
;
iDestruct
"Hi2'"
as
%
Hi2
.
as
(
i2
)
"[Hi2' #Hi2]"
;
iDestruct
"Hi2'"
as
%
Hi2
.
rewrite
>
not_elem_of_union
,
elem_of_singleton
in
Hi2
;
destruct
Hi2
.
rewrite
>
not_elem_of_union
,
elem_of_singleton
in
Hi2
;
destruct
Hi2
.
iMod
(
"Hclose"
$!
(
State
p
({[
i1
;
i2
]}
∪
I
∖
{[
i
]}))
with
"[]"
)
as
"Hγ"
.
iMod
(
"Hclose"
$!
(
State
p
({[
i1
;
i2
]}
∪
I
∖
{[
i
]}))
{[
Change
i1
;
Change
i2
]}
with
"[]"
)
as
"Hγ"
.
{
iSplit
;
first
by
eauto
using
split_step
.
{
iSplit
;
first
by
eauto
using
split_step
.
rewrite
/
barrier_inv
/=.
iNext
.
iFrame
"Hl"
.
rewrite
/
barrier_inv
/=.
iNext
.
iFrame
"Hl"
.
by
iApply
(
ress_split
with
"HQ Hi1 Hi2 HQR"
).
}
by
iApply
(
ress_split
with
"HQ Hi1 Hi2 HQR"
).
}
...
...
theories/proofmode/tactics.v
View file @
ae510d09
...
@@ 17,7 +17,7 @@ Declare Reduction env_cbv := cbv [
...
@@ 17,7 +17,7 @@ Declare Reduction env_cbv := cbv [
envs_split_go
envs_split
].
envs_split_go
envs_split
].
Ltac
env_cbv
:
=
Ltac
env_cbv
:
=
match
goal
with

?u
=>
let
v
:
=
eval
env_cbv
in
u
in
change
v
end
.
match
goal
with

?u
=>
let
v
:
=
eval
env_cbv
in
u
in
change
v
end
.
Ltac
env_reflexivity
:
=
env_cbv
;
reflexivity
.
Ltac
env_reflexivity
:
=
env_cbv
;
exact
eq_refl
.
(** * Misc *)
(** * Misc *)
(* Tactic Notation tactics cannot return terms *)
(* Tactic Notation tactics cannot return terms *)
...
@@ 364,21 +364,34 @@ Notation "( H $! x1 .. xn 'with' pat )" :=
...
@@ 364,21 +364,34 @@ Notation "( H $! x1 .. xn 'with' pat )" :=
(
ITrm
H
(
hcons
x1
..
(
hcons
xn
hnil
)
..)
pat
)
(
at
level
0
,
x1
,
xn
at
level
9
).
(
ITrm
H
(
hcons
x1
..
(
hcons
xn
hnil
)
..)
pat
)
(
at
level
0
,
x1
,
xn
at
level
9
).
Notation
"( H 'with' pat )"
:
=
(
ITrm
H
hnil
pat
)
(
at
level
0
).
Notation
"( H 'with' pat )"
:
=
(
ITrm
H
hnil
pat
)
(
at
level
0
).
(*
There is some hacky stuff going on here (most probably there is a Coq bug).
Holes  like unresolved type class instances  in the argument `xs` are
resolved at arbitrary moments. It seems that tactics like `apply`, `split` and
`eexists` trigger type class search to resolve these holes. To avoid TC being
triggered too eagerly, this tactic uses `refine` at various places instead of
`apply`.
TODO: Investigate what really is going on. Is there a related to Cog bug #5752?
When should holes in an `open_constr` be resolved?
*)
Local
Tactic
Notation
"iSpecializeArgs"
constr
(
H
)
open_constr
(
xs
)
:
=
Local
Tactic
Notation
"iSpecializeArgs"
constr
(
H
)
open_constr
(
xs
)
:
=
let
rec
go
xs
:
=
let
rec
go
xs
:
=
lazymatch
xs
with
lazymatch
xs
with

hnil
=>
idtac

hnil
=>
apply
id
(* Finally, trigger TC *)

hcons
?x
?xs
=>

hcons
?x
?xs
=>
eapply
tac_forall_specialize
with
_
H
_
_
_;
(* (i:=H) (a:=x) *)
eapply
tac_forall_specialize
with
_
H
_
_
_;
(* (i:=H) (a:=x) *)
[
env_reflexivity

fail
1
"iSpecialize:"
H
"not found"
[
env_reflexivity

fail
"iSpecialize:"
H
"not found"

apply
_


typeclasses
eauto

let
P
:
=
match
goal
with

IntoForall
?P
_
=>
P
end
in
let
P
:
=
match
goal
with

IntoForall
?P
_
=>
P
end
in
fail
1
"iSpecialize: cannot instantiate"
P
"with"
x
fail
"iSpecialize: cannot instantiate"
P
"with"
x

exists
x
;
split
;
[
env_reflexivity

go
xs
]]

lazymatch
goal
with
(* Force [A] in [ex_intro] to deal with coercions. *)


∃
_
:
?A
,
_
=>
refine
(@
ex_intro
A
_
x
(
conj
_
_
))
end
;
[
env_reflexivity

go
xs
]]
end
in
end
in
go
xs
.
go
xs
.
Local
Tactic
Notation
"iSpecializePat"
constr
(
H
)
constr
(
pat
)
:
=
Local
Tactic
Notation
"iSpecializePat"
open_
constr
(
H
)
constr
(
pat
)
:
=
let
solve_to_wand
H1
:
=
let
solve_to_wand
H1
:
=
apply
_

apply
_

let
P
:
=
match
goal
with

IntoWand
_
?P
_
_
=>
P
end
in
let
P
:
=
match
goal
with

IntoWand
_
?P
_
_
=>
P
end
in
...
...
theories/tests/proofmode.v
View file @
ae510d09
From
iris
.
proofmode
Require
Import
tactics
.
From
iris
.
proofmode
Require
Import
tactics
.
From
iris
.
base_logic
.
lib
Require
Import
invariants
.
From
iris
.
base_logic
.
lib
Require
Import
invariants
.
From
stdpp
Require
Import
gmap
.
Set
Default
Proof
Using
"Type"
.
Set
Default
Proof
Using
"Type"
.
Section
tests
.
Section
tests
.
...
@@ 117,6 +118,12 @@ Proof. iIntros "H HP HQ". by iApply ("H" with "[$]"). Qed.
...
@@ 117,6 +118,12 @@ Proof. iIntros "H HP HQ". by iApply ("H" with "[$]"). Qed.
Lemma
test_iExist_coercion
(
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
.
Proof
.
iIntros
"HP"
.
iExists
(
0
:
nat
).
iApply
(
"HP"
$!
(
0
:
nat
)).
Qed
.
Lemma
test_iExist_tc
`
{
Collection
A
C
}
P
:
(
∃
x1
x2
:
gset
positive
,
P

∗
P
)%
I
.
Proof
.
iExists
{[
1
%
positive
]},
∅
.
auto
.
Qed
.
Lemma
test_iSpecialize_tc
P
:
(
∀
x
y
z
:
gset
positive
,
P
)

∗
P
.
Proof
.
iIntros
"H"
.
iSpecialize
(
"H"
$!
∅
{[
1
%
positive
]}
∅
).
done
.
Qed
.
Lemma
test_iAssert_modality
P
:
(==>
False
)

∗
==>
P
.
Lemma
test_iAssert_modality
P
:
(==>
False
)

∗
==>
P
.
Proof
.
iIntros
.
iAssert
False
%
I
with
"[>  //]"
as
%[].
Qed
.
Proof
.
iIntros
.
iAssert
False
%
I
with
"[>  //]"
as
%[].
Qed
.
...
...
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