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Rodolphe Lepigre
Iris
Commits
df7f6381
Commit
df7f6381
authored
Feb 25, 2016
by
Robbert Krebbers
Browse files
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Plain Diff
Move and rename some tactics.
parent
c905411d
Changes
4
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4 changed files
with
25 additions
and
29 deletions
+25
-29
algebra/upred_tactics.v
algebra/upred_tactics.v
+9
-19
barrier/proof.v
barrier/proof.v
+5
-7
heap_lang/wp_tactics.v
heap_lang/wp_tactics.v
+3
-3
prelude/tactics.v
prelude/tactics.v
+8
-0
No files found.
algebra/upred_tactics.v
View file @
df7f6381
...
...
@@ -146,19 +146,10 @@ Tactic Notation "ecancel" open_constr(Ps) :=
close
Ps
(@
nil
(
uPred
M
))
ltac
:
(
fun
Qs
=>
cancel
Qs
)
end
.
(* Some more generic uPred tactics.
TODO: Naming. *)
Ltac
revert_intros
tac
:
=
lazymatch
goal
with
|
|-
∀
_
,
_
=>
let
H
:
=
fresh
in
intro
H
;
revert_intros
tac
;
revert
H
|
|-
_
=>
tac
end
.
(** Assumes a goal of the shape P ⊑ ▷ Q. Alterantively, if Q
is built of ★, ∧, ∨ with ▷ in all branches; that will work, too.
Will turn this goal into P ⊑ Q and strip ▷ in P below ★, ∧, ∨. *)
Ltac
u_
strip_later
:
=
Ltac
strip_later
:
=
let
rec
strip
:
=
lazymatch
goal
with
|
|-
(
_
★
_
)
⊑
▷
_
=>
...
...
@@ -190,23 +181,22 @@ Ltac u_strip_later :=
|
|-
_
⊑
▷
_
=>
apply
later_mono
;
reflexivity
(* We fail if we don't find laters in all branches. *)
end
in
revert_intros
ltac
:
(
etrans
;
[|
shape_Q
]
;
in
intros_revert
ltac
:
(
etrans
;
[|
shape_Q
]
;
etrans
;
last
eapply
later_mono
;
first
solve
[
strip
]).
(** Transforms a goal of the form ∀ ..., ?0... → ?1 ⊑ ?2
into True ⊑ ∀..., ■?0... → ?1 → ?2, applies tac, and
the moves all the assumptions back. *)
Ltac
u_revert_all
:
=
(* TODO: this name may be a big too general *)
Ltac
revert_all
:
=
lazymatch
goal
with
|
|-
∀
_
,
_
=>
let
H
:
=
fresh
in
intro
H
;
u_
revert_all
;
|
|-
∀
_
,
_
=>
let
H
:
=
fresh
in
intro
H
;
revert_all
;
(* TODO: Really, we should distinguish based on whether this is a
dependent function type or not. Right now, we distinguish based
on the sort of the argument, which is suboptimal. *)
first
[
apply
(
const_intro_impl
_
_
_
H
)
;
clear
H
|
revert
H
;
apply
forall_elim'
]
|
|-
?C
⊑
_
=>
trans
(
True
∧
C
)%
I
;
first
(
apply
equiv_entails_sym
,
left_id
,
_;
reflexivity
)
;
apply
impl_elim_l'
|
|-
?C
⊑
_
=>
apply
impl_entails
end
.
(** This starts on a goal of the form ∀ ..., ?0... → ?1 ⊑ ?2.
...
...
@@ -215,8 +205,8 @@ Ltac u_revert_all :=
applies [tac] on the goal (now of the form _ ⊑ _), and then reverts the
Coq assumption so that we end up with the same shape as where we started,
but with an additional assumption ★-ed to the context *)
Ltac
u_
l
ö
b
tac
:
=
u_
revert_all
;
Ltac
l
ö
b
tac
:
=
revert_all
;
(* Add a box *)
etrans
;
last
(
eapply
always_elim
;
reflexivity
)
;
(* We now have a goal for the form True ⊑ P, with the "original" conclusion
...
...
@@ -233,7 +223,7 @@ Ltac u_löb tac :=
|
|-
_
⊑
(
■
_
→
_
)
=>
apply
impl_intro_l
,
const_elim_l
;
let
H
:
=
fresh
in
intro
H
;
go
;
revert
H
(* This is the "bottom" of the goal, where we see the impl introduced
by u_revert_all as well as the ▷ from löb_strong and the □ we added. *)
by u
Pred
_revert_all as well as the ▷ from löb_strong and the □ we added. *)
|
|-
▷
□
?R
⊑
(
?L
→
_
)
=>
apply
impl_intro_l
;
trans
(
L
★
▷
□
R
)%
I
;
first
(
eapply
equiv_entails
,
always_and_sep_r
,
_;
reflexivity
)
;
...
...
barrier/proof.v
View file @
df7f6381
...
...
@@ -81,7 +81,7 @@ Proof.
do
4
(
rewrite
big_sepS_insert
;
last
set_solver
).
rewrite
!
fn_lookup_insert
fn_lookup_insert_ne
//
!
fn_lookup_insert
.
rewrite
3
!
assoc
.
apply
sep_mono
.
-
rewrite
saved_prop_agree
.
u_
strip_later
.
-
rewrite
saved_prop_agree
.
strip_later
.
apply
wand_intro_l
.
rewrite
[(
_
★
(
_
-
★
Π★
{
set
_
}
_
))%
I
]
comm
!
assoc
wand_elim_r
.
rewrite
(
big_sepS_delete
_
I
i
)
//.
rewrite
[(
_
★
Π★
{
set
_
}
_
)%
I
]
comm
[(
_
★
Π★
{
set
_
}
_
)%
I
]
comm
-!
assoc
.
...
...
@@ -116,8 +116,7 @@ Proof.
rewrite
[(
▷
_
★
_
)%
I
]
comm
-!
assoc
.
eapply
wand_apply_l
.
{
by
rewrite
<-
later_wand
,
<-
later_intro
.
}
{
by
rewrite
later_sep
.
}
u_strip_later
.
apply
:
(
eq_rewrite
R
Q
(
λ
x
,
x
)%
I
)
;
eauto
with
I
.
strip_later
.
apply
:
(
eq_rewrite
R
Q
(
λ
x
,
x
)%
I
)
;
eauto
with
I
.
Qed
.
(** Actual proofs *)
...
...
@@ -181,7 +180,7 @@ Proof.
apply
const_elim_sep_l
=>
Hs
.
destruct
p
;
last
done
.
rewrite
{
1
}/
barrier_inv
=>/={
Hs
}.
rewrite
later_sep
.
eapply
wp_store
with
(
v'
:
=
'
0
)
;
eauto
with
I
ndisj
.
u_
strip_later
.
cancel
[
l
↦
'
0
]%
I
.
strip_later
.
cancel
[
l
↦
'
0
]%
I
.
apply
wand_intro_l
.
rewrite
-(
exist_intro
(
State
High
I
)).
rewrite
-(
exist_intro
∅
).
rewrite
const_equiv
/=
;
last
by
eauto
using
signal_step
.
rewrite
left_id
-
later_intro
{
2
}/
barrier_inv
-!
assoc
.
apply
sep_mono_r
.
...
...
@@ -212,7 +211,7 @@ Proof.
apply
const_elim_sep_l
=>
Hs
.
rewrite
{
1
}/
barrier_inv
=>/=.
rewrite
later_sep
.
eapply
wp_load
;
eauto
with
I
ndisj
.
rewrite
-!
assoc
.
apply
sep_mono_r
.
u_
strip_later
.
rewrite
-!
assoc
.
apply
sep_mono_r
.
strip_later
.
apply
wand_intro_l
.
destruct
p
.
{
(* a Low state. The comparison fails, and we recurse. *)
rewrite
-(
exist_intro
(
State
Low
I
))
-(
exist_intro
{[
Change
i
]}).
...
...
@@ -242,8 +241,7 @@ Proof.
apply
wand_intro_l
.
rewrite
[(
heap_ctx
_
★
_
)%
I
]
sep_elim_r
.
rewrite
[(
sts_own
_
_
_
★
_
)%
I
]
sep_elim_r
[(
sts_ctx
_
_
_
★
_
)%
I
]
sep_elim_r
.
rewrite
!
assoc
[(
_
★
saved_prop_own
i
Q
)%
I
]
comm
!
assoc
saved_prop_agree
.
wp_op
>
;
last
done
.
intros
_
.
u_strip_later
.
wp_if
.
wp_op
;
[|
done
]=>
_
.
wp_if
.
eapply
wand_apply_r
;
[
done
..|].
eapply
wand_apply_r
;
[
done
..|].
apply
:
(
eq_rewrite
Q'
Q
(
λ
x
,
x
)%
I
)
;
last
by
eauto
with
I
.
rewrite
eq_sym
.
eauto
with
I
.
...
...
heap_lang/wp_tactics.v
View file @
df7f6381
...
...
@@ -12,7 +12,7 @@ Ltac wp_strip_later :=
|
|-
_
⊑
▷
_
=>
apply
later_intro
|
|-
_
⊑
_
=>
reflexivity
end
in
revert_intros
ltac
:
(
first
[
u_
strip_later
|
etrans
;
[|
go
]
]
).
in
intros_revert
ltac
:
(
first
[
strip_later
|
etrans
;
[|
go
]
]
).
Ltac
wp_bind
K
:
=
lazymatch
eval
hnf
in
K
with
|
[]
=>
idtac
...
...
@@ -29,10 +29,10 @@ Ltac wp_finish :=
try
(
eapply
pvs_intro
;
match
goal
with
|-
_
⊑
wp
_
_
_
=>
simpl
|
_
=>
fail
end
)
|
_
=>
idtac
end
in
simpl
;
revert_intros
go
.
end
in
simpl
;
intros_revert
go
.
Tactic
Notation
"wp_rec"
">"
:
=
u_
l
ö
b
ltac
:
(
(* Find the redex and apply wp_rec *)
l
ö
b
ltac
:
(
(* Find the redex and apply wp_rec *)
idtac
;
(* <https://coq.inria.fr/bugs/show_bug.cgi?id=4584> *)
lazymatch
goal
with
|
|-
_
⊑
wp
?E
?e
?Q
=>
reshape_expr
e
ltac
:
(
fun
K
e'
=>
...
...
prelude/tactics.v
View file @
df7f6381
...
...
@@ -228,6 +228,14 @@ Ltac setoid_subst :=
|
H
:
@
equiv
?A
?e
_
?x
|-
_
=>
symmetry
in
H
;
setoid_subst_aux
(@
equiv
A
e
)
x
end
.
(** The tactic [intros_revert tac] introduces all foralls/arrows, performs tac,
and then reverts them. *)
Ltac
intros_revert
tac
:
=
lazymatch
goal
with
|
|-
∀
_
,
_
=>
let
H
:
=
fresh
in
intro
H
;
intros_revert
tac
;
revert
H
|
|-
_
=>
tac
end
.
(** Given a tactic [tac2] generating a list of terms, [iter tac1 tac2]
runs [tac x] for each element [x] until [tac x] succeeds. If it does not
suceed for any element of the generated list, the whole tactic wil fail. *)
...
...
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