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Iris
Fairis
Commits
faf2018e
Commit
faf2018e
authored
Feb 20, 2016
by
Ralf Jung
Browse files
make u_strip_later more clever; also use it for wp_strip_later
parent
6428df91
Changes
2
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heap_lang/tests.v
View file @
faf2018e
...
...
@@ 61,7 +61,7 @@ Section LiftingTests.
Lemma
Pred_spec
n
E
Φ
:
▷
Φ
(
LitV
(
n

1
))
⊑

Pred
'
n
@
E
{{
Φ
}}
.
Proof
.
wp_lam
>
;
apply
later_mono
;
wp_op
=>
?
;
wp_if
.
wp_lam
.
wp_op
=>
?
;
wp_if
.

wp_op
.
wp_op
.
(
*
TODO
:
Can
we
use
the
wp
tactic
again
here
?
It
seems
that
the
tactic
fails
if
there
are
goals
being
generated
.
That
should
not
be
the
case
.
*
)
...
...
heap_lang/wp_tactics.v
View file @
faf2018e
From
heap_lang
Require
Export
tactics
substitution
.
Import
uPred
.
(
*
TODO
:
The
next
6
tactics
are
not
wp

specific
at
all
.
They
should
move
elsewhere
.
*
)
(
*
TODO
:
The
next
5
tactics
are
not
wp

specific
at
all
.
They
should
move
elsewhere
.
*
)
Ltac
revert_intros
tac
:=
lazymatch
goal
with


∀
_
,
_
=>
let
H
:=
fresh
in
intro
H
;
revert_intros
tac
;
revert
H


_
=>
tac
end
.
Ltac
wp_strip_later
:=
let
rec
go
:=
lazymatch
goal
with


_
⊑
(
_
★
_
)
=>
apply
sep_mono
;
go


_
⊑
▷
_
=>
apply
later_intro


_
⊑
_
=>
reflexivity
end
in
revert_intros
ltac
:
(
etrans
;
[

go
]).
(
**
Assumes
a
goal
of
the
shape
P
⊑
▷
Q
.
Will
get
rid
of
▷
in
P
below
★
,
∧
and
∨
.
*
)
(
**
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
:=
let
rec
strip
:=
match
goal
with
lazy
match
goal
with


(
_
★
_
)
⊑
▷
_
=>
etrans
;
last
(
eapply
equiv_spec
,
later_sep
);
apply
sep_mono
;
strip
...
...
@@ 34,7 +27,25 @@ Ltac u_strip_later :=


▷
_
⊑
▷
_
=>
apply
later_mono
;
reflexivity


_
⊑
▷
_
=>
apply
later_intro
;
reflexivity
end
in
etrans
;
last
eapply
later_mono
;
first
solve
[
strip
].
in
let
rec
shape_Q
:=
lazymatch
goal
with


_
⊑
(
_
★
_
)
=>
(
*
Force
the
later
on
the
LHS
to
be
top

level
,
matching
laters
below
★
on
the
RHS
*
)
etrans
;
first
(
apply
equiv_spec
;
symmetry
;
apply
later_sep
;
reflexivity
);
(
*
Match
the
arm
recursively
*
)
apply
sep_mono
;
shape_Q


_
⊑
(
_
∧
_
)
=>
etrans
;
first
(
apply
equiv_spec
;
symmetry
;
apply
later_and
;
reflexivity
);
apply
sep_mono
;
shape_Q


_
⊑
(
_
∨
_
)
=>
etrans
;
first
(
apply
equiv_spec
;
symmetry
;
apply
later_or
;
reflexivity
);
apply
sep_mono
;
shape_Q


_
⊑
▷
_
=>
apply
later_mono
;
reflexivity
(
*
We
fail
if
we
don
'
t
find
laters
in
all
branches
.
*
)
end
in
revert_intros
ltac
:
(
etrans
;
[

shape_Q
];
etrans
;
last
eapply
later_mono
;
first
solve
[
strip
]).
(
*
ssreflect

locks
the
part
after
the
⊑
*
)
(
*
FIXME
:
I
tried
doing
a
lazymatch
to
only
apply
the
tactic
if
the
goal
has
shape
⊑
,
...
...
@@ 47,28 +58,31 @@ Ltac u_lock_goal := revert_intros ltac:(apply uPred_lock_conclusion).
Ltac
u_revert_all
:=
lazymatch
goal
with


∀
_
,
_
=>
let
H
:=
fresh
in
intro
H
;
u_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
'
]
(
*
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
(
rewrite
[(
True
★
C
)
%
I
]
left_id
;
reflexivity
);
apply
wand_elim_l
'
first
(
rewrite
[(
True
★
C
)
%
I
]
left_id
;
reflexivity
);
apply
wand_elim_l
'
end
.
(
**
This
starts
on
a
goal
of
the
form
∀
...,
?
0.
..
→
?
1
⊑
?
2.
It
applies
l
ö
b
where
all
the
Coq
assumptions
have
been
turned
into
logical
assumptions
,
then
moves
all
the
Coq
assumptions
back
out
to
the
context
,
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
.
*
)
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
.
[
tac
]
is
a
thunk
because
I
found
no
other
way
to
prevent
Coq
from
expandig
matches
too
early
.
*
)
Ltac
u_l
ö
b
tac
:=
u_lock_goal
;
u_revert_all
;
(
*
We
now
have
a
goal
for
the
form
True
⊑
P
,
with
the
"original"
conclusion
being
locked
.
*
)
apply
l
ö
b_strong
;
etransitivity
;
first
(
apply
equiv_spec
;
symmetry
;
apply
(
left_id
_
_
_
);
reflexivity
);
(
*
Now
introduce
again
all
the
things
that
we
reverted
,
and
at
the
bottom
,
do
the
work
*
)
(
*
Now
introduce
again
all
the
things
that
we
reverted
,
and
at
the
bottom
,
do
the
work
*
)
let
rec
go
:=
lazymatch
goal
with


_
⊑
(
∀
_
,
_
)
=>
apply
forall_intro
;
...
...
@@ 76,13 +90,21 @@ Ltac u_löb tac :=


_
⊑
(
■
_
→
_
)
=>
apply
impl_intro_l
,
const_elim_l
;
let
H
:=
fresh
in
intro
H
;
go
;
revert
H


▷
?
R
⊑
(
?
L

★
locked
_
)
=>
apply
wand_intro_l
;
(
*
TODO
:
Do
sth
.
more
robust
than
rewriting
.
*
)
trans
(
▷
L
★
▷
R
)
%
I
;
first
(
apply
sep_mono_l
,
later_intro
;
reflexivity
);
trans
(
▷
(
L
★
R
))
%
I
;
first
(
apply
equiv_spec
,
later_sep
;
reflexivity
);
unlock
;
tac
unlock
;
tac
()
end
in
go
.
(
**
wp

specific
helper
tactics
*
)
(
*
First
try
to
productively
strip
off
laters
;
if
that
fails
,
at
least
cosmetically
get
rid
of
laters
in
the
conclusion
.
*
)
Ltac
wp_strip_later
:=
let
rec
go
:=
lazymatch
goal
with


_
⊑
(
_
★
_
)
=>
apply
sep_mono
;
go


_
⊑
▷
_
=>
apply
later_intro


_
⊑
_
=>
reflexivity
end
in
revert_intros
ltac
:
(
first
[
u_strip_later

etrans
;
[

go
]
]
).
Ltac
wp_bind
K
:=
lazymatch
eval
hnf
in
K
with

[]
=>
idtac
...
...
@@ 101,16 +123,16 @@ Ltac wp_finish :=

_
=>
idtac
end
in
simpl
;
revert_intros
go
.
Tactic
Notation
"wp_rec"
:=
u_l
ö
b
ltac
:
((
*
Find
the
redex
and
apply
wp_rec
*
)
match
goal
with
Tactic
Notation
"wp_rec"
">"
:=
u_l
ö
b
ltac
:
(
fun
_
=>
(
*
Find
the
redex
and
apply
wp_rec
*
)
lazy
match
goal
with


_
⊑
wp
?
E
?
e
?
Q
=>
reshape_expr
e
ltac
:
(
fun
K
e
'
=>
match
eval
cbv
in
e
'
with

App
(
Rec
_
_
_
)
_
=>
wp_bind
K
;
etrans
;
[

eapply
wp_rec
;
reflexivity
];
wp_finish
end
)
end
;
apply
later_mono
)
.
end
).
Tactic
Notation
"wp_rec"
:=
wp_rec
>
;
wp_strip_later
.
Tactic
Notation
"wp_lam"
">"
:=
match
goal
with
...
...
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