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Joshua Yanovski
iriscoq
Commits
1b172b22
Commit
1b172b22
authored
Feb 24, 2016
by
Ralf Jung
Browse files
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move generic upred tactics from wp_tactics to upred_tactics
parent
0ef28164
Changes
2
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2 changed files
with
98 additions
and
95 deletions
+98
95
algebra/upred_tactics.v
algebra/upred_tactics.v
+97
1
heap_lang/wp_tactics.v
heap_lang/wp_tactics.v
+1
94
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algebra/upred_tactics.v
View file @
1b172b22
From
algebra
Require
Export
upred
.
From
algebra
Require
Export
upred_big_op
.
Import
uPred
.
Module
upred_reflection
.
Section
upred_reflection
.
Context
{
M
:
cmraT
}
.
...
...
@@ 89,7 +90,7 @@ Module upred_reflection. Section upred_reflection.
Proof
.
intros
??
.
rewrite
!
eval_flatten
.
rewrite
(
flatten_cancel
e1
e1
'
ns
)
// (flatten_cancel e2 e2' ns) //; csimpl.
rewrite
!
fmap_app
!
big_sep_app
.
apply
uPred
.
sep_mono_r
.
rewrite
!
fmap_app
!
big_sep_app
.
apply
sep_mono_r
.
Qed
.
Class
Quote
(
Σ
1
Σ
2
:
list
(
uPred
M
))
(
P
:
uPred
M
)
(
e
:
expr
)
:=
{}
.
...
...
@@ 144,3 +145,98 @@ Tactic Notation "ecancel" open_constr(Ps) :=


@
uPred_entails
?
M
_
_
=>
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
:=
let
rec
strip
:=
lazymatch
goal
with


(
_
★
_
)
⊑
▷
_
=>
etrans
;
last
(
eapply
equiv_entails_sym
,
later_sep
);
apply
sep_mono
;
strip


(
_
∧
_
)
⊑
▷
_
=>
etrans
;
last
(
eapply
equiv_entails_sym
,
later_and
);
apply
sep_mono
;
strip


(
_
∨
_
)
⊑
▷
_
=>
etrans
;
last
(
eapply
equiv_entails_sym
,
later_or
);
apply
sep_mono
;
strip


▷
_
⊑
▷
_
=>
apply
later_mono
;
reflexivity


_
⊑
▷
_
=>
apply
later_intro
;
reflexivity
end
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_entails
,
later_sep
;
reflexivity
);
(
*
Match
the
arm
recursively
*
)
apply
sep_mono
;
shape_Q


_
⊑
(
_
∧
_
)
=>
etrans
;
first
(
apply
equiv_entails
,
later_and
;
reflexivity
);
apply
sep_mono
;
shape_Q


_
⊑
(
_
∨
_
)
=>
etrans
;
first
(
apply
equiv_entails
,
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
]).
(
**
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
:=
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
'
]


?
C
⊑
_
=>
trans
(
True
∧
C
)
%
I
;
first
(
apply
equiv_entails_sym
,
left_id
,
_
;
reflexivity
);
apply
impl_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
,
but
with
an
additional
assumption
★

ed
to
the
context
*
)
Ltac
u_l
ö
b
tac
:=
u_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
being
locked
.
*
)
apply
l
ö
b_strong
;
etransitivity
;
first
(
apply
equiv_entails
,
left_id
,
_
;
reflexivity
);
apply:
always_intro
;
(
*
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
;
let
H
:=
fresh
in
intro
H
;
go
;
revert
H


_
⊑
(
■
_
→
_
)
=>
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
l
ö
b_strong
and
the
□
we
added
.
*
)


▷
□
?
R
⊑
(
?
L
→
_
)
=>
apply
impl_intro_l
;
trans
(
L
★
▷
□
R
)
%
I
;
first
(
eapply
equiv_entails
,
always_and_sep_r
,
_
;
reflexivity
);
tac
end
in
go
.
heap_lang/wp_tactics.v
View file @
1b172b22
From
algebra
Require
Export
upred_tactics
.
From
heap_lang
Require
Export
tactics
substitution
.
Import
uPred
.
(
*
TODO
:
The
next
few
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
.
(
**
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
:=
lazymatch
goal
with


(
_
★
_
)
⊑
▷
_
=>
etrans
;
last
(
eapply
equiv_entails_sym
,
later_sep
);
apply
sep_mono
;
strip


(
_
∧
_
)
⊑
▷
_
=>
etrans
;
last
(
eapply
equiv_entails_sym
,
later_and
);
apply
sep_mono
;
strip


(
_
∨
_
)
⊑
▷
_
=>
etrans
;
last
(
eapply
equiv_entails_sym
,
later_or
);
apply
sep_mono
;
strip


▷
_
⊑
▷
_
=>
apply
later_mono
;
reflexivity


_
⊑
▷
_
=>
apply
later_intro
;
reflexivity
end
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_entails
,
later_sep
;
reflexivity
);
(
*
Match
the
arm
recursively
*
)
apply
sep_mono
;
shape_Q


_
⊑
(
_
∧
_
)
=>
etrans
;
first
(
apply
equiv_entails
,
later_and
;
reflexivity
);
apply
sep_mono
;
shape_Q


_
⊑
(
_
∨
_
)
=>
etrans
;
first
(
apply
equiv_entails
,
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
]).
(
**
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
:=
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
'
]


?
C
⊑
_
=>
trans
(
True
∧
C
)
%
I
;
first
(
apply
equiv_entails_sym
,
left_id
,
_
;
reflexivity
);
apply
impl_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
,
but
with
an
additional
assumption
★

ed
to
the
context
*
)
Ltac
u_l
ö
b
tac
:=
u_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
being
locked
.
*
)
apply
l
ö
b_strong
;
etransitivity
;
first
(
apply
equiv_entails
,
left_id
,
_
;
reflexivity
);
apply:
always_intro
;
(
*
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
;
let
H
:=
fresh
in
intro
H
;
go
;
revert
H


_
⊑
(
■
_
→
_
)
=>
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
l
ö
b_strong
and
the
□
we
added
.
*
)


▷
□
?
R
⊑
(
?
L
→
_
)
=>
apply
impl_intro_l
;
trans
(
L
★
▷
□
R
)
%
I
;
first
(
eapply
equiv_entails
,
always_and_sep_r
,
_
;
reflexivity
);
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
.
*
)
...
...
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