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Iris
Fairis
Commits
2ee38008
Commit
2ee38008
authored
Feb 25, 2016
by
Robbert Krebbers
Browse files
Merge branch 'master' of gitlab.mpisws.org:FP/iriscoq
Conflicts: prelude/tactics.v
parents
df7f6381
77a15fea
Changes
6
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algebra/cofe.v
View file @
2ee38008
...
...
@@ 40,8 +40,6 @@ Tactic Notation "cofe_subst" :=

H
:@
dist
?
A
?
d
?
n
_
?
x

_
=>
symmetry
in
H
;
setoid_subst_aux
(
@
dist
A
d
n
)
x
end
.
Tactic
Notation
"solve_ne"
:=
intros
;
solve_proper
.
Record
chain
(
A
:
Type
)
`
{
Dist
A
}
:=
{
chain_car
:>
nat
→
A
;
chain_cauchy
n
i
:
n
<
i
→
chain_car
i
≡
{
n
}
≡
chain_car
(
S
n
)
...
...
algebra/sts.v
View file @
2ee38008
...
...
@@ 77,7 +77,7 @@ Proof. by intros ??? ?? [??]; split; apply up_preserving. Qed.
Global
Instance
up_set_preserving
:
Proper
((
⊆
)
==>
flip
(
⊆
)
==>
(
⊆
))
up_set
.
Proof
.
intros
S1
S2
HS
T1
T2
HT
.
rewrite
/
up_set
.
f_equiv
;
last
done
.
move
=>
s1
s2
Hs
.
simpl
in
HT
.
by
apply
up_preserving
.
f_equiv
.
move
=>
s1
s2
Hs
.
simpl
in
HT
.
by
apply
up_preserving
.
Qed
.
Global
Instance
up_set_proper
:
Proper
((
≡
)
==>
(
≡
)
==>
(
≡
))
up_set
.
Proof
.
by
intros
S1
S2
[
??
]
T1
T2
[
??
];
split
;
apply
up_set_preserving
.
Qed
.
...
...
algebra/upred.v
View file @
2ee38008
...
...
@@ 648,7 +648,7 @@ Proof. intros; apply (anti_symm _); auto using const_intro. Qed.
Lemma
equiv_eq
{
A
:
cofeT
}
P
(
a
b
:
A
)
:
a
≡
b
→
P
⊑
(
a
≡
b
).
Proof
.
intros
>
;
apply
eq_refl
.
Qed
.
Lemma
eq_sym
{
A
:
cofeT
}
(
a
b
:
A
)
:
(
a
≡
b
)
⊑
(
b
≡
a
).
Proof
.
apply
(
eq_rewrite
a
b
(
λ
b
,
b
≡
a
)
%
I
);
auto
using
eq_refl
.
solve_
ne
.
Qed
.
Proof
.
apply
(
eq_rewrite
a
b
(
λ
b
,
b
≡
a
)
%
I
);
auto
using
eq_refl
.
solve_
proper
.
Qed
.
(
*
BI
connectives
*
)
Lemma
sep_mono
P
P
'
Q
Q
'
:
P
⊑
Q
→
P
'
⊑
Q
'
→
(
P
★
P
'
)
⊑
(
Q
★
Q
'
).
...
...
barrier/proof.v
View file @
2ee38008
...
...
@@ 52,19 +52,17 @@ Definition recv (l : loc) (R : iProp) : iProp :=
saved_prop_own
i
Q
★
▷
(
Q

★
R
))
%
I
.
(
**
Setoids
*
)
(
*
These
lemmas
really
ought
to
be
doable
by
just
calling
a
tactic
.
It
is
just
application
of
already
registered
congruence
lemmas
.
*
)
Global
Instance
waiting_ne
n
:
Proper
(
dist
n
==>
(
=
)
==>
dist
n
)
waiting
.
Proof
.
intros
P
P
'
HP
I
?
<
.
rewrite
/
waiting
.
by
setoid_rewrite
HP
.
Qed
.
Proof
.
solve_proper
.
Qed
.
Global
Instance
barrier_inv_ne
n
l
:
Proper
(
dist
n
==>
pointwise_relation
_
(
dist
n
)
)
(
barrier_inv
l
).
Proof
.
intros
P
P
'
HP
[[]];
rewrite
/
barrier_inv
//=. by setoid_rewrite HP
. Qed.
Proper
(
dist
n
==>
eq
==>
dist
n
)
(
barrier_inv
l
).
Proof
.
solve_proper
.
Qed
.
Global
Instance
barrier_ctx_ne
n
γ
l
:
Proper
(
dist
n
==>
dist
n
)
(
barrier_ctx
γ
l
).
Proof
.
intros
P
P
'
HP
.
rewrite
/
barrier_ctx
.
by
setoid_rewrite
HP
.
Qed
.
Proof
.
solve_proper
.
Qed
.
Global
Instance
send_ne
n
l
:
Proper
(
dist
n
==>
dist
n
)
(
send
l
).
Proof
.
intros
P
P
'
HP
.
rewrite
/
send
.
by
setoid_rewrite
HP
.
Qed
.
Proof
.
solve_proper
.
Qed
.
Global
Instance
recv_ne
n
l
:
Proper
(
dist
n
==>
dist
n
)
(
recv
l
).
Proof
.
intros
R
R
'
HR
.
rewrite
/
recv
.
by
setoid_rewrite
HR
.
Qed
.
Proof
.
solve_proper
.
Qed
.
(
**
Helper
lemmas
*
)
Lemma
waiting_split
i
i1
i2
Q
R1
R2
P
I
:
...
...
prelude/tactics.v
View file @
2ee38008
...
...
@@ 228,6 +228,73 @@ Ltac setoid_subst :=

H
:
@
equiv
?
A
?
e
_
?
x

_
=>
symmetry
in
H
;
setoid_subst_aux
(
@
equiv
A
e
)
x
end
.
(
**
f_equiv
solves
goals
of
the
form
"f _ = f _"
,
for
any
relation
and
any
number
of
arguments
,
by
looking
for
appropriate
"Proper"
instances
.
If
it
cannot
solve
an
equality
,
it
will
leave
that
to
the
user
.
*
)
Ltac
f_equiv
:=
(
*
Deal
with
"pointwise_relation"
*
)
try
lazymatch
goal
with


pointwise_relation
_
_
_
_
=>
intros
?
end
;
(
*
repeatedly
apply
congruence
lemmas
and
use
the
equalities
in
the
hypotheses
.
*
)
first
[
reflexivity

assumption

symmetry
;
assumption

match
goal
with
(
*
We
support
matches
on
both
sides
,
*
if
*
they
concern
the
same
or
provably
equal
variables
.
TODO:
We
should
support
different
variables
,
provided
that
we
can
derive
contradictions
for
the
off

diagonal
cases
.
*
)


?
R
(
match
?
x
with
_
=>
_
end
)
(
match
?
x
with
_
=>
_
end
)
=>
destruct
x
;
f_equiv


?
R
(
match
?
x
with
_
=>
_
end
)
(
match
?
y
with
_
=>
_
end
)
=>
subst
y
;
f_equiv
(
*
First
assume
that
the
arguments
need
the
same
relation
as
the
result
*
)


?
R
(
?
f
?
x
)
(
?
f
_
)
=>
let
H
:=
fresh
"Proper"
in
assert
(
Proper
(
R
==>
R
)
f
)
as
H
by
(
eapply
_
);
apply
H
;
clear
H
;
f_equiv


?
R
(
?
f
?
x
?
y
)
(
?
f
_
_
)
=>
let
H
:=
fresh
"Proper"
in
assert
(
Proper
(
R
==>
R
==>
R
)
f
)
as
H
by
(
eapply
_
);
apply
H
;
clear
H
;
f_equiv
(
*
Next
,
try
to
infer
the
relation
*
)
(
*
TODO
:
If
some
of
the
arguments
are
the
same
,
we
could
also
query
for
"pointwise_relation"
'
s
.
But
that
leads
to
a
combinatorial
explosion
about
which
arguments
are
and
which
are
not
the
same
.
*
)


?
R
(
?
f
?
x
)
(
?
f
_
)
=>
let
R1
:=
fresh
"R"
in
let
H
:=
fresh
"Proper"
in
let
T
:=
type
of
x
in
evar
(
R1
:
relation
T
);
assert
(
Proper
(
R1
==>
R
)
f
)
as
H
by
(
subst
R1
;
eapply
_
);
subst
R1
;
apply
H
;
clear
H
;
f_equiv


?
R
(
?
f
?
x
?
y
)
(
?
f
_
_
)
=>
let
R1
:=
fresh
"R"
in
let
R2
:=
fresh
"R"
in
let
H
:=
fresh
"Proper"
in
let
T1
:=
type
of
x
in
evar
(
R1
:
relation
T1
);
let
T2
:=
type
of
y
in
evar
(
R2
:
relation
T2
);
assert
(
Proper
(
R1
==>
R2
==>
R
)
f
)
as
H
by
(
subst
R1
R2
;
eapply
_
);
subst
R1
R2
;
apply
H
;
clear
H
;
f_equiv
end

idtac
(
*
Let
the
user
solve
this
goal
*
)
].
(
**
solve_proper
solves
goals
of
the
form
"Proper (R1 ==> R2)"
,
for
any
number
of
relations
.
All
the
actual
work
is
done
by
f_equiv
;
solve_proper
just
introduces
the
assumptions
and
unfolds
the
first
head
symbol
.
*
)
Ltac
solve_proper
:=
(
*
Introduce
everything
*
)
intros
;
repeat
lazymatch
goal
with


Proper
_
_
=>
intros
???


(
_
==>
_
)
%
signature
_
_
=>
intros
???
end
;
(
*
Unfold
the
head
symbol
,
which
is
the
one
we
are
proving
a
new
property
about
*
)
lazymatch
goal
with


?
R
(
?
f
_
_
_
_
)
(
?
f
_
_
_
_
)
=>
unfold
f


?
R
(
?
f
_
_
_
)
(
?
f
_
_
_
)
=>
unfold
f


?
R
(
?
f
_
_
)
(
?
f
_
_
)
=>
unfold
f


?
R
(
?
f
_
)
(
?
f
_
)
=>
unfold
f
end
;
solve
[
f_equiv
].
(
**
The
tactic
[
intros_revert
tac
]
introduces
all
foralls
/
arrows
,
performs
tac
,
and
then
reverts
them
.
*
)
Ltac
intros_revert
tac
:=
...
...
program_logic/saved_prop.v
View file @
2ee38008
...
...
@@ 43,6 +43,6 @@ Section saved_prop.
rewrite
agree_equivI
later_equivI
/=
;
apply
later_mono
.
rewrite
{
2
}
(
iProp_fold_unfold
P
)
{
2
}
(
iProp_fold_unfold
Q
).
apply
(
eq_rewrite
(
iProp_unfold
P
)
(
iProp_unfold
Q
)
(
λ
Q
'
:
iPreProp
Λ
_
,
iProp_fold
(
iProp_unfold
P
)
≡
iProp_fold
Q
'
)
%
I
);
solve_
ne

auto
with
I
.
iProp_fold
(
iProp_unfold
P
)
≡
iProp_fold
Q
'
)
%
I
);
solve_
proper

auto
with
I
.
Qed
.
End
saved_prop
.
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