Skip to content
GitLab
Menu
Projects
Groups
Snippets
Loading...
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in
Toggle navigation
Menu
Open sidebar
CHARGUERAUD Arthur
cfml
Commits
e819bd58
Commit
e819bd58
authored
Mar 07, 2016
by
charguer
Browse files
overapps
parent
01378833
Changes
1
Hide whitespace changes
Inline
Side-by-side
lib/coq/CFSpec.v
View file @
e819bd58
...
...
@@ -72,7 +72,7 @@ Proof using.
do
2
rewrite
<-
heap_union_assoc
.
fequal
.
rewrite
heap_union_comm
.
rewrite
~
<-
heap_union_assoc
.
rew_disjoint
*
.
*
)
Admitted
.
Admitted
.
(
*
faster
*
)
(
*
Qed
.
...
...
@@ -90,7 +90,143 @@ Proof using. intros. applys* local_wframe. Qed.
(
********************************************************************
)
(
*
**
Generic
of
[
app
N
]
*
)
(
*
**
Generic
notation
for
list
of
args
*
)
Notation
"[ x1 ]"
:=
((
dyn
x1
)
::
nil
)
(
at
level
0
,
x1
at
level
00
)
:
arglist
.
Notation
"[ x1 x2 ]"
:=
((
dyn
x1
)
::
(
dyn
x2
)
::
nil
)
(
at
level
0
,
x1
at
level
0
,
x2
at
level
0
)
:
arglist
.
Notation
"[ x1 x2 x3 ]"
:=
((
dyn
x1
)
::
(
dyn
x2
)
::
(
dyn
x3
)
::
nil
)
(
at
level
0
,
x1
at
level
0
,
x2
at
level
0
,
x3
at
level
0
)
:
arglist
.
Delimit
Scope
arglist
with
arglist
.
(
********************************************************************
)
(
*
**
Definition
of
[
App
]
*
)
Fixpoint
AppDef
(
f
:
func
)
(
xs
:
list
dynamic
)
B
(
H
:
hprop
)
(
Q
:
B
->
hprop
)
:
Prop
:=
match
xs
with
|
nil
=>
False
|
(
dyn
x
)
::
nil
=>
app_basic
f
x
H
Q
|
(
dyn
x
)
::
xs
=>
app_basic
f
x
H
(
fun
g
=>
Hexists
H
'
,
H
'
\
*
\
[
AppDef
g
xs
H
'
Q
])
end
.
Notation
"'App' f xs"
:=
(
@
AppDef
f
(
xs
)
%
arglist
_
)
(
at
level
68
,
f
at
level
0
,
xs
at
level
0
)
:
charac
.
Open
Scope
charac
.
Definition
demo_arglist
:=
forall
f
(
xs
:
list
int
)
(
x
y
:
int
)
B
H
(
Q
:
B
->
hprop
),
App
f
[
x
y
]
H
Q
.
(
********************************************************************
)
(
*
**
Definition
of
[
curried
]
*
)
Fixpoint
curried
(
n
:
nat
)
(
f
:
func
)
:
Prop
:=
match
n
with
|
O
=>
False
|
S
O
=>
True
|
S
n
=>
forall
A
(
x
:
A
),
app_basic
f
x
\
[]
(
fun
g
=>
\
[
curried
n
g
/
\
forall
xs
B
H
(
Q
:
B
->
hprop
),
App
f
((
dyn
x
)
::
xs
)
H
Q
->
App
g
xs
H
Q
])
end
.
(
********************************************************************
)
(
*
**
Lemma
for
over
-
applications
*
)
Lemma
App_hd_nonnil_unfold
:
forall
(
f
:
func
)
A
(
x
:
A
)
(
xs
:
list
dynamic
)
B
(
H
:
hprop
)
(
Q
:
B
->
hprop
),
(
length
xs
>=
1
)
%
nat
->
App
f
((
dyn
x
)
::
xs
)
H
Q
=
app_basic
f
x
H
(
fun
g
=>
Hexists
H
'
,
H
'
\
*
\
[
AppDef
g
xs
H
'
Q
]).
Proof
using
.
intros
.
destruct
xs
.
rew_list
in
*
.
math
.
auto
.
Qed
.
Lemma
App_over
:
forall
xs
ys
f
B
H
(
Q
:
B
->
hprop
),
(
length
xs
>
0
)
%
nat
->
(
length
ys
>
0
)
%
nat
->
App
f
(
xs
++
ys
)
H
Q
=
App
f
xs
H
(
fun
g
=>
Hexists
H
'
,
H
'
\
*
\
[
App
g
ys
H
'
Q
]).
Proof
using
.
induction
xs
.
rew_list
.
math
.
introv
N1
N2
.
rew_list
.
destruct
a
as
[
A
x
].
destruct
xs
.
rew_list
.
simpl
.
destruct
ys
.
rew_list
in
*
.
math
.
auto
.
sets_eq
xs
'
:
(
d
::
xs
).
do
2
(
rewrite
App_hd_nonnil_unfold
;
[
|
subst
;
rew_list
;
math
]).
fequal
.
apply
func_ext_1
.
intros
g
.
apply
func_equal_1
.
auto
.
apply
func_ext_1
.
intros
H
'
.
fequal
.
fequal
.
apply
IHxs
.
subst
.
rew_list
.
math
.
math
.
Qed
.
Lemma
App_over
'
:
forall
n
xs
f
B
H
(
Q
:
B
->
hprop
),
(
0
<
n
<
length
xs
)
%
nat
->
App
f
xs
H
Q
=
App
f
(
take
n
xs
)
H
(
fun
g
=>
Hexists
H
'
,
H
'
\
*
\
[
App
g
(
drop
n
xs
)
H
'
Q
]).
Proof
using
.
introv
N
.
forwards
*
(
M
&
E1
&
E2
)
:
take_and_drop
n
xs
.
math
.
set
(
xs
'
:=
xs
)
at
1.
change
xs
with
xs
'
in
M
.
rewrite
M
.
subst
xs
'
.
rewrite
App_over
;
try
math
.
auto
.
Qed
.
(
********************************************************************
)
(
*
**
Lemma
for
partial
-
applications
*
)
(
*
bug
...
Axiom
App
:
forall
(
f
:
func
)
(
xs
:
list
dynamic
)
B
(
H
:
hprop
)
(
Q
:
B
->
hprop
),
Prop
.
Implicit
Arguments
App
[[
B
]].
Print
App
.
Arguments
App
f
%
heap_scope
xs
%
arglist
H
%
heap_scope
Q
%
heap_scope
.
*
)
(
*
TODO
:
why
not
Coercion
id
(
P
:
Prop
)
:
hprop
:=
\
[
P
].
Error:
Sortclass
cannot
be
a
source
class
.
*
)
(
*
Inductive
arglist
:
nat
->
Type
:=
|
arglist_nil
:
arglist
0
...
...
@@ -104,7 +240,7 @@ Fixpoint app (n : nat) (X : arglist n) (f:func) (B:Type) (H:hprop) (Q:B->hprop)
app_basic
f
x
H
(
fun
g
:
func
=>
Hexists
H
'
,
H
'
\
*
\
[
app
xs
g
H
'
Q
])
end
.
*
)
(
*
[
app
n
xs
f
B
H
Q
]
...
...
@@ -119,7 +255,7 @@ Definition app
Proof
.
induction
1
;
intros
f
B
H
Q
.
(
*
exact
(
H
==>
Q
f
).
*
)
exact
True
.
exact
True
.
exact
(
app_basic
f
x
H
(
fun
g
=>
Hexists
H
'
,
H
'
\
*
\
[
IHX
g
B
H
'
Q
])).
Defined
.
...
...
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment