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Rodolphe Lepigre
Iris
Commits
23b0e16b
Commit
23b0e16b
authored
Jul 06, 2014
by
Ralf Jung
Browse files
add and almost prove the soundness (adequacy) theorem as it appears in the writeup
parent
688d3287
Changes
1
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Inline
Side-by-side
iris.v
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23b0e16b
...
...
@@ -1169,6 +1169,37 @@ Qed.
-
simpl
comp_list
;
now
erewrite
comm
,
pcm_op_unit
by
apply
_
.
Qed
.
Program
Definition
cons_pred
(
φ
:
value
-=>
Prop
)
:
value
-
n
>
Props
:
=
n
[(
fun
v
=>
pcmconst
(
mkUPred
(
fun
n
r
=>
φ
v
)
_
))].
Next
Obligation
.
firstorder
.
Qed
.
Next
Obligation
.
intros
x
y
H_xy
P
n
r
.
simpl
.
rewrite
H_xy
.
tauto
.
Qed
.
Next
Obligation
.
intros
x
y
H_xy
P
m
r
.
simpl
in
H_xy
.
destruct
n
.
-
intros
LEZ
.
exfalso
.
omega
.
-
intros
_
.
simpl
.
assert
(
H_xy'
:
equiv
x
y
)
by
assumption
.
rewrite
H_xy'
.
tauto
.
Qed
.
Theorem
soundness_obs
m
e
(
φ
:
value
-=>
Prop
)
n
e'
tp
σ
σ
'
(
HT
:
valid
(
ht
m
(
ownS
σ
)
e
(
cons_pred
φ
)))
(
HSN
:
stepn
n
([
e
],
σ
)
(
e'
::
tp
,
σ
'
))
(
HV
:
is_value
e'
)
:
φ
(
exist
_
e'
HV
).
Proof
.
edestruct
(
soundness
_
_
_
_
_
0
_
_
_
_
fdEmpty
(
ex_own
_
σ
,
pcm_unit
_
)
1
HT
HSN
)
as
[
w'
[
r'
[
s'
[
H_wle
[
H_phi
_
]
]
]
]
].
-
simpl
.
hnf
.
exists
(
pcm_unit
_
).
rewrite
pcm_op_unit
by
intuition
.
reflexivity
.
-
rewrite
Plus
.
plus_comm
.
simpl
.
split
.
+
admit
.
(* TODO: rewrite comm. does not work though?? *)
+
exists
(
fdEmpty
(
V
:
=
res
)).
simpl
.
split
;
[
reflexivity
|].
intros
i
_
.
split
;
[
tauto
|].
intros
_
_
[].
-
exact
H_phi
.
Qed
.
End
Soundness
.
Section
HoareTripleProperties
.
...
...
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