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c85f63e2
Commit
c85f63e2
authored
Feb 11, 2015
by
Ralf Jung
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refactor wp adequacy: add and use a dedicated lemma for "preserving wptp"
parent
9b6f2c6e
Changes
4
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4 changed files
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220 additions
and
196 deletions
+220
-196
iris_core.v
iris_core.v
+9
-2
iris_wp.v
iris_wp.v
+179
-194
lang.v
lang.v
+27
-0
lib/ModuRes/PCM.v
lib/ModuRes/PCM.v
+5
-0
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iris_core.v
View file @
c85f63e2
Require
Import
world_prop
core_lang
lang
masks
.
Require
Import
world_prop
core_lang
masks
.
Require
Import
ModuRes
.
PCM
ModuRes
.
UPred
ModuRes
.
BI
ModuRes
.
PreoMet
ModuRes
.
Finmap
.
Require
Import
ModuRes
.
PCM
ModuRes
.
UPred
ModuRes
.
BI
ModuRes
.
PreoMet
ModuRes
.
Finmap
.
Module
IrisRes
(
RL
:
PCM_T
)
(
C
:
CORE_LANG
)
<
:
PCM_T
.
Module
IrisRes
(
RL
:
PCM_T
)
(
C
:
CORE_LANG
)
<
:
PCM_T
.
...
@@ -10,7 +10,7 @@ Module IrisRes (RL : PCM_T) (C : CORE_LANG) <: PCM_T.
...
@@ -10,7 +10,7 @@ Module IrisRes (RL : PCM_T) (C : CORE_LANG) <: PCM_T.
End
IrisRes
.
End
IrisRes
.
Module
IrisCore
(
RL
:
PCM_T
)
(
C
:
CORE_LANG
).
Module
IrisCore
(
RL
:
PCM_T
)
(
C
:
CORE_LANG
).
Module
Export
L
:
=
Lang
C
.
Export
C
.
Module
Export
R
:
=
IrisRes
RL
C
.
Module
Export
R
:
=
IrisRes
RL
C
.
Module
Export
WP
:
=
WorldProp
R
.
Module
Export
WP
:
=
WorldProp
R
.
...
@@ -310,6 +310,13 @@ Module IrisCore (RL : PCM_T) (C : CORE_LANG).
...
@@ -310,6 +310,13 @@ Module IrisCore (RL : PCM_T) (C : CORE_LANG).
|
(
x
::
xs
)%
list
=>
Some
x
·
comp_list
xs
|
(
x
::
xs
)%
list
=>
Some
x
·
comp_list
xs
end
.
end
.
Lemma
comp_list_app
rs1
rs2
:
comp_list
(
rs1
++
rs2
)
==
comp_list
rs1
·
comp_list
rs2
.
Proof
.
induction
rs1
;
simpl
comp_list
;
[
now
rewrite
pcm_op_unit
by
apply
_
|].
now
rewrite
IHrs1
,
assoc
.
Qed
.
Definition
cod
(
m
:
nat
-
f
>
res
)
:
list
res
:
=
List
.
map
snd
(
findom_t
m
).
Definition
cod
(
m
:
nat
-
f
>
res
)
:
list
res
:
=
List
.
map
snd
(
findom_t
m
).
Definition
comp_map
(
m
:
nat
-
f
>
res
)
:
option
res
:
=
comp_list
(
cod
m
).
Definition
comp_map
(
m
:
nat
-
f
>
res
)
:
option
res
:
=
comp_list
(
cod
m
).
...
...
iris_wp.v
View file @
c85f63e2
This diff is collapsed.
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lang.v
View file @
c85f63e2
...
@@ -159,4 +159,31 @@ Module Lang (C : CORE_LANG).
...
@@ -159,4 +159,31 @@ Module Lang (C : CORE_LANG).
-
symmetry
in
EQK
;
now
apply
fill_noinv
in
EQK
.
-
symmetry
in
EQK
;
now
apply
fill_noinv
in
EQK
.
Qed
.
Qed
.
(* Reflexive, transitive closure of the step relation *)
Inductive
steps
:
cfg
->
cfg
->
Prop
:
=
|
steps_refl
ρ
:
steps
ρ
ρ
|
stepn_trans
ρ
1
ρ
2
ρ
3
:
step
ρ
1
ρ
2
->
steps
ρ
2
ρ
3
->
steps
ρ
1
ρ
3
.
Inductive
stepn
:
nat
->
cfg
->
cfg
->
Prop
:
=
|
stepn_O
ρ
:
stepn
O
ρ
ρ
|
stepn_S
ρ
1
ρ
2
ρ
3
n
(
HS
:
step
ρ
1
ρ
2
)
(
HSN
:
stepn
n
ρ
2
ρ
3
)
:
stepn
(
S
n
)
ρ
1
ρ
3
.
Lemma
steps_stepn
ρ
1
ρ
2
:
steps
ρ
1
ρ
2
->
exists
n
,
stepn
n
ρ
1
ρ
2
.
Proof
.
induction
1
.
-
eexists
.
eauto
using
stepn
.
-
destruct
IHsteps
as
[
n
IH
].
eexists
.
eauto
using
stepn
.
Qed
.
Lemma
stepn_steps
n
ρ
1
ρ
2
:
stepn
n
ρ
1
ρ
2
->
steps
ρ
1
ρ
2
.
Proof
.
induction
1
;
now
eauto
using
steps
.
Qed
.
End
Lang
.
End
Lang
.
lib/ModuRes/PCM.v
View file @
c85f63e2
...
@@ -150,6 +150,11 @@ Section Order.
...
@@ -150,6 +150,11 @@ Section Order.
erewrite
pcm_op_zero
in
EQ
by
apply
_;
contradiction
.
erewrite
pcm_op_zero
in
EQ
by
apply
_;
contradiction
.
Qed
.
Qed
.
Lemma
unit_min
r
:
pcm_unit
_
⊑
r
.
Proof
.
exists
r
;
now
erewrite
comm
,
pcm_op_unit
by
apply
_
.
Qed
.
End
Order
.
End
Order
.
Section
Exclusive
.
Section
Exclusive
.
...
...
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