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Xiaojie Guo
rt-proofs
Commits
14cb2cfe
Commit
14cb2cfe
authored
Dec 29, 2015
by
Felipe Cerqueira
Browse files
Clean-up code
parent
2ad89199
Changes
22
Hide whitespace changes
Inline
Side-by-side
Makefile
View file @
14cb2cfe
...
...
@@ -14,7 +14,7 @@
#
# This Makefile was generated by the command line :
# coq_makefile
B
ertogna
ResponseTimeDefsEDF
.v
B
ertogna
ResponseTimeDefsJitter
.v
B
ertogna
ResponseTimeDefs
.v
B
ertogna
ResponseTimeEDFC
omp.v
B
ertogna
ResponseTimeFPJitter
.v
B
ertogna
ResponseTimeFP.v divround
.v extralib.v ExtraRelations.v
G
uan
Defs
.v
G
uan
FP.v helper
.v
I
nterference
Defs
.v
J
ob
Defs
.v
P
latform
Defs
.v
P
riority
Defs
.v
R
esponse
T
ime
Defs
.v
S
chedulability
Defs
.v
S
chedule
Defs
.v ssromega.v
T
ask
A
rrival
Defs
.v
T
ask
Def
s.v Vbase.v
W
orkload
DefsJ
itter.v
W
orkload
Defs
.v
# coq_makefile
b
ertogna
_edf_comp
.v
b
ertogna
_edf_theory
.v
b
ertogna
_fp_comp
.v
b
ertogna
_fp_jitter_c
omp.v
b
ertogna
_fp_jitter_theory
.v
b
ertogna
_fp_theory
.v extralib.v ExtraRelations.v
g
uan
_fp_comp
.v
g
uan
_fp_theory
.v
i
nterference.v
j
ob.v
p
latform.v
p
riority.v
r
esponse
_t
ime.v
s
chedulability.v
s
chedule.v ssromega.v
t
ask
_a
rrival.v
t
ask
.v util_divround.v util_lemma
s.v Vbase.v
w
orkload
_j
itter.v
w
orkload.v
#
.DEFAULT_GOAL
:=
all
...
...
@@ -80,31 +80,31 @@ endif
# #
######################
VFILES
:=
BertognaResponseTimeDefsEDF.v
\
BertognaResponseTimeDefsJitter.v
\
BertognaResponseTimeDefs.v
\
BertognaResponseTimeEDFComp.v
\
BertognaResponseTimeFPJitter.v
\
BertognaResponseTimeFP.v
\
divround.v
\
VFILES
:=
bertogna_edf_comp.v
\
bertogna_edf_theory.v
\
bertogna_fp_comp.v
\
bertogna_fp_jitter_comp.v
\
bertogna_fp_jitter_theory.v
\
bertogna_fp_theory.v
\
extralib.v
\
ExtraRelations.v
\
GuanDefs.v
\
GuanFP.v
\
helper.v
\
InterferenceDefs.v
\
JobDefs.v
\
PlatformDefs.v
\
PriorityDefs.v
\
ResponseTimeDefs.v
\
SchedulabilityDefs.v
\
ScheduleDefs.v
\
guan_fp_comp.v
\
guan_fp_theory.v
\
interference.v
\
job.v
\
platform.v
\
priority.v
\
response_time.v
\
schedulability.v
\
schedule.v
\
ssromega.v
\
TaskArrivalDefs.v
\
TaskDefs.v
\
task_arrival.v
\
task.v
\
util_divround.v
\
util_lemmas.v
\
Vbase.v
\
W
orkload
DefsJ
itter.v
\
W
orkload
Defs
.v
w
orkload
_j
itter.v
\
w
orkload.v
-include
$(addsuffix .d,$(VFILES))
.SECONDARY
:
$(addsuffix .d
,
$(VFILES))
...
...
B
ertogna
ResponseTimeEDFC
omp.v
→
b
ertogna
_edf_c
omp.v
View file @
14cb2cfe
Require
Import
Vbase
S
chedule
Defs
B
ertogna
ResponseTimeDefsEDF
divround
helper
ssreflect
ssrbool
eqtype
ssrnat
seq
fintype
bigop
div
path
tuple
.
Require
Import
Vbase
s
chedule
b
ertogna
_edf_theory
util_divround
util_lemmas
ssreflect
ssrbool
eqtype
ssrnat
seq
fintype
bigop
div
path
.
Module
ResponseTimeIterationEDF
.
...
...
B
ertogna
ResponseTimeDefsEDF
.v
→
b
ertogna
_edf_theory
.v
View file @
14cb2cfe
Require
Import
Vbase
T
ask
Defs
JobDefs
T
ask
A
rrival
Defs
S
chedule
Defs
PlatformDefs
W
orkload
Defs
S
chedulability
Defs
P
riority
Defs
ResponseTimeDefs
BertognaResponseTimeDefs
divround
helper
ssreflect
ssrbool
eqtype
ssrnat
seq
fintype
bigop
div
path
tuple
.
Require
Import
Vbase
t
ask
job
t
ask
_a
rrival
s
chedule
platform
w
orkload
s
chedulability
p
riority
response_time
bertogna_fp_theory
util_divround
util_lemmas
ssreflect
ssrbool
eqtype
ssrnat
seq
fintype
bigop
div
path
.
Module
ResponseTimeAnalysisEDF
.
...
...
B
ertogna
ResponseTimeFP
.v
→
b
ertogna
_fp_comp
.v
View file @
14cb2cfe
Require
Import
Vbase
S
chedule
Defs
B
ertogna
ResponseTimeDefs
divround
helper
ssreflect
ssrbool
eqtype
ssrnat
seq
fintype
bigop
div
path
tuple
.
Require
Import
Vbase
s
chedule
b
ertogna
_fp_theory
util_divround
util_lemmas
ssreflect
ssrbool
eqtype
ssrnat
seq
fintype
bigop
div
path
.
Module
ResponseTimeIterationFP
.
...
...
B
ertogna
ResponseTimeFPJitter
.v
→
b
ertogna
_fp_jitter_comp
.v
View file @
14cb2cfe
Require
Import
Vbase
JobDefs
TaskDefs
ScheduleDefs
TaskArrivalDefs
PriorityDefs
WorkloadDefsJitter
BertognaResponseTimeDefsJitter
InterferenceDefs
divround
helper
Require
Import
Vbase
job
task
schedule
task_arrival
priority
workload_jitter
bertogna_fp_jitter_theory
interference
platform
schedulability
response_time
util_divround
util_lemmas
ssreflect
ssrbool
eqtype
ssrnat
seq
fintype
bigop
div
path
tuple
.
Module
ResponseTimeIterationFPWithJitter
.
Import
Job
ScheduleOfTaskWithJitter
SporadicTaskset
SporadicTaskArrival
Priority
WorkloadWithJitter
ResponseTimeAnalysisJitter
Interference
.
Import
Job
ScheduleOfTaskWithJitter
SporadicTaskset
SporadicTaskArrival
Priority
WorkloadWithJitter
ResponseTimeAnalysisJitter
Interference
Platform
Schedulability
ResponseTime
.
Section
Analysis
.
...
...
B
ertogna
ResponseTimeDefsJitter
.v
→
b
ertogna
_fp_jitter_theory
.v
View file @
14cb2cfe
Require
Import
Vbase
T
ask
Defs
JobDefs
T
ask
A
rrival
Defs
S
chedule
Defs
PlatformDefs
WorkloadDefsJitter
BertognaR
esponse
T
ime
Defs
S
chedulability
Defs
P
riority
Defs
ResponseTimeDefs
divround
helper
Require
Import
Vbase
t
ask
job
t
ask
_a
rrival
s
chedule
platform
workload_jitter
r
esponse
_t
ime
s
chedulability
p
riority
interference
workload
util_divround
util_lemmas
ssreflect
ssrbool
eqtype
ssrnat
seq
fintype
bigop
div
path
tuple
.
Module
ResponseTimeAnalysisJitter
.
Import
Job
SporadicTaskset
ScheduleOfTaskWithJitter
Schedulability
ResponseTime
Priority
SporadicTaskArrival
.
Export
WorkloadWithJitter
ResponseTimeAnalysis
.
Import
Job
SporadicTaskset
ScheduleOfTaskWithJitter
Schedulability
ResponseTime
Priority
SporadicTaskArrival
Platform
Interference
Workload
.
Export
WorkloadWithJitter
.
Section
InterferenceBoundJitter
.
...
...
@@ -570,7 +570,7 @@ Module ResponseTimeAnalysisJitter.
rewrite
big_seq_cond
[
\
sum_
(
i
<-
_
|
true
)
_
]
big_seq_cond
.
apply
leq_sum
;
move
=>
tsk_k
/
andP
[
HPk
_
]
;
destruct
tsk_k
as
[
tsk_k
R_k
].
specialize
(
ALL
(
tsk_k
,
R_k
)
HPk
).
unfold
interference_bound
,
workload_bound
,
x
in
*.
unfold
interference_bound
_jitter
,
workload_bound
,
x
in
*.
fold
(
interferes_with_tsk
)
;
destruct
(
interferes_with_tsk
tsk_k
)
eqn
:
INTERFk
;
[
rewrite
andbT
in
ALL
;
rewrite
andbT
|
by
rewrite
andbF
min0n
].
destruct
(
tsk_k
\
in
ts
)
eqn
:
INk
;
last
by
rewrite
min0n
.
...
...
B
ertogna
ResponseTimeDefs
.v
→
b
ertogna
_fp_theory
.v
View file @
14cb2cfe
Require
Import
Vbase
T
ask
Defs
JobDefs
T
ask
A
rrival
Defs
S
chedule
Defs
PlatformDefs
WorkloadDefs
S
chedulability
Defs
P
riority
Defs
ResponseTimeDefs
InterferenceDefs
divround
helper
Require
Import
Vbase
t
ask
job
t
ask
_a
rrival
s
chedule
platform
workload
s
chedulability
p
riority
response_time
interference
util_divround
util_lemmas
ssreflect
ssrbool
eqtype
ssrnat
seq
fintype
bigop
div
path
tuple
.
Module
ResponseTimeAnalysis
.
...
...
G
uan
FP
.v
→
g
uan
_fp_comp
.v
View file @
14cb2cfe
Require
Import
Vbase
JobDefs
TaskDefs
ScheduleDefs
TaskArrivalDefs
PriorityDefs
WorkloadDefsJitter
GuanDefs
divround
helper
Require
Import
Vbase
job
task
schedule
task_arrival
priority
workload_jitter
guan_fp_theory
util_divround
util_lemmas
ssreflect
ssrbool
eqtype
ssrnat
seq
fintype
bigop
div
path
tuple
.
Module
ResponseTimeIterationFPGuan
.
...
...
G
uan
Defs
.v
→
g
uan
_fp_theory
.v
View file @
14cb2cfe
Require
Import
Vbase
T
ask
Defs
JobDefs
T
ask
A
rrival
Defs
S
chedule
Defs
PlatformDefs
WorkloadDefs
BertognaResponseTimeDefs
S
chedulability
Defs
P
riority
Defs
I
nterference
Defs
PlatformDefs
R
esponse
T
ime
Defs
divround
helper
Require
Import
Vbase
t
ask
job
t
ask
_a
rrival
s
chedule
platform
workload
bertogna_fp_theory
s
chedulability
p
riority
i
nterference
platform
r
esponse
_t
ime
util_
divround
util_lemmas
ssreflect
ssrbool
eqtype
ssrnat
seq
fintype
bigop
div
path
tuple
.
Module
ResponseTimeAnalysisGuan
.
...
...
I
nterference
Defs
.v
→
i
nterference.v
View file @
14cb2cfe
Require
Import
Vbase
T
ask
Defs
JobDefs
S
chedule
Defs
P
riority
Defs
W
orkload
Defs
divround
helper
ssreflect
ssrbool
eqtype
ssrnat
seq
fintype
bigop
.
Require
Import
Vbase
t
ask
job
s
chedule
p
riority
w
orkload
util_
divround
util_lemmas
ssreflect
ssrbool
eqtype
ssrnat
seq
fintype
bigop
.
Module
Interference
.
...
...
J
ob
Defs
.v
→
j
ob.v
View file @
14cb2cfe
Require
Import
T
ask
Defs
helper
ssrnat
ssrbool
eqtype
.
Require
Import
t
ask
util_lemmas
ssrnat
ssrbool
eqtype
.
Module
Job
.
...
...
P
latform
Defs
.v
→
p
latform.v
View file @
14cb2cfe
Require
Import
Vbase
TaskDefs
ScheduleDefs
JobDefs
PriorityDefs
InterferenceDefs
helper
Require
Import
Vbase
task
schedule
job
priority
interference
util_lemmas
ssreflect
ssrbool
eqtype
ssrnat
seq
fintype
bigop
.
Module
Platform
.
...
...
P
riority
Defs
.v
→
p
riority.v
View file @
14cb2cfe
Require
Import
Vbase
ExtraRelations
TaskDefs
JobDefs
ScheduleDefs
(*TaskArrivalDefs*)
Require
Import
Vbase
task
job
schedule
ssreflect
ssrbool
eqtype
ssrnat
seq
.
Set
Implicit
Arguments
.
...
...
R
esponse
T
ime
Defs
.v
→
r
esponse
_t
ime.v
View file @
14cb2cfe
Require
Import
Vbase
T
ask
Defs
JobDefs
T
ask
A
rrival
Defs
S
chedule
Def
s
helper
ssreflect
ssrbool
eqtype
ssrnat
seq
fintype
bigop
.
Require
Import
Vbase
t
ask
job
t
ask
_a
rrival
s
chedule
util_lemma
s
ssreflect
ssrbool
eqtype
ssrnat
seq
fintype
bigop
.
Module
ResponseTime
.
...
...
S
chedulability
Defs
.v
→
s
chedulability.v
View file @
14cb2cfe
Require
Import
Vbase
T
ask
Defs
S
chedule
Defs
Require
Import
Vbase
t
ask
s
chedule
ssreflect
eqtype
ssrbool
ssrnat
seq
.
Module
Schedulability
.
...
...
S
chedule
Defs
.v
→
s
chedule.v
View file @
14cb2cfe
Require
Import
Vbase
J
ob
Defs
TaskDefs
helper
Require
Import
Vbase
j
ob
task
util_lemmas
ssreflect
ssrbool
eqtype
ssrnat
seq
fintype
bigop
.
Definition
time
:
=
nat
.
...
...
T
ask
Defs
.v
→
t
ask.v
View file @
14cb2cfe
Require
Import
Vbase
helper
ssrnat
ssrbool
eqtype
fintype
seq
.
Require
Import
Vbase
util_lemmas
ssrnat
ssrbool
eqtype
fintype
seq
.
Module
SporadicTask
.
...
...
T
ask
A
rrival
Defs
.v
→
t
ask
_a
rrival.v
View file @
14cb2cfe
Require
Import
Vbase
T
ask
Defs
JobDefs
ScheduleDefs
helper
Require
Import
Vbase
t
ask
job
schedule
util_lemmas
ssreflect
ssrbool
eqtype
ssrnat
seq
fintype
bigop
.
Module
SporadicTaskArrival
.
...
...
divround.v
→
util_
divround.v
View file @
14cb2cfe
File moved
helper
.v
→
util_lemmas
.v
View file @
14cb2cfe
...
...
@@ -359,24 +359,6 @@ Proof.
Qed
.
Lemma
fun_mon_iter_mon
:
forall
(
f
:
nat
->
nat
)
x0
x1
x2
(
LE
:
x1
<=
x2
)
(
MIN
:
f
0
>=
x0
)
(
MON
:
forall
x1
x2
,
x1
<=
x2
->
f
x1
<=
f
x2
),
iter
x1
f
x0
<=
iter
x2
f
x0
.
Proof
.
ins
;
revert
LE
;
revert
x2
;
rewrite
leq_as_delta
;
intros
delta
.
induction
x1
;
try
rewrite
add0n
.
{
destruct
delta
;
first
by
apply
leqnn
.
apply
leq_trans
with
(
n
:
=
f
0
)
;
first
by
apply
MIN
.
by
rewrite
iterS
MON
.
}
{
rewrite
iterS
-
addn1
-
addnA
[
1
+
delta
]
addnC
addnA
addn1
iterS
.
by
apply
MON
,
IHx1
.
}
Qed
.
Lemma
fun_mon_iter_mon'
:
forall
(
f
:
nat
->
nat
)
x0
x1
x2
(
LE
:
x1
<=
x2
)
(
MIN
:
f
x0
>=
x0
)
(
MON
:
forall
x1
x2
,
x1
<=
x2
->
f
x1
<=
f
x2
),
...
...
@@ -806,46 +788,4 @@ Proof.
last
by
apply
leq_trans
with
(
n
:
=
t2
).
rewrite
->
big_cat_nat
with
(
p
:
=
t2'
)
(
n
:
=
t2
)
;
try
(
by
done
)
;
simpl
.
by
rewrite
addnC
-
addnA
;
apply
leq_addr
.
Qed
.
(*Program Definition fun_ord_to_nat2 {n} {T} (x0: T) (f: 'I_n -> T)
(x : nat) : T :=
match (x < n) with
true => (f _)
| false => x0
end.
Next Obligation.
eby eapply Ordinal, Logic.eq_sym.
Defined.
Lemma eq_fun_ord_to_nat2 :
forall n {T: Type} x0 (f: 'I_n -> T) (x: 'I_n),
(fun_ord_to_nat2 x0 f) x = f x.
Proof.
ins. unfold fun_ord_to_nat2.
des_eqrefl.
by f_equal; apply ord_inj.
by destruct x; ins; rewrite i in EQ.
Qed.
(* For all x: 'I_n (i.e., x < n), the conversion preserves equality. *)
Program Definition eq_fun_ord_to_nat :
forall n {T: Type} x0 (f: 'I_n -> T) (x: 'I_n),
(fun_ord_to_nat x0 f) x = f x :=
fun n T x0 f x =>
match ltn_ord x in eq _ b return
(
(if b as b' return b = b' -> T then
fun (H : b = true) => f (@Ordinal n x ( H))
else fun _ => x0) Logic.eq_refl = f x
)
-> fun_ord_to_nat x0 f x = f x
with
| Logic.eq_refl => _
end (Logic.eq_refl (f x)).
Next Obligation.
destruct x; simpl.
f_equal; f_equal.
exact: bool_irrelevance.
Qed.*)
\ No newline at end of file
Qed
.
\ No newline at end of file
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