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Felipe Cerqueira
rtproofs
Commits
03101ea9
Commit
03101ea9
authored
Jan 08, 2016
by
Felipe Cerqueira
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Improve theorem statement about response time bound
parent
11a82d9b
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bertogna_fp_comp.v
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bertogna_fp_comp.v
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03101ea9
...
...
@@ 599,11 +599,13 @@ Module ResponseTimeIterationFP.
Hypothesis
H_global_scheduling_invariant
:
FP_scheduling_invariant_holds
job_cost
job_task
num_cpus
rate
sched
ts
higher_eq_priority
.
Definition
no_deadline_missed_by_task
(
tsk
:
sporadic_task
)
:=
Let
no_deadline_missed_by_task
(
tsk
:
sporadic_task
)
:=
task_misses_no_deadline
job_cost
job_deadline
job_task
rate
sched
tsk
.
Definition
no_deadline_missed_by_job
:=
Let
no_deadline_missed_by_job
:=
job_misses_no_deadline
job_cost
job_deadline
rate
sched
.
Let
response_time_bounded_by
(
tsk
:
sporadic_task
)
:=
is_response_time_bound_of_task
job_cost
job_task
tsk
rate
sched
.
(
*
In
the
following
lemma
,
we
prove
that
any
response

time
bound
contained
in
R_list
is
safe
.
The
proof
follows
by
induction
on
the
task
set
:
...
...
@@ 618,9 +620,7 @@ Module ResponseTimeIterationFP.
forall
rt_bounds
tsk
R
,
R_list
ts
=
Some
rt_bounds
>
(
tsk
,
R
)
\
in
rt_bounds
>
forall
j
:
JobIn
arr_seq
,
job_task
j
=
tsk
>
completed
job_cost
rate
sched
j
(
job_arrival
j
+
R
).
response_time_bounded_by
tsk
R
.
Proof
.
rename
H_valid_job_parameters
into
JOBPARAMS
,
H_valid_task_parameters
into
TASKPARAMS
,
H_restricted_deadlines
into
RESTR
,
H_completed_jobs_dont_execute
into
COMP
,
...
...
@@ 769,11 +769,12 @@ Module ResponseTimeIterationFP.
Theorem
fp_schedulability_test_yields_response_time_bounds
:
forall
tsk
,
tsk
\
in
ts
>
exists
R
,
R
<=
task_deadline
tsk
/
\
forall
(
j
:
JobIn
arr_seq
),
job_task
j
=
tsk
>
completed
job_cost
rate
sched
j
(
job_arrival
j
+
R
).
if
R_list
ts
is
Some
rt_bounds
then
exists
R
,
(
tsk
,
R
)
\
in
rt_bounds
/
\
R
<=
task_deadline
tsk
/
\
response_time_bounded_by
tsk
R
else
False
.
Proof
.
intros
tsk
IN
.
unfold
fp_schedulable
in
*
.
...
...
@@ 783,7 +784,7 @@ Module ResponseTimeIterationFP.
destruct
(
R_list
ts
)
as
[
rt_bounds

];
last
by
ins
.
exploit
(
TASKS
rt_bounds
tsk
);
[
by
ins

clear
TASKS
;
intro
EX
].
destruct
EX
as
[
EX
_
];
specialize
(
EX
IN
);
des
.
exists
R
;
split
.
exists
R
;
repeat
split
;
try
(
by
done
)
.
by
apply
DL
with
(
rt_bounds0
:=
rt_bounds
).
by
ins
;
apply
(
BOUNDS
rt_bounds
tsk
).
Qed
.
...
...
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