Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
R
rt-proofs
Project overview
Project overview
Details
Activity
Releases
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Issues
0
Issues
0
List
Boards
Labels
Service Desk
Milestones
Merge Requests
0
Merge Requests
0
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Operations
Operations
Incidents
Environments
Analytics
Analytics
CI / CD
Repository
Value Stream
Wiki
Wiki
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
Sophie Quinton
rt-proofs
Commits
8c68c87a
Commit
8c68c87a
authored
Oct 06, 2016
by
Felipe Cerqueira
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Add schedule construction based on prefixes
parent
aac7e9a3
Changes
2
Hide whitespace changes
Inline
Side-by-side
Showing
2 changed files
with
112 additions
and
1 deletion
+112
-1
Makefile
Makefile
+2
-1
model/uni/transformation/construction.v
model/uni/transformation/construction.v
+110
-0
No files found.
Makefile
View file @
8c68c87a
...
...
@@ -14,7 +14,7 @@
#
# This Makefile was generated by the command line :
# coq_makefile -f _CoqProject ./util/ssromega.v ./util/seqset.v ./util/sorting.v ./util/minmax.v ./util/powerset.v ./util/all.v ./util/ord_quantifier.v ./util/nat.v ./util/sum.v ./util/bigord.v ./util/counting.v ./util/tactics.v ./util/induction.v ./util/list.v ./util/divround.v ./util/bigcat.v ./util/fixedpoint.v ./util/notation.v ./analysis/global/jitter/bertogna_fp_comp.v ./analysis/global/jitter/interference_bound_edf.v ./analysis/global/jitter/workload_bound.v ./analysis/global/jitter/bertogna_edf_comp.v ./analysis/global/jitter/bertogna_fp_theory.v ./analysis/global/jitter/interference_bound.v ./analysis/global/jitter/interference_bound_fp.v ./analysis/global/jitter/bertogna_edf_theory.v ./analysis/global/parallel/bertogna_fp_comp.v ./analysis/global/parallel/interference_bound_edf.v ./analysis/global/parallel/workload_bound.v ./analysis/global/parallel/bertogna_edf_comp.v ./analysis/global/parallel/bertogna_fp_theory.v ./analysis/global/parallel/interference_bound.v ./analysis/global/parallel/interference_bound_fp.v ./analysis/global/parallel/bertogna_edf_theory.v ./analysis/global/basic/bertogna_fp_comp.v ./analysis/global/basic/interference_bound_edf.v ./analysis/global/basic/workload_bound.v ./analysis/global/basic/bertogna_edf_comp.v ./analysis/global/basic/bertogna_fp_theory.v ./analysis/global/basic/interference_bound.v ./analysis/global/basic/interference_bound_fp.v ./analysis/global/basic/bertogna_edf_theory.v ./analysis/apa/bertogna_fp_comp.v ./analysis/apa/interference_bound_edf.v ./analysis/apa/workload_bound.v ./analysis/apa/bertogna_edf_comp.v ./analysis/apa/bertogna_fp_theory.v ./analysis/apa/interference_bound.v ./analysis/apa/interference_bound_fp.v ./analysis/apa/bertogna_edf_theory.v ./analysis/uni/basic/workload_bound_fp.v ./analysis/uni/basic/fp_rta_comp.v ./analysis/uni/basic/fp_rta_theory.v ./model/arrival_sequence.v ./model/task.v ./model/task_arrival.v ./model/partitioned/schedulability.v ./model/partitioned/schedule.v ./model/priority.v ./model/global/workload.v ./model/global/schedulability.v ./model/global/jitter/interference_edf.v ./model/global/jitter/interference.v ./model/global/jitter/job.v ./model/global/jitter/constrained_deadlines.v ./model/global/jitter/schedule.v ./model/global/jitter/platform.v ./model/global/response_time.v ./model/global/basic/interference_edf.v ./model/global/basic/interference.v ./model/global/basic/constrained_deadlines.v ./model/global/basic/schedule.v ./model/global/basic/platform.v ./model/job.v ./model/time.v ./model/arrival_bounds.v ./model/apa/interference_edf.v ./model/apa/interference.v ./model/apa/affinity.v ./model/apa/constrained_deadlines.v ./model/apa/platform.v ./model/uni/workload.v ./model/uni/schedulability.v ./model/uni/schedule_of_task.v ./model/uni/response_time.v ./model/uni/schedule.v ./model/uni/basic/arrival_bounds.v ./model/uni/basic/busy_interval.v ./model/uni/basic/platform.v ./model/uni/service.v ./implementation/arrival_sequence.v ./implementation/task.v ./implementation/global/jitter/arrival_sequence.v ./implementation/global/jitter/task.v ./implementation/global/jitter/bertogna_edf_example.v ./implementation/global/jitter/job.v ./implementation/global/jitter/bertogna_fp_example.v ./implementation/global/jitter/schedule.v ./implementation/global/parallel/bertogna_edf_example.v ./implementation/global/parallel/bertogna_fp_example.v ./implementation/global/basic/bertogna_edf_example.v ./implementation/global/basic/bertogna_fp_example.v ./implementation/global/basic/schedule.v ./implementation/job.v ./implementation/apa/arrival_sequence.v ./implementation/apa/task.v ./implementation/apa/bertogna_edf_example.v ./implementation/apa/job.v ./implementation/apa/bertogna_fp_example.v ./implementation/apa/schedule.v ./implementation/uni/basic/fp_rta_example.v ./implementation/uni/basic/schedule.v -o Makefile
# coq_makefile -f _CoqProject ./util/ssromega.v ./util/seqset.v ./util/sorting.v ./util/minmax.v ./util/powerset.v ./util/all.v ./util/ord_quantifier.v ./util/nat.v ./util/sum.v ./util/bigord.v ./util/counting.v ./util/tactics.v ./util/induction.v ./util/list.v ./util/divround.v ./util/bigcat.v ./util/fixedpoint.v ./util/notation.v ./analysis/global/jitter/bertogna_fp_comp.v ./analysis/global/jitter/interference_bound_edf.v ./analysis/global/jitter/workload_bound.v ./analysis/global/jitter/bertogna_edf_comp.v ./analysis/global/jitter/bertogna_fp_theory.v ./analysis/global/jitter/interference_bound.v ./analysis/global/jitter/interference_bound_fp.v ./analysis/global/jitter/bertogna_edf_theory.v ./analysis/global/parallel/bertogna_fp_comp.v ./analysis/global/parallel/interference_bound_edf.v ./analysis/global/parallel/workload_bound.v ./analysis/global/parallel/bertogna_edf_comp.v ./analysis/global/parallel/bertogna_fp_theory.v ./analysis/global/parallel/interference_bound.v ./analysis/global/parallel/interference_bound_fp.v ./analysis/global/parallel/bertogna_edf_theory.v ./analysis/global/basic/bertogna_fp_comp.v ./analysis/global/basic/interference_bound_edf.v ./analysis/global/basic/workload_bound.v ./analysis/global/basic/bertogna_edf_comp.v ./analysis/global/basic/bertogna_fp_theory.v ./analysis/global/basic/interference_bound.v ./analysis/global/basic/interference_bound_fp.v ./analysis/global/basic/bertogna_edf_theory.v ./analysis/apa/bertogna_fp_comp.v ./analysis/apa/interference_bound_edf.v ./analysis/apa/workload_bound.v ./analysis/apa/bertogna_edf_comp.v ./analysis/apa/bertogna_fp_theory.v ./analysis/apa/interference_bound.v ./analysis/apa/interference_bound_fp.v ./analysis/apa/bertogna_edf_theory.v ./analysis/uni/basic/workload_bound_fp.v ./analysis/uni/basic/fp_rta_comp.v ./analysis/uni/basic/fp_rta_theory.v ./model/arrival_sequence.v ./model/task.v ./model/task_arrival.v ./model/partitioned/schedulability.v ./model/partitioned/schedule.v ./model/priority.v ./model/global/workload.v ./model/global/schedulability.v ./model/global/jitter/interference_edf.v ./model/global/jitter/interference.v ./model/global/jitter/job.v ./model/global/jitter/constrained_deadlines.v ./model/global/jitter/schedule.v ./model/global/jitter/platform.v ./model/global/response_time.v ./model/global/basic/interference_edf.v ./model/global/basic/interference.v ./model/global/basic/constrained_deadlines.v ./model/global/basic/schedule.v ./model/global/basic/platform.v ./model/job.v ./model/time.v ./model/arrival_bounds.v ./model/apa/interference_edf.v ./model/apa/interference.v ./model/apa/affinity.v ./model/apa/constrained_deadlines.v ./model/apa/platform.v ./model/uni/workload.v ./model/uni/
transformation/construction.v ./model/uni/
schedulability.v ./model/uni/schedule_of_task.v ./model/uni/response_time.v ./model/uni/schedule.v ./model/uni/basic/arrival_bounds.v ./model/uni/basic/busy_interval.v ./model/uni/basic/platform.v ./model/uni/service.v ./implementation/arrival_sequence.v ./implementation/task.v ./implementation/global/jitter/arrival_sequence.v ./implementation/global/jitter/task.v ./implementation/global/jitter/bertogna_edf_example.v ./implementation/global/jitter/job.v ./implementation/global/jitter/bertogna_fp_example.v ./implementation/global/jitter/schedule.v ./implementation/global/parallel/bertogna_edf_example.v ./implementation/global/parallel/bertogna_fp_example.v ./implementation/global/basic/bertogna_edf_example.v ./implementation/global/basic/bertogna_fp_example.v ./implementation/global/basic/schedule.v ./implementation/job.v ./implementation/apa/arrival_sequence.v ./implementation/apa/task.v ./implementation/apa/bertogna_edf_example.v ./implementation/apa/job.v ./implementation/apa/bertogna_fp_example.v ./implementation/apa/schedule.v ./implementation/uni/basic/fp_rta_example.v ./implementation/uni/basic/schedule.v -o Makefile
#
.DEFAULT_GOAL
:=
all
...
...
@@ -176,6 +176,7 @@ VFILES:=util/ssromega.v\
model/apa/constrained_deadlines.v
\
model/apa/platform.v
\
model/uni/workload.v
\
model/uni/transformation/construction.v
\
model/uni/schedulability.v
\
model/uni/schedule_of_task.v
\
model/uni/response_time.v
\
...
...
model/uni/transformation/construction.v
0 → 100644
View file @
8c68c87a
Require
Import
rt
.
util
.
all
.
Require
Import
rt
.
model
.
job
rt
.
model
.
arrival_sequence
.
Require
Import
rt
.
model
.
uni
.
schedule
.
From
mathcomp
Require
Import
ssreflect
ssrbool
ssrfun
eqtype
ssrnat
fintype
bigop
seq
path
finfun
.
Module
ScheduleConstruction
.
Import
Job
ArrivalSequence
UniprocessorSchedule
.
(* In this section, we construct a schedule recursively by augmenting prefixes. *)
Section
ConstructionFromPrefixes
.
Context
{
Job
:
eqType
}.
(* Let arr_seq be any arrival sequence.*)
Variable
arr_seq
:
arrival_sequence
Job
.
(* Assume we are given a function that takes an existing schedule prefix
up to interval [0, t) and returns what should be scheduled at time t. *)
Variable
build_schedule
:
schedule
arr_seq
->
time
->
option
(
JobIn
arr_seq
).
(* Then, starting from the empty schedule as a base, ... *)
Definition
empty_schedule
:
schedule
arr_seq
:
=
fun
t
=>
None
.
(* ...we can update individual times using the build_schedule function, ... *)
Definition
update_schedule
(
prev_sched
:
schedule
arr_seq
)
(
t_next
:
time
)
:
schedule
arr_seq
:
=
fun
t
=>
if
t
==
t_next
then
build_schedule
prev_sched
t
else
prev_sched
t
.
(* ...which recursively generates schedule prefixes up to time t_max. *)
Fixpoint
schedule_prefix
(
t_max
:
time
)
:
schedule
arr_seq
:
=
if
t_max
is
t_prev
.+
1
then
update_schedule
(
schedule_prefix
t_prev
)
t_prev
.+
1
else
update_schedule
empty_schedule
0
.
(* Based on the schedule prefixes, we construct a complete schedule. *)
Definition
build_schedule_from_prefixes
:
=
fun
t
=>
schedule_prefix
t
t
.
(* In this section, we prove some lemmas about the construction. *)
Section
Lemmas
.
(* Let sched be the generated schedule. *)
Let
sched
:
=
build_schedule_from_prefixes
.
(* First, we show that the scheduler preserves its prefixes. *)
Lemma
prefix_construction_same_prefix
:
forall
t
t_max
,
t
<=
t_max
->
schedule_prefix
t_max
t
=
sched
t
.
Proof
.
intros
t
t_max
LEt
.
induction
t_max
;
first
by
rewrite
leqn0
in
LEt
;
move
:
LEt
=>
/
eqP
EQ
;
subst
.
rewrite
leq_eqVlt
in
LEt
.
move
:
LEt
=>
/
orP
[/
eqP
EQ
|
LESS
]
;
first
by
subst
.
{
feed
IHt_max
;
first
by
done
.
unfold
schedule_prefix
,
update_schedule
at
1
.
assert
(
FALSE
:
t
==
t_max
.+
1
=
false
).
{
by
apply
negbTE
;
rewrite
neq_ltn
LESS
orTb
.
}
rewrite
FALSE
.
by
rewrite
-
IHt_max
.
}
Qed
.
(* If the generation function only depends on the service
received by jobs during the schedule prefix, ...*)
Hypothesis
H_depends_only_on_service
:
forall
sched1
sched2
t
,
(
forall
j
,
service
sched1
j
t
=
service
sched2
j
t
)
->
build_schedule
sched1
t
=
build_schedule
sched2
t
.
(* ...then we can prove that the final schedule, at any time t,
is exactly the result of the construction function. *)
Lemma
prefix_construction_uses_function
:
forall
t
,
sched
t
=
build_schedule
sched
t
.
Proof
.
intros
t
.
feed
(
prefix_construction_same_prefix
t
t
)
;
[
by
done
|
intros
EQ
].
rewrite
-{}
EQ
.
induction
t
as
[
t
IH
]
using
strong_ind
.
destruct
t
.
{
rewrite
/=
/
update_schedule
eq_refl
.
apply
H_depends_only_on_service
.
by
intros
j
;
rewrite
/
service
/
service_during
big_geq
//
big_geq
//.
}
{
rewrite
/=
/
update_schedule
eq_refl
.
apply
H_depends_only_on_service
.
intros
j
;
rewrite
/
service
/
service_during
.
rewrite
big_nat_recr
//=
big_nat_recr
//=
;
f_equal
.
apply
eq_big_nat
;
move
=>
i
/=
LT
.
rewrite
/
service_at
/
scheduled_at
.
by
rewrite
prefix_construction_same_prefix
;
last
by
apply
ltnW
.
}
Qed
.
End
Lemmas
.
End
ConstructionFromPrefixes
.
End
ScheduleConstruction
.
\ No newline at end of file
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