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PROSA - Formally Proven Schedulability Analysis
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Lasse Blaauwbroek
PROSA - Formally Proven Schedulability Analysis
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0c43c153
Commit
0c43c153
authored
5 years ago
by
Björn Brandenburg
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define notion of job progress / lack of progress
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restructuring/analysis/definitions/progress.v
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Require
Export
rt
.
restructuring
.
analysis
.
facts
.
behavior
.
service
.
(** * Job Progress (or Lack Thereof) *)
(** In the following section, we define a notion of "job progress", and
conversely a notion of a lack of progress. *)
Section
Progress
.
(** Consider any type of jobs with a known cost... *)
Context
{
Job
:
JobType
}
.
Context
`{
JobCost
Job
}
.
(** ... and any kind of schedule. *)
Context
{
PState
:
Type
}
.
Context
`{
ProcessorState
Job
PState
}
.
(** For a given job and a given schedule... *)
Variable
sched
:
schedule
PState
.
Variable
j
:
Job
.
Section
NotionsOfProgress
.
(** ...and two ordered points in time... *)
Variable
t1
t2
:
nat
.
Hypothesis
H_t1_before_t2
:
t1
<=
t2
.
(** ... we say that the job has progressed between the two points iff its
total received service has increased. *)
Definition
job_has_progressed
:=
service
sched
j
t1
<
service
sched
j
t2
.
(** Conversely, if the accumulated service does not change, there is no
progress. *)
Definition
no_progress
:=
service
sched
j
t1
==
service
sched
j
t2
.
(** We note that the negation of the former is equivalent to the latter
definition. *)
Lemma
no_progress_equiv
:
~~
job_has_progressed
<->
no_progress
.
Proof
.
rewrite
/
job_has_progressed
/
no_progress
.
split
.
{
rewrite
-
leqNgt
leq_eqVlt
=>
/
orP
[
EQ
|
LT
];
first
by
rewrite
eq_sym
.
exfalso
.
have
MONO
:
service
sched
j
t1
<=
service
sched
j
t2
by
apply
service_monotonic
.
have
NOT_MONO
:
~~
(
service
sched
j
t1
<=
service
sched
j
t2
)
by
apply
/
negPf
;
apply
ltn_geF
.
move
:
NOT_MONO
=>
/
negP
NOT_MONO
.
contradiction
.
}
{
move
=>
/
eqP
->
.
rewrite
-
leqNgt
.
by
apply
service_monotonic
.
}
Qed
.
End
NotionsOfProgress
.
(** For convenience, we define a lack of progress also in terms of given
reference point [t] and the length of the preceding interval of
inactivity [delta], meaning that no progress has been made for at least
[delta] time units. *)
Definition
no_progress_for
(
t
:
instant
)
(
delta
:
duration
)
:=
no_progress
(
t
-
delta
)
t
.
End
Progress
.
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