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Sergey Bozhko
rt-proofs
Commits
45853287
Commit
45853287
authored
Jun 04, 2019
by
Maxime Lesourd
Committed by
Björn Brandenburg
Jun 05, 2019
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applied naming convention to behavior
parent
557ced9d
Changes
3
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3 changed files
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12 additions
and
12 deletions
+12
-12
restructuring/behavior/arrival/arrival_sequence.v
restructuring/behavior/arrival/arrival_sequence.v
+4
-4
restructuring/behavior/facts/arrivals.v
restructuring/behavior/facts/arrivals.v
+7
-7
restructuring/behavior/schedule/schedule.v
restructuring/behavior/schedule/schedule.v
+1
-1
No files found.
restructuring/behavior/arrival/arrival_sequence.v
View file @
45853287
...
...
@@ -51,18 +51,18 @@ Section ValidArrivalSequence.
(* We say that arrival times are consistent if any job that arrives in the
sequence has the corresponding arrival time. *)
Definition
arrival_times_are_consistent
:
=
Definition
consistent_arrival_times
:
=
forall
j
t
,
arrives_at
arr_seq
j
t
->
job_arrival
j
=
t
.
(* We say that the arrival sequence is a set iff it doesn't contain duplicate
jobs at any given time. *)
Definition
arrival_sequence_
is_a_set
:
=
forall
t
,
uniq
(
jobs_arriving_at
arr_seq
t
).
Definition
arrival_sequence_
uniq
:
=
forall
t
,
uniq
(
jobs_arriving_at
arr_seq
t
).
(* We say that the arrival sequence is valid iff it is a set and arrival times
are consistent *)
Definition
arrival_sequence_is_valid
:
=
arrival_times_are_consistent
/\
arrival_sequence_is_a_set
.
Definition
valid_arrival_sequence
:
=
consistent_arrival_times
/\
arrival_sequence_uniq
.
End
ValidArrivalSequence
.
...
...
restructuring/behavior/facts/arrivals.v
View file @
45853287
...
...
@@ -78,8 +78,8 @@ Section ArrivalSequencePrefix.
Section
ArrivalTimes
.
(* Assume that job arrival times are consistent. *)
Hypothesis
H_
arrival_times_are_consistent
:
arrival_times_are_consistent
arr_seq
.
Hypothesis
H_
consistent_arrival_times
:
consistent_arrival_times
arr_seq
.
(* First, we prove that if a job belongs to the prefix
(jobs_arrived_before t), then it arrives in the arrival sequence. *)
...
...
@@ -88,7 +88,7 @@ Section ArrivalSequencePrefix.
j
\
in
jobs_arrived_between
t1
t2
->
arrives_in
arr_seq
j
.
Proof
.
rename
H_
arrival_times_are_consistent
into
CONS
.
rename
H_
consistent_arrival_times
into
CONS
.
intros
j
t1
t2
IN
.
apply
mem_bigcat_nat_exists
in
IN
.
move
:
IN
=>
[
arr
[
IN
_
]].
...
...
@@ -103,7 +103,7 @@ Section ArrivalSequencePrefix.
j
\
in
jobs_arrived_between
t1
t2
->
arrived_between
j
t1
t2
.
Proof
.
rename
H_
arrival_times_are_consistent
into
CONS
.
rename
H_
consistent_arrival_times
into
CONS
.
intros
j
t1
t2
IN
.
apply
mem_bigcat_nat_exists
in
IN
.
move
:
IN
=>
[
t0
[
IN
/=
LT
]].
...
...
@@ -131,7 +131,7 @@ Section ArrivalSequencePrefix.
arrived_between
j
t1
t2
->
j
\
in
jobs_arrived_between
t1
t2
.
Proof
.
rename
H_
arrival_times_are_consistent
into
CONS
.
rename
H_
consistent_arrival_times
into
CONS
.
move
=>
j
t1
t2
[
a_j
ARRj
]
BEFORE
.
have
SAME
:
=
ARRj
;
apply
CONS
in
SAME
;
subst
a_j
.
by
apply
mem_bigcat_nat
with
(
j
:
=
(
job_arrival
j
)).
...
...
@@ -140,10 +140,10 @@ Section ArrivalSequencePrefix.
(* Next, we prove that if the arrival sequence doesn't contain duplicate
jobs, the same applies for any of its prefixes. *)
Lemma
arrivals_uniq
:
arrival_sequence_
is_a_set
arr_seq
->
arrival_sequence_
uniq
arr_seq
->
forall
t1
t2
,
uniq
(
jobs_arrived_between
t1
t2
).
Proof
.
rename
H_
arrival_times_are_consistent
into
CONS
.
rename
H_
consistent_arrival_times
into
CONS
.
unfold
jobs_arrived_up_to
;
intros
SET
t1
t2
.
apply
bigcat_nat_uniq
;
first
by
done
.
intros
x
t
t'
IN1
IN2
.
...
...
restructuring/behavior/schedule/schedule.v
View file @
45853287
...
...
@@ -85,7 +85,7 @@ Section Schedule.
(* We say that the schedule is valid iff
- jobs come from some arrival sequence
- a job can only be scheduled if it has arrived and is not completed yet *)
Definition
schedule_is_valid
(
arr_seq
:
arrival_sequence
Job
)
:
=
Definition
valid_schedule
(
arr_seq
:
arrival_sequence
Job
)
:
=
jobs_come_from_arrival_sequence
arr_seq
/\
jobs_must_arrive_to_execute
/\
completed_jobs_dont_execute
.
...
...
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