Commit d574638e authored by Felipe Cerqueira's avatar Felipe Cerqueira
Browse files

Add lemma about pending job + comments

parent 8e5fabfe
......@@ -117,8 +117,8 @@ Module Schedule.
End ValidSchedules.
(* In this section, we prove some basic lemmas about service. *)
Section ServiceLemmas.
(* In this section, we prove some basic lemmas about a job. *)
Section JobLemmas.
(* Consider an arrival sequence, ...*)
Context {Job: eqType}.
......@@ -333,7 +333,41 @@ Module Schedule.
End Arrival.
End ServiceLemmas.
Section Pending.
(* Assume that jobs must arrive to execute. *)
Hypothesis H_jobs_must_arrive:
jobs_must_arrive_to_execute sched.
(* Assume that completed jobs do not execute. *)
Hypothesis H_completed_jobs:
completed_jobs_dont_execute job_cost sched.
(* Then, if job j is scheduled, it must be pending. *)
Lemma scheduled_implies_pending:
forall t,
scheduled sched j t ->
pending job_cost sched j t.
rename H_jobs_must_arrive into ARRIVE,
H_completed_jobs into COMP.
unfold jobs_must_arrive_to_execute, completed_jobs_dont_execute in *.
intros t SCHED.
unfold pending; apply/andP; split; first by apply ARRIVE.
apply/negP; unfold not; intro COMPLETED.
have BUG := COMP j t.+1.
rewrite leqNgt in BUG; move: BUG => /negP BUG; apply BUG.
unfold service; rewrite -addn1 big_nat_recr // /=.
apply leq_add;
first by move: COMPLETED => /eqP COMPLETED; rewrite -COMPLETED.
rewrite lt0n; apply/eqP; red; move => /eqP NOSERV.
rewrite -not_scheduled_no_service in NOSERV.
by rewrite SCHED in NOSERV.
End Pending.
End JobLemmas.
(* In this section, we prove some lemmas about the list of jobs
scheduled at time t. *)
......@@ -347,6 +381,7 @@ Module Schedule.
Context {num_cpus: nat}.
Variable sched: schedule num_cpus arr_seq.
(* A job is in the list of scheduled jobs iff it is scheduled. *)
Lemma mem_scheduled_jobs_eq_scheduled :
forall j t,
j \in jobs_scheduled_at sched t = scheduled sched j t.
......@@ -369,9 +404,11 @@ Module Schedule.
Section Uniqueness.
(* Suppose there's no job parallelism. *)
Hypothesis H_no_parallelism :
jobs_dont_execute_in_parallel sched.
(* Then, the list of jobs scheduled at any time t has no duplicates. *)
Lemma scheduled_jobs_uniq :
forall t,
uniq (jobs_scheduled_at sched t).
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