Library prosa.implementation.refinements.FP.preemptive_sched

Require Export prosa.analysis.facts.preemption.task.preemptive.
Require Export prosa.analysis.facts.preemption.rtc_threshold.preemptive.
Require Export prosa.analysis.facts.readiness.sequential.
Require Export prosa.analysis.definitions.tardiness.
Require Export prosa.implementation.facts.ideal_uni.prio_aware.
Require Export prosa.implementation.definitions.task.

Fully-Preemptive Fixed-Priority Schedules

In this section, we prove that the fully-preemptive preemption policy under fixed-priority schedules is valid, and that the scheduling policy is respected at each preemption point.

This file does not contain novel facts; it is used to uniform POET's certificates and minimize their verbosity.

Section Schedule.

In this file, we adopt the Prosa standard implementation of jobs and tasks.

Definition Task := [eqType of concrete_task ].
Definition Job := [eqType of concrete_job ].

Consider any arrival sequence with consistent arrivals, ...

Variable arr_seq : arrival_sequence Job.
Hypothesis H_arrival_times_are_consistent : consistent_arrival_times arr_seq.

... assume sequential readiness, ...

Instance sequential_ready_instance : JobReady Job (ideal.processor_state Job) :=
sequential_ready_instance arr_seq.

... and consider any fully-preemptive, fixed-priority schedule.

  #[local] Existing Instance fully_preemptive_job_model.
  #[local] Existing Instance NumericFPAscending.
  Definition sched := uni_schedule arr_seq.

First, we remark that such a schedule is valid.

  Remark sched_valid :
    valid_schedule sched arr_seq.
  Proof.
    apply uni_schedule_valid ⇒ //.
    by apply sequential_readiness_nonclairvoyance.
  Qed.

Finally, we show that the fixed-priority policy is respected at each preemption point.

  Lemma respects_policy_at_preemption_point :
    respects_FP_policy_at_preemption_point arr_seq sched (NumericFPAscending Task).
  Proof.
    apply schedule_respects_policy ⇒ //; rt_eauto.
    by apply sequential_readiness_nonclairvoyance.
  Qed.

End Schedule.