Library prosa.implementation.refinements.EDF.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.basic.
Require Export prosa.analysis.definitions.tardiness.
Require Export prosa.implementation.facts.ideal_uni.prio_aware.
Require Export prosa.implementation.definitions.task.
Require Export prosa.model.priority.edf.

Fully-Preemptive Earliest-Deadline-First Schedules

In this section, we prove that the fully-preemptive preemption policy under earliest-deadline-first 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 := concrete_task : eqType.
Definition Job := concrete_job : eqType.

Consider any valid arrival sequence, ...

Variable arr_seq : arrival_sequence Job.
Hypothesis H_valid_arrivals : valid_arrival_sequence arr_seq.

... assume basic readiness, ...

Instance basic_ready_instance : JobReady Job (ideal.processor_state Job) :=
basic.basic_ready_instance.

... and consider any fully-preemptive, earliest-deadline-first schedule.

  #[local] Existing Instance fully_preemptive_job_model.
  #[local] Existing Instance EDF.
  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 basic_readiness_nonclairvoyance.
  Qed.

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

  Lemma respects_policy_at_preemption_point_edf_fp :
    respects_JLFP_policy_at_preemption_point arr_seq sched (EDF Job).
  Proof.
    apply schedule_respects_policy ⇒ //; auto with basic_rt_facts.
    by apply basic_readiness_nonclairvoyance.
  Qed.

End Schedule.