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 := [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 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.