Library prosa.classic.model.schedule.uni.nonpreemptive.platform

Require Import prosa.classic.util.all.
Require Import prosa.classic.model.arrival.basic.task prosa.classic.model.arrival.basic.job prosa.classic.model.priority prosa.classic.model.arrival.basic.task_arrival.
Require Import prosa.classic.model.schedule.uni.schedule
               prosa.classic.model.schedule.uni.basic.platform.
Require Import prosa.classic.model.schedule.uni.nonpreemptive.schedule.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq fintype bigop.

Module NonpreemptivePlatform.

  Import Job SporadicTaskset UniprocessorSchedule Priority.

  Section Properties.

    Context {sporadic_task: eqType}.

    Context {Job: eqType}.
    Variable job_arrival: Job time.
    Variable job_cost: Job time.
    Variable job_task: Job sporadic_task.

    Variable arr_seq: arrival_sequence Job.

    Variable sched: schedule Job.

    Let job_completed_by := completed_by job_cost sched.
    Let job_scheduled_at := scheduled_at sched.

    Section PreemptionPoint.

      Definition is_preemption_point' (t: time) :=
        t = 0
         sched (t-1) = None
         j, scheduled_at sched j (t - 1) job_completed_by j t.

      Definition is_preemption_point (t: time) :=
        t = 0 j, job_scheduled_at j (t - 1) job_completed_by j t.

      Lemma defitions_of_preemption_point_are_equal:
         t, is_preemption_point t is_preemption_point' t.

    End PreemptionPoint.

    Section Execution.

      Definition work_conserving := Platform.work_conserving job_cost.

    End Execution.

    Section FP.

      Variable higher_eq_priority: FP_policy sporadic_task.

      Definition respects_FP_policy_at_preemption_point :=
         j j_hp t,
          arrives_in arr_seq j
          backlogged job_arrival job_cost sched j t
          scheduled_at sched j_hp t
          is_preemption_point t
          higher_eq_priority (job_task j_hp) (job_task j).

    End FP.

    Section JLFP.

      Variable higher_eq_priority: JLFP_policy Job.

      Definition respects_JLFP_policy_at_preemption_point :=
         j j_hp t,
          arrives_in arr_seq j
          backlogged job_arrival job_cost sched j t
          scheduled_at sched j_hp t
          is_preemption_point t
          higher_eq_priority j_hp j.

    End JLFP.

  End Properties.

End NonpreemptivePlatform.