Library prosa.classic.implementation.uni.basic.fp_rta_example

Require Import prosa.classic.util.all.
Require Import prosa.classic.model.arrival.basic.job prosa.classic.model.arrival.basic.task prosa.classic.model.priority.
Require Import prosa.classic.model.schedule.uni.schedule prosa.classic.model.schedule.uni.schedulability.
Require Import prosa.classic.analysis.uni.basic.workload_bound_fp
               prosa.classic.analysis.uni.basic.fp_rta_comp.
Require Import prosa.classic.implementation.job prosa.classic.implementation.task
               prosa.classic.implementation.arrival_sequence.
Require Import prosa.classic.implementation.uni.basic.schedule.
From mathcomp Require Import ssreflect ssrbool ssrnat eqtype seq bigop div.

Module ResponseTimeAnalysisFP.

  Import Job UniprocessorSchedule SporadicTaskset Priority Schedulability
         WorkloadBoundFP ResponseTimeIterationFP.
  Import ConcreteJob ConcreteTask ConcreteArrivalSequence ConcreteScheduler.

  Section ExampleRTA.

    Let tsk1 := {| task_id := 1; task_cost := 1; task_period := 4; task_deadline := 5|}.
    Let tsk2 := {| task_id := 2; task_cost := 1; task_period := 6; task_deadline := 5|}.
    Let tsk3 := {| task_id := 3; task_cost := 1; task_period := 6; task_deadline := 6|}.

    Program Let ts := Build_set [:: tsk1; tsk2; tsk3] _.

    Fact ts_has_valid_parameters:
      valid_sporadic_taskset task_cost task_period task_deadline ts.

    Let RTA_claimed_bounds :=
      fp_claimed_bounds task_cost task_period task_deadline (RM task_period).
    Let schedulability_test :=
      fp_schedulable task_cost task_period task_deadline (RM task_period).

    Fact RTA_yields_these_bounds :
      RTA_claimed_bounds ts = Some [:: (tsk1, 1); (tsk2, 3); (tsk3, 3)].

    Fact schedulability_test_succeeds :
      schedulability_test ts = true.


    Let arr_seq := periodic_arrival_sequence ts.

    Let higher_eq_priority := FP_to_JLDP job_task (RM task_period).

    Fact priority_is_total:
      ∀ t, total (higher_eq_priority t).

    Let sched := scheduler job_arrival job_cost arr_seq higher_eq_priority.

    Let no_deadline_missed_by :=
      task_misses_no_deadline job_arrival job_cost job_deadline job_task arr_seq sched.

    Corollary ts_is_schedulable:
      ∀ tsk,
        tsk \in ts →
        no_deadline_missed_by tsk.

  End ExampleRTA.

End ResponseTimeAnalysisFP.