Library prosa.model.priority.deadline_monotonic


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Welcome to Coq 8.11.2 (June 2020)

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Require Export prosa.model.priority.classes.

Deadline-Monotonic Fixed-Priority Policy

We define the notion of deadline-monotonic task priorities, i.e., the classic FP policy in which tasks are prioritized in order of their relative deadlines.
Instance DM (Task : TaskType) `{TaskDeadline Task} : FP_policy Task :=
{
  hep_task (tsk1 tsk2 : Task) := task_deadline tsk1 ≤ task_deadline tsk2
}.

In this section, we prove a few basic properties of the DM policy.
Section Properties.

Consider any kind of tasks with relative deadlines...
  Context {Task : TaskType}.
  Context `{TaskDeadline Task}.

...and jobs stemming from these tasks.
  Context {Job : JobType}.
  Context `{JobTask Job Task}.

DM is reflexive.
  Lemma DM_is_reflexive : reflexive_priorities.

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1 subgoal (ID 43)
  
  Task : TaskType
  H : TaskDeadline Task
  Job : JobType
  H0 : JobTask Job Task
  ============================
  reflexive_priorities

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  Proof. by move⇒ ?; rewrite /hep_job_at /JLFP_to_JLDP /hep_job /FP_to_JLFP /hep_task /DM.
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No more subgoals.

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Qed.

DM is transitive.
  Lemma DM_is_transitive : transitive_priorities.

(* ----------------------------------[ coqtop ]---------------------------------

1 subgoal (ID 51)
  
  Task : TaskType
  H : TaskDeadline Task
  Job : JobType
  H0 : JobTask Job Task
  ============================
  transitive_priorities

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  Proof. by intros t y x z; apply leq_trans.
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No more subgoals.

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Qed.

DM is total.
  Lemma DM_is_total : total_priorities.

(* ----------------------------------[ coqtop ]---------------------------------

1 subgoal (ID 59)
  
  Task : TaskType
  H : TaskDeadline Task
  Job : JobType
  H0 : JobTask Job Task
  ============================
  total_priorities

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 Proof. by move⇒ t j1 j2; apply leq_total.
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No more subgoals.

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Qed.

End Properties.

We add the above lemmas into a "Hint Database" basic_facts, so Coq will be able to apply them automatically.
Hint Resolve
     DM_is_reflexive
     DM_is_transitive
     DM_is_total
  : basic_facts.