Library prosa.model.priority.numeric_fixed_priority

Numeric Fixed Task Priorities

We define the notion of arbitrary numeric fixed task priorities, i.e., tasks are prioritized in order of user-provided numeric priority values, where numerically smaller values indicate lower priorities (as for instance it is the case in Linux).
First, we define a new task parameter task_priority that maps each task to a numeric priority value.
Based on this parameter, we define the corresponding FP policy.
Instance NumericFP (Task : TaskType) `{TaskPriority Task} : FP_policy Task :=
  hep_task (tsk1 tsk2 : Task) := task_priority tsk1 task_priority tsk2

In this section, we prove a few basic properties of numeric fixed priorities.
Section Properties.

Consider any kind of tasks with specified priorities...
  Context {Task : TaskType}.
  Context `{TaskPriority Task}.

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

The resulting priority policy is reflexive.
  Lemma NFP_is_reflexive : reflexive_priorities.
  Proof. by move⇒ ?; rewrite /hep_job_at /JLFP_to_JLDP /hep_job /FP_to_JLFP /hep_task /NumericFP. Qed.

The resulting priority policy is transitive.
  Lemma NFP_is_transitive : transitive_priorities.
    movet y x z.
    rewrite /hep_job_at /JLFP_to_JLDP /hep_job /FP_to_JLFP /hep_task /NumericFP.
    by movePRIO_yx PRIO_zy; apply leq_trans with (n := task_priority (job_task y)).

The resulting priority policy is total.
  Lemma NFP_is_total : total_priorities.
  Proof. by movet j1 j2; apply leq_total. 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
  : basic_facts.