Library prosa.analysis.facts.readiness.basic

Require Export prosa.model.readiness.basic.
Require Export prosa.analysis.facts.behavior.completion.
Require Export prosa.analysis.definitions.readiness.

Section LiuAndLaylandReadiness.

Consider any kind of jobs ...
  Context {Job : JobType}.

... and any kind of processor state.
  Context {PState : ProcessorState Job}.

Suppose jobs have an arrival time and a cost.
  Context `{JobArrival Job} `{JobCost Job}.

Assume a basic (i.e., Liu & Layland) readiness model under which any pending job is ready.
  Context {RM : JobReady Job PState}.
  Hypothesis H_basic_readiness : basic_readiness RM.

The Liu & Layland readiness model is trivially non-clairvoyant.
  Fact basic_readiness_nonclairvoyance :
    nonclairvoyant_readiness RM.

Consider any job arrival sequence ...
  Variable arr_seq : arrival_sequence Job.

... and any schedule of these jobs.
  Variable sched : schedule PState.

In the basic Liu & Layland model, a schedule satisfies that only ready jobs execute as long as jobs must arrive to execute and completed jobs don't execute, which we note with the following theorem.
  Lemma basic_readiness_compliance :
    jobs_must_arrive_to_execute sched →
    completed_jobs_dont_execute sched →
    jobs_must_be_ready_to_execute sched.

Consider a JLFP policy that indicates a reflexive higher-or-equal priority relation.
  Context {JLFP : JLFP_policy Job}.
  Hypothesis H_priority_is_reflexive : reflexive_job_priorities JLFP.

We show that the basic readiness model is a work-bearing readiness model. That is, at any time instant t, if a job j is pending, then there exists a job (namely j itself) with higher-or-equal priority that is ready at time t.
  Fact basic_readiness_is_work_bearing_readiness :
    work_bearing_readiness RM arr_seq sched.

End LiuAndLaylandReadiness.

We add the above lemma into a "Hint Database" basic_rt_facts, so Coq will be able to apply it automatically.
Global Hint Resolve basic_readiness_is_work_bearing_readiness : basic_rt_facts.