Library prosa.implementation.priority.fifo

Require Export prosa.model.priority.fifo.
Require Export prosa.analysis.facts.hyperperiod.

FIFO Priority Policy

We define a basic FIFO priority policy, under which jobs are prioritized in order of their arrival times. The FIFO policy belongs to the class of JLFP policies.

#[local] Instance FIFO (Job : JobType) `{JobArrival Job} : JLFP_policy Job :=
{
hep_job (j1 j2 : Job) := job_arrival j1 ≤ job_arrival j2
}.

In this section, we prove a few basic properties of the FIFO policy.

Section Properties.

Consider any type of jobs with arrival times.

Context {Job : JobType} `{JobArrival Job}.

Under the concrete FIFO implementation, hep_job is exactly arrival order.

  Fact FIFO_hep_job :
    ∀ j1 j2,
      @hep_job Job (FIFO Job) j1 j2 = (job_arrival j1 ≤ job_arrival j2 ).

FIFO is reflexive.

Fact FIFO_is_reflexive :
reflexive_job_priorities (FIFO Job).

FIFO is transitive.

Fact FIFO_is_transitive :
transitive_job_priorities (FIFO Job).

FIFO is total.

Fact FIFO_is_total :
total_job_priorities (FIFO Job).

The concrete FIFO implementation is indeed a FIFO policy.

Fact FIFO_is_FIFO_policy :
policy_is_FIFO (FIFO Job).

End Properties.

FIFO's arrival order repeats with a periodic workload.

Section FIFOHyperperiodPriorities.

Consider periodic tasks and their jobs.

Context {Task : TaskType} `{PeriodicModel Task}.
Context {Job : JobType} `{JobTask Job Task} `{JobArrival Job}.

Consider a task set with valid periods ...

Variable ts : TaskSet Task.
Hypothesis H_valid_periods : valid_periods ts.

... generating a valid arrival sequence of jobs of these tasks ...

  Variable arr_seq : arrival_sequence Job.
  Hypothesis H_valid_arrival_sequence : valid_arrival_sequence arr_seq.
  Hypothesis H_all_jobs_from_taskset : all_jobs_from_taskset arr_seq ts.

... with periodic releases continuing indefinitely.

Hypothesis H_periodic_arrivals : taskset_respects_periodic_task_model arr_seq ts.
Hypothesis H_infinite_jobs : tasks_have_infinite_arrivals arr_seq ts.

Shifting two jobs by one hyperperiod preserves their arrival order.

Fact FIFO_priorities_consistent_across_hyperperiods :
priorities_consistent_across_hyperperiods ts arr_seq (FIFO Job).

End FIFOHyperperiodPriorities.

We add the above lemmas into a "Hint Database" basic_rt_facts, so Rocq will be able to apply them automatically.

Global Hint Resolve
  FIFO_is_FIFO_policy
  FIFO_is_reflexive
  FIFO_is_transitive
  FIFO_is_total
  FIFO_priorities_consistent_across_hyperperiods
  : basic_rt_facts.