Library prosa.model.processor.spin

From mathcomp Require Import all_ssreflect.
Require Export prosa.behavior.all.

In the following, we define a processor state that includes the possibility of spinning, where spinning jobs do not progress (= don't get any service).

NB: For now, the definition serves only to document how this can be done; it is not actually used anywhere in the library.

Section State.

Consider any type of jobs.

Variable Job: JobType.

We define the state of a processor at a given time to be one of three possible cases: either a specific job is scheduled and makes progress Progress j, a specific job is scheduled but makes not useful progress Spin j, or the processor is idle Idle.

  Inductive processor_state :=
    Idle
  | Spin (j : Job)
  | Progress (j : Job).

Next, we define the semantics of the processor state with spinning.

Section Service.

Let j denote any job.

Variable j : Job.

It is scheduled in a given state s iff the state is not idle and j is the job mentioned in the state.

    Definition spin_scheduled_on (s : processor_state) (_ : unit) : bool :=
      match s with
      | Idle ⇒ false
      | Spin j' ⇒ j' == j
      | Progress j' ⇒ j' == j
      end.

In contrast, job j receives service only if the given state s is Progress j.

    Definition spin_service_on (s : processor_state) (_ : unit) : work :=
      match s with
      | Idle ⇒ 0
      | Spin j' ⇒ 0
      | Progress j' ⇒ j' == j
      end.

  End Service.

Finally, we connect the above definitions with the generic Prosa interface for abstract processor states.

  Program Definition pstate_instance : ProcessorState Job :=
    {|
      State := processor_state;
      scheduled_on := spin_scheduled_on;
      service_on := spin_service_on
    |}.
  Next Obligation.
    move: r H.
    case: s=>//= j' _.
    rewrite /nat_of_bool.
    by case: ifP.
  Qed.
End State.