Library prosa.model.processor.varspeed

In the following, we define a model of processors with variable execution speeds.

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 variable-speed processor at a given time to be one of two possible cases: either a specific job is scheduled and progresses with a specific speed, or the processor is idle. Here, Idle k denotes a scenario where the processor could have generated k units of service, but there is no job being scheduled at that time instant.

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

Next, we define the semantics of the variable-speed processor state.

Section Service.

Consider any job j.

Variable j : Job.

Job j is scheduled in a given state s if s is not idle and j matches the job recorded in s.

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

The processor state Idle k indicates that the processor is ready to produce k units of supply; however, no job is scheduled. If the processor is in state Progress j k, it produces k unit of work at a given time instant.

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

If it is scheduled in state s, job j receives service proportional to the speed recorded in the state.

    Definition varspeed_service_on (s : processor_state) (_ : unit) : work :=
      match s with
      | Idle _ ⇒ 0
      | Progress j' speed ⇒ if j' == j then speed else 0
      end.

  End Service.

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

  Program Definition pstate_instance : ProcessorState Job :=
    {|
      State := processor_state;
      scheduled_on := varspeed_scheduled_on;
      supply_on := varspeed_supply_on;
      service_on := varspeed_service_on
    |}.
  Next Obligation. by move⇒ j [] //= s ; case: eqP. Qed.
  Next Obligation. by move⇒ j [] //= j' v _; case: ifP. Qed.

End State.