NB: This requires bumping up the "depth" parameter of `rt_auto` and `rt_eauto`.

As a benefit, it becomes possible to automatically use RBFs in the
context of periodic tasks, sporadic tasks, and tasks with arrival
curves. Full example:

```
Require Import prosa.model.task.arrival.periodic.
Require Import prosa.model.task.arrival.periodic_as_sporadic.
Require Import prosa.model.task.arrival.sporadic_as_curve.
Require Import prosa.model.task.arrival.curve_as_rbf.

Section AutoArrivalModelConversion.

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

  Variable ts : TaskSet Task.

  Variable arr_seq : arrival_sequence Job.
  Hypothesis H_consistent_arrivals: consistent_arrival_times arr_seq.
  Hypothesis H_uniq_arr_seq: arrival_sequence_uniq arr_seq.

  Hypothesis H_valid_periods : valid_periods ts.
  Hypothesis H_respects : taskset_respects_periodic_task_model arr_seq ts.

  Context `{JobCost Job} `{TaskCost Task}.
  Hypothesis H_valid_costs : jobs_have_valid_job_costs.

  (** Interpret as an RBF. *)

  Goal valid_taskset_request_bound_function ts (task_max_rbf max_arrivals).
  Proof. by rt_auto. Qed.

  Goal taskset_respects_max_request_bound arr_seq ts.
  Proof. rt_eauto. Qed.

End AutoArrivalModelConversion.
```

This commit makes it possible to transparently interpret periodic
tasks as sporadic tasks, and sporadic tasks as tasks with an arrival
curve, such that all proof obligations can satisfied by `rt_auto` and
`rt_eauto`. Full example:

```
Require Import prosa.model.task.arrival.periodic.
Require Import prosa.model.task.arrival.periodic_as_sporadic.
Require Import prosa.model.task.arrival.sporadic_as_curve.

Section AutoArrivalModelConversion.

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

  Variable ts : TaskSet Task.

  Variable arr_seq : arrival_sequence Job.
  Hypothesis H_consistent_arrivals: consistent_arrival_times arr_seq.
  Hypothesis H_uniq_arr_seq: arrival_sequence_uniq arr_seq.

  Hypothesis H_valid_periods : valid_periods ts.

  Hypothesis H_respects : taskset_respects_periodic_task_model arr_seq ts.

  (** 1. Interpret as sporadic: *)
  Goal valid_taskset_inter_arrival_times ts.
  Proof. by rt_auto. Qed.

  Goal taskset_respects_sporadic_task_model ts arr_seq.
  Proof. by rt_auto. Qed.

  (** 2. Interpret as an arrival curve. *)
  Goal valid_taskset_arrival_curve ts max_arrivals.
  Proof. by rt_auto. Qed.

  Goal taskset_respects_max_arrivals arr_seq ts.
  Proof. by rt_eauto. Qed.

End AutoArrivalModelConversion.

```

- move all to `prosa.model.task.arrival`
- unify names to `${FOO}_as_${BAR}.v`

Arguments about sporadic tasks do not reason about offsets as future
arrival times are unknown.

Marco Maida authored 2 years ago and Björn Brandenburg committed 2 years ago

- Slightly change `valid_nonpreemptive_readiness` so that `sched` is a
  parameter. This way, the proposition can be assumed to hold only for a
  certain schedule (making weaker assumptions).

- Modify `prev_job_nonpreemptive, to unconditionally get
  `jobs_must_be_ready_to_execute`.
  
- Revise lemmas accordingly. 

Kimaya Bedarkar authored 3 years ago and Björn Brandenburg committed 3 years ago

From a spec readability PoV, it's unfortunate that the policy that is
being respected doesn't show up in the code. The subject of definitions
should show up as an explicit argument, even if it is implicit
everywhere else. This is however difficult to realize for the current
`respects_policy_at_preemption_time` predicate due to difficulties with
coercion technicalities (see further details below).

Therefore, instead of `respects_policy_at_preemption_time`, we now have:

* `respects_JLDP_policy_at_preemption_point`
* `respects_JLFP_policy_at_preemption_point`
* `respects_FP_policy_at_preemption_point`

Further details: RT-PROOFS/rt-proofs!188 (comment 78569)

Closes: #82

Pierre Roux authored 3 years ago and Björn Brandenburg committed 3 years ago

This ensures all hypotheses in behavior have corresponding trivial lemmas
in `analysis.facts.all` that enable to exploit them, which makes them 
easier to discover with `Search`.

This also makes the code more robust to potential changes in the precise way
these hypotheses are stated.

Sergey Bozhko authored 3 years ago and Björn Brandenburg committed 3 years ago

This commit renames scope [basic_facts] into [basic_rt_facts] to
highlight the that lemmas collected in the scope are real-time (rt)
theory lemmas.

These new tactics are just shorthand for [(e)auto with basic_rt_facts].

Deprecation only works for notations, it is a noop on definitions.
There is now a warning in Coq, https://github.com/coq/coq/pull/15760
to avoid this in future releases.

Pierre Roux authored 3 years ago and Björn Brandenburg committed 3 years ago

...and many other proofs:

- Simplify proof of conversion_preserves_equivalence
- Simplify proofs in analysis/facts/behavior/service.v
- Simplify proofs in analysis/facts/behavior/deadlines.v
- Simplify proofs in analysis/facts/behavior/arrivals.v
- Fix order of arguments in identical_prefix_inclusion
- Simplify proofs in analysis/facts/behavior/completion.v