Library prosa.model.priority.numeric_fixed_priority

Numeric Fixed Task Priorities

We define the notion of arbitrary numeric fixed task priorities, i.e., tasks are prioritized in order of user-provided numeric priority values, where numerically smaller values indicate lower priorities (as for instance it is the case in Linux).
First, we define a new task parameter task_priority that maps each task to a numeric priority value.
Based on this parameter, we define the corresponding FP policy.
Instance NumericFP (Task : TaskType) `{TaskPriority Task} : FP_policy Task :=
{
  hep_task (tsk1 tsk2 : Task) := task_priority tsk1 task_priority tsk2
}.

In this section, we prove a few basic properties of numeric fixed priorities.
Section Properties.

Consider any kind of tasks with specified priorities...
  Context {Task : TaskType}.
  Context `{TaskPriority Task}.

...and jobs stemming from these tasks.
  Context {Job : JobType}.
  Context `{JobTask Job Task}.

The resulting priority policy is reflexive.
The resulting priority policy is transitive.
The resulting priority policy is total.
We add the above lemmas into a "Hint Database" basic_facts, so Coq will be able to apply them automatically.
Hint Resolve
     NFP_is_reflexive
     NFP_is_transitive
     NFP_is_total
  : basic_facts.