From 6a1dfeb365f91db6ce48b1b123c07d22cb7011ca Mon Sep 17 00:00:00 2001
From: Kimaya Bedarkar <kbedarka@mpi-sws.org>
Date: Wed, 19 Feb 2025 10:57:51 +0100
Subject: [PATCH] add proc state facts
---
analysis/facts/model/ideal_uni_exceed.v | 133 ++++++++++++++++++++++++
1 file changed, 133 insertions(+)
create mode 100644 analysis/facts/model/ideal_uni_exceed.v
diff --git a/analysis/facts/model/ideal_uni_exceed.v b/analysis/facts/model/ideal_uni_exceed.v
new file mode 100644
index 000000000..b30a00b3c
--- /dev/null
+++ b/analysis/facts/model/ideal_uni_exceed.v
@@ -0,0 +1,133 @@
+Require Import prosa.model.processor.ideal_uni_exceed.
+Require Export prosa.model.processor.platform_properties.
+
+(** In the following section, we prove some general properties about the
+ ideal uniprocessor with exceedance processor state. *)
+Section ExceedanceProcStateProperties.
+
+ (** In this section, we consider any type of jobs. *)
+ Context `{Job : JobType}.
+
+ (** First we prove that the processor state provides unit supply. *)
+ Lemma eps_is_unit_supply : unit_supply_proc_model (exceedance_proc_state Job).
+ Proof.
+ rewrite /unit_supply_proc_model.
+ move => s.
+ destruct s => //=.
+ all : by rewrite /supply_in //=;rewrite sum_unit1.
+ Qed.
+
+ (** The usually opaque predicates are made transparent for this section
+ to enable us to prove some processor properties. *)
+ Local Transparent scheduled_in scheduled_on service_on.
+
+ (** A job [j] is said to be [scheduled_at] some time [t] if and only if the
+ processor state at that time is [NominalExecution j] or
+ [ExceedanceExecution j]. *)
+ Lemma scheduled_at_procstate (sched : schedule (exceedance_proc_state Job)) j t:
+ scheduled_at sched j t <->
+ sched t = NominalExecution j \/ sched t = ExceedanceExecution j.
+ Proof.
+ split.
+ - move => SCHED.
+ rewrite /scheduled_at /scheduled_in in SCHED.
+ move : SCHED => /existsP [c SCHEDON].
+ unfold scheduled_on in SCHEDON.
+ simpl in SCHEDON.
+ unfold exceedance_scheduled_on in *.
+ destruct (sched t); try done.
+ + left.
+ by move : SCHEDON => /eqP <-.
+ + right.
+ by move : SCHEDON => /eqP <-.
+ - rewrite /scheduled_at.
+ move => [-> | -> ]; rewrite /scheduled_in /scheduled_on //=; by apply /existsP => //=.
+ Qed.
+
+
+ (** Next we prove that the processor model under consideration is a uniprocessor
+ model i.e., only one job can be scheduled at any time instant. *)
+ Lemma eps_is_uniproc : uniprocessor_model (exceedance_proc_state Job).
+ Proof.
+ rewrite /uniprocessor_model.
+ move => j1 j2 sched t SCHED1 SCHED2.
+ rewrite /scheduled_at /scheduled_in in SCHED1, SCHED2.
+ move : SCHED1 => /existsP [c SCHED1].
+ move : SCHED2 => /existsP [c' SCHED2].
+ rewrite /scheduled_on //= /exceedance_scheduled_on in SCHED1, SCHED2.
+ destruct (sched t) eqn: EQ; try done.
+ - move : SCHED1 => /eqP <-.
+ by move : SCHED2 => /eqP <-.
+ - move : SCHED1 => /eqP <-.
+ by move : SCHED2 => /eqP <-.
+ Qed.
+
+ (** Next, we prove that the processor model under consideration is fully
+ consuming i.e., all the supply offered is consumed by the scheduled job. *)
+ Lemma eps_is_fully_consuming :
+ fully_consuming_proc_model (exceedance_proc_state Job).
+ Proof.
+ rewrite /fully_consuming_proc_model.
+ move => j sched t SCHED1.
+ rewrite /scheduled_at /scheduled_in in SCHED1.
+ apply scheduled_at_procstate in SCHED1.
+ move : SCHED1 => [SCHED1 | SCHED1].
+ - by rewrite /service_at /service_in /exceedance_service_on /supply_at /supply_in
+ !/exceedance_service_on //= SCHED1 sum_unit1 // sum_unit1 //
+ /exceedance_service_on /exceedance_supply_on eq_refl.
+ - by rewrite /service_at /service_in /exceedance_service_on /supply_at /supply_in
+ !/exceedance_service_on //= SCHED1 sum_unit1 // sum_unit1 //
+ /exceedance_service_on /exceedance_supply_on eq_refl.
+ Qed.
+
+ (** Finally we prove that the processor model under consideration is unit
+ service i.e., it provides at most one unit of service at any time instant. *)
+ Lemma eps_is_unit_service : unit_service_proc_model (exceedance_proc_state Job).
+ Proof.
+ rewrite /unit_service_proc_model.
+ move => j pstate.
+ rewrite /service_in /service_on //= sum_unit1 /exceedance_service_on.
+ destruct pstate =>//=.
+ by apply leq_b1.
+ Qed.
+
+End ExceedanceProcStateProperties.
+
+(** Next, we prove some general properties specific to the
+ ideal uniprocessor with exceedance processor state. *)
+Section ExceedanceProcStateProperties1.
+
+ (** In this section we consider any type of jobs. *)
+ Context `{Job : JobType}.
+
+ (** First let us define the notion of exceedance execution. A processor state
+ is said to be an exceedance execution state if is equal to
+ [ExceedanceExecution j] for some [j]. *)
+ Definition is_exceedance_exec (pstate : (exceedance_proc_state Job)) :=
+ match pstate with
+ |ExceedanceExecution _ => true
+ |_ => false
+ end.
+ Local Transparent scheduled_in scheduled_on service_on.
+
+
+ (** Next, let us consider any schedule of the [exceedance_proc_state]. *)
+ Variable sched : schedule (exceedance_proc_state Job).
+
+ (** We prove that the schedule being in blackout at any time [t] is equivalent
+ to the processor state at [t] being an exceedance execution state. *)
+ Lemma blackout_implies_exceedance_execution t :
+ is_blackout sched t = is_exceedance_exec (sched t).
+ Proof.
+ rewrite /is_blackout /has_supply /supply_at /supply_in
+ /is_exceedance_exec //= sum_unit1 /exceedance_supply_on.
+ destruct (sched t) eqn : PSTATE; try done.
+ Qed.
+
+End ExceedanceProcStateProperties1.
+
+Global Hint Resolve
+ eps_is_uniproc
+ eps_is_unit_supply
+ eps_is_fully_consuming
+ : basic_rt_facts.
--
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