update task and job models in preparation of aRTA port

Also removes an unnecessary module in rt.util.epsilon.

model/schedule/uni/limited/abstract_RTA/abstract_rta.v

@@ -15,8 +15,8 @@ From mathcomp Require Import ssreflect ssrbool eqtype ssrnat seq path fintype bi
     of uniprocessor scheduling of real-time tasks with arbitrary arrival models. *)
 Module AbstractRTA. 
 
-  Import Job Epsilon UniprocessorSchedule Service ResponseTime 
-         AbstractRTADefinitions AbstractRTALockInService AbstractRTAReduction. 
+  Import Job UniprocessorSchedule Service ResponseTime  AbstractRTADefinitions
+         AbstractRTALockInService AbstractRTAReduction. 
 
   (* In this section we prove that the maximum among the solutions of the response-time bound 
      recurrence is a response time bound for tsk. Note that in this section we do not rely on 

model/schedule/uni/limited/abstract_RTA/abstract_seq_rta.v

@@ -23,7 +23,7 @@ From mathcomp Require Import ssreflect ssrbool eqtype ssrnat seq path fintype bi
     and sequential jobs. *)
 Module AbstractSeqRTA. 
 
-  Import Job Epsilon ArrivalCurves TaskArrival ScheduleOfTask UniprocessorSchedule Workload
+  Import Job ArrivalCurves TaskArrival ScheduleOfTask UniprocessorSchedule Workload
          Service ResponseTime MaxArrivalsWorkloadBound 
          AbstractRTADefinitions AbstractRTALockInService AbstractRTAReduction AbstractRTA. 
 

model/schedule/uni/limited/abstract_RTA/definitions.v

@@ -9,7 +9,7 @@ From mathcomp Require Import ssreflect ssrbool eqtype ssrnat seq path fintype bi
     of uniprocessor scheduling of real-time tasks with arbitrary arrival models. *)
 Module AbstractRTADefinitions. 
 
-  Import Job Epsilon UniprocessorSchedule.
+  Import Job UniprocessorSchedule.
 
   (* In this section, we introduce all the abstract notions required by the analysis. *)
   Section Definitions.

model/schedule/uni/limited/abstract_RTA/reduction_of_search_space.v

@@ -10,7 +10,7 @@ From mathcomp Require Import ssreflect ssrbool eqtype ssrnat seq path fintype bi
    
 Module AbstractRTAReduction. 
 
-  Import Epsilon UniprocessorSchedule.
+  Import UniprocessorSchedule.
 
   (* The response-time analysis we are presenting in this series of documents is based on searching 
      over all possible values of A, the relative arrival time of the job respective to the beginning 

model/schedule/uni/limited/abstract_RTA/sufficient_condition_for_lock_in_service.v

@@ -12,7 +12,7 @@ From mathcomp Require Import ssreflect ssrbool eqtype ssrnat seq path fintype bi
     receives enough service to become nonpreemptive. *)
 Module AbstractRTALockInService. 
 
-  Import Job Epsilon UniprocessorSchedule Service  AbstractRTADefinitions.
+  Import Job UniprocessorSchedule Service  AbstractRTADefinitions.
 
   (* Previously we defined the notion of lock-in service (see limited.schedule.v file). 
      Lock-in service is the amount of service after which a job cannot be preempted until 

model/schedule/uni/limited/edf/nonpr_reg/concrete_models/response_time_bound.v

@@ -25,7 +25,7 @@ From mathcomp Require Import ssreflect ssrbool eqtype ssrnat seq path fintype bi
     (4) EDF with floating nonpreemptive regions. *)
 Module RTAforConcreteModels.
 
-  Import Epsilon Job ArrivalCurves TaskArrival Priority UniprocessorSchedule Workload Service
+  Import Job ArrivalCurves TaskArrival Priority UniprocessorSchedule Workload Service
          ResponseTime MaxArrivalsWorkloadBound LimitedPreemptionPlatform ModelWithLimitedPreemptions
          RTAforEDFwithBoundedNonpreemptiveSegmentsWithArrivalCurves NonpreemptiveSchedule
          FullyNonPreemptivePlatform FullyPreemptivePlatform AbstractRTAforEDFwithArrivalCurves.

model/schedule/uni/limited/edf/nonpr_reg/response_time_bound.v

@@ -21,7 +21,7 @@ From mathcomp Require Import ssreflect ssrbool eqtype ssrnat seq path fintype bi
 (** In this module we prove a general RTA theorem for EDF-schedulers. *)
 Module RTAforEDFwithBoundedNonpreemptiveSegmentsWithArrivalCurves.
 
-  Import Epsilon Job ArrivalCurves TaskArrival Priority  UniprocessorSchedule Workload Service
+  Import Job ArrivalCurves TaskArrival Priority  UniprocessorSchedule Workload Service
          ResponseTime MaxArrivalsWorkloadBound LimitedPreemptionPlatform RBF 
          AbstractRTAforEDFwithArrivalCurves BusyIntervalJLFP PriorityInversionIsBounded. 
 

model/schedule/uni/limited/edf/response_time_bound.v

@@ -24,7 +24,7 @@ From mathcomp Require Import ssreflect ssrbool eqtype ssrnat seq path fintype bi
     EDF uniprocessor scheduling of real-time tasks with arbitrary arrival models.  *)
 Module AbstractRTAforEDFwithArrivalCurves.
   
-  Import Job Epsilon ArrivalCurves TaskArrival ScheduleOfTask Priority
+  Import Job ArrivalCurves TaskArrival ScheduleOfTask Priority
          UniprocessorSchedule Workload Service ResponseTime MaxArrivalsWorkloadBound
          BusyIntervalJLFP LimitedPreemptionPlatform RBF Service JLFPInstantiation.
  

model/schedule/uni/limited/fixed_priority/nonpr_reg/concrete_models/response_time_bound.v

@@ -24,7 +24,7 @@ From mathcomp Require Import ssreflect ssrbool eqtype ssrnat seq path fintype bi
     (4) FP with floating nonpreemptive regions. *)
 Module RTAforConcreteModels.
 
-  Import Epsilon Job ArrivalCurves TaskArrival Priority UniprocessorSchedule Workload Service
+  Import Job ArrivalCurves TaskArrival Priority UniprocessorSchedule Workload Service
          ResponseTime MaxArrivalsWorkloadBound LimitedPreemptionPlatform ModelWithLimitedPreemptions
          RTAforFPwithBoundedNonpreemptiveSegmentsWithArrivalCurves NonpreemptiveSchedule
          FullyNonPreemptivePlatform FullyPreemptivePlatform.

model/schedule/uni/limited/fixed_priority/nonpr_reg/response_time_bound.v

@@ -21,7 +21,7 @@ From mathcomp Require Import ssreflect ssrbool eqtype ssrnat seq path fintype bi
 (** In this module we prove a general RTA theorem for FP-schedulers *)
 Module RTAforFPwithBoundedNonpreemptiveSegmentsWithArrivalCurves.
 
-  Import Epsilon Job ArrivalCurves TaskArrival Priority  UniprocessorSchedule Workload Service
+  Import Job ArrivalCurves TaskArrival Priority  UniprocessorSchedule Workload Service
          ResponseTime MaxArrivalsWorkloadBound LimitedPreemptionPlatform RBF
          AbstractRTAforFPwithArrivalCurves BusyIntervalJLFP PriorityInversionIsBounded. 
 

model/schedule/uni/limited/fixed_priority/response_time_bound.v

@@ -25,7 +25,7 @@ From mathcomp Require Import ssreflect ssrbool eqtype ssrnat seq path fintype bi
     FP uniprocessor scheduling of real-time tasks with arbitrary arrival models.  *)
 Module AbstractRTAforFPwithArrivalCurves.
    
-  Import Epsilon Job ArrivalCurves TaskArrival Priority ScheduleOfTask
+  Import Job ArrivalCurves TaskArrival Priority ScheduleOfTask
          UniprocessorSchedule Workload Service ResponseTime MaxArrivalsWorkloadBound
          LimitedPreemptionPlatform RBF BusyIntervalJLFP JLFPInstantiation.
   

model/schedule/uni/limited/platform/definitions.v

@@ -16,7 +16,7 @@ From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq fintype
    predicate for various preemption models. *)
 Module LimitedPreemptionPlatform.
 
-  Import Epsilon Job SporadicTaskset UniprocessorSchedule Priority Service.
+  Import Job SporadicTaskset UniprocessorSchedule Priority Service.
   
   (* In this section, we define a processor platform with limited preemptions. *)
   Section Properties.

model/schedule/uni/limited/platform/limited.v

@@ -13,7 +13,7 @@ From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq fintype
     model with floating nonpreemptive regions. *)
 Module ModelWithLimitedPreemptions.
 
-  Import Epsilon Job NondecreasingSequence UniprocessorSchedule LimitedPreemptionPlatform.
+  Import Job NondecreasingSequence UniprocessorSchedule LimitedPreemptionPlatform.
 
   (* In this section, we instantiate can_be_preempted for the model with fixed preemption points and
      the model with floating nonpreemptive regions. We also prove that the definitions are correct. *)

model/schedule/uni/limited/platform/nonpreemptive.v

@@ -17,7 +17,7 @@ From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq fintype
    can_be_preempted for the fully nonpreemptive model and prove its correctness. *)
 Module FullyNonPreemptivePlatform.
 
-  Import Epsilon Job SporadicTaskset UniprocessorSchedule Priority
+  Import Job SporadicTaskset UniprocessorSchedule Priority
          Service LimitedPreemptionPlatform.
   
   Section FullyNonPreemptiveModel.

model/schedule/uni/limited/platform/preemptive.v

@@ -16,7 +16,7 @@ From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq fintype
    can_be_preempted for the fully preemptive model and prove its correctness. *)
 Module FullyPreemptivePlatform.
 
-  Import Epsilon Job SporadicTaskset UniprocessorSchedule Priority
+  Import Job SporadicTaskset UniprocessorSchedule Priority
          Service LimitedPreemptionPlatform.
   
   Section FullyPreemptiveModel.

model/schedule/uni/limited/platform/priority_inversion_is_bounded.v

@@ -15,7 +15,7 @@ From mathcomp Require Import ssreflect ssrbool eqtype ssrnat seq path fintype bi
     is bounded. *)
 Module PriorityInversionIsBounded.
 
-  Import Epsilon Job Priority UniprocessorSchedule LimitedPreemptionPlatform BusyIntervalJLFP. 
+  Import Job Priority UniprocessorSchedule LimitedPreemptionPlatform BusyIntervalJLFP. 
 
   Section PriorityInversionIsBounded.
 

model/schedule/uni/limited/schedule.v

@@ -7,7 +7,7 @@ From mathcomp Require Import ssreflect ssrbool eqtype ssrnat seq fintype bigop.
 
 (* In this file, we provide additional definitions and 
    lemmas about lock-in-serivce-compliant schedules. *)
-  Import Job Epsilon Service UniprocessorSchedule.
+  Import Job Service UniprocessorSchedule.
 
   Section Definitions.
 

restructuring/behavior/job.v

 From rt.restructuring.behavior Require Export time.
-From mathcomp Require Export eqtype.
+From mathcomp Require Export eqtype ssrnat.
 
 (* Throughout the library we assume that jobs have decidable equality *)
-
 Definition JobType := eqType.
 
 (* Definition of a generic type of parameter relating jobs to a discrete cost *)
-
 Class JobCost (J : JobType) := job_cost : J -> duration.
 
 (* Definition of a generic type of parameter for job_arrival *)
-
 Class JobArrival (J : JobType) := job_arrival : J -> instant.
 
 (* Definition of a generic type of parameter relating jobs to an absolute deadline *)
 Class JobDeadline (J : JobType) := job_deadline : J -> instant.
 
 (* Definition of a generic type of release jitter parameter. *)
-Class JobJitter (J : JobType) := job_jitter : J -> duration.
-
+Class JobJitter (J : JobType) := job_jitter : J -> duration.
\ No newline at end of file

restructuring/model/job.v

+From rt.restructuring.behavior Require Export time job.
+From mathcomp Require Export eqtype ssrnat.
+
+(* In this section, we introduce properties of a job. *)
+Section PropertesOfJob.
+
+  (* Assume that job costs are known. *)
+  Context {Job : JobType}.
+  Context `{JobCost Job}.
+
+  (* Consider an arbitrary job. *)
+  Variable j: Job.
+
+  (* The job cost must be positive. *)
+  Definition job_cost_positive := job_cost j > 0.
+
+End PropertesOfJob.
\ No newline at end of file

restructuring/model/schedule/priority_based/preemptive.v

@@ -25,4 +25,5 @@ Section Priority.
       backlogged sched j t ->
       scheduled_at sched j_hp t ->
       hep_job_at t j_hp j.
+  
 End Priority.