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PROSA - Formally Proven Schedulability Analysis
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RT-PROOFS
PROSA - Formally Proven Schedulability Analysis
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fe812c5c
Commit
fe812c5c
authored
2 years ago
by
Pierre Roux
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Draft: Initiate a Prosa Tutorial
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fe812c5c
...
...
@@ -351,7 +351,7 @@ only serves a documentation purpose) in which one can
add variables
|*)
(** Given any job type with decidable equality, ... *)
Variable
Job
:
JobType
.
Variable
Job
:
JobType
.
(*|
which can be used in further definitions in the section
|*)
...
...
@@ -390,8 +390,8 @@ are available
Section
JobProperties
.
(** Consider any job arrival sequence. *)
Context
{
Job
:
JobType
}
.
Variable
arr_seq
:
arrival_sequence
Job
.
Context
{
Job
:
JobType
}
.
Variable
arr_seq
:
arrival_sequence
Job
.
(** First, we define the sequence of jobs arriving at time t. *)
Definition
arrivals_at
(
t
:
instant
)
:=
arr_seq
t
.
...
...
@@ -417,11 +417,11 @@ with such a function. This is expressed by the following definitions:
Section
ValidArrivalSequence
.
(** Assume that job arrival times are known. *)
Context
{
Job
:
JobType
}
.
Context
{
Job
:
JobType
}
.
Context
`{
JobArrival
Job
}
.
(** Consider any job arrival sequence. *)
Variable
arr_seq
:
arrival_sequence
Job
.
Variable
arr_seq
:
arrival_sequence
Job
.
(** We say that arrival times are consistent if any job that arrives
in the sequence has the corresponding arrival time. *)
...
...
@@ -447,11 +447,11 @@ about individual jobs.
Section
ArrivalTimeProperties
.
(** Assume that job arrival times are known. *)
Context
{
Job
:
JobType
}
.
Context
{
Job
:
JobType
}
.
Context
`{
JobArrival
Job
}
.
(** Let j be any job. *)
Variable
j
:
Job
.
Variable
j
:
Job
.
(** We say that job j has arrived at time t iff it arrives
at some time t_0 with t_0 <= t. *)
...
...
@@ -474,11 +474,11 @@ jobs arriving in some time interval.
Section
ArrivalSequencePrefix
.
(** Assume that job arrival times are known. *)
Context
{
Job
:
JobType
}
.
Context
{
Job
:
JobType
}
.
Context
`{
JobArrival
Job
}
.
(** Consider any job arrival sequence. *)
Variable
arr_seq
:
arrival_sequence
Job
.
Variable
arr_seq
:
arrival_sequence
Job
.
(** By concatenation, we construct the list of jobs that arrived
in the interval <<[t1, t2)>>. *)
...
...
@@ -954,10 +954,10 @@ Section Monotonicity.
Context
{
Job
:
JobType
}
{
PState
:
ProcessorState
Job
}
.
(** Consider any given schedule... *)
Variable
sched
:
schedule
PState
.
Variable
sched
:
schedule
PState
.
(** ...and a given job that is to be scheduled. *)
Variable
j
:
Job
.
Variable
j
:
Job
.
(** We observe that the amount of service received
is monotonic by definition. *)
...
...
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