Getting Your Hands Dirty

B Training Course

Event-B Examples

Fuel Level

This example demonstrates how to specify a software and to implement it by using a modular architecture.

Measuring fuel level in a tank

We are considering to estimate the remaining amount of fuel in a tank. This information is critical for a plane, for example, because an error in the estimation might lead to a crash.

So we would like to develop a piece of software that would make the pilot aware of the situation (fuel level below a given capacity). This is in fact the main property of our software, independently from the way the fuel level is estimated.

As the sensors are likely to provide inaccurate / erroneous measures, the architecture of the system includes redundancy (2 ultrasonic level sensors, 3 flowmeters) and the estimation of the fuel left in the tank is performed in two steps:

- initial level in the tank is estimated with the 2 ultrasonic level sensors (minimum value of the two measures)
- each cycle, current level is estimated by substracting the maximum value given by the 3 flowmeters)

When the estimated level is less or equal to a given value, an alarm is raised.

β

With the B modelling, the objective is:

- estimating the remaining amount of fuel
- making the pilot aware of any fuel shortage

The resulting modelling contains 7 files:

- fuel0 is the top level specification of our software.
- fuel_i is its implementation, that requires services from measure and utils
- measure is a basic machine, in charge of acquiring data from sensors. This component is implemented manually.
- utils is a stateless machine offering 2 services: minimum of 2 NATURAL numbers, maximum of 3 NATURAL numbers.
- utils_i is its implementation
- ctx contains the definition of constants
- ctx_i is its implementation. The values of the constants are provided, in order to be checked against their properties. Constants are then demonstrated to be implementable.

The machine fuel0 contains two operations:

- compute_initial_level: initial estimation of the amount of fuel in the tank
- compute_remaining_fuel: called repeatidly to estimate consumption and remaining fuel

The main property of this component is: (estimated_level <= WARNING_CAPACITY => status = LOW_LEVEL)

The variable status is used to raise an alarm.

β

MACHINE fuel0

SEES

ctx

VARIABLES

estimated_level,

estimated_consumption,

status

INVARIANT

/* Typing */

estimated_level : 0..TANK_CAPACITY &

estimated_consumption : 0 ..MAX_CONSUMPTION &

status : tSTATUS &

/* Security property */

(estimated_level <= WARNING_CAPACITY => status = LOW_LEVEL)

INITIALISATION

estimated_level := 0 ||

estimated_consumption := 0 ||

status := LOW_LEVEL

OPERATIONS

compute_initial_level =

BEGIN

estimated_level, status :(

estimated_level: 0..TANK_CAPACITY &

status : tSTATUS &

(estimated_level <= WARNING_CAPACITY => status = LOW_LEVEL))

END

;

compute_remaining_fuel =

BEGIN

estimated_level, estimated_consumption, status :(

estimated_level: 0..TANK_CAPACITY &

estimated_consumption : 0..MAX_CONSUMPTION &

status : tSTATUS &

(estimated_level <= estimated_level$0) &

(estimated_level <= WARNING_CAPACITY => status = LOW_LEVEL))

END

END

This implementation fuel_i implements the two operations defined in fuel0, and imports services from measure and utils.

IMPLEMENTATION fuel_i

REFINES fuel0

SEES ctx

IMPORTS

measure,

utils

β

CONCRETE_VARIABLES

estimated_level ,

estimated_consumption ,

status

β

INITIALISATION

estimated_level := 0 ;

estimated_consumption := 0 ;

status := LOW_LEVEL

β

OPERATIONS

compute_initial_level =

VAR m1, m2 IN

m1, m2 <-- measure_level;

estimated_level <-- minimum(m1, m2);

IF estimated_level <= WARNING_CAPACITY

THEN

status := LOW_LEVEL

ELSE

status := NOMINAL

END

END

;

compute_remaining_fuel =

VAR m1, m2, m3 IN

m1, m2, m3 <-- measure_consumption;

estimated_consumption <-- maximum(m1,m2,m3);

IF estimated_consumption >= estimated_level

THEN

estimated_level := 0

ELSE

estimated_level := estimated_level - estimated_consumption

END;

IF estimated_level <= WARNING_CAPACITY

THEN

status := LOW_LEVEL

END

END

END

The component measure provides two services: measure_level and measure_consumption. These two operations have to be developped manually.

MACHINE measure

SEES ctx

β

OPERATIONS

m1, m2 <-- measure_level =

BEGIN

m1 :: 0..TANK_CAPACITY ||

m2 :: 0..TANK_CAPACITY

END;

β

m1, m2, m3 <-- measure_consumption =

BEGIN

m1 :: 0..MAX_CONSUMPTION ||

m2 :: 0..MAX_CONSUMPTION ||

m3 :: 0..MAX_CONSUMPTION

END

END

The component utils provides two services: minimum and maximum.

MACHINE utils

β

OPERATIONS

rr <-- minimum(aa, bb) =

PRE

aa: NAT &

bb: NAT

THEN

rr := min({aa, bb})

END;

β

rr <-- maximum(aa, bb, cc) =

PRE

aa: NAT &

bb: NAT &

cc: NAT

THEN

rr := max({aa, bb, cc})

END

END

The component utils_i implements the two services defined in utils

IMPLEMENTATION utils_i

β

REFINES utils

β

OPERATIONS

rr <-- minimum ( aa , bb) =

BEGIN

IF aa >= bb

THEN

rr := bb

ELSE

rr := aa

END

END

;

rr <-- maximum ( aa , bb , cc ) =

BEGIN

IF aa >= bb

THEN

IF aa >= cc THEN

rr := aa

ELSE

rr := cc

END

ELSIF bb >= cc THEN

rr := bb

ELSE

rr := cc

END

END

END

The component ctx contains the constants of the software.

MACHINE ctx

β

SETS

tSTATUS = {NOMINAL, LOW_LEVEL}

β

CONSTANTS

TANK_CAPACITY, /* max quantity of fuel in the tank */

MAX_CONSUMPTION, /* max quantity of fuel consumed in a cycle */

WARNING_CAPACITY /* low fuel level */

β

PROPERTIES

TANK_CAPACITY : NAT1 &

MAX_CONSUMPTION : NAT1 &

WARNING_CAPACITY : NAT1 &

MAX_CONSUMPTION < TANK_CAPACITY &

WARNING_CAPACITY < TANK_CAPACITY

END

The component ctx_i contains the values of the constants.

IMPLEMENTATION ctx_i

REFINES ctx

β

VALUES

TANK_CAPACITY = 1000;

MAX_CONSUMPTION = 10;

WARNING_CAPACITY = 100

END

Once the project is created (software development), add the various machines starting with ctx, utild, measure, then fuel0. Then create the implementations. Each time, create the component empty then copy-paste the contents from this page.

Once all the components are in the project:

- generate the proof obligations (button Po on the toolbar)
- execute the proof in force 0 (button F0 on the toolbar)
- execute the proof in force 1 (button F1 on the toolbar)

You should obtain the following status below from the Top-Bottom graphical view. The color green indicates that the components are fully proven.

Project structure: the lines are decomposition links (fuel_i imports measure and utils components)

When everything is proved:

- generate C code for the implementations fuel_i, Utils_i, and Ctx_i,
- Generate C code for the machine Measure: you obtain a skeleton for your C file. Complete measure.c manually, using for example a random number generator to simulate fuel consumption.
- Create main.c such as

`void main(void ) { `

` fuel0__compute_initial_level();`

` while(fuel0__estimated_level>0) {`

` fuel0__compute_remaining_fuel();`

` printf("Consumption = %d, Level = %d, status = %d\n",`

` fuel0__estimated_consumption,`

` fuel0__estimated_level,`

` fuel0__status);`

` }`

`}`

- Compile main.c fuel0.cpp utils.c measure.c
- Execute the resulting software

Last modified 6mo ago

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Formal specification

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