Switch
This example demonstrates how to specify a stateless function and how to implement it.
A railroad switch is a mechanical installation enabling railway trains to be guided from one track to another at a railway junction. The position of the switch is safety-related. We are considering a control/command system in charge of safely determining the position of the switch. Redudancy is mandatory to take into account sensor failures, leading to a switch equipped with 3 sensors to determine its position. These sensors provide 3 measures: m1, m2, and m3.
The possible values are :
- normal (right position)
- reverse (left position)
- void (middle position while the switch is moving from a position to another)
We have to specify a function
pos <-- estimate (m1, m2, m3) = ...
calculating an estimate of the switch position, considering that:
- if at least, one normal and one reverse are measured, then the result is void.
- if all measures are void, then the result is void.
- in all other cases, it should return normal or reverse
As usual, the modelling solution is not unique.
We could for example make explicit the value of the return value pos for each value of m1, m2, m3. We could also have a more elegant solution, where we are not obliged to list every single case:
MACHINE switch
SETS
POSITION = {normal,reverse,void}
OPERATIONS
pos <-- estimate(m1,m2,m3) =
PRE
m1: POSITION &
m2: POSITION &
m3: POSITION
THEN
SELECT
normal: {m1,m2,m3} &
reverse /: {m1,m2,m3}
THEN
pos:=normal
WHEN
reverse: {m1,m2,m3} &
normal /: {m1,m2,m3}
THEN
pos:=reverse
ELSE
pos:=void
END
END
END
This model doesn’t generate any non-obvious proof obligation, as there is no variable, no invariant and no properties to verify.
The next step of this example is to implement this specification. We are now obliged to make explicit the algorithm:
IMPLEMENTATION switch_1
REFINES switch
OPERATIONS
pos <-- estimate(m1,m2,m3) =
CASE m1 OF
EITHER normal THEN
IF m2 = reverse or m3 = reverse THEN
pos:=void
ELSE
pos:=normal
END
OR reverse THEN
IF m2 = normal or m3 = normal THEN
pos:=void
ELSE
pos:=reverse
END
ELSE
CASE m2 OF
EITHER normal THEN
IF m3 = reverse THEN
pos:=void
ELSE
pos:=normal
END
OR reverse THEN
IF m3 = normal THEN
pos:=void
ELSE
pos:=reverse
END
ELSE
pos:=m3
END
END
END
END
END
The implementation is automatically demonstrated to comply with its specification.
The resulting C code, generated by ComenC from the implementation is given below:
switch.h
#ifndef _switch_h
#define _switch_h
#include <stdbool.h>
typedef enum {
switch__normal,
switch__reverse,
switch__void
} switch__POSITION;
extern void switch__INITIALISATION(void);
extern void switch__estimate(
switch__POSITION switch__m1,
switch__POSITION switch__m2,
switch__POSITION switch__m3,
switch__POSITION *switch__pos);
#endif
switch.c
#include <stdbool.h>
#include "switch.h"
void switch__INITIALISATION(void) {
}
void switch__estimate(
switch__POSITION switch__m1,
switch__POSITION switch__m2,
switch__POSITION switch__m3,
switch__POSITION *switch__pos) {
switch (switch__m1) {
case switch__normal:
if ((switch__m2 == switch__reverse) || (switch__m3 == switch__reverse)) {
*switch__pos = switch__void;
} else {
*switch__pos = switch__normal;
}
break;
case switch__reverse:
if ((switch__m2 == switch__normal) || (switch__m3 == switch__normal)) {
*switch__pos = switch__void;
} else {
*switch__pos = switch__reverse;
}
break;
default:
switch (switch__m2) {
case switch__normal:
if (switch__m3 == switch__reverse) {
*switch__pos = switch__void;
} else {
*switch__pos = switch__normal;
}
break;
case switch__reverse:
if (switch__m3 == switch__normal) {
*switch__pos = switch__void;
} else {
*switch__pos = switch__reverse;
}
break;
default:
*switch__pos = switch__m3;
break;
}
break;
}
}
Last modified 1yr ago