Clarify how pre(y) is determined during initialization

[casella]

Section 3.7.5, operator 3.24 states

The first value of pre(y) is determined in the initialization phase.

Section 8.6 then states that it is possible to add the equation pre(vc) = startExpression to the initialization problem by setting vc(start = startExpression, fixed = true)

What is not 100% clear to me is whether it is really necessary to do so in case vc is completely determined as a function of time. Consider this MWE:

model TestInitDiscrete
  Boolean b;
  Boolean b1(start = true);
  Boolean bs(start = false, fixed = true);
equation
  b = if time < 0.5 then false else true;
  b1 = b;
  when pre(b1) and pre(bs)==false then
    bs = true;
  end when;
end TestInitDiscrete;

Both Dymola and OpenModelica automatically add fixed = true to b1, which makes pre(b1) = true at initialization. This seems a bit odd to me, given that b1 is always false for time < 0.5.

Is this the intended behaviour? If so, maybe we should clarify it more explicitly, perhaps in a non-normative section of the text.

[kabdelhak]

From my perspective the question here is which equation should be added to the initial system? Is it

pre(b1) = b1.start;

or

pre(b1) = b1;

(or is it even something else?)

The first equation can always be added since the system will solve for b1. The second one, which you seem to imply should be added, can only be added safely if b1 can be solved during initialization independently of the value of pre(b1).

For the following example one could not use the second equation since it would create an algebraic loop without solution during initialization, while the first equation would allow a proper initialization.

model TestInitDiscrete
  Boolean b;
  Boolean b1(start = true);
  Boolean bs(start = false, fixed = true);
equation
  b = if time < 0.5 then false else true;
  when {initial(), sample(0.1,0.1)} then
    b1 = not pre(b1);
  end when;
  when pre(b1) and pre(bs)==false then
    bs = true;
  end when;
end TestInitDiscrete;

Should compilers figure this out and add the appropriate equation? From my understanding most compilers currently always use the first approach.

[henrikt-ma]

SystemModeler also automatically treats b1 as having fixed initialization.

Regarding automatic introduction of pre(b1) = b1;, I don't see where it would come from.

[JohannesKrauseGitH]

Same in SimulationX, pre(b1) = b1.start; is added.

[HansOlsson]

This is specified in https://specification.modelica.org/master/equations.html#initialization-initial-equation-and-initial-algorithm as far as I can see:

• A missing initial value of a discrete-time variable (see section 4.5 – this does not include parameter and constant variables) which does not influence the simulation result, may be automatically set to the start value or its default without informing the user. For example, variables assigned in a when-clause which are not accessed outside of the when-clause and where pre is not explicitly used on these variables, do not have an effect on the simulation.
• A start-attribute that is not fixed may be treated as fixed with a diagnostic.

The only clarifications needed I could see are:

• Reference to the initialization section
• More structure to the initialization section