Computing fixpoint in Lustre node

Question

1) Exam 29.07.2021 problem 5: The fixpoint of y2 is computed without the special value [.] although the result of  (0 fby pre(y1)) has values [.].

2) Exam 06.04.2021 problem 5: The fixpoint of y2 is computed with the special values [.] in the result of (1 fby x2).

Both problems deal with a Lustre node. Why is the fixpoint computation done without the special value [.] in the first given exam?

Answer 1

There is no special difference between the two; we are just computing the least fixpoint starting with the least sequence (the empty sequence). The fixpoint in one exam does not have values [.] while the other one has these values. So, it is just because the function used in the fixpoint iteration creates these values (with the when operator) while other one does not.