Write a full program

Does that mean using only the code section of some try-it-online tool?

writes another program

Does that mean generting an executable/script file? Or only printing the program is enough?

The length of each program must tend toward infinity as the sequence continues.

I guess you mean that every generated program must be longer than the program who generated it, right?

And what is each program supposed to do? Output something to the screen? Do some calculation?

Does that mean using only the code section of some try-it-online tool?

I don't really get what you mean by this. I was under the impression that anything runnable without needing to add anything counted as a full program.

Does that mean generting an executable/script file? Or only printing the program is enough?

Outputting source code; will edit

I guess you mean that every generated program must be longer than the program who generated it, right?

Not necessarily; I worded it that way specifically so that say, if the first program source code has 200 chars, second has 300, third has 250, fourth has 400... it would still be valid as the sequence tends towards infinity even though there can be some regressions

And what is each program supposed to do? Output something to the screen? Do some calculation?

Output the source of the next program