falls-dann-sonst
would be more correct, since "wenn" is temporal, like the English "when".
Many Germans often use these wrongly in everyday speech, but mathematicians like Friedrich L. Bauer probably wouldn't.
The other German word "falls" is sometimes also translated as "if" but it carries a slightly different connotation. In typical use "falls" is used for an unlikely condition: "falls es morgen regnen sollte" -> "if it were to rain tomorrow". If "wenn" was used instead of "falls", the connotation would be more like a 50/50 probability. In the end, the if/when split of English is really not the same as the falls/wenn split of German. For computer programming "wenn" would likely have been preferred by German programmers.
Nope, "wenn" is both "if" and "when", it's not limited to time.