[buccaneer81]

My assumption, when I saw the movie in 1968 or so, was that HAL was regressing to his early programming, and that the song was something that his early trainers had exposed him to when they were teaching him human language.

Exactly. HAL stated earlier in the movie that he was activated at the University of Illinois-Urbana on January 12, 1992 and that Professor So-and-so had taught him the song as one of his first programming efforts.

[Frantzie]

I always thought the part about HAL computer company was in Urbana, IL. I wonder if it was because the university or because he could not use IBM and it was sort of in the same northern middle America like Armonk/Binghampton, NY area.