I first heard this tune in Die Hard 3. After all I like Bruce Willis since third grade. It got stuck in my head. After a few days of out loud humming it was time to find it. It's called
Waltz of the Banker
After some time searching I found out that the original tune is actually a popular traditional Irish anti-war and anti-recruiting song. It is generally dated to the early 19th century. The original refers to the soldiers from Athy, County Kildare that fought in "Sulloon" (Ceylon - present day Sri Lanka) for the East India Company (in what history knows as the Kandyan Wars though the term was not familiar to the Irish). It has become a definitive anti-war song. It's called
Johnny I Hardly Knew Ye
Check out the refrain:
Ye haven't an arm, ye haven't a leg, hurroo, hurroo
Ye haven't an arm, ye haven't a leg, hurroo, hurroo
Ye haven't an arm, ye haven't a leg
Ye're an armless, boneless, chickenless egg
Ye'll have to be put with a bowl out to beg
Oh Johnny I hardly knew ye.
There's one more version I found. It's a popular song of the American Civil War that expressed people's longing for the return of their friends and relatives who were fighting in the war. That's called