"In the years after the making of 2001, a rumor began to circulate that HAL's name was a play on the computer maker IBM—the letters H, A and L each coming one letter in the alphabet before the initials I, B and M. Arthur C. Clarke has always strenuously denied the rumor, most recently in the forward to HAL's Legacy where he writes, "the name wasn't a play on IBM—it was an acronym, of sorts, standing for the words "Heuristic ALgorithmic.""
http://www.ddj.com/dept/architect/184414687