The HAL Project - HAL 9000
As is clearly stated in the novel (Chapter 16), HAL stands for Heuristically programmed ALgorithmic computer. However, about once a week some character spots the fact that HAL is one letter ahead of IBM, and promptly assumes that Stanley and I were taking a crack at the estimable institution … As it happened, IBM had given us a good deal of help, so we were quite embarrassed by this, and would have changed the name had we spotted the coincidence.