On the occur-check free Prolog programs

In most PROLOG implementations, for efficiency occur-check is omitted from the unification algorithm. This paper provides natural syntactic conditions that allow the occur-check to be safely omitted. The established results apply to most well-known PROLOG programs, including those that use difference lists, and seem to explain why this omission does not lead in practice to any complications. When applying these results to general programs, we show their usefulness for proving absence of floundering. Finally, we propose a program transformation that transforms every program into a program for which only the calls to the built-in unification predicate need to be resolved by a unification algorithm with the occur-check.