Every LOOP program can be simulated using a WHILE program. In other words, the set of all LOOP-computable functions is a subset^{1} of all WHILE-computable functions:
\[L O O P \subseteq W H I L E.\]
Proofs: 1
Please note that the conversion is not true. One reason for this is because all LOOP-computable functions are total, but there are also partially WHILE-computable functions (which are not total). ↩