Just so you know, there's half a dozen of equally plausible hypotheses about REM function, and dozens more of more fantastical. Most amusing one yet is about synthesis of molecular chaperones that guard against aggregation of chains produced during NREM. But honestly we just don't know.

Personally I agree with Marcus Schmidt and his idea of "energy allocation function of sleep". Basically it says that distinct physiological states provide viable configurations of priorities for vital functions that allow for the lowest possible energy expenditure over the whole cycle. I.e. there's no single specific function of REM sleep, it hosts all functions that are too costly to prioritize during other states, and the same is true for NREM.