A small study of Canadian infants and toddlers found that those who slept most at night were making significantly more progress in executive functions than those who slept less at night, even if the latter group also had daytime sleep. These functions include impulse control, memory and mental flexibility. The researchers controlled for parents’ education and income and children’s general cognition, but the link between night-time sleep and development of cognitive skills remained. These finding support similar research findings on schoolchildren.

Might this also apply to older children and adults? That would be interesting to know!
Annie Bernier, Stephanie M. Carlson, Stéphanie Bordeleau, Julie Carrier. Relations Between Physiological and Cognitive Regulatory Systems: Infant Sleep Regulation and Subsequent Executive Functioning. Child Development, 2010; 81 (6)