I was at the library today, and since I felt kinda tired I took a 15-minute nap with my head on the table. 
Anyway, I noticed that I was more startled than normal when my phone alarm rang, and I actually felt quite rested, much more rested than I usually do when I don’t fall asleep.
The thing is just that I don’t have a clear memory of actually having fallen asleep, I sort of felt like I was more or less awake the whole time but started “drifting off”, so to speak - but still I felt rested in a way as if I had fallen asleep.
What was this?
Sounds like it, yep. You probably did fall asleep without noticing it. In fact, I fall asleep without noticing it every night… Can’t get my bloody WILD to work 