Annotate repeat, replace and every?

I tried to annotate a few (trivial) fns from core. I expect it's a bit naive and broken but here it is anyway.

I will need to read more about typed racket and try to understand some of the annotations you made already in order to go forward.
Some whitespace got killed in the process too!

Anyway it is fun and a good exercise, I would love to do more of this at our local usergroup once I understand a bit better how things work. 

Max