Unfortunately, I'm too unsophisticated to be able to gain much insight from the CBPV papers. There's an introduction to CBPV for more mortal-like folks. Other material is hard to find.
What caught my eye was the following code sample from Paul Blain Levy's (rhymes with "all plain Stevie") PhD thesis:
thunk(print "hello1"; λz. print "we just popped" z; ...)
So, apparently you can do stuff in a function before you're even taking arguments. Interested!
Maybe one of you can provide more information about this interesting new thing?!