What is the type of a continuation in Racket? And how to determine current continuation looking at a call/cc invocation? (e.g : Is it a correct strategy to assume that the current continuation is what follows immediately after call/cc closing bracket?)
A continuation is a procedure (in the sense that it's callable and returns true for procedure?), albeit a special one that does not return to the caller of the continuation.
The value(s) you call the continuation with will become the return value(s) of the call/cc invocation that created it.
Example:
> (define $k #f)
> (call-with-values (lambda () (call/cc (lambda (k)
(set! $k k))))
(case-lambda (() "Zero values")
((x) "One value")
((x y) "Two values")
((x y z) "Three values")))
"One value"
> (procedure? $k)
#t
> ($k)
"Zero values"
> ($k 1)
"One value"
> ($k 1 2)
"Two values"
> ($k 1 2 3)
"Three values"
> ($k 1 2 3 4)
#<case-lambda-procedure>: arity mismatch;
the expected number of arguments does not match the given number