So for I am trying to figure out this whole call/cc thing in Scheme. Below is the code I am working with:
(+ 1 (call/cc
(lambda (k)
(if (number? k)
(call/cc (lambda (k) (k (- 1 k))))
(k 4)))))
So here we start adding the two arguments in the first parenthesis. 1 and the rest which we have to evaluate because of eager evaluation. So we have a call/cc which accepts one arguments, a function, which the call/cc evaluates by calling. (am I right?) And at the same time it holds the rest of what has happened so far in our first parenthesis, namely (+ 1 []), which is the "continuation". (am I right?) So we call lambda k with the continuation as I have just described, (+ 1 []). In the function it then asks if this is a number, which it is not and does the "then". I get "lost" here, what does this second call/cc do? What is (k 4) invoked, to make this whole thing evaluate to 5?
You're pretty close! All of your questions are right, I think.
The function you pass to call/cc takes one argument (k in your example), and it's a way to return a value to the current continuation. k is a function of one argument. When you call that function with a value, that value is returned to and stands in place of the _ in this: (+ 1 _).
So in your example, (number? k) is never true, and the second call to call/cc is never executed. (Even if it were, it would fail with a runtime error where (- 1 k) subtracts a function from 1.) So it actually executes the "else" branch: (k 4), which returns 4 to (+ 1 4) so the result is 5.
Hope that's clear!