I ran into this code on Wikipedia:
(define (pyth x y k) (* x x (lambda (x2) (* y y (lambda (y2) (+ x2 y2 (lambda (x2py2) (sqrt x2py2 k)))))))) The article says that that code is the Continuation-Passing version of another piece of code:
(define (pyth x y) (sqrt (+ (* x x) (* y y)))) However, I'm quite confused: How does that even work? How do you multiply a number by a lambda here? (* x x (lambda ...))
In the Wikipedia example, * doesn't mean the same thing as * in the conventional example.
I would rewrite the Wikipedia example as:
(define (pyth x y k) (cps-* x x (lambda (x2) (cps-* y y (lambda (y2) (cps-+ x2 y2 (lambda (x2py2) (cps-sqrt x2py2 k)))))))) In this form, each of the cps-xxx functions perform the operation indicated and then pass the result to the last argument. You could call it like this:
(pyth 2 3 display) which would multiply 2 and 3, giving 6, and then passing 6 to display. (Actually you would want to pass the result to a cps-display that displayed its initial argument(s) and then called another function specified as its last parameter).
*&,+&andsqrt&, i.e. a convention where an ampersand is appended to each function which accepts a continuation as the last parameter. It took me a while nevertheless to understand that these functions are not part of Scheme's standard operators, but implemented explicitly.