Problem with lambda

Hi

I'm trying to learn common lisp "by example" out of some course based on scheme. Here's my adaptation of the classic Newton algorithm to find square roots:

(defun fixed-point (f start)
  (defvar tolerance 0.00001)
  (labels ((close-enough? (u v)
             (< (abs (- u v)) tolerance))
            (iter (old new)
              (if (close-enough? old new)
                new
                (iter new (funcall f new)))))
  (iter start (funcall f start))))
  
(defvar dx 0.00001)
(defun deriv (f)
               #'(lambda (x) (/ (- (funcall f (+ x dx)) 
                                  (funcall f x)) 
                               dx)))

(defun newton (f guess)
  (labels ((df () (deriv f)))
    (fixed-point 
      #'(lambda (x) (- x (/ (funcall f x) ((df) x)))) 
      guess)))

(defun mysqrt-newton (x)
  (labels ((square (x) (* x x)))
    (newton #'(lambda (y) (- x (square y))) 1))) 

(mysqrt-newton 2)

The problem is with expression ((df) x) - it is supposed to return the value of a derivative of f in x. (df) should return a function being derivative of f. Apparently it doesn't because I get an error: SYSTEM::EPAND-FORM (DF) should be a lambda expression. But it is, isn't it?

Please help.

wilku wrote:The problem is with expression ((df) x) - it is supposed to return the value of a derivative of f in x. (df) should return a function being derivative of f. Apparently it doesn't because I get an error: SYSTEM::EPAND-FORM (DF) should be a lambda expression. But it is, isn't it?

No, it isn't a lambda expression, but it evaluates to a lambda expression. You have to use funcall: (funcall (df) x).

In CL, the first element in a form must be either a symbol (naming a function or a macro) or an explicit lambda expression, like:

cl-user> ((lambda (x) (+ x 1)) 2)
3

This you don't need anyway, you already have let.

Unlike Scheme, Common Lisp separates variable and function namespaces. In this case, I would say it loses to Scheme.

It took me 15 more minutes to understand this even though you explained it very clearly.
This says something about the level of abstraction of higher functions (or my intelectual abilities )
Thank you for the answer.