I write the newton-method to find root from Scheme example in elisp as
#+begin_src emacs-lisp :session sicp :lexical t
(defun deriv(g)
(lambda (x)
(/ (- (funcall g (+ x dx)) (funcall g x))
dx)))
(defvar dx 0.00001)
(defvar tolerance 0.00001)
(defun fixed-point(f guess)
(defun close-enoughp(v1 v2)
(< (abs (- v1 v2)) tolerance))
(let ((next (funcall f guess)))
(if (close-enoughp guess next)
next
(fixed-point f next))))
(defun newton-transform(g)
(lambda (x)
(- x (/ (funcall g x) (funcall (funcall #'deriv g) x)))))
(defun newton-method(g guess)
(fixed-point (funcall #'newton-transform g) guess))
(defun curt(x)
(newton-method (lambda (y) (- (* y y y) x))
1.0))
(curt 12)
#+end_src
#+RESULTS:
: 2.2894284851069058
It works but observe the twisted code:
(defun newton-transform(g)
(lambda (x)
(- x (/ (funcall g x) (funcall (funcall #'deriv g) x)))))
Three funcalls, in which I could not imagine bad if more depths of closures.
Is there an alternative solution to the problem with elisp? (I guess it de-appreciates closures)
A couple of the functions calls can be simplified, and we should implement @sds's advice regarding function names and conventions - like this:
(defvar dx 0.00001)
(defvar tolerance 0.00001)
(defun deriv (g)
(lambda (x)
(/ (- (funcall g (+ x dx)) (funcall g x))
dx)))
(defun close-enough-p (v1 v2)
(< (abs (- v1 v2)) tolerance))
(defun try (f guess)
(let ((next (funcall f guess)))
(if (close-enough-p guess next)
next
(try f next))))
(defun fixed-point (f first-guess)
(try f first-guess))
(defun newton-transform (g)
(lambda (x)
(- x (/ (funcall g x)
(funcall (deriv g) x)))))
(defun newton-method (g guess)
(fixed-point (newton-transform g) guess))
(defun curt (x)
(newton-method (lambda (y) (- (* y y y) x))
1.0))
Notice that we don't need to use funcall when invoking functions previously defined and named, such as deriv and newton-transform.