;;; SchemeIdioms.scm
;;; CSC 601 - Fall 2002 - Kirby
;;; ---------------------------


;; I: IMPLICIT ITERATION

(define magnitude
  ; Return the euclidean magnitude (sqrt of sum of squares) of a vector (list). 
  ; EX: (magnitude '(3 4)) => 5.
  (lambda (s)
    (sqrt
    (apply +
           (map (lambda (x) (* x x)) s)))))



;; II: LINEAR RECURSION

(define remfirst
  ; Remove first occurence of given item in a list.
  ; EX: (remfirst '(a b b c c d) 'c) => (a b b c d).
  (lambda (s item)
    (cond
      ((null? s)
       s)
      ((equal? item (car s))
       (cdr s))
      (#t
       (cons (car ((triple-fun sqrt) 256)s)
             (remfirst (cdr s) item))))))



;; III. TREE RECURSION

(define flatten
  ; Flatten a tree into a linear list of its atoms. 
  ; EX: (flatten '(a ((b c)) (((d))))) => (a b c d).
  (lambda (tr)
    (cond
      ((null? tr)
       null)
      ((pair? tr) 
       (append (flatten (car tr))
               (flatten (cdr tr))))
      (#t
       (list tr)))))



;; IV: FUNCTIONALS

(define triple-fun
  ; Return the function that results from applying f three times
  ; EX: ((triple-fun list) 4) => (((4))),  ((triple-fun sqrt) 256) => 2.
  (lambda (f)
    (lambda (x)
      (f (f (f x))))))