teaching machines

CS 330 Lecture 33 – Higher-order

April 25, 2012 by Chris Johnson. Filed under
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cs330, lectures, spring 2012.

Agenda

• program this
• double, square, cosine
• higher-order functions
• map and filter
• variable-length argument lists
• symbolic differentiation

TODO

• Introduction Google’s MapReduce: http://code.google.com/edu/parallel/mapreduce-tutorial.html.

Program This

Choose one:

• Write contains, which takes two arguments: a list and an atom. Return true if the list contains the atom.
• Write nth-element, which returns the the nth-element (starting at 0) of the list.

Code

hof.ss

(define first car)
(define rest cdr)

(define contains
  (lambda (l item)
    (cond
      ((null? l) #f)
      ((= (first l) item) #t)
      (else (contains (rest l) item)))))

(define nth-element
  (lambda (l index)
    (cond
      ((null? l) '())
      ((= index 0) (first l))
      (else (nth-element (rest l) (- index 1))))))


(define double
  (lambda (l)
    (cond
      ((null? l) '())
      (else (cons (* 2 (first l)) (double (rest l)))))))

(define lsin
  (lambda (l)
    (cond
      ((null? l) '())
      (else (cons (sin (first l)) (lsin (rest l)))))))

(define square
  (lambda (l)
    (cond
      ((null? l) '())
      (else (cons (* (first l) (first l)) (square (rest l)))))))


(define mymap
  (lambda (f l)
    (cond
      ((null? l) '())
      (else (cons (f (first l)) (mymap f (rest l)))))))

(define differentiate
  (lambda (f)
    (cond
      ((number? f) 0)
      ((equal? 'x f) 1)
      ((equal? '+ (first f))
       (list '+ 
             (differentiate (nth-element f 1))
             (differentiate (nth-element f 2))))
      ((equal? '* (first f))
       (list '+
             (list '* (nth-element f 1) (differentiate (nth-element f 2)))
             (list '* (nth-element f 2) (differentiate (nth-element f 1)))))
      (else (display 'Idunno)))))


;(define (contains l item)
  

Haiku