Lecture 2 Solutions

[See ex6solns for solutions to first two problems]

Sum-list:

(define sum-list
  (lambda (lst)
    (if (null? lst)
        0
        (+ (car lst) (sum-list (cdr lst))))))
;cdr'ing down

Build list of numbers:

(define build-list-of-numbers
  (lambda (start end)
    (if (> start end)
        nil
        (cons start (build-list-of-numbers (+ start 1) end)))))
;cons'ing up

Delete Number:

(define delnum
  (lambda (element lst)
    (if (null? lst)
        lst
        (if (= (car lst) element)
            (cdr lst)
            (delnum element (cdr lst))))))
 

Higher Order procedures

Integrate:

(define square (lambda (x) (* x x)))

(define rect
  (lambda (fx0 fx1 dx)
    (* fx1 dx)))

(define trap
  (lambda (fx0 fx1 dx)
    (* (/ (+ fx0 fx1) 2) dx)))

(define integrate
  (lambda (start end dx)
    (if (>= start end)
        0
        (+ (trap (square start) (square (+ start dx)) dx)
           (integrate (+ start dx) end dx)))))

;integrate using functions
;f is the function to integrate
;areaf is the function to use to compute area under the curve

(define fintegrate
  (lambda (f areaf start end dx)
    (if (>= start end)
        0
        (+ (areaf (f start) (f (+ start dx)) dx)
           (fintegrate f areaf (+ start dx) end dx)))))

Lines:

(define make-line
  (lambda (m b)
     (lambda (x)
       (+ (* m x) b))))

(define diag (make-line 1 0)
(diag 3)
;Value: 3


Map:

(define map
  (lambda (proc lst)
    (if (null? lst)
        nil
        (cons (proc (car lst))
              (map proc (cdr lst))))))

Filter:

(define filter
  (lambda (pred lst)
    (if (null? lst)
        nil
        (if (pred (car lst))
            (cons (car lst) (filter pred (cdr lst)))
            (filter pred (cdr lst))))))

Nth-prime:

(define nth-prime
  (lambda (n)
    (list-ref
     (filter prime?
             (build-list-of-numbers 2 (expt 2 n)))
     n)))