6.090 IAP '05 - Lecture 6 Solutions

(define (sum f x y dx)
  (if (> x y)
      0
      (+ (f x)
         (sum f (+ x dx) y dx))))

(define (make-adder amt)
  (lambda (x) (+ x amt)))

(define add-3 (make-adder 3))

(add-3 5)
;Value: 8

(define compose
  (lambda (f g)
    (lambda (x)
      (f (g x)))))

(define square (lambda (x) (* x x)))
(define inc (lambda (x) (+ x 1)))

(define inc-square (compose square inc))

(inc-square 3)


4
;Value: 4
;Type: num

(+ 1 1)
;Value: 2
;Type: num

(lambda (x) (+ x 1))
;Value: compound-procedure
;Type: num -> num

(lambda (x) (= x 1))
;Value: compound-procedure
;Type: num -> bool

(define square
  (lambda (x) (* x x)))
;Value: unspecified

square
;Value: compound-procedure
;Type: num -> num

(square 5)
;Value: 25
;Type: num

(define a
  (lambda (f) (+ (f 5) 1)))
;Value: unspecified

a
;Value: compound-procedure
;Type: (num -> num) -> num

(a square)
;Value: 26
;Type: num

(define b
  (lambda (x y)
    (+ (a x) y)))
;Value: unspecified

b
;Value: compound-procedure
;Type: (num -> num), num -> num

(b square 4)
;Value: 30
;Type: num

(define c
  (lambda (x)
    (lambda (y)
      (+ x y))))
;Value: unspecified

c
;Value: compound-procedure
;Type: num -> (num -> num)

(c 5)
;Value: compound-procedure
;Type: num -> num