;Problem Set 2 Solutions
;January 19, 2006
;Grant Oladipo

;;;;;;;;;;
;Problem 1
;;;;;;;;;;

(display "Problem 1\n")

(lambda (x y z) x)
;a. Special form type
;b. procedure
;c. #<procedure:7:0>

((lambda (x y) (+ x y)) 4 (+ 3 4))
;a. Combination (special form lambda inside evaluates to a procedure)
;b. 11
;c. 11

((lambda (happy tiger) (if (= tiger 4) (+ happy tiger) happy)) 4 5)
;a. Combination (special form lambda inside with special form if inside; lambda evaluates to a procedure)
;b. 4
;c. 4

((lambda (wow this works) (wow this works)) - 7 5)
;a. Combination (special form lambda inside evaluates to a procedure)
;b. 2
;c. 2

;((lambda (wow this works) (works wow this)) 7 - 5)
;a. Combination (special form lambda inside evaluates to a procedure)
;b. error
;c. procedure application: expected procedure, given: 5; arguments were: 7 #<primitive:->

((if (= 4 5)
     (lambda (x) (+ x 3))
     (lambda (x) (+ x 5)))
 7)
;a. Combination (special form if that returns one of two special form lambdas that evaluates to a procedures)
;b. 12
;c. 12

(define x 2)
;a. Special form define
;b. unspecified
;c. unspecified

((lambda (x) (+ x x)) 5)
;a. Combination (special form lambda inside that evaluates to a procedure)
;b. 10
;c. 10

((lambda (yummy) (* yummy yummy)) 5)
;a. Combination (special form lambda inside that evaluates to a procedure)
;b. 25
;c. 25

;yummy
;a. name
;b. error
;c. reference to undefined identifier: yummy

;;;;;;;;;;
;Problem 2
;;;;;;;;;;

(display "\nProblem 2\n")

;a. Sign

(define sign 
  (lambda (number)
    (if (> number 0)
        1
        (if (= number 0)
            0
            -1))))

(sign 104)
(sign 0)
(sign (- 4 6))

;b. Beautiful-Rectangle

(define beautiful-rectangle
  (lambda (width)
    (* width (/ (+ (sqrt 5) 1) 2))))

(beautiful-rectangle 34.5)
(beautiful-rectangle 1)

;c. Positive-Root

(define positive-root
  (lambda (a b c)
    (if (> 0 (- (* b b) (* 4 a c)))
        "complex roots"
        (/ (+ (- b) (sqrt (- (* b b) (* 4 a c)))) (* 2 a)))))

(positive-root 1 -2 1)
(positive-root 3 1 3)

;d. Censor

(define (substring? str substr)
  (let ((strlen (string-length str)))
    (if (< strlen (string-length substr))
        #f
        (if (string=? substr (substring str 0 (string-length substr)))
            #t
            (substring? (substring str 1 strlen) substr)))))

(define censor
  (lambda (s)
    (if (substring? s "scheme sucks")
        "BEEP"
        s)))

(censor "I love scheme; it's so cool!")
(censor "Dunno, but I think scheme sucks a lot")

;;;;;;;;;;
;Problem 3
;;;;;;;;;;

(display "\nProblem 3\n")

;a. Slow-Multiply

(define slow-mul
  (lambda (a b)
    (if (= b 0)
        0
        (+ a (slow-mul a (- b 1))))))

(slow-mul 3 4)
(slow-mul 5 9)

;b. Even

(define even?
  (lambda (number)
    (if (< number 2)
        (= number 0)
        (even? (- number 2)))))

(even? 24)
(even? 9)