; CS101, Spring 2013
; Lab 2 

; Defining unnamed procedures using the lambda special form.

(display "\n         CS101 Lab 2, Spring 2013\n")
(display "\n               SOLUTIONS \n\n")
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(display "Problem 1(a): Writing a Fahrenheit to Celsius converter:\n\n")
; 
;     Define an unnamed Racket procedure that consumes a single
;     input (representing the temperature in Fahrenheit) and returns   
;     as output the corresponding temperature in Celsius.
;     
;     The appropriate conversion formula is:  c = 5(f-32)/9.
;     (You'll have to change this expression a little to get it
;     into the form of a Racket expression.)
;     
;     Make sure that you test your unnamed procedure on the
;     following examples:
;     
;            f = 32, f = 212, and f = -40.
;     


;; WRITE THE LAMBDA EXPRESSION HERE IN A PRINTF STATEMENT. PUT THE LAMBDA
;; EXPRESSION IN A STRING TO PRINT.
(printf "Solution is:  ~a~%~%" "(lambda (f) (/ (* 5 (- f 32)) 9))")

;; THERE SHOULD BE 3 SEPARATE CALLS TO PRINTF, AS SHOWN BELOW. 
;;
;; EACH PRINTF EXPRESSION SHOULD HAVE 3 ARGUMENTS:
;;     1ST ARG: the string "~a degrees F = ~a degrees C~%~%" (GIVEN),
;;     2ND ARG: a number representing the temperature in degrees Fahrenheit,
;;     3RD ARG: a call to the lambda function you wrote above, passing in the 
;;              degrees Fahrenheit as an argument to the lambda function.
(printf "~a degrees F = ~a degrees C~%~%" 
        32 ((lambda (f) (/ (* 5 (- f 32)) 9)) 32))
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(printf "~a degrees F = ~a degrees C~%~%" 
        212 ((lambda (f) (/ (* 5 (- f 32)) 9)) 212))
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(printf "~a degrees F = ~a degrees C~%~%" 
        -40 ((lambda (f) (/ (* 5 (- f 32)) 9)) -40))

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(display "Problem 1(b): Naming the lambda expression from part 1(a):\n\n")
; 
;     Use a define special form to name the lambda expression you wrote 
;     for part (a). Call the function fahr->cels.
;     
;     Test your procedure on the following examples:  
;     
;                f = 32, f = 212, and f = -40.
;     


;; DEFINE THE FAHR->CELS FUNCTION HERE.
(define fahr->cels
  (lambda (f) 
    (/ (* 5 (- f 32)) 9)))

;; CALL FAHR->CELS WITH THE SAME INPUTS YOU USED IN PART 1(a), USING THREE
;; PRINTF STATEMENTS WITH THE SAME NUMBER OF ARGUMENTS AS THE PRINTFS IN 1(a)
;; (3 SEPARATE PRINTF STATEMENTS).
(printf "~a degrees F = ~a degrees C~%~%" 32 (fahr->cels 32))
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(printf "~a degrees F = ~a degrees C~%~%" 212 (fahr->cels 212))
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(printf "~a degrees F = ~a degrees C~%~%" -40 (fahr->cels -40))

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(display "Problem 2(a): Writing a function to calculate slope:\n\n")
; 
;     Define an unnamed Racket procedure that consumes four           
;     inputs--x1, y1, x2, y2--representing the coordinates of
;     two points in the xy-plane: (x1, y1) and (x2, y2), and 
;     returns as output the slope of the line segment joining
;     these two points.
;     
;     The appropriate formula is:  (y2 - y1) / (x2 - x1).
;     (You'll have to change this expression a little to get 
;     it into the form of a Racket expression.) You may assume
;     that x1 and x2 are different.
;     
;     Make sure that you test the unnamed procedure on the
;     following examples:  
;     
;     x1 = 0, y1 = 0, x2 = 1, y2 = 1
;     
;     x1 = 0, y1 = 0, x2 = 3, y2 = 12
;     
;     x1 = 1, y1 = 2, x2 = 8, y2 = 15
;     


;; WRITE THE LAMBDA EXPRESSION IN A PRINTF STATEMENT. PUT THE LAMBDA
;; EXPRESSION IN A STRING TO PRINT.
(printf "Solution is:  ~a~%~%" 
        "(lambda (x1 y1 x2 y2) (/ (- y2 y1) (- x2 x1)))")

;; CALL THE LAMBDA EXPRESSION ON THE 3 SETS OF INPUTS GIVEN ABOVE 
;; EACH PRINTF EXPRESSION SHOULD HAVE 6 ARGUMENTS:
;;     1ST ARG: the string "Slope when x1=~a, y1=~a, x2=~a, y2=~a is ~a~%~%"
;;              (STRING IS GIVEN BELOW FOR EACH SET OF ARGUMENTS),
;;     2ND THROUGH 5TH ARGS: values for x1, x2, y1, and y2
;;     6TH ARG: a call to the lambda function you wrote above, passing in 
;;              x1 x2 y1 and y2.
(printf "Slope when x1=~a, y1=~a, x2=~a, y2=~a is ~a~%~%"
        0 0 1 1 ((lambda (x1 y1 x2 y2) (/ (- y2 y1) (- x2 x1))) 0 0 1 1))
(printf "Slope when x1=~a, y1=~a, x2=~a, y2=~a is ~a~%~%"
        0 0 3 12 ((lambda (x1 y1 x2 y2) (/ (- y2 y1) (- x2 x1))) 0 0 3 12))
(printf "Slope when x1=~a, y1=~a, x2=~a, y2=~a is ~a~%~%"
        1 2 8 15 ((lambda (x1 y1 x2 y2) (/ (- y2 y1) (- x2 x1))) 1 2 8 15))
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(display "Problem 2(b): Naming the lambda expression from part 2(a):\n\n")
; 
;     Use a define special form to name the lambda expression you wrote 
;     for part 2(a). Call the function slope.
;     
;     Test the slope procedure on the same examples as you did in part
;     2(a).
;     


;; DEFINE THE SLOPE FUNCTION HERE.
(define slope
  (lambda (x1 y1 x2 y2) 
    (/ (- y2 y1) (- x2 x1))))

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;; CALL FAHR->CELS WITH THE SAME INPUTS YOU USED IN PART 2(a) 
;; (3 SEPARATE PRINTF STATEMENTS WITH 6 ARGUMENTS EACH).
(printf "Slope when x1=~a, y1=~a, x2=~a, y2=~a is ~a~%~%"
        0 0 1 1 (slope 0 0 1 1))
(printf "Slope when x1=~a, y1=~a, x2=~a, y2=~a is ~a~%~%"
        0 0 3 12 (slope 0 0 3 12))
(printf "Slope when x1=~a, y1=~a, x2=~a, y2=~a is ~a~%~%"
        1 2 8 15 (slope 1 2 8 15))

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