2015-09-28

posted Sep 28, 2015, 6:24 AM by Samuel Konstantinovich   [ updated Sep 28, 2015, 6:24 AM ]
Goal: Keeping the fun in functions.

We have already seen the define statement:
(define  label   v)   ; where v can be any value, expression, or function

Math notation of functions:
We can define functions like in math, the math notation is as follows:
f(x) = x + 1  
f is the name of the function
(x) is the parameter
x+1 is what to do with the parameters

or

sum(a,b) = a + b
sum is the name
a and b are parameters
a + b is what to do with the function

SCHEME notation of functions:

(define  f ???? )

we need a way to create a function

(lambda (parameters) expression )


(lambda (x) (+ x 1) )   ; this is scheme for the x+1 function


(define f   (lambda (x) (+ x 1) )
; this is like f(x) = x + 1


(define add (lambda (x y) (+ x y)))
;this is like add(x,y) = x + y 

;Try to make it readable:
(define label
 (lambda
   (parameters)
   v  ) )
;Break up v into new lines as well if needed.

(define add 
   (lambda 
      (x y) 
      (+ x y)))


;Lambda is a function that creates a function.
;the first parameter is a list of labels that the function will use as parameters
;the second parameter is the expression that uses the label to calculate the result

;This is one way to write a distance function that takes
;two sets of coordinates (x1,y1) and (x2,y2)
(define dist
  (lambda  (x1 y1 x2 y2)  (sqrt (+ (sq (- x1 x2)  ) (sq (- y1 y2))))))
;test cases to see if your function works
(dist 0 0 3 4)
(dist 1 1 2 2)


;A better way is to break it up into smaller pieces
;and use new lines to help readability
(define dist
  (lambda
      (x1 y1 x2 y2)
      (sqrt (+
              (* (- x1 x2) (- x1 x2))
              (* (- y1 y2) (- y1 y2)) ))))
(dist 0 0 3 4)
(dist 1 1 2 2)


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