Representing Data Structures

representing_data_structures.scm

; 2.2 Representing data with procedures

(define (make-point x y)(cons x y))
(define (x-point point) (car point))
(define (y-point point) (cdr point))

(define a-point (make-point 0 0))
(define b-point (make-point 2 2))
(x-point a-point)
(y-point a-point)

(define (make-segment start-point end-point)(cons start-point end-point))
(define (start-point segment) (car segment))
(define (end-point segment) (cdr segment))

(define segment (make-segment a-point b-point))

(define (mid-point segment)
  (make-point (/ (+ (x-point (start-point segment)) (x-point (end-point segment))) 2)
              (/ (+ (y-point (start-point segment)) (y-point (end-point segment))) 2)))

(mid-point segment)

; 2.4: Representing data AS procedures

(define (24cons x y)
  (lambda (m) (m x y)))

(define (24car z)
  (z (lambda (p q) p)))

(define (24cdr z)
  (z (lambda (p q) q)))

(24car (24cons 2 3))
(24cdr (24cons 2 3))

; 2.5: Another implementation of the data as procedures that yields the same thing (because 2^a * 3^b is a function (unique) in a and b).
; The point: the implementation details don't matter. The data is defined by its behavior, not its content or storage or format. 

(define (25cons a b)
  (* (expt 2 a) (expt 3 b))
  )

(define (25car cawns)
  (if (= 0 (remainder cawns 2))
      (+ 1 (25car (/ cawns 2)))
      0)
  )

(define (25cdr cawns)
  (if (= 0 (remainder cawns 3))
      (+ 1 (25cdr (/ cawns 3)))
      0)
  )

(define example (25cons 5 7))  ; 69984
(25car example)                ; 5
(25cdr example)                ; 7


; 2.6: Representing a primitive (numbers) as procedures

(define zero (lambda (f) (lambda (x) x)))

(define (add-1 n)
  (lambda (f) (lambda (x) (f ((n f) x)))))

(define (inc x) (+ 1 x))
(define one (lambda (f x) (f x)))
(define two (lambda (f x) (f (f x))))
(define three (lambda (f x) (f (f (f x)))))