Exercises

Exercise 2.2

Consider the problem of representing line segments in a plane. Each segment is represented as a pair of points: a starting point and an ending point. Define a constructor make-segment and selectors start-segment and end-segment that define the representation of segments in terms of points. Furthermore, a point can be represented as a pair of numbers: the $x$ coordinate and the $y$ coordinate. Accordingly, specify a constructor make-point and selectors x-point and y-point that define this representation. Finally, using your selectors and constructors, define a function midpoint-segment that takes a line segment as argument and returns its midpoint (the point whose coordinates are the average of the coordinates of the endpoints). To try your functions, you'll need a way to print points:

(defun print-point (p)
  (io:format "(~p, ~p)~n" (list (x-point p)
                                (y-point p))))

Exercise 2.3

Implement a representation for rectangles in a plane. (Hint: You may want to make use of exercise 2.2.) In terms of your constructors and selectors, create functions that compute the perimeter and the area of a given rectangle. Now implement a different representation for rectangles. Can you design your system with suitable abstraction barriers, so that the same perimeter and area functions will work using either representation?