 Due date: 11/06
Purpose:
The goal of this problem set is to help you design structurally recursive
and generative recursive functions, dealing with all forms of data. You
must learn to pinpoint which design approach each function uses and whether
or not using an accumulatorstyle is useful or not.
Drill:
HtDP: 31.3.1, 31.3.2, 31.3.3, 31.3.4, 31.3.5, 31.3.6, 31.3.7, 31.3.8,
32.2: all exercises or 32.3: all exercises
Required Problems:
Note: You must annotate each function with the design
strategy that you used:
 domain knowledge (algebra, physics, watching traffic lights)
 function composition: a function that contains a conditional is
not designed via function composition; expressions such as (f w
(g x y) z) is about all you may use then;
 structural design, on the 6th argument
 structural design, on the 4th and 6th argument (if you choose this
option, also document which of the three situations you are working with)
 generative design;
 design of abstraction over structural repetition;
 design of abstraction over genrec repetition.
If you use a design "with accumulators", be sure to explain the connection
between the local recursion argument, the accumulator, and the initial
argument; otherwise you can't get credit. You may also use a design "with
existing abstractions" if you use one of the functions from page 313.
 Design the function
render , which consumes enumerations,
nested arbitrarily deep, and renders them:
(definestruct ul (list))
(definestruct ol (list))
;; Enum is one of:
;;  (makeul LOI)
;;  (makeol LOI)
;; LOI is one of:
;;  (cons Item empty)
;;  (cons Item LOI)
;; Item is one of:
;;  String
;;  Enum
Here is a somewhat complex illustration of its output:
Domain knowledge: We will use Safari's rendering
strategy for nested unordered lists. That is, the outermost unordered
list uses bullets (•); the first nested level comes with circles
(ο); the third level's anchor is square. For all levels below
the third one, Safari uses the square. As always, a nested enumeration
is offset by one blank line and every item (including nested
enumerations) are separated by a blank space from their anchor.
 Project:
Modify your solution of problem 3.4 so that the ball performs its complete
movement in one tick. That is, the ball moves for an entire tick and
bounces as many timesoff the wall, off the paddleas possible according
to its initial velocity and location.
The idea is to move the ball to the closest obstacle, to bounce it, and to
repeat this process for the remaining fraction of time.
Domain knowledge: If an object O moves
from P to Q at velocity V , it has
traveled for a time equal to the distance between those two points divided
by the O 's speed, which is the magnitude of V .
Dually, one tick minus the time traveled for moving from P to
Q is the remaining fraction of a tick that remains to move
the ball.  Stop when the fraction of time has gotten too smal. Keep in
mind that it is better to compare floating point numbers with < or ≤
than with =.
