CS 2500 Lab 9: Highway to Abstraction

• Work in pairs
• Change roles often!
• Follow the design recipe for every problem.

Exit 1: Function Warm-Up

Exercise 1:

Design a function that consumes an list of numbers ln and checks if 0 is a member of ln.

Exercise 2:

Design a function that consumes an list of numbers ln and checks if 6 is a member of ln.

Exercise 3:

Abstract over the previous two functions to design a function that consumes an list of numbers ln and a number n and checks if n is a member of ln.

Exercise 4:

Design a function that consumes an list of numbers ln and filters out all members of ln that are greater than 3.

Exercise 5:

Design a function that consumes an list of numbers ln and a number n and filters out all numbers less than n in ln.

Exercise 6:

Abstract over the previous two functions.

Exit 2: Parametric Data Definitions

     (define-struct unop (fun expr)) 
     (define-struct binop (fun left right))
     (define-struct var (x)) 
     
     ;; An NAExpr is one of
     ;; -- (make-var String)
     ;; -- (make-unop [Number -> Number] NAExpr)
     ;; -- (make-binop [Number Number -> Number] NAExpr NAExpr)
     ;; -- Number
   

Exercise 7:

An NAExpr is an arithmetic expression on Numbers. Give the data definition for an arithmetic expression of Booleans, BAExpr.

(Hint: Unary operators on Booleans include functions things not, and binary operators on Booleans include functions like and and or.)

Exercise 8:

Abstract over the two previous data definitions to obtain a data definition for a generic arithmetic expression. That is:

   ;; For any X, a [GAExpr X] is one of:
   ;; . . . ?

Exercise 9:

Design a function that consumes a generic arithmetic expression and counts all occurrences of constants (i.e., not variables or operations but the last case of the data definition).

Exercise 10:

Design a function that consumes a generic arithmetic expression, a String s and a value v and replaces all occurences of (make-var s) in the expression with v.

What kind of data does v have to be? What is the contract of your function?

Exit 3: Even More Parametric Data Definitions

When people stand in a queue (a line), they stay in order. New people enqueue (get in line) at the back, and when it’s their turn, people dequeue from the front.

A queue comes with five operations:

• enqueue adds an element at the end of the queue
• dequeue removes an element at the front and returns the remaining queue
• queue-head returns the element at the head of the queue
• empty-queue? tells whether a queue is empty
• make-empty-queue creates a new, empty queue

We will represent queues (somewhat inefficiently) using lists.

Here is a data definition for a queue of numbers is the following:

     ;; An NQueue is one of:
     ;; -- empty
     ;; -- (cons Number NQueue)
     ;; where the front of the NQueue is the first item in the list,
     ;; and the back of the NQueue is the final element of the list.

Exercise 11:

Give the data definition for a queue of strings.

Exercise 12:

Abstract over the two previous data definitions to obtain a data definition for a generic queue.

Exercise 13:

Design the five functions mentioned above for generic queues.

Can all of these functions succeed and return a sensible answer for all queues? If not, some of the functions may need to signal an error. See checked functions in Section 8.4.