WRIGHT STATE UNIVERSITY
Department of Computer Science and Engineering

Assignment 1 (Due: (Ex. 1) April 11 and (Ex. 2) April 30) (10 pts)

## 1. Recursive Definitions (2.5 pts)

EOPL 2nd ed. Text. Pages 26-27. Exercise 1.16: 1, 2, 4. Exercise 1.17: 1, 3.

EOPL 3rd ed. Text. Pages 27-29. Exercises 1.18, 1.26, 1.27. Exercises 1.30, 1.34.

## 2. Abstract Data Types (5 + 2.5 pts)

We explore the relationship between algebraic (axiomatic) specification of a (generic) data type and its implementation. You are required to specify the ADT Map1 that supports the following operations described only informally here:

• map: Yields the empty map.
• clear: Takes a map m and yields the empty map.
• containsKey: Takes a map m and a key k as input, and checks if m has k.
• containsValue: Takes a map m and a value v as input, and checks if m has v bound to some key.
• equals: Takes two maps m and n as input, and checks if m and n are equivalent, that is, contain similar bindings.
• get: Takes a map m and a key k as input, and yields the value bound to k in m.
• isEmpty: Takes a map m as input, and checks if m is empty.
• put: Takes a map m, a key k, and a value v as input, and yields a new map that behaves like m except that k is bound to v.
• remove: Takes a map m and a key k as input, and yields a new map which has k deleted from m (if it were present).
• size: Takes a map m as input, and yields the number of key-value pairs in m.
1. Specify the syntax and semantics of the ADT Map using algebraic (axiomatic) approach.
2. Give an implementation of the ADT Map in Scheme.

Note:  The ADT specs are written in functional style and as such do not support assignments. For example, put(m,k,v) does not change the state of the existing map m. Instead, conceptually, it creates a new map by "cloning'' m and then modifying the copy by inserting the new k-v binding.

What to hand-in?

Submit your well-documented solutions to (i) problem 1 in  defn.scm (containing Scheme functions including signature, test calls and outcomes (see Design Recipe and the sample given below)) and (ii) problem 2 in adt.scm (containing algebraic specs of the ADT as comments and a conforming  implementation in Scheme) by executing the following turn-in command on unixapps1.wright.edu.  (Make sure the solution files can be loaded and run in Racket without any modification.)

Sample "Well-documented" Definition

; HtDP book Exercise 5.1.2
;
Develop the function ``` check-guess```. It consumes two numbers, ``` guess``` and ``` target```.
; Depending on how `guess` relates to `target`, the function produces one of the following three answers: ``` ;'TooSmall```, ``` 'Perfect```, or `'TooLarge`.

; CONTRACT: check-guess : number   number -> { TooSmall, Perfect, TooLarge }
; PURPOSE:  check-guess takes two numbers - a guess and a target, and
;           returns a symbol TooSmall, Perfect or TooLarge
;           depending on whether target is more, equal or less than guess
; CODE:
(define (check-guess guess target)
(cond [(> guess target) 'TooLarge ]
[(< guess target) 'TooSmall ]
[(= guess target) 'Perfect ]
)
)
; TEST CASES and EXPECTED OUTCOMES
;(in general, focus on boundary conditions and coverage)
(check-guess 3 5) "should be" 'TooSmall
(check-guess 5 5) "should be" 'Perfect
(check-guess 7 5) "should be" 'TooLarge

#### Footnotes

... Map1
Reference: java.util.Map