Notes: Tuesday 10 September 2002

Assignments Due

• Now: Problem Set 2
• 12 September: Read Ch 5.3-5.10
• 19 September: Problem Set 3
• Lab hours this week (Small Hall): Thursday, 5-7pm (Sol); 7-9pm (Tiffany); Sunday 4-6pm (Mike), 6-8pm (Serge)

Notes and Questions

What are the advantages and disadvantages of using abstract data types?

Specifying Abstract Data Types

• Overview: what does the type represent. Should always include:
  • Mutability/Immutability (e.g., A StringSet is a mutable set of Strings.)
  • Abstract Notation (e.g., A typical StringSet is { x1, , xn }.)
• Operations: specifications for constructors and methods clients use Describe in terms of abstract notation introduced in overview.
  • Ways to create objects of the data type
    • Creators: create new objects of the ADT from parameters of other types
    • Producers: create new objects of the ADT from parameters of the ADT type (and other types)
  • Ways to observe properties: observers
  • Ways to change properties: mutators (mutable data types only)

StringSet Specification

public class StringSet
    // OVERVIEW: StringSets are unbounded, mutable sets of
    //     Strings.  A typical StringSet is { x1, ..., xn }
    public StringSet () 
        // EFFECTS: Initializes this to be empty: { }
    public void insert (String s) 
        // MODIFIES: this
        // EFFECTS: Adds x to the elements of this: 
        //       this_post = this_pre U { s }
    public boolean isIn (String s) {
        // EFFECTS: Returns true iff s is an element of this.
    public int size () 
        // EFFECTS: Returns the number of elements in this.

Representation Invariant

The Representation Invariant expresses properties all legitimate objects of the ADT must satisfy. It is a function from concrete representation to boolean:

I: C → boolean

To check correctness we assume all objects passed in to a procedure satisfy the invariant and prove all objects satisfy the invariant before leaving the implementation code.

public class StringSet {
   // OVERVIEW: StringSets are unbounded, mutable sets of Strings.
   //    A typical StringSet is {x1, ..., xn}

   // Representation:
   private Vector rep;

   // RepInvariant (c) = c contains no duplicates && c != null

Abstraction Function

The Abstraction Function maps a concrete state to an abstract state:

AF: C → A

It is a function from concrete representation to the abstract notation introduced in overview specification.

   // AF (c) = { AFString (c.els[i]) | 0 <= i < c.els.size () }

It is better to have 100 functions operate on one data structure than 10 functions on 10 data structures.

Alan Perlis

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University of Virginia Department of Computer Science CS 201J: Engineering Software

Sponsored by the National Science Foundation

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