David Evans cs.virginia/evans

1. Lecture 5: Implementing Data Abstractions David Evans http://www.cs.virginia.edu/evans CS201J: Engineering Software University of Virginia Computer Science

2. Menu • Data Abstraction • Specifying Abstract Data Types • Implementing Abstract Data Types CS 201J Fall 2003

3. Abstract Data Types • Separate what you can do with data from how it is represented • Client interacts with data through provided operations according to their specifications • Implementation chooses how to represent data and implement its operations CS 201J Fall 2003

4. Data Abstraction in Java • A class defines a new data type • Use private instance variables to hide the choice of representation • private declarations are only visible inside the class CS 201J Fall 2003

5. Up and Down Clients manipulate an abstract data type by calling its operations (methods and constructors) clients down up Abstract Type Concrete Representation class implementation The representation of an abstract data type is visible only in the class implementation. CS 201J Fall 2003

6. StringSet clients s.isIn () { “test”, “okay” } down up Abstract Type Concrete Representation private Vector res; class implementation public boolean isIn () { … } CS 201J Fall 2003

7. Advantages/Disadvantages • More code to write and maintain • Run-time overhead (time to call method) • Client doesn’t need to know about representation • Localize impact of changes CS 201J Fall 2003

8. StringSet Example • StringSet abstract data type: represent a set of strings • Support mathematical set operations: insert, isIn, size • Create an empty set CS 201J Fall 2003

9. Specifying Abstract Data Types • Overview: what does the type represent • Mutability/Immutability A StringSet is a mutable set of Strings. • Abstract Notation A typical StringSet is { x1, …, xn }. • Operations: specifications for constructors and methods clients use • Describe in terms of abstract notation introduced in overview. CS 201J Fall 2003

10. 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. CS 201J Fall 2003

11. Components of Data Abstractions • 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 CS 201J Fall 2003

12. StringSet Operations • Creators StringSet () • Producers none • Observers isIn, size • Mutators insert 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. CS 201J Fall 2003

13. Using Abstract Data Types • PS1, PS2 • Client interacts with data type using the methods as described in the specification • Client does not know the concrete representation CS 201J Fall 2003

14. Implementing Abstract Data Types CS 201J Fall 2003

15. Choosing a Representation • Need a concrete data representation to store the state • Think about how methods will be implemented • A good representation choice should: • Enable easy implementations of all methods • Allow performance-critical methods to be implemented efficiently CS 201J Fall 2003

16. StringSet Representation • Option 1: private String [] rep; • Recall Java arrays are bounded • Easy to implement most methods, hard to implement insert • Option 2: private Vector rep; • Easy to implement all methods • Performance may be worse than for array CS 201J Fall 2003

17. Implementing StringSet public class StringSet { // OVERVIEW: StringSets are unbounded, mutable sets of Strings. // A typical StringSet is {x1, ..., xn} // Representation: private Vector rep; public StringSet () { // EFFECTS: Initializes this to be empty: { } rep = new Vector (); } public void insert (String s) { // MODIFIES: this // EFFECTS: Adds s to the elements of this: // this_post = this_pre U { s } rep.add (s); } Could this implementation of insert be correct? CS 201J Fall 2003

18. It depends… public int size () { // EFFECTS: Returns the number of elements in this. StringSet uniqueels = new StringSet (); for (int i = 0; i < rep.size (); i++) { String current = (String) rep.elementAt (i); if (uniqueels.isIn (current)) { ; } else { uniqueels.insert (current); } } return uniqueels.rep.size (); } CS 201J Fall 2003

19. Is it correct? public int size () { // EFFECTS: Returns the number of // elements in this. return rep.size (); } public void insert (String s) { if (!isIn (s)) rep.add (s); } CS 201J Fall 2003

20. Reasoning About Data Abstractions • How can we possibly implement data abstractions correctly if correctness of one method depends on how other methods are implemented? • How can we possibly test a data abstraction implementation if there are complex interdependencies between methods? CS 201J Fall 2003

21. What must we know to know size is correct? • This implementation is correct only if we know the rep does not contain duplicates public int size () { // EFFECTS: Returns the number of // elements in this. return rep.size (); } CS 201J Fall 2003

22. Rep Invariant • The Representation Invariant expresses properties all legitimate objects of the ADT must satisfy I: C→ boolean Function from concrete representation to boolean. • Helps us reason about correctness of methods independently CS 201J Fall 2003

23. Reasoning with Rep Invariants • Prove all objects satisfy the invariant before leaving the implementation code • Assume all objects passed in satisfy the invariant REQUIRES: Rep Invariant is true for this (and any other reachable ADT objects) EFFECTS: Rep Invariant is true for all new and modified ADT object on exit. CS 201J Fall 2003

24. Rep Invariant for StringSet 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 CS 201J Fall 2003

25. Implementing Insert? public void insert (String s) { // MODIFIES: this // EFFECTS: Adds s to the elements of this: // this_post = this_pre U { s } rep.add (s); } Not a correct implementation: after it returns this might not satisfy the rep invariant! CS 201J Fall 2003

26. Implementing Insert public void insert (String s) { // MODIFIES: this // EFFECTS: Adds s to the elements of this: // this_post = this_pre U { s } if (!isIn (s)) { rep.add (s); } } Possibly correct implementation: we need to know how to map rep to abstraction notation to know if this_post = this_pre U { s } CS 201J Fall 2003

27. Tomorrow in Section • Return PS2 • Consider how to implement the Graph datatype specified in your notes • Think about possible representations before tomorrow’s class CS 201J Fall 2003