CS 3500 Assignment #1
Assigned:  Friday, 7 September 2012
Due:  Friday, 14 September 2012

The purpose of this assignment is:

 * To review basic Java programming concepts
 * To review static methods in Java
 * To review the Java API (application programming interface)
 * To acquaint you with the development system you choose to use
 * To learn the required process for submitting homework in this course
 * To begin our study of abstraction-based software design with an
   algebraic specification for an abstract data type of immutable sets

You will complete an implementation in Java of the FSet ADT
that is specified below.  Collaboration between students is
forbidden on this assignment.  You are responsible for keeping your
code hidden from all other students.  Turn in your work on this
assignment before 10 pm on the due date by following instructions
on the course's main assignments web page,
http://www.ccs.neu.edu/home/vkp/3500-fl12/Assignments.html

Your file of Java code should begin with a block comment that lists
    1.  Your name, as you want the instructor to write it.
    2.  Your email address.
    3.  Any remarks that you wish to make to the instructor.

Part of your grade will depend on the quality and correctness of your
code, part will depend on the readability of your code (comments and
indentation), and part will depend on how well you follow the procedure
above for submitting your work.  Late assignments may be discounted,
and very late assignments may be discarded.

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Your assignment is to write the code for a single file, FSet.java,
that implements the specification below.  A test program
(/net/course/cs3500vkpf12/Assignments/A1/TestFSet.java) will be provided.

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Specification of the FSet ADT.

FSet is an immutable abstract data type whose values represent
finite sets with elements of type Double.

The FSet ADT shall be implemented in Java, and will be tested
using Sun's Java 2 Runtime Environment, Standard Edition, version 1.6.0.
The code for this implementation shall be in the default package, and
shall define a public class named FSet.  The operations of the
FSet class shall be provided by the following public methods
of the FSet class:


Signature:

  Static methods:

    emptySet  :                                 ->  FSet
    insert    : FSet x Double                   ->  FSet
    add       : FSet x Double                   ->  FSet
    size      : FSet                            ->  int
    isEmpty   : FSet                            ->  boolean
    contains  : FSet x Double                   ->  boolean
    isSubset  : FSet x FSet                     ->  boolean
    absent    : FSet x Double                   ->  FSet
    union     : FSet x FSet                     ->  FSet
    intersect : FSet x FSet                     ->  FSet

  Dynamic methods (for which the receiver is an FSet):
    toString  :                                 ->  String
    equals    :  Object                         ->  boolean
    hashCode  :                                 ->  int

Restrictions:

    Null arguments may not be passed to any of the above methods
    except for equals(Object).

Algebraic specification:

    FSet.add (s, k)  =  s                      if FSet.contains (s, k)
    FSet.add (s, k)  =  FSet.insert (s, k)     if ! (FSet.contains (s, k))

    FSet.size (FSet.emptySet())  =  0
    FSet.size (FSet.insert (s0, k0))
        =  FSet.size (s0)                      if FSet.contains (s0, k0)
    FSet.size (FSet.insert (s0, k0))
        =  1 + FSet.size (s0)                  if ! (FSet.contains (s0, k0))

    FSet.isEmpty (FSet.emptySet())  =  true
    FSet.isEmpty (FSet.insert(s0, k0))  =  false

    FSet.contains (FSet.emptySet(), k)  =  false
    FSet.contains (FSet.insert (s0, k0), k)
        =  true                                if k.equals(k0)
    FSet.contains (FSet.insert (s0, k0), k)
        =  FSet.contains (s0, k)               if ! (k.equals(k0))

    FSet.isSubset (FSet.emptySet(), s2)  =  true
    FSet.isSubset (FSet.insert (s0, k0), s2)
        =  FSet.isSubset (s0, s2)              if FSet.contains (s2, k0)
    FSet.isSubset (FSet.insert (s0, k0), s2)
        =  false                               if ! (FSet.contains (s2, k0))

    FSet.absent (FSet.emptySet(), k)  =  FSet.emptySet()
    FSet.absent (FSet.insert (s0, k0), k)
        =  FSet.absent (s0, k)                 if k.equals(k0)
    FSet.absent (FSet.insert (s0, k0), k)
        =  FSet.insert (FSet.absent (s0, k), k0)
                                               if ! (k.equals(k0))

    FSet.union (FSet.emptySet(), s2)  =  s2
    FSet.union (FSet.insert (s0, k0), s2)
        =  FSet.union (s0, s2)                 if FSet.contains (s2, k0)
    FSet.union (FSet.insert (s0, k0), s2)
        =  FSet.insert (FSet.union (s0, s2), k0)
                                               if ! (FSet.contains (s2, k0))

    FSet.intersect (FSet.emptySet(), s2)  =  FSet.emptySet()
    FSet.intersect (FSet.insert (s0, k0), s2)
        =  FSet.insert (FSet.intersect (s0, s2), k0)
                                               if FSet.contains (s2, k0)
    FSet.intersect (FSet.insert (s0, k0), s2)
        =  FSet.intersect (s0, s2)
                                               if ! (FSet.contains (s2, k0))

    s.toString() = "{...(" + FSet.size(s) + " elements)...}"

Values of the FSet ADT shall also implement the public
dynamic methods equals(Object) and hashCode() such that

    If s1 is a value of the FSet ADT, then

        s1.equals(null) returns false.

    If s1 is a value of the FSet ADT, but x is not, then

        s1.equals(x) returns false.

    If s1 and s2 are values of the FSet ADT, then
    s1.equals(s2) if and only if

        for every Double k

            FSet.contains (s1, k) if and only if FSet.contains (s2, k)

    If s1 and s2 are values of the FSet ADT, and

        s1.equals(s2)

    then s1.hashCode() == s2.hashCode().

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