org.jmlspecs.models.resolve
Class NaturalNumber

java.lang.Object
  java.lang.Number
      org.jmlspecs.models.resolve.NaturalNumber

All Implemented Interfaces:

AntisymmetricCompareTo, Cloneable, Comparable, CompareTo, JMLType, PreorderedCompareTo, ReflexiveCompareTo, Serializable, TotalCompareTo, TotallyOrderedCompareTo, TotalPreorderedCompareTo, TransitiveCompareTo

public class NaturalNumber

extends Number

implements TotallyOrderedCompareTo, JMLType

The natural numbers. These are essentially unlimited in size.

Version:

$Revision: 1.26 $

Author:

Gary T. Leavens

See Also:

BigInteger, JMLFiniteInteger

Class Specifications

private invariant this.value.compareTo(java.math.BigInteger.ZERO) >= 0; public invariant this.owner == null; public invariant org.jmlspecs.models.resolve.NaturalNumber.ZERO != null&&org.jmlspecs.models.resolve.NaturalNumber.ZERO.equals(valueOf(0)); public invariant org.jmlspecs.models.resolve.NaturalNumber.ONE != null&&org.jmlspecs.models.resolve.NaturalNumber.ONE.equals(valueOf(1)); private constraint_redundantly this.value == \old(this.value); public constraint org.jmlspecs.models.resolve.NaturalNumber.ZERO == \old(org.jmlspecs.models.resolve.NaturalNumber.ZERO); public constraint org.jmlspecs.models.resolve.NaturalNumber.ONE == \old(org.jmlspecs.models.resolve.NaturalNumber.ONE);

Specifications inherited from class Object

represents objectState <- org.jmlspecs.lang.JMLDataGroup.IT; public represents _getClass <- \typeof(this);

Specifications inherited from interface AntisymmetricCompareTo

instance public invariant ( \forall org.jmlspecs.models.resolve.AntisymmetricCompareTo x, y; x != null&&y != null&&x.isComparableTo(y)&&y.isComparableTo(x); x.compareTo(y) <= 0&&y.compareTo(x) <= 0 ==> x.compareTo(y) == 0); instance public invariant_redundantly ( \forall org.jmlspecs.models.resolve.AntisymmetricCompareTo x, y; x != null&&y != null&&x.isComparableTo(y)&&y.isComparableTo(x); x.compareTo(y) >= 0&&y.compareTo(x) >= 0 ==> x.compareTo(y) == 0);

Specifications inherited from interface Comparable

instance public invariant ( \forall java.lang.Comparable x; x != null; x.compareTo(x) == 0); instance public invariant ( \forall java.lang.Comparable x, y; x != null&&y != null&&this.definedComparison(x,y)&&this.definedComparison(y,x); this.sgn(x.compareTo(y)) == -this.sgn(y.compareTo(x))); instance public invariant ( \forall int n; n == -1||n == 1; ( \forall java.lang.Comparable x, y, z; x != null&&y != null&&z != null&&this.definedComparison(x,y)&&this.definedComparison(y,z)&&this.definedComparison(x,z); this.sgn(x.compareTo(y)) == n&&this.sgn(y.compareTo(z)) == n ==> this.sgn(x.compareTo(z)) == n)); instance public invariant ( \forall int n; n == -1||n == 1; ( \forall java.lang.Comparable x, y, z; x != null&&y != null&&z != null&&this.definedComparison(x,y)&&this.definedComparison(y,z)&&this.definedComparison(x,z); (this.sgn(x.compareTo(y)) == 0&&this.sgn(y.compareTo(z)) == n||this.sgn(x.compareTo(y)) == n&&this.sgn(y.compareTo(z)) == 0) ==> this.sgn(x.compareTo(z)) == n)); instance public invariant ( \forall java.lang.Comparable x, y, z; x != null&&y != null&&z != null&&this.definedComparison(x,y)&&this.definedComparison(x,z)&&this.definedComparison(y,z); this.sgn(x.compareTo(y)) == 0 ==> this.sgn(x.compareTo(z)) == this.sgn(y.compareTo(z)));

Specifications inherited from interface ReflexiveCompareTo

instance public invariant ( \forall org.jmlspecs.models.resolve.ReflexiveCompareTo x; x != null; x.isComparableTo(x)&&x.compareTo(x) == 0);

Specifications inherited from interface TransitiveCompareTo

instance public invariant ( \forall org.jmlspecs.models.resolve.TransitiveCompareTo x, y, z; x != null&&y != null&&z != null&&x.isComparableTo(y)&&y.isComparableTo(z); x.compareTo(y) < 0&&y.compareTo(z) < 0 ==> x.isComparableTo(z)&&x.compareTo(z) < 0); instance public invariant ( \forall org.jmlspecs.models.resolve.TransitiveCompareTo x, y, z; x != null&&y != null&&z != null&&x.isComparableTo(y)&&y.isComparableTo(z); x.compareTo(y) <= 0&&y.compareTo(z) <= 0 ==> x.isComparableTo(z)&&x.compareTo(z) <= 0); instance public invariant ( \forall org.jmlspecs.models.resolve.TransitiveCompareTo x, y, z; x != null&&y != null&&z != null&&x.isComparableTo(y)&&y.isComparableTo(z); x.compareTo(y) == 0&&y.compareTo(z) == 0 ==> x.isComparableTo(z)&&x.compareTo(z) == 0); instance public invariant_redundantly ( \forall org.jmlspecs.models.resolve.TransitiveCompareTo x, y, z; x != null&&y != null&&z != null&&x.isComparableTo(y)&&y.isComparableTo(z); x.compareTo(y) >= 0&&y.compareTo(z) >= 0 ==> x.isComparableTo(z)&&x.compareTo(z) >= 0); instance public invariant_redundantly ( \forall org.jmlspecs.models.resolve.TransitiveCompareTo x, y, z; x != null&&y != null&&z != null&&x.isComparableTo(y)&&y.isComparableTo(z); x.compareTo(y) > 0&&y.compareTo(z) > 0 ==> x.isComparableTo(z)&&x.compareTo(z) > 0);

Model Field Summary

 

Model fields inherited from class java.lang.Object

_getClass, objectState, theString

 

Ghost Field Summary

 

Ghost fields inherited from class java.lang.Object

objectTimesFinalized, owner

 

Field Summary
private static NaturalNumber	intMaxVal           The maximum integer as a natural number.
static NaturalNumber	ONE           The natural number one.
private  BigInteger	value           The value of this natural number.
static NaturalNumber	ZERO           The natural number zero.

 

Constructor Summary

NaturalNumber()           Initialize this natural number to zero.

NaturalNumber(non_null BigInteger val)           Initialize this natural number to the given BigInteger value.

NaturalNumber(long val)           Initialize this natural number to the given long value.

 

Model Method Summary

 

Model methods inherited from class java.lang.Object

hashValue

 

Model methods inherited from interface org.jmlspecs.models.resolve.CompareTo

isComparableTo

 

Model methods inherited from interface org.jmlspecs.models.resolve.TotalCompareTo

isComparableTo

 

Model methods inherited from interface java.lang.Comparable

definedComparison, sgn

 

Method Summary
NaturalNumber	add(non_null NaturalNumber val)           Return the sum of this natural number and the given one.
BigInteger	bigIntegerValue()           Return the BigInteger value of this natural number.
Object	clone()           Return a clone of this object.
int	compareTo(non_null Object o)           Compare this to obj, returning negative if this is strictly less than obj, 0 if they are equal, and positive otherwise.
int	compareTo(non_null BigInteger val)
int	compareTo(non_null NaturalNumber val)           Return negative if this natural numbers strictly less than the given one, 0 if they are equal, and positive if this natural numbers is strictly greater than the given one.
NaturalNumber	divide(non_null NaturalNumber val)           Return the quotient of this natural number divided by the given one.
boolean	divides(non_null NaturalNumber val)           Tell if this natural number divides the given one evenly.
double	doubleValue()
boolean	equals(nullable Object x)           Tell if this object is equal to the given argument.
float	floatValue()
NaturalNumber	gcd(non_null NaturalNumber val)           Return the greatest common denominator of this number and the given number.
int	hashCode()           Return a hash code for this object.
int	intValue()
boolean	isZero()           Tell if this object is equal to zero.
long	longValue()
NaturalNumber	max(non_null NaturalNumber val)           Return the smaller of the given natural number and this one.
NaturalNumber	min(non_null NaturalNumber val)           Return the smaller of the given natural number and this one.
NaturalNumber	mod(non_null NaturalNumber m)           Return this natural number modulo the given one.
NaturalNumber	multiply(non_null NaturalNumber val)           Return the product of this natural number and the given one.
NaturalNumber	pow(int exponent)           Return this natural number multiplied by itself the given number of times.
NaturalNumber	pow(non_null NaturalNumber exponent)           Return this natural number multiplied by itself the given number of times.
NaturalNumber	remainder(non_null NaturalNumber val)           Return the remainder of this natural number divided by the given one.
NaturalNumber	shiftLeft(int n)           Return this natural number left shifted the given number of bits.
NaturalNumber	shiftRight(int n)           Return this natural number right shifted the given number of bits.
NaturalNumber	suc()           Return the successor of this natural number.
static NaturalNumber	suc(non_null NaturalNumber v)           Return the successor of the given natural number.
String	toString()
static NaturalNumber	valueOf(long val)           Return a natural number with the given value.

 

Methods inherited from class java.lang.Number

byteValue, shortValue

 

Methods inherited from class java.lang.Object

finalize, getClass, notify, notifyAll, wait, wait, wait

 

Field Detail

value

private final BigInteger value

The value of this natural number.

Specifications: non_null
is in groups: objectState

ZERO

public static final NaturalNumber ZERO

The natural number zero.

See Also:

NaturalNumber(), ONE

Specifications: non_null

ONE

public static final NaturalNumber ONE

The natural number one.

See Also:

NaturalNumber(long), valueOf(long), ZERO

Specifications: non_null

intMaxVal

private static final NaturalNumber intMaxVal

The maximum integer as a natural number.

Specifications: non_null

NaturalNumber

public NaturalNumber()

Initialize this natural number to zero.

See Also:

ZERO, NaturalNumber(long), NaturalNumber(BigInteger)

Specifications: (class)pure

public normal_behavior
assignable objectState, owner;
ensures this.isZero();

NaturalNumber

public NaturalNumber(long val)
              throws IllegalArgumentException

Initialize this natural number to the given long value.

Throws:

IllegalArgumentException

See Also:

NaturalNumber(), NaturalNumber(BigInteger), valueOf(long)

Specifications: (class)pure

public normal_behavior
requires val >= 0;
assignable objectState, owner;
ensures this.longValue() == val;

     also

signals (java.lang.IllegalArgumentException) val < 0;

NaturalNumber

public NaturalNumber(non_null BigInteger val)
              throws IllegalArgumentException

Initialize this natural number to the given BigInteger value.

Throws:

IllegalArgumentException

See Also:

NaturalNumber(), NaturalNumber(BigInteger)

Specifications: (class)pure

public normal_behavior
requires val != null&&val.compareTo(java.math.BigInteger.ZERO) >= 0;
assignable objectState, owner;
ensures this.bigIntegerValue().equals(val);

valueOf

public static NaturalNumber valueOf(long val)

Return a natural number with the given value.

See Also:

NaturalNumber(long), NaturalNumber(BigInteger)

Specifications: pure non_null

public normal_behavior
requires val >= 0;
ensures \result != null&&\result .equals(new org.jmlspecs.models.resolve.NaturalNumber(val));

    implies_that

requires val >= 0;

suc

public NaturalNumber suc()

Return the successor of this natural number.

See Also:

suc(NaturalNumber), add(org.jmlspecs.models.resolve.NaturalNumber), ONE

Specifications: non_null (class)pure

public normal_behavior
ensures \result != null&&\result .equals(this.add(org.jmlspecs.models.resolve.NaturalNumber.ONE));

suc

public static NaturalNumber suc(non_null NaturalNumber v)

Return the successor of the given natural number.

See Also:

suc(), add(org.jmlspecs.models.resolve.NaturalNumber)

Specifications: pure non_null

public normal_behavior
requires v != null;
ensures \result != null&&\result .equals(v.suc());
ensures_redundantly \result != null&&\result .equals(v.add(org.jmlspecs.models.resolve.NaturalNumber.ONE));

add

public NaturalNumber add(non_null NaturalNumber val)

Return the sum of this natural number and the given one.

See Also:

suc(), add(org.jmlspecs.models.resolve.NaturalNumber)

Specifications: non_null (class)pure

public normal_behavior
requires val != null;

{|

requires val.equals(org.jmlspecs.models.resolve.NaturalNumber.ZERO);
ensures \result != null&&\result .equals(this);

also

forall org.jmlspecs.models.resolve.NaturalNumber v;
requires !(val.equals(org.jmlspecs.models.resolve.NaturalNumber.ZERO));
ensures v != null&&v.suc().equals(val) ==> \result != null&&\result .equals(this.add(v).suc());

|}

    for_example

public normal_example
requires val != null&&val.equals(new org.jmlspecs.models.resolve.NaturalNumber(3))&&this.equals(new org.jmlspecs.models.resolve.NaturalNumber(7));
ensures \result != null&&\result .equals(new org.jmlspecs.models.resolve.NaturalNumber(10));

multiply

public NaturalNumber multiply(non_null NaturalNumber val)

Return the product of this natural number and the given one.

See Also:

divide(org.jmlspecs.models.resolve.NaturalNumber)

Specifications: non_null (class)pure

public normal_behavior
requires val != null;

{|

requires val.equals(org.jmlspecs.models.resolve.NaturalNumber.ZERO);
ensures \result != null&&\result .isZero();

also

forall org.jmlspecs.models.resolve.NaturalNumber v;
requires !(val.equals(org.jmlspecs.models.resolve.NaturalNumber.ZERO));
ensures v != null&&v.suc().equals(val) ==> \result != null&&\result .equals(this.add(this.multiply(v)));

|}

    implies_that

public normal_behavior
requires val != null&&val.equals(org.jmlspecs.models.resolve.NaturalNumber.ONE);
ensures \result != null&&\result .equals(this);

    for_example

public normal_example
requires val != null&&val.equals(new org.jmlspecs.models.resolve.NaturalNumber(3))&&this.equals(new org.jmlspecs.models.resolve.NaturalNumber(7));
ensures \result != null&&\result .equals(new org.jmlspecs.models.resolve.NaturalNumber(21));

divide

public NaturalNumber divide(non_null NaturalNumber val)

Return the quotient of this natural number divided by the given one.

See Also:

multiply(org.jmlspecs.models.resolve.NaturalNumber)

Specifications: non_null (class)pure

public normal_behavior
forall org.jmlspecs.models.resolve.NaturalNumber quot;
forall org.jmlspecs.models.resolve.NaturalNumber rem;
requires val != null&&!val.equals(org.jmlspecs.models.resolve.NaturalNumber.ZERO);
ensures quot != null&&rem != null&&rem.compareTo(this) < 0&&this.equals(rem.add(quot.multiply(val))) ==> \result .equals(quot);

     also

public exceptional_behavior
requires val != null&&val.equals(org.jmlspecs.models.resolve.NaturalNumber.ZERO);
signals_only java.lang.ArithmeticException;

    implies_that

public normal_behavior
requires val != null&&val.equals(org.jmlspecs.models.resolve.NaturalNumber.ONE);
ensures \result != null&&\result .equals(this);

    for_example

public normal_example
requires val != null&&val.equals(new org.jmlspecs.models.resolve.NaturalNumber(3))&&this.equals(new org.jmlspecs.models.resolve.NaturalNumber(22));
ensures \result != null&&\result .equals(new org.jmlspecs.models.resolve.NaturalNumber(7));

remainder

public NaturalNumber remainder(non_null NaturalNumber val)

Return the remainder of this natural number divided by the given one.

See Also:

divide(org.jmlspecs.models.resolve.NaturalNumber)

Specifications: non_null (class)pure

public normal_behavior
forall org.jmlspecs.models.resolve.NaturalNumber quot;
forall org.jmlspecs.models.resolve.NaturalNumber rem;
requires val != null&&!val.equals(org.jmlspecs.models.resolve.NaturalNumber.ZERO);
ensures quot != null&&rem != null&&rem.compareTo(this) < 0&&this.equals(rem.add(quot.multiply(val))) ==> \result .equals(rem);

     also

public exceptional_behavior
requires val != null&&val.equals(org.jmlspecs.models.resolve.NaturalNumber.ZERO);
signals_only java.lang.ArithmeticException;

    implies_that

public normal_behavior
requires val != null&&val.equals(org.jmlspecs.models.resolve.NaturalNumber.ONE);
ensures \result != null&&\result .equals(org.jmlspecs.models.resolve.NaturalNumber.ZERO);

    for_example

public normal_example
requires val != null&&val.equals(new org.jmlspecs.models.resolve.NaturalNumber(3))&&this.equals(new org.jmlspecs.models.resolve.NaturalNumber(22));
ensures \result != null&&\result .equals(new org.jmlspecs.models.resolve.NaturalNumber(1));

pow

public NaturalNumber pow(non_null NaturalNumber exponent)
                  throws OutOfMemoryError

Return this natural number multiplied by itself the given number of times.

Throws:

OutOfMemoryError

See Also:

multiply(org.jmlspecs.models.resolve.NaturalNumber), pow(int)

Specifications: non_null (class)pure

public normal_behavior
requires exponent != null;

{|

requires !this.isZero()&&exponent.equals(org.jmlspecs.models.resolve.NaturalNumber.ZERO);
ensures \result != null&&\result .equals(org.jmlspecs.models.resolve.NaturalNumber.ONE);

also

forall org.jmlspecs.models.resolve.NaturalNumber v;
requires !(exponent.equals(org.jmlspecs.models.resolve.NaturalNumber.ZERO))&&exponent.compareTo(java.math.BigInteger.valueOf(2147483647)) <= 0;
ensures v != null&&v.suc().equals(exponent) ==> \result != null&&\result .equals(this.multiply(this.pow(v)));

|}

    implies_that

public normal_behavior
requires exponent != null&&exponent.equals(org.jmlspecs.models.resolve.NaturalNumber.ONE);
ensures \result != null&&\result .equals(this);

     also

public normal_behavior
requires exponent != null&&this.isZero()&&!exponent.isZero()&&exponent.compareTo(java.math.BigInteger.valueOf(2147483647)) <= 0;
ensures \result != null&&\result .equals(org.jmlspecs.models.resolve.NaturalNumber.ZERO);
ensures_redundantly \result != null&&\result .equals(this);

    for_example

public normal_example
requires exponent != null&&exponent.equals(new org.jmlspecs.models.resolve.NaturalNumber(3))&&this.equals(new org.jmlspecs.models.resolve.NaturalNumber(3));
ensures \result != null&&\result .equals(new org.jmlspecs.models.resolve.NaturalNumber(27));

pow

public NaturalNumber pow(int exponent)

Return this natural number multiplied by itself the given number of times.

See Also:

multiply(org.jmlspecs.models.resolve.NaturalNumber), pow(NaturalNumber)

Specifications: non_null (class)pure

public normal_behavior
requires exponent >= 0;

{|

requires !this.isZero()&&exponent == 0;
ensures \result != null&&\result .equals(org.jmlspecs.models.resolve.NaturalNumber.ONE);

also

forall int v;
requires exponent != 0;
ensures v+1 == exponent ==> \result != null&&\result .equals(this.multiply(this.pow(v)));

|}

    implies_that

public normal_behavior
requires exponent == 1;
ensures \result != null&&\result .equals(this);

gcd

public NaturalNumber gcd(non_null NaturalNumber val)

Return the greatest common denominator of this number and the given number.

Specifications: non_null (class)pure

public normal_behavior
forall org.jmlspecs.models.resolve.NaturalNumber n;
requires !this.isZero()&&val != null&&!val.isZero();
ensures n != null&&n.divides(this)&&n.divides(val)&&( \forall org.jmlspecs.models.resolve.NaturalNumber m; m != null&&m.divides(this)&&m.divides(val); n.compareTo(m) >= 0) ==> \result .equals(n);

     also

public normal_behavior
requires this.isZero()&&val != null&&val.isZero();
ensures \result .isZero();

    for_example

public normal_example
requires val != null&&val.equals(new org.jmlspecs.models.resolve.NaturalNumber(12))&&this.equals(new org.jmlspecs.models.resolve.NaturalNumber(30));
ensures \result != null&&\result .equals(new org.jmlspecs.models.resolve.NaturalNumber(6));

mod

public NaturalNumber mod(non_null NaturalNumber m)

Return this natural number modulo the given one.

See Also:

remainder(org.jmlspecs.models.resolve.NaturalNumber)

Specifications: non_null (class)pure

public normal_behavior
requires m != null&&!m.isZero();
ensures \result .equals(this.remainder(m));

     also

public exceptional_behavior
requires m != null&&m.equals(org.jmlspecs.models.resolve.NaturalNumber.ZERO);
signals_only java.lang.ArithmeticException;

shiftLeft

public NaturalNumber shiftLeft(int n)

Return this natural number left shifted the given number of bits.

See Also:

shiftRight(int), pow(int)

Specifications: non_null (class)pure

public normal_behavior
requires n >= 0;
ensures \result != null&&\result .equals(this.multiply(new org.jmlspecs.models.resolve.NaturalNumber(2).pow(new org.jmlspecs.models.resolve.NaturalNumber(n))));

     also

public normal_behavior
requires n <= 0;
ensures \result != null&&\result .equals(this.shiftRight(java.lang.Math.abs(n)));

    implies_that

public normal_behavior
requires n == 0;
ensures \result != null&&\result .equals(this);

shiftRight

public NaturalNumber shiftRight(int n)

Return this natural number right shifted the given number of bits.

See Also:

shiftLeft(int), pow(int)

Specifications: non_null (class)pure

public normal_behavior
requires n >= 0;
ensures \result != null&&\result .equals(this.divide(new org.jmlspecs.models.resolve.NaturalNumber(2).pow(new org.jmlspecs.models.resolve.NaturalNumber(n))));

     also

public normal_behavior
requires n <= 0;
ensures \result != null&&\result .equals(this.shiftLeft(java.lang.Math.abs(n)));

compareTo

public int compareTo(non_null NaturalNumber val)

Return negative if this natural numbers strictly less than the given one, 0 if they are equal, and positive if this natural numbers is strictly greater than the given one.

See Also:

compareTo(Object), equals(java.lang.Object)

Specifications: (class)pure

public normal_behavior
requires val != null;
ensures \result == this.bigIntegerValue().compareTo(val.bigIntegerValue());

Specifications inherited from overridden method compareTo(Object o) in interface Comparable:
       pure

public behavior
requires o != null;
ensures (* \result is negative if this is "less than" o *);
ensures (* \result is 0 if this is "equal to" o *);
ensures (* \result is positive if this is "greater than" o *);
signals_only java.lang.ClassCastException;
signals (java.lang.ClassCastException) (* the class of o prohibits it from being compared to this *);

     also

public behavior
requires o != null&&o instanceof java.lang.Comparable;
ensures this.definedComparison((java.lang.Comparable)o,this);
ensures o == this ==> \result == 0;
ensures this.sgn(\result ) == -this.sgn(((java.lang.Comparable)o).compareTo(this));
signals (java.lang.ClassCastException) !this.definedComparison((java.lang.Comparable)o,this);

Specifications inherited from overridden method compareTo(Object obj) in interface TotalCompareTo:
       pure

     also

public behavior
requires obj != null;
ensures obj instanceof org.jmlspecs.models.resolve.TotalCompareTo;
signals_only java.lang.ClassCastException;
signals (java.lang.ClassCastException) !(obj instanceof org.jmlspecs.models.resolve.TotalCompareTo);

Specifications inherited from overridden method compareTo(Object obj) in interface CompareTo:
       pure

public behavior
requires obj != null;
ensures this.isComparableTo(obj);
ensures (* returns if this is comparable to obj *);
signals_only org.jmlspecs.models.resolve.UndefinedException, java.lang.ClassCastException;
signals (org.jmlspecs.models.resolve.UndefinedException e) (* no comparison between this and obj is defined *)&&e != null;
signals (java.lang.ClassCastException e) (* obj's type prevents it from being compared to this *)&&e != null;

compareTo

public int compareTo(non_null BigInteger val)

Specifications: (class)pure

public normal_behavior
ensures \result == this.bigIntegerValue().compareTo(val);

Specifications inherited from overridden method compareTo(Object o) in interface Comparable:
       pure

public behavior
requires o != null;
ensures (* \result is negative if this is "less than" o *);
ensures (* \result is 0 if this is "equal to" o *);
ensures (* \result is positive if this is "greater than" o *);
signals_only java.lang.ClassCastException;
signals (java.lang.ClassCastException) (* the class of o prohibits it from being compared to this *);

     also

public behavior
requires o != null&&o instanceof java.lang.Comparable;
ensures this.definedComparison((java.lang.Comparable)o,this);
ensures o == this ==> \result == 0;
ensures this.sgn(\result ) == -this.sgn(((java.lang.Comparable)o).compareTo(this));
signals (java.lang.ClassCastException) !this.definedComparison((java.lang.Comparable)o,this);

Specifications inherited from overridden method compareTo(Object obj) in interface TotalCompareTo:
       pure

     also

public behavior
requires obj != null;
ensures obj instanceof org.jmlspecs.models.resolve.TotalCompareTo;
signals_only java.lang.ClassCastException;
signals (java.lang.ClassCastException) !(obj instanceof org.jmlspecs.models.resolve.TotalCompareTo);

Specifications inherited from overridden method compareTo(Object obj) in interface CompareTo:
       pure

public behavior
requires obj != null;
ensures this.isComparableTo(obj);
ensures (* returns if this is comparable to obj *);
signals_only org.jmlspecs.models.resolve.UndefinedException, java.lang.ClassCastException;
signals (org.jmlspecs.models.resolve.UndefinedException e) (* no comparison between this and obj is defined *)&&e != null;
signals (java.lang.ClassCastException e) (* obj's type prevents it from being compared to this *)&&e != null;

compareTo

public int compareTo(non_null Object o)
              throws ClassCastException

Description copied from interface: CompareTo

Compare this to obj, returning negative if this is strictly less than obj, 0 if they are equal, and positive otherwise.

Specified by:

compareTo in interface CompareTo

Throws:

ClassCastException

Specifications: (class)pure

     also

public normal_behavior
requires o != null&&o instanceof org.jmlspecs.models.resolve.NaturalNumber;
requires this.equals(o);
ensures \result == 0;

Specifications inherited from overridden method compareTo(Object o) in interface Comparable:
       pure

public behavior
requires o != null;
ensures (* \result is negative if this is "less than" o *);
ensures (* \result is 0 if this is "equal to" o *);
ensures (* \result is positive if this is "greater than" o *);
signals_only java.lang.ClassCastException;
signals (java.lang.ClassCastException) (* the class of o prohibits it from being compared to this *);

     also

public behavior
requires o != null&&o instanceof java.lang.Comparable;
ensures this.definedComparison((java.lang.Comparable)o,this);
ensures o == this ==> \result == 0;
ensures this.sgn(\result ) == -this.sgn(((java.lang.Comparable)o).compareTo(this));
signals (java.lang.ClassCastException) !this.definedComparison((java.lang.Comparable)o,this);

Specifications inherited from overridden method compareTo(Object obj) in interface TotalCompareTo:
       pure

     also

public behavior
requires obj != null;
ensures obj instanceof org.jmlspecs.models.resolve.TotalCompareTo;
signals_only java.lang.ClassCastException;
signals (java.lang.ClassCastException) !(obj instanceof org.jmlspecs.models.resolve.TotalCompareTo);

Specifications inherited from overridden method compareTo(Object obj) in interface CompareTo:
       pure

public behavior
requires obj != null;
ensures this.isComparableTo(obj);
ensures (* returns if this is comparable to obj *);
signals_only org.jmlspecs.models.resolve.UndefinedException, java.lang.ClassCastException;
signals (org.jmlspecs.models.resolve.UndefinedException e) (* no comparison between this and obj is defined *)&&e != null;
signals (java.lang.ClassCastException e) (* obj's type prevents it from being compared to this *)&&e != null;

equals

public boolean equals(nullable Object x)

Tell if this object is equal to the given argument.

Specified by:

equals in interface JMLType

Overrides:

equals in class Object

See Also:

compareTo(Object), compareTo(NaturalNumber), equals(java.lang.Object)

Specifications: (class)pure

Specifications inherited from overridden method equals(Object obj) in class Object:
       pure

public normal_behavior
requires obj != null;
ensures (* \result is true when obj is "equal to" this object *);

     also

public normal_behavior
requires this == obj;
ensures \result ;

     also

public code normal_behavior
requires obj != null;
ensures \result <==> this == obj;

     also

diverges false;
ensures obj == null ==> !\result ;

Specifications inherited from overridden method equals(Object ob2) in interface JMLType:
       pure

     also

public normal_behavior
ensures \result ==> ob2 != null&&(* ob2 is not distinguishable from this, except by using mutation or == *);

    implies_that

public normal_behavior

{|

requires ob2 != null&&ob2 instanceof org.jmlspecs.models.JMLType;
ensures ((org.jmlspecs.models.JMLType)ob2).equals(this) == \result ;

also

requires ob2 == this;
ensures \result <==> true;

|}

clone

public Object clone()

Description copied from interface: JMLType

Return a clone of this object.

Specified by:

clone in interface JMLType

Overrides:

clone in class Object

Specifications: (class)pure

Specifications inherited from overridden method in class Object:
       non_null

protected normal_behavior
requires this instanceof java.lang.Cloneable;
assignable \nothing;
ensures \result != null;
ensures \typeof(\result ) == \typeof(this);
ensures (* \result is a clone of this *);

     also

protected normal_behavior
requires this.getClass().isArray();
assignable \nothing;
ensures \elemtype(\typeof(\result )) == \elemtype(\typeof(this));
ensures ((java.lang.Object[])\result ).length == ((java.lang.Object[])this).length;
ensures ( \forall int i; 0 <= i&&i < ((java.lang.Object[])this).length; ((java.lang.Object[])\result )[i] == ((java.lang.Object[])this)[i]);

     also

requires this.getClass().isArray();
assignable \nothing;
ensures \elemtype(\typeof(\result )) == \elemtype(\typeof(this));
ensures java.lang.reflect.Array.getLength(\result ) == java.lang.reflect.Array.getLength(this);
ensures ( \forall int i; 0 <= i&&i < java.lang.reflect.Array.getLength(this); ( \exists java.lang.Object result_i; result_i == java.lang.reflect.Array.get(\result ,i); (result_i == null&&java.lang.reflect.Array.get(this,i) == null)||(result_i != null&&result_i.equals(java.lang.reflect.Array.get(this,i)))));

     also

protected exceptional_behavior
requires !(this instanceof java.lang.Cloneable);
assignable \nothing;
signals_only java.lang.CloneNotSupportedException;

     also

protected normal_behavior
requires \elemtype(\typeof(this)) <: \type(java.lang.Object);
assignable \nothing;
ensures \elemtype(\typeof(\result )) == \elemtype(\typeof(this));
ensures ((java.lang.Object[])\result ).length == ((java.lang.Object[])this).length;
ensures ( \forall int i; 0 <= i&&i < ((java.lang.Object[])this).length; ((java.lang.Object[])\result )[i] == ((java.lang.Object[])this)[i]);

     also

protected normal_behavior
requires \elemtype(\typeof(this)) == \type(int);
assignable \nothing;
ensures \elemtype(\typeof(\result )) == \elemtype(\typeof(this));
ensures ((int[])\result ).length == ((int[])this).length;
ensures ( \forall int i; 0 <= i&&i < ((int[])this).length; ((int[])\result )[i] == ((int[])this)[i]);

     also

protected normal_behavior
requires \elemtype(\typeof(this)) == \type(byte);
assignable \nothing;
ensures \elemtype(\typeof(\result )) == \elemtype(\typeof(this));
ensures ((byte[])\result ).length == ((byte[])this).length;
ensures ( \forall int i; 0 <= i&&i < ((byte[])this).length; ((byte[])\result )[i] == ((byte[])this)[i]);

     also

protected normal_behavior
requires \elemtype(\typeof(this)) == \type(char);
assignable \nothing;
ensures \elemtype(\typeof(\result )) == \elemtype(\typeof(this));
ensures ((char[])\result ).length == ((char[])this).length;
ensures ( \forall int i; 0 <= i&&i < ((char[])this).length; ((char[])\result )[i] == ((char[])this)[i]);

     also

protected normal_behavior
requires \elemtype(\typeof(this)) == \type(long);
assignable \nothing;
ensures \elemtype(\typeof(\result )) == \elemtype(\typeof(this));
ensures ((long[])\result ).length == ((long[])this).length;
ensures ( \forall int i; 0 <= i&&i < ((long[])this).length; ((long[])\result )[i] == ((long[])this)[i]);

     also

protected normal_behavior
requires \elemtype(\typeof(this)) == \type(short);
assignable \nothing;
ensures \elemtype(\typeof(\result )) == \elemtype(\typeof(this));
ensures ((short[])\result ).length == ((short[])this).length;
ensures ( \forall int i; 0 <= i&&i < ((short[])this).length; ((short[])\result )[i] == ((short[])this)[i]);

     also

protected normal_behavior
requires \elemtype(\typeof(this)) == \type(boolean);
assignable \nothing;
ensures \elemtype(\typeof(\result )) == \elemtype(\typeof(this));
ensures ((boolean[])\result ).length == ((boolean[])this).length;
ensures ( \forall int i; 0 <= i&&i < ((boolean[])this).length; ((boolean[])\result )[i] == ((boolean[])this)[i]);

     also

protected normal_behavior
requires \elemtype(\typeof(this)) == \type(float);
assignable \nothing;
ensures \elemtype(\typeof(\result )) == \elemtype(\typeof(this));
ensures ((float[])\result ).length == ((float[])this).length;
ensures ( \forall int i; 0 <= i&&i < ((float[])this).length; (java.lang.Float.isNaN(((float[])\result )[i])&&java.lang.Float.isNaN(((float[])this)[i]))||((float[])\result )[i] == ((float[])this)[i]);

     also

protected normal_behavior
requires \elemtype(\typeof(this)) == \type(double);
assignable \nothing;
ensures \elemtype(\typeof(\result )) == \elemtype(\typeof(this));
ensures ((double[])\result ).length == ((double[])this).length;
ensures ( \forall int i; 0 <= i&&i < ((double[])this).length; (java.lang.Double.isNaN(((double[])\result )[i])&&java.lang.Double.isNaN(((double[])this)[i]))||((double[])\result )[i] == ((double[])this)[i]);

Specifications inherited from overridden method in interface JMLType:
       pure

     also

public normal_behavior
ensures \result != null;
ensures \result instanceof org.jmlspecs.models.JMLType;
ensures ((org.jmlspecs.models.JMLType)\result ).equals(this);

    implies_that

ensures \result != null&&\typeof(\result ) <: \type(org.jmlspecs.models.JMLType);

isZero

public boolean isZero()

Tell if this object is equal to zero.

See Also:

ZERO, compareTo(NaturalNumber), equals(java.lang.Object)

Specifications: (class)pure

public normal_behavior
ensures \result <==> this.equals(org.jmlspecs.models.resolve.NaturalNumber.ZERO);
ensures_redundantly \result <==> this.compareTo(org.jmlspecs.models.resolve.NaturalNumber.ZERO) == 0;
ensures_redundantly \result <==> this.equals(new org.jmlspecs.models.resolve.NaturalNumber());

divides

public boolean divides(non_null NaturalNumber val)

Tell if this natural number divides the given one evenly.

See Also:

remainder(org.jmlspecs.models.resolve.NaturalNumber), mod(org.jmlspecs.models.resolve.NaturalNumber)

Specifications: (class)pure

public normal_behavior
requires val != null;
ensures \result <==> !this.isZero()&&val.remainder(this).equals(org.jmlspecs.models.resolve.NaturalNumber.ZERO);

min

public NaturalNumber min(non_null NaturalNumber val)

Return the smaller of the given natural number and this one.

See Also:

max(org.jmlspecs.models.resolve.NaturalNumber), compareTo(NaturalNumber)

Specifications: (class)pure

public normal_behavior
requires val != null;

{|

requires this.compareTo(val) <= 0;
ensures \result != null&&\result .equals(this);

also

requires val.compareTo(this) <= 0;
ensures \result != null&&\result .equals(val);

|}

max

public NaturalNumber max(non_null NaturalNumber val)

Return the smaller of the given natural number and this one.

See Also:

max(org.jmlspecs.models.resolve.NaturalNumber), compareTo(NaturalNumber)

Specifications: (class)pure

public normal_behavior
requires val != null;

{|

requires this.compareTo(val) >= 0;
ensures \result != null&&\result .equals(this);

also

requires val.compareTo(this) >= 0;
ensures \result != null&&\result .equals(val);

|}

hashCode

public int hashCode()

Description copied from interface: JMLType

Return a hash code for this object.

Specified by:

hashCode in interface JMLType

Overrides:

hashCode in class Object

Specifications: (class)pure

Specifications inherited from overridden method in class Object:

public behavior
assignable objectState;
ensures (* \result is a hash code for this object *);

     also

public code normal_behavior
assignable \nothing;

Specifications inherited from overridden method in interface JMLType:
       pure

toString

public String toString()

Overrides:

toString in class Object

Specifications: (class)pure

Specifications inherited from overridden method in class Object:
       non_null

public normal_behavior
assignable objectState;
ensures \result != null&&\result .equals(this.theString);
ensures (* \result is a string representation of this object *);

     also

public code normal_behavior
assignable \nothing;
ensures \result != null&&(* \result is the instance's class name, followed by an @, followed by the instance's hashcode in hex *);

     also

public code model_program { ... }

    implies_that

assignable objectState;
ensures \result != null;

bigIntegerValue

public BigInteger bigIntegerValue()

Return the BigInteger value of this natural number.

See Also:

intValue(), longValue()

Specifications: non_null (class)pure

public normal_behavior
ensures \result != null&&new org.jmlspecs.models.resolve.NaturalNumber(\result ).equals(this);

intValue

public int intValue()

Specifications: (class)pure

Specifications inherited from overridden method in class Number:
       pure

public normal_behavior
ensures (* \result is an int approximation to the value of this object *);

longValue

public long longValue()

Specifications: (class)pure

Specifications inherited from overridden method in class Number:
       pure

public normal_behavior
ensures (* \result is an long approximation to the value of this object *);

floatValue

public float floatValue()

Specifications: (class)pure

Specifications inherited from overridden method in class Number:
       pure

public normal_behavior
ensures (* \result is an float approximation to the value of this object *);

doubleValue

public double doubleValue()

Specifications: (class)pure

Specifications inherited from overridden method in class Number:
       pure

public normal_behavior
ensures (* \result is an double approximation to the value of this object *);