Class Booleans

java.lang.Object

org.episteme.core.mathematics.sets.Booleans

All Implemented Interfaces:

Iterable<Boolean>, AbelianMonoid<Boolean>, Magma<Boolean>, Monoid<Boolean>, Semiring<Boolean>, FiniteSet<Boolean>, Set<Boolean>

public final class Booleans
extends Object
implements Semiring<Boolean>, FiniteSet<Boolean>

The structure of Boolean values (𝔹 = {0, 1}).

This class represents the structure of Booleans.

Since:

1.0

Author:

Gemini AI (Google DeepMind)

See Also:

• * @author Silvere Martin-Michiellot

Method Summary

Modifier and Type	Method	Description
Boolean	add(Boolean a, Boolean b)	Returns the sum of two elements (additive notation).
boolean	contains(Boolean element)	Tests whether this set contains the specified element.
String	description()	Returns a human-readable description of this set.
static Booleans	getInstance()
boolean	isEmpty()	Returns true if this set contains no elements.
boolean	isMultiplicationCommutative()	Tests whether multiplication is commutative in this semiring.
Iterator<Boolean>	iterator()	Returns an iterator over the elements in this set.
Boolean	multiply(Boolean a, Boolean b)	Returns the product of two elements.
Boolean	one()	Returns the multiplicative identity (one element).
Boolean	operate(Boolean a, Boolean b)	Performs the binary operation on two elements.
long	size()	Returns the number of elements in this set (its cardinality).
Stream<Boolean>	stream()	Returns a sequential Stream with this set as its source.
String	toString()
Boolean	zero()	Returns the additive identity (zero element).

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface AbelianMonoid

identity, isCommutative

Methods inherited from interface Iterable

forEach, spliterator

Methods inherited from interface Monoid

isAssociative

Methods inherited from interface Semiring

pow

Method Details

getInstance

public static Booleans getInstance()

operate

public Boolean operate(Boolean a,
 Boolean b)

Description copied from interface: Magma

Performs the binary operation on two elements.

This is the fundamental operation of a magma. The result must be an element of this magma (closure property).

Properties: None required (not necessarily associative or commutative)

Specified by:

operate in interface Magma<Boolean>

Parameters:

a - the first operand

b - the second operand

Returns:

the result of a ∗ b

See Also:

• Magma.isAssociative()
• Magma.isCommutative()

add

public Boolean add(Boolean a,
 Boolean b)

Description copied from interface: AbelianMonoid

Returns the sum of two elements (additive notation).

Delegates to Magma.operate(Object, Object).

Specified by:

add in interface AbelianMonoid<Boolean>

Parameters:

a - the first addend

b - the second addend

Returns:

a + b

zero

public Boolean zero()

Description copied from interface: AbelianMonoid

Returns the additive identity (zero element).

Delegates to AbelianMonoid.identity().

Specified by:

zero in interface AbelianMonoid<Boolean>

Returns:

the zero element

multiply

public Boolean multiply(Boolean a,
 Boolean b)

Description copied from interface: Semiring

Returns the product of two elements.

Multiplication must be associative and distribute over addition.

Specified by:

multiply in interface Semiring<Boolean>

Parameters:

a - the first factor

b - the second factor

Returns:

a × b

one

public Boolean one()

Description copied from interface: Semiring

Returns the multiplicative identity (one element).

Satisfies: 1 × a = a × 1 = a for all elements a.

Specified by:

one in interface Semiring<Boolean>

Returns:

the multiplicative identity

isMultiplicationCommutative

public boolean isMultiplicationCommutative()

Description copied from interface: Semiring

Tests whether multiplication is commutative in this semiring.

Specified by:

isMultiplicationCommutative in interface Semiring<Boolean>

Returns:

true if multiplication commutes

contains

public boolean contains(Boolean element)

Description copied from interface: Set

Tests whether this set contains the specified element.

This is the fundamental operation of a set - membership testing.

Specified by:

contains in interface Set<Boolean>

Parameters:

element - the element to test for membership

Returns:

true if this set contains the element, false otherwise

See Also:

• Set.isEmpty()
• invalid reference

  #size()

isEmpty

public boolean isEmpty()

Description copied from interface: Set

Returns true if this set contains no elements.

The empty set (∅) is a fundamental concept in set theory. It is the unique set containing no elements.

Specified by:

isEmpty in interface Set<Boolean>

Returns:

true if this set is empty

size

public long size()

Description copied from interface: FiniteSet

Returns the number of elements in this set (its cardinality).

Specified by:

size in interface FiniteSet<Boolean>

Returns:

the cardinality of this set

description

public String description()

Description copied from interface: Set

Returns a human-readable description of this set.

Examples:

• "ℝ (Real Numbers)"
• "ℤ/12ℤ (Integers modulo 12)"
• "{1, 2, 3, 4, 5}"

Specified by:

description in interface Set<Boolean>

Returns:

a description of this set

iterator

public Iterator<Boolean> iterator()

Description copied from interface: FiniteSet

Returns an iterator over the elements in this set.

Specified by:

iterator in interface FiniteSet<Boolean>

Specified by:

iterator in interface Iterable<Boolean>

Returns:

an iterator over the elements in this set

stream

public Stream<Boolean> stream()

Description copied from interface: FiniteSet

Returns a sequential Stream with this set as its source.

Specified by:

stream in interface FiniteSet<Boolean>

Returns:

a stream over the elements in this set

toString

public String toString()

Overrides:

toString in class Object