orbital.logic.functor
Class Predicates

java.lang.Object
  orbital.logic.functor.Predicates

public final class Predicates
extends java.lang.Object

Predicate Implementations.

Author:

André Platzer

See Also:

Functionals

Stereotype:

Module

Field Summary

static BinaryPredicate	equal =.
static VoidPredicate	FALSE false = ⊥.
static BinaryPredicate	greater >.
static BinaryPredicate	greaterEqual ≥.
static BinaryPredicate	less <.
static BinaryPredicate	lessEqual ≤.
static Predicates	predicates Class alias object.
static VoidPredicate	TRUE true = ⊤.
static BinaryPredicate	unequal ≠.

Method Summary

Methods inherited from class java.lang.Object

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

Field Detail

predicates

public static final Predicates predicates

Class alias object.

TRUE

public static final VoidPredicate TRUE

true = ⊤.

FALSE

public static final VoidPredicate FALSE

false = ⊥.

equal

public static final BinaryPredicate equal

=. In first-order logic, equality "=" is uniquely determined by

• reflexive, i.e. ∀x (x=x)
• substitutive, ∀φ∈Formula(Σ) a=b,φ ⊨ φ[a→b]

Attributes:

equivalent, congruent for all f, P, substitutive

unequal

public static final BinaryPredicate unequal

≠.

Inequality is defined as x≠y :⇔ ¬(x=y).

See Also:

equal

Attributes:

irreflexive, symmetric

less

public static final BinaryPredicate less

<.

It is true that x<y ⇔ x≤y ∧ x≠y.

See Also:

Comparable

Attributes:

strict order

greater

public static final BinaryPredicate greater

>.

It is defined as x>y :⇔ y<x.

See Also:

Comparable

Attributes:

strict order

lessEqual

public static final BinaryPredicate lessEqual

≤.

It is true that x≤y ⇔ x<y ∨ x<y.

See Also:

Comparable

Attributes:

order

greaterEqual

public static final BinaryPredicate greaterEqual

≥.

It is defined as x≥y :⇔ y≤x.

See Also:

Comparable

Attributes:

order