Packages

case class SkolemFunctions(skolemDefs: Map[Const, Expr]) extends Product with Serializable

List of definitions of Skolem symbols.

A Skolem definition is similar but slightly different from the epsilon operator:

Syntactically it is a map s_i → λx_1 .. λx_n Qy φ(x_1, .., x_n, y), where Q is a quantifier. Then s_i(x_1, .., x_n) is the Skolem term used for the formula Qy φ(x_1, .., x_n, y), where Qy is strong.

This Skolem term corresponds to the epsilon term εy φ(x_1, .., x_n, y) or εy ¬φ(x_1, .., x_n), depending on whether Q is ∃ or ∀. The reason we don't use epsilon terms directly is that this makes it impossible to deskolemize a formula based on just the Skolem definitions: for example both ∃x ∀y φ and ∃x ¬∃y¬ φ would define their Skolem functions using the same epsilon terms.

Source
SkolemFunctions.scala
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Inherited
  1. SkolemFunctions
  2. Serializable
  3. Product
  4. Equals
  5. AnyRef
  6. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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Visibility
  1. Public
  2. Protected

Instance Constructors

  1. new SkolemFunctions(skolemDefs: Map[Const, Expr])

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##: Int
    Definition Classes
    AnyRef → Any
  3. def +(sym: Const, defn: Expr): SkolemFunctions
  4. def ->[B](y: B): (SkolemFunctions, B)
    Implicit
    This member is added by an implicit conversion from SkolemFunctions toArrowAssoc[SkolemFunctions] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  7. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @IntrinsicCandidate()
  8. def dependencyOrder: Vector[Const]
  9. def ensuring(cond: (SkolemFunctions) => Boolean, msg: => Any): SkolemFunctions
    Implicit
    This member is added by an implicit conversion from SkolemFunctions toEnsuring[SkolemFunctions] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  10. def ensuring(cond: (SkolemFunctions) => Boolean): SkolemFunctions
    Implicit
    This member is added by an implicit conversion from SkolemFunctions toEnsuring[SkolemFunctions] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  11. def ensuring(cond: Boolean, msg: => Any): SkolemFunctions
    Implicit
    This member is added by an implicit conversion from SkolemFunctions toEnsuring[SkolemFunctions] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  12. def ensuring(cond: Boolean): SkolemFunctions
    Implicit
    This member is added by an implicit conversion from SkolemFunctions toEnsuring[SkolemFunctions] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  13. def epsilonDefinitions: Vector[(Const, Expr)]
  14. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  15. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @IntrinsicCandidate()
  16. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  17. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  18. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  19. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  20. def orderedDefinitions: Vector[(Const, Expr)]
  21. def productElementNames: Iterator[String]
    Definition Classes
    Product
  22. val skolemDefs: Map[Const, Expr]
  23. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  24. def toString(): String
    Definition Classes
    SkolemFunctions → AnyRef → Any
  25. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  26. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  27. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])

Shadowed Implicit Value Members

  1. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from SkolemFunctions toany2stringadd[SkolemFunctions] performed by method any2stringadd in scala.Predef.
    Shadowing
    This implicitly inherited member is shadowed by one or more members in this class.
    To access this member you can use a type ascription:
    (skolemFunctions: any2stringadd[SkolemFunctions]).+(other)
    Definition Classes
    any2stringadd

Deprecated Value Members

  1. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.Throwable]) @Deprecated
    Deprecated
  2. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from SkolemFunctions toStringFormat[SkolemFunctions] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @deprecated @inline()
    Deprecated

    (Since version 2.12.16) Use formatString.format(value) instead of value.formatted(formatString), or use the f"" string interpolator. In Java 15 and later, formatted resolves to the new method in String which has reversed parameters.

  3. def [B](y: B): (SkolemFunctions, B)
    Implicit
    This member is added by an implicit conversion from SkolemFunctions toArrowAssoc[SkolemFunctions] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @deprecated
    Deprecated

    (Since version 2.13.0) Use -> instead. If you still wish to display it as one character, consider using a font with programming ligatures such as Fira Code.

Inherited from Serializable

Inherited from Product

Inherited from Equals

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromSkolemFunctions to any2stringadd[SkolemFunctions]

Inherited by implicit conversion StringFormat fromSkolemFunctions to StringFormat[SkolemFunctions]

Inherited by implicit conversion Ensuring fromSkolemFunctions to Ensuring[SkolemFunctions]

Inherited by implicit conversion ArrowAssoc fromSkolemFunctions to ArrowAssoc[SkolemFunctions]

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