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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  1. SkolemFunctions
  2. Serializable
  3. Serializable
  4. Product
  5. Equals
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  7. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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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 to ArrowAssoc[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[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  8. val dependencyOrder: Seq[Const]
  9. def ensuring(cond: (SkolemFunctions) ⇒ Boolean, msg: ⇒ Any): SkolemFunctions
    Implicit
    This member is added by an implicit conversion from SkolemFunctions to Ensuring[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 to Ensuring[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 to Ensuring[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 to Ensuring[SkolemFunctions] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  13. def epsilonDefinitions: Seq[(Const, Expr)]
  14. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  15. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  16. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from SkolemFunctions to StringFormat[SkolemFunctions] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  17. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
  18. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  19. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  20. final def notify(): Unit
    Definition Classes
    AnyRef
  21. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  22. def orderedDefinitions: Seq[(Const, Expr)]
  23. val skolemDefs: Map[Const, Expr]
  24. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  25. def toString(): String
    Definition Classes
    SkolemFunctions → AnyRef → Any
  26. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  27. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  28. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  29. def [B](y: B): (SkolemFunctions, B)
    Implicit
    This member is added by an implicit conversion from SkolemFunctions to ArrowAssoc[SkolemFunctions] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Shadowed Implicit Value Members

  1. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from SkolemFunctions to any2stringadd[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

Inherited from Serializable

Inherited from Serializable

Inherited from Product

Inherited from Equals

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd from SkolemFunctions to any2stringadd[SkolemFunctions]

Inherited by implicit conversion StringFormat from SkolemFunctions to StringFormat[SkolemFunctions]

Inherited by implicit conversion Ensuring from SkolemFunctions to Ensuring[SkolemFunctions]

Inherited by implicit conversion ArrowAssoc from SkolemFunctions to ArrowAssoc[SkolemFunctions]

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