Packages

object fol2

Provides a simple intuitionistic proof of ¬p ∨ p ⊢ ¬¬p ⊃ p. Applying the CERES method will create a non-intuitionistic proof but reductive cut-elimination will always create an intuitionistic one. Therefore this is an example that CERES produces cut-free proofs which reductive cut-elimination cannot.

Source
fol2.scala
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  1. final def !=(arg0: Any): Boolean
    Definition Classes
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  2. final def ##(): Int
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  3. final def ==(arg0: Any): Boolean
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  4. final def asInstanceOf[T0]: T0
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  5. val ax: LogicalAxiom
  6. lazy val ceres_cutfree: LKProof
  7. def clone(): AnyRef
    Attributes
    protected[java.lang]
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    @native() @throws( ... )
  8. val cut_left: OrRightRule
  9. val cut_right: ImpRightRule
  10. final def eq(arg0: AnyRef): Boolean
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  11. def equals(arg0: Any): Boolean
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  12. def finalize(): Unit
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    @throws( classOf[java.lang.Throwable] )
  13. final def getClass(): Class[_]
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    @native()
  14. def hashCode(): Int
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    @native()
  15. final def isInstanceOf[T0]: Boolean
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  16. final def ne(arg0: AnyRef): Boolean
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  17. final def notify(): Unit
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    @native()
  18. final def notifyAll(): Unit
    Definition Classes
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    @native()
  19. val p1: NegLeftRule
  20. val p2: NegRightRule
  21. val p3: NegLeftRule
  22. val p4: OrLeftRule
  23. val p5: NegLeftRule
  24. val p6: NegRightRule
  25. val p7: OrLeftRule
  26. val proof: CutRule
  27. lazy val reductive_cutfree: LKProof
  28. final def synchronized[T0](arg0: ⇒ T0): T0
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  29. def toString(): String
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  30. final def wait(): Unit
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  31. final def wait(arg0: Long, arg1: Int): Unit
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  32. final def wait(arg0: Long): Unit
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