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
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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
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    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @IntrinsicCandidate()
  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: AnyRef): Boolean
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  12. final def getClass(): Class[_ <: AnyRef]
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  13. def hashCode(): Int
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  14. final def isInstanceOf[T0]: Boolean
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  15. final def ne(arg0: AnyRef): Boolean
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  16. final def notify(): Unit
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  17. final def notifyAll(): Unit
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    @native() @IntrinsicCandidate()
  18. val p1: NegLeftRule
  19. val p2: NegRightRule
  20. val p3: NegLeftRule
  21. val p4: OrLeftRule
  22. val p5: NegLeftRule
  23. val p6: NegRightRule
  24. val p7: OrLeftRule
  25. val proof: CutRule
  26. lazy val reductive_cutfree: LKProof
  27. final def synchronized[T0](arg0: => T0): T0
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  28. def toString(): String
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  29. final def wait(arg0: Long, arg1: Int): Unit
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  30. final def wait(arg0: Long): Unit
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  31. final def wait(): Unit
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  1. def finalize(): Unit
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