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object ReductiveCutElimination

This object implements a version of Gentzen's cut-elimination proof for our sequent calculus LK. For details, please refer to the documentation of the apply methods.

Source
reductiveCutElimination.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. def apply(proof: LKProof, cleanStructRules: Boolean = true): LKProof

    This methods implements a version of Gentzen's cut-elimination proof using the (known to be terminating) strategy of reducing a left-uppermost cut.

    This methods implements a version of Gentzen's cut-elimination proof using the (known to be terminating) strategy of reducing a left-uppermost cut. The algorithm terminates when all cuts have been eliminated.

    proof

    The proof to subject to cut-elimination or restructuring.

    cleanStructRules

    Tells the algorithm whether or not to clean the structural rules default value is on, i.e. clean the structural rules

    returns

    A proof.

  5. final def asInstanceOf[T0]: T0
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  6. def clone(): AnyRef
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  7. def eliminateInduction(proof: LKProof, cleanStructRules: Boolean = true)(implicit ctx: Context): LKProof
  8. final def eq(arg0: AnyRef): Boolean
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  9. def equals(arg0: Any): Boolean
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  10. def finalize(): Unit
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  11. final def getClass(): Class[_]
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  12. def hashCode(): Int
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  13. def introOrCut(proof: LKProof, formula: Formula): Boolean

    Checks if the last rule in proof is a leaf, a cut rule, or a weakening rule on the given formula.

    Checks if the last rule in proof is a leaf, a cut rule, or a weakening rule on the given formula.

    proof

    The proof we are checking.

    formula

    The formula we are checking.

    returns

    True is structure is correct or false if not.

  14. def isACNF(proof: LKProof): Boolean

    This method checks whether a proof is in ACNF

    This method checks whether a proof is in ACNF

    proof

    The proof to check for in ACNF.

    returns

    True if proof is in ACNF, False otherwise.

  15. def isACNFTop(proof: LKProof): Boolean

    This method checks whether a proof is in ACNF top

    This method checks whether a proof is in ACNF top

    proof

    The proof to check for in ACNF top.

    returns

    True if proof is in ACNF, False otherwise.

  16. def isCutFree(proof: LKProof): Boolean

    This method checks whether a proof is cut-free.

    This method checks whether a proof is cut-free.

    proof

    The proof to check for cut-freeness.

    returns

    True if proof does not contain the cut rule, False otherwise.

  17. final def isInstanceOf[T0]: Boolean
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  18. final def ne(arg0: AnyRef): Boolean
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  19. final def notify(): Unit
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  20. final def notifyAll(): Unit
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  21. def reduceToACNF(proof: LKProof, cleanStructRules: Boolean = true): LKProof

    Reduces proof to ACNF using reductive cut elimination

    Reduces proof to ACNF using reductive cut elimination

    proof

    The proof to subject to cut-elimination or restructuring.

    cleanStructRules

    Tells the algorithm whether or not to clean the structural rules default value is on, i.e. clean the structural rules

    returns

    A proof.

  22. def reduceToACNFTop(proof: LKProof, cleanStructRules: Boolean = true): LKProof

    Reduces proof to ACNF top using reductive cut elimination

    Reduces proof to ACNF top using reductive cut elimination

    proof

    The proof to subject to cut-elimination or restructuring.

    cleanStructRules

    Tells the algorithm whether or not to clean the structural rules default value is on, i.e. clean the structural rules

    returns

    A proof.

  23. final def synchronized[T0](arg0: ⇒ T0): T0
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