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class ReductiveCutElimination extends AnyRef

Source
reductiveCutElimination.scala
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  1. by any2stringadd
  2. by StringFormat
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Instance Constructors

  1. new ReductiveCutElimination()

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from ReductiveCutElimination to any2stringadd[ReductiveCutElimination] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (ReductiveCutElimination, B)
    Implicit
    This member is added by an implicit conversion from ReductiveCutElimination to ArrowAssoc[ReductiveCutElimination] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. def apply(proof: LKProof, reduction: (LKProof) ⇒ Option[(LKProof, SequentConnector)], cleanStructRules: Boolean = true): LKProof

    Transforms a proof by applying a reduction until some specified criterion is satisfied.

    Transforms a proof by applying a reduction until some specified criterion is satisfied.

    proof

    The proof to which the transformation is applied.

    reduction

    A local reduction function.

    cleanStructRules

    Indicates whether structural rules are cleaned after each step.

    returns

    A proof that is obtained from the given proof by applying the reduction function iteratively and simultaneously to all lowermost redexes of the current proof until the specified criterion is satisfied.

  7. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  8. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  9. def eliminateAllByUppermost(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.

    cleanStructRules

    Tells algorithm to clean struct rules or not. Default is on

    returns

    The cut-free proof.

  10. def eliminateInduction(proof: LKProof, cleanStructRules: Boolean = true)(implicit ctx: Context): LKProof

    Eliminates inductions from a proof.

    Eliminates inductions from a proof.

    proof

    The proof to which the transformation is applied.

    cleanStructRules

    Indicates whether structural rules are cleaned during the reduction.

    ctx

    Defines constants, types, etc.

    returns

    A proof obtained by repeated application of induction unfolding; equality reduction and free-cut elimination. The reduction ends if there is no more unfoldable induction i.e. there is no induction inference with constructor form induction term.

  11. def eliminateToACNFByUppermost(proof: LKProof, cleanStructRules: Boolean = true): LKProof

    This algorithm implements a generalization of the Gentzen method which reduces all cuts to atomic cuts.

    This algorithm implements a generalization of the Gentzen method which reduces all cuts to atomic cuts.

    proof

    The proof to subject to cut-elimination.

    cleanStructRules

    Tells algorithm to clean struct rules or not. Default is on

    returns

    The cut-free proof.

  12. def eliminateToACNFTopByUppermost(proof: LKProof, cleanStructRules: Boolean = true): LKProof

    This algorithm implements a generalization of the Gentzen method which reduces all cuts to atomic cuts and pushes these cuts to the leaves of the proof.

    This algorithm implements a generalization of the Gentzen method which reduces all cuts to atomic cuts and pushes these cuts to the leaves of the proof.

    proof

    The proof to subject to cut-elimination.

    cleanStructRules

    Tells algorithm to clean struct rules or not. Default is on

    returns

    The cut-free proof.

  13. def ensuring(cond: (ReductiveCutElimination) ⇒ Boolean, msg: ⇒ Any): ReductiveCutElimination
    Implicit
    This member is added by an implicit conversion from ReductiveCutElimination to Ensuring[ReductiveCutElimination] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  14. def ensuring(cond: (ReductiveCutElimination) ⇒ Boolean): ReductiveCutElimination
    Implicit
    This member is added by an implicit conversion from ReductiveCutElimination to Ensuring[ReductiveCutElimination] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  15. def ensuring(cond: Boolean, msg: ⇒ Any): ReductiveCutElimination
    Implicit
    This member is added by an implicit conversion from ReductiveCutElimination to Ensuring[ReductiveCutElimination] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  16. def ensuring(cond: Boolean): ReductiveCutElimination
    Implicit
    This member is added by an implicit conversion from ReductiveCutElimination to Ensuring[ReductiveCutElimination] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  17. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  18. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  19. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  20. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from ReductiveCutElimination to StringFormat[ReductiveCutElimination] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  21. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  22. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  23. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  24. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  25. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  26. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  27. var recordSteps: Boolean
  28. val steps: Buffer[LKProof]
  29. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  30. def toString(): String
    Definition Classes
    AnyRef → Any
  31. def unfoldInductions(proof: LKProof, cleanStructRules: Boolean = true)(implicit ctx: Context): LKProof

    Unfolds all induction inference with induction term in constructor form.

    Unfolds all induction inference with induction term in constructor form.

    proof

    The proof to which this transformation is applied.

    cleanStructRules

    Indicates whether the structural rules are cleaned during the reduction.

    ctx

    Defines constants, inductive types, etc.

    returns

    A proof of the same end-sequent which contains no induction inference with induction term in constructor form.

  32. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  33. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  34. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  35. def [B](y: B): (ReductiveCutElimination, B)
    Implicit
    This member is added by an implicit conversion from ReductiveCutElimination to ArrowAssoc[ReductiveCutElimination] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Inherited from AnyRef

Inherited from Any

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

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

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

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

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