Class/Object

at.logic.gapt.proofs.lk

ReductiveCutElimination

Related Docs: object ReductiveCutElimination | package lk

Permalink

class ReductiveCutElimination extends AnyRef

Source
reductiveCutElimination.scala
Linear Supertypes
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. ReductiveCutElimination
  2. AnyRef
  3. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. All

Instance Constructors

  1. new ReductiveCutElimination()

    Permalink

Value Members

  1. final def !=(arg0: Any): Boolean

    Permalink
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int

    Permalink
    Definition Classes
    AnyRef → Any
  3. def +(other: String): String

    Permalink
    Implicit information
    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)

    Permalink
    Implicit information
    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

    Permalink
    Definition Classes
    AnyRef → Any
  6. def apply(proof: LKProof, pred_done: (LKProof) ⇒ Boolean, pred_cut: (LKProof, LKProof) ⇒ Boolean): LKProof

    Permalink

    This methods implements a version of Gentzen's cut-elimination proof parameterized by a strategy given by pred_cut and pred_done.

    This methods implements a version of Gentzen's cut-elimination proof parameterized by a strategy given by pred_cut and pred_done.

    The method traverses an LKProof recursively from the bottom up. When it reaches a cut, the method calls pred_cut(global, sub), where global is complete proof under consideration, while sub is the subproof of global ending in the cut. If this call returns true, the cut is reduced using the usual Gentzen cut-elimination rules. If the call returns false, the traversion continues.

    After every application of a reduction, pred_done(global) is called. If it returns true, the algorithm terminates, returning the current proof. If it returns false, the algorithm continues to traverse the proof.

    This means that pred_cut and pred_done allow the definition of a (not necessarily terminating!) cut-elimination strategy. A standard implementation (reducing left-uppermost cuts until the proof is cut-free) is provided by another apply method in this class.

    proof

    The proof to subject to cut-elimination.

    pred_done

    A predicate deciding when to terminate the algorithm.

    pred_cut

    A predicate deciding whether or not to reduce a cut encountered when traversing the proof.

    returns

    The proof as it is after pred_done returns true.

  7. final def asInstanceOf[T0]: T0

    Permalink
    Definition Classes
    Any
  8. def clone(): AnyRef

    Permalink
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  9. def eliminateAllByUppermost(proof: LKProof): LKProof

    Permalink

    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.

    returns

    The cut-free proof.

  10. def ensuring(cond: (ReductiveCutElimination) ⇒ Boolean, msg: ⇒ Any): ReductiveCutElimination

    Permalink
    Implicit information
    This member is added by an implicit conversion from ReductiveCutElimination to Ensuring[ReductiveCutElimination] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  11. def ensuring(cond: (ReductiveCutElimination) ⇒ Boolean): ReductiveCutElimination

    Permalink
    Implicit information
    This member is added by an implicit conversion from ReductiveCutElimination to Ensuring[ReductiveCutElimination] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  12. def ensuring(cond: Boolean, msg: ⇒ Any): ReductiveCutElimination

    Permalink
    Implicit information
    This member is added by an implicit conversion from ReductiveCutElimination to Ensuring[ReductiveCutElimination] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  13. def ensuring(cond: Boolean): ReductiveCutElimination

    Permalink
    Implicit information
    This member is added by an implicit conversion from ReductiveCutElimination to Ensuring[ReductiveCutElimination] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  14. final def eq(arg0: AnyRef): Boolean

    Permalink
    Definition Classes
    AnyRef
  15. def equals(arg0: Any): Boolean

    Permalink
    Definition Classes
    AnyRef → Any
  16. def finalize(): Unit

    Permalink
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  17. def formatted(fmtstr: String): String

    Permalink
    Implicit information
    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()
  18. final def getClass(): Class[_]

    Permalink
    Definition Classes
    AnyRef → Any
  19. def hashCode(): Int

    Permalink
    Definition Classes
    AnyRef → Any
  20. final def isInstanceOf[T0]: Boolean

    Permalink
    Definition Classes
    Any
  21. final def ne(arg0: AnyRef): Boolean

    Permalink
    Definition Classes
    AnyRef
  22. final def notify(): Unit

    Permalink
    Definition Classes
    AnyRef
  23. final def notifyAll(): Unit

    Permalink
    Definition Classes
    AnyRef
  24. var recordSteps: Boolean

    Permalink
  25. val steps: Buffer[LKProof]

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

    Permalink
    Definition Classes
    AnyRef
  27. def toString(): String

    Permalink
    Definition Classes
    AnyRef → Any
  28. final def wait(): Unit

    Permalink
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  29. final def wait(arg0: Long, arg1: Int): Unit

    Permalink
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  30. final def wait(arg0: Long): Unit

    Permalink
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  31. def [B](y: B): (ReductiveCutElimination, B)

    Permalink
    Implicit information
    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]

Ungrouped