case class ContractionRule(subProof: NDProof, aux1: SequentIndex, aux2: SequentIndex) extends UnaryNDProof with CommonRule with Product with Serializable

An NDProof ending with a contraction:

        (π)
    A, A, Γ :- B
   --------------ctr
     A, Γ :- B

subProof

The subproof π.

aux1

The index of one occurrence of A.

aux2

The index of the other occurrence of A.

Source
nd.scala
Type Hierarchy
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Inherited
  1. ContractionRule
  2. Serializable
  3. CommonRule
  4. ContextRule
  5. UnaryNDProof
  6. NDProof
  7. SequentProof
  8. DagProof
  9. Product
  10. Equals
  11. AnyRef
  12. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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Visibility
  1. Public
  2. Protected

Instance Constructors

  1. new ContractionRule(subProof: NDProof, aux1: SequentIndex, aux2: SequentIndex)

    subProof

    The subproof π.

    aux1

    The index of one occurrence of A.

    aux2

    The index of the other occurrence of A.

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 ContractionRule toany2stringadd[ContractionRule] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (ContractionRule, B)
    Implicit
    This member is added by an implicit conversion from ContractionRule toArrowAssoc[ContractionRule] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. def NDRuleCreationException(message: String): NDRuleCreationException
    Attributes
    protected
    Definition Classes
    NDProof
  7. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  8. val aux1: SequentIndex
  9. val aux2: SequentIndex
  10. def auxFormulas: Seq[Seq[Formula]]

    A list of lists containing the auxiliary formulas of the rule.

    A list of lists containing the auxiliary formulas of the rule. The first list constains the auxiliary formulas in the first premise and so on.

    Definition Classes
    SequentProof
  11. def auxIndices: Seq[Seq[SequentIndex]]

    A list of lists of SequentIndices denoting the auxiliary formula(s) of the rule.

    A list of lists of SequentIndices denoting the auxiliary formula(s) of the rule. The first list contains the auxiliary formulas in the first premise and so on.

    Definition Classes
    ContractionRuleSequentProof
  12. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @IntrinsicCandidate()
  13. lazy val conclusion: Sequent[Formula]

    The conclusion of the rule.

    The conclusion of the rule.

    Definition Classes
    ContextRuleSequentProof
  14. def contexts: Seq[Sequent[Formula]]
    Attributes
    protected
    Definition Classes
    ContextRule
  15. def dagLike: DagLikeOps[NDProof]

    Operations that view the sub-proofs as a DAG, which ignore duplicate sub-proofs, see DagProof.DagLikeOps for a list.

    Operations that view the sub-proofs as a DAG, which ignore duplicate sub-proofs, see DagProof.DagLikeOps for a list.

    Definition Classes
    DagProof
  16. def depth: Int

    Depth of the proof, which is the maximum length of a path you can take via immediateSubProofs.

    Depth of the proof, which is the maximum length of a path you can take via immediateSubProofs.

    Definition Classes
    DagProof
  17. final def endSequent: Sequent[Formula]

    The end-sequent of the rule.

    The end-sequent of the rule.

    Definition Classes
    NDProof
  18. def ensuring(cond: (ContractionRule) => Boolean, msg: => Any): ContractionRule
    Implicit
    This member is added by an implicit conversion from ContractionRule toEnsuring[ContractionRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  19. def ensuring(cond: (ContractionRule) => Boolean): ContractionRule
    Implicit
    This member is added by an implicit conversion from ContractionRule toEnsuring[ContractionRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  20. def ensuring(cond: Boolean, msg: => Any): ContractionRule
    Implicit
    This member is added by an implicit conversion from ContractionRule toEnsuring[ContractionRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  21. def ensuring(cond: Boolean): ContractionRule
    Implicit
    This member is added by an implicit conversion from ContractionRule toEnsuring[ContractionRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  22. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  23. def equals(that: Any): Boolean
    Definition Classes
    DagProof → Equals → AnyRef → Any
  24. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from ContractionRule toStringFormat[ContractionRule] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  25. def formulasToBeDeleted: Seq[Seq[SequentIndex]]
    Attributes
    protected
    Definition Classes
    ContextRule
  26. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @IntrinsicCandidate()
  27. def getSequentConnector: SequentConnector

    The object connecting the lower and upper sequents.auxFormulas.

    The object connecting the lower and upper sequents.auxFormulas.

    Definition Classes
    UnaryNDProof
  28. val hashCode: Int
    Definition Classes
    DagProof
  29. def immediateSubProofs: Seq[NDProof]

    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    UnaryNDProofDagProof
  30. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  31. def longName: String

    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  32. val mainFormula: Formula
  33. def mainFormulaSequent: Sequent[Formula]
    Definition Classes
    ContractionRuleContextRule
  34. def mainFormulas: Seq[Formula]

    The list of main formulas of the rule.

    The list of main formulas of the rule.

    Definition Classes
    SequentProof
  35. def mainIndices: Vector[SequentIndex]

    A list of SequentIndices denoting the main formula(s) of the rule.

    A list of SequentIndices denoting the main formula(s) of the rule.

    Definition Classes
    ContextRuleSequentProof
  36. def name: String

    The name of this rule (in symbols).

    The name of this rule (in symbols).

    Definition Classes
    ContractionRuleDagProof
  37. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  38. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  39. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  40. def occConnectors: IndexedSeq[SequentConnector]

    A list of occurrence connectors, one for each immediate subproof.

    A list of occurrence connectors, one for each immediate subproof.

    Definition Classes
    ContextRuleSequentProof
  41. def premise: Sequent[Formula]

    The upper sequent of the rule.

    The upper sequent of the rule.

    Definition Classes
    UnaryNDProof
  42. def premises: Seq[Sequent[Formula]]

    The upper sequents of the rule.

    The upper sequents of the rule.

    Definition Classes
    SequentProof
  43. def productElementNames: Iterator[String]
    Definition Classes
    Product
  44. def stepString(subProofLabels: Map[Any, String]): String
    Attributes
    protected
    Definition Classes
    SequentProofDagProof
  45. val subProof: NDProof

    The immediate subproof of the rule.

    The immediate subproof of the rule.

    Definition Classes
    ContractionRuleUnaryNDProof
  46. def subProofAt(pos: List[Int]): NDProof

    Returns the subproof at the given position: p.subProofAt(Nil) is p itself; p.subProofAt(i :: is) is the ith subproof of p.subProofAt(is).

    Returns the subproof at the given position: p.subProofAt(Nil) is p itself; p.subProofAt(i :: is) is the ith subproof of p.subProofAt(is).

    Definition Classes
    DagProof
  47. def subProofs: Set[NDProof]

    Set of all (transitive) sub-proofs including this.

    Set of all (transitive) sub-proofs including this.

    Definition Classes
    DagProof
  48. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  49. def toString(): String
    Definition Classes
    DagProof → AnyRef → Any
  50. def treeLike: TreeLikeOps[NDProof]

    Operations that view the sub-proofs as a tree, see DagProof.TreeLikeOps for a list.

    Operations that view the sub-proofs as a tree, see DagProof.TreeLikeOps for a list.

    Definition Classes
    DagProof
  51. def validateIndices(premise: HOLSequent, antecedentIndices: Seq[SequentIndex]): Unit

    Checks whether indices are in the right place and premise is defined at all of them.

    Checks whether indices are in the right place and premise is defined at all of them.

    premise

    The sequent to be checked.

    antecedentIndices

    Indices that should be in the antecedent.

    Attributes
    protected
    Definition Classes
    NDProof
  52. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  53. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  54. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])

Deprecated Value Members

  1. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.Throwable]) @Deprecated @deprecated
    Deprecated

    (Since version ) see corresponding Javadoc for more information.

  2. def [B](y: B): (ContractionRule, B)
    Implicit
    This member is added by an implicit conversion from ContractionRule toArrowAssoc[ContractionRule] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @deprecated
    Deprecated

    (Since version 2.13.0) Use -> instead. If you still wish to display it as one character, consider using a font with programming ligatures such as Fira Code.

Inherited from Serializable

Inherited from CommonRule

Inherited from ContextRule[Formula, NDProof]

Inherited from UnaryNDProof

Inherited from NDProof

Inherited from SequentProof[Formula, NDProof]

Inherited from DagProof[NDProof]

Inherited from Product

Inherited from Equals

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromContractionRule to any2stringadd[ContractionRule]

Inherited by implicit conversion StringFormat fromContractionRule to StringFormat[ContractionRule]

Inherited by implicit conversion Ensuring fromContractionRule to Ensuring[ContractionRule]

Inherited by implicit conversion ArrowAssoc fromContractionRule to ArrowAssoc[ContractionRule]

Ungrouped