Class/Object

at.logic.gapt.proofs.lkNew

ForallRightRule

Related Docs: object ForallRightRule | package lkNew

Permalink

case class ForallRightRule(subProof: LKProof, aux: SequentIndex, eigenVariable: Var, quantifiedVariable: Var) extends UnaryLKProof with Product with Serializable

An LKProof ending with a universal quantifier on the right:

          (π)
     Γ :- Δ, A[x\α]
    ---------------∀:r
     Γ :- Δ, ∀x.A
This rule is only applicable if the eigenvariable condition is satisfied: α must not occur freely in Γ :- Δ.

subProof

The proof π.

aux

The index of A[x\α].

eigenVariable

The variable α.

quantifiedVariable

The variable x.

Linear Supertypes
Serializable, Serializable, UnaryLKProof, LKProof, SequentProof[HOLFormula, LKProof], DagProof[LKProof], Product, Equals, AnyRef, Any
Type Hierarchy Learn more about scaladoc diagrams
Ordering
  1. Alphabetic
  2. By inheritance
Inherited
  1. ForallRightRule
  2. Serializable
  3. Serializable
  4. UnaryLKProof
  5. LKProof
  6. SequentProof
  7. DagProof
  8. Product
  9. Equals
  10. AnyRef
  11. 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 ForallRightRule(subProof: LKProof, aux: SequentIndex, eigenVariable: Var, quantifiedVariable: Var)

    Permalink

    subProof

    The proof π.

    aux

    The index of A[x\α].

    eigenVariable

    The variable α.

    quantifiedVariable

    The variable x.

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 ForallRightRule to any2stringadd[ForallRightRule] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (ForallRightRule, B)

    Permalink
    Implicit information
    This member is added by an implicit conversion from ForallRightRule to ArrowAssoc[ForallRightRule] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean

    Permalink
    Definition Classes
    AnyRef → Any
  6. final def asInstanceOf[T0]: T0

    Permalink
    Definition Classes
    Any
  7. val aux: SequentIndex

    Permalink

    The index of A[x\α].

  8. val auxFormula: HOLFormula

    Permalink
  9. def auxFormulas: Seq[Seq[HOLFormula]]

    Permalink

    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
  10. def auxIndices: Seq[Seq[SequentIndex]]

    Permalink

    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
    ForallRightRuleSequentProof
  11. def clone(): AnyRef

    Permalink
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  12. def conclusion: HOLSequent

    Permalink

    The conclusion of the rule.

    The conclusion of the rule.

    Definition Classes
    LKProofSequentProof
  13. val context: Sequent[HOLFormula]

    Permalink
  14. def dagLikeForeach(f: (LKProof) ⇒ Unit): Set[LKProof]

    Permalink

    Iterate over all sub-proofs including this in post-order, ignoring duplicates.

    Iterate over all sub-proofs including this in post-order, ignoring duplicates.

    returns

    Set of all visited sub-proofs including this.

    Definition Classes
    DagProof
  15. def dagLikePostOrder: Seq[LKProof]

    Permalink

    A sequence of all sub-proofs including this in post-order, ignoring duplicates.

    A sequence of all sub-proofs including this in post-order, ignoring duplicates.

    Definition Classes
    DagProof
  16. val eigenVariable: Var

    Permalink

    The variable α.

  17. def endSequent: Sequent[HOLFormula]

    Permalink

    The end-sequent of the rule.

    The end-sequent of the rule.

    Definition Classes
    ForallRightRuleLKProof
  18. def ensuring(cond: (ForallRightRule) ⇒ Boolean, msg: ⇒ Any): ForallRightRule

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

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

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

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

    Permalink
    Definition Classes
    AnyRef
  23. def finalize(): Unit

    Permalink
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  24. def foreach(f: (LKProof) ⇒ Unit): Unit

    Permalink

    Iterate over all sub-proofs including this in post-order.

    Iterate over all sub-proofs including this in post-order.

    Definition Classes
    DagProof
  25. def formatted(fmtstr: String): String

    Permalink
    Implicit information
    This member is added by an implicit conversion from ForallRightRule to StringFormat[ForallRightRule] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  26. final def getClass(): Class[_]

    Permalink
    Definition Classes
    AnyRef → Any
  27. def getOccConnector: OccConnector

    Permalink

    The object connecting the lower and upper sequents.

    The object connecting the lower and upper sequents.

    Definition Classes
    ForallRightRuleUnaryLKProof
  28. val hashCode: Int

    Permalink
    Definition Classes
    DagProof → AnyRef → Any
  29. def immediateSubProofs: Seq[LKProof]

    Permalink

    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    UnaryLKProofDagProof
  30. final def isInstanceOf[T0]: Boolean

    Permalink
    Definition Classes
    Any
  31. def longName: String

    Permalink

    The name of the rule (in words).

    The name of the rule (in words).

    Definition Classes
    DagProof
  32. val mainFormula: HOLFormula

    Permalink
  33. def mainFormulas: Seq[HOLFormula]

    Permalink

    The list of main formulas of the rule.

    The list of main formulas of the rule.

    Definition Classes
    SequentProof
  34. def mainIndices: Seq[Suc]

    Permalink

    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
    ForallRightRuleSequentProof
  35. def name: String

    Permalink

    The name of the rule (in symbols).

    The name of the rule (in symbols).

    Definition Classes
    ForallRightRuleDagProof
  36. final def ne(arg0: AnyRef): Boolean

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

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

    Permalink
    Definition Classes
    AnyRef
  39. def occConnectors: Seq[OccConnector]

    Permalink

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

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

    Definition Classes
    UnaryLKProofSequentProof
  40. def postOrder: Seq[LKProof]

    Permalink

    A sequence of all sub-proofs including this in post-order.

    A sequence of all sub-proofs including this in post-order.

    Definition Classes
    DagProof
  41. def premise: HOLSequent

    Permalink

    The upper sequent of the rule.

    The upper sequent of the rule.

    Definition Classes
    UnaryLKProof
  42. def premises: Seq[Sequent[HOLFormula]]

    Permalink

    The upper sequents of the rule.

    The upper sequents of the rule.

    Definition Classes
    SequentProof
  43. val quantifiedVariable: Var

    Permalink

    The variable x.

  44. def stepString(subProofLabels: Map[Any, String]): String

    Permalink
    Attributes
    protected
    Definition Classes
    SequentProofDagProof
  45. val subProof: LKProof

    Permalink

    The proof π.

    The proof π.

    Definition Classes
    ForallRightRuleUnaryLKProof
  46. def subProofs: Set[LKProof]

    Permalink

    Set of all sub-proofs including this.

    Set of all sub-proofs including this.

    Definition Classes
    DagProof
  47. final def synchronized[T0](arg0: ⇒ T0): T0

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

    Permalink
    Definition Classes
    DagProof → AnyRef → Any
  49. def validateIndices(premise: HOLSequent, antecedentIndices: Seq[SequentIndex], succedentIndices: Seq[SequentIndex]): Unit

    Permalink

    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.

    succedentIndices

    Indices that should be in the succedent.

    Attributes
    protected
    Definition Classes
    LKProof
  50. final def wait(): Unit

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

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

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

    Permalink
    Implicit information
    This member is added by an implicit conversion from ForallRightRule to ArrowAssoc[ForallRightRule] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Inherited from Serializable

Inherited from Serializable

Inherited from UnaryLKProof

Inherited from LKProof

Inherited from SequentProof[HOLFormula, LKProof]

Inherited from DagProof[LKProof]

Inherited from Product

Inherited from Equals

Inherited from AnyRef

Inherited from Any

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

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

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

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

Ungrouped