Packages

case class ForallLeftRule(subProof: LKProof, aux: SequentIndex, A: Formula, term: Expr, v: Var) extends UnaryLKProof with CommonRule with Product with Serializable

An LKProof ending with a universal quantifier on the left:

           (π)
     A[x\t], Γ :- Δ
    ----------------∀:l
      ∀x.A, Γ :- Δ

subProof

The proof π.

aux

The index of A[x\t].

A

The formula A.

term

The term t.

v

The variable x.

Source
lk.scala
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. ForallLeftRule
  2. Serializable
  3. Serializable
  4. CommonRule
  5. ContextRule
  6. UnaryLKProof
  7. LKProof
  8. SequentProof
  9. DagProof
  10. Product
  11. Equals
  12. AnyRef
  13. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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Visibility
  1. Public
  2. All

Instance Constructors

  1. new ForallLeftRule(subProof: LKProof, aux: SequentIndex, A: Formula, term: Expr, v: Var)

    subProof

    The proof π.

    aux

    The index of A[x\t].

    A

    The formula A.

    term

    The term t.

    v

    The variable x.

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 ForallLeftRule to any2stringadd[ForallLeftRule] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (ForallLeftRule, B)
    Implicit
    This member is added by an implicit conversion from ForallLeftRule to ArrowAssoc[ForallLeftRule] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. val A: Formula
  7. def LKRuleCreationException(message: String): LKRuleCreationException
    Attributes
    protected
    Definition Classes
    LKProof
  8. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  9. val aux: 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
    ForallLeftRuleSequentProof
  12. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate() @throws( ... )
  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[LKProof]

    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
    LKProof
  18. def ensuring(cond: (ForallLeftRule) ⇒ Boolean, msg: ⇒ Any): ForallLeftRule
    Implicit
    This member is added by an implicit conversion from ForallLeftRule to Ensuring[ForallLeftRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  19. def ensuring(cond: (ForallLeftRule) ⇒ Boolean): ForallLeftRule
    Implicit
    This member is added by an implicit conversion from ForallLeftRule to Ensuring[ForallLeftRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  20. def ensuring(cond: Boolean, msg: ⇒ Any): ForallLeftRule
    Implicit
    This member is added by an implicit conversion from ForallLeftRule to Ensuring[ForallLeftRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  21. def ensuring(cond: Boolean): ForallLeftRule
    Implicit
    This member is added by an implicit conversion from ForallLeftRule to Ensuring[ForallLeftRule] 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 ForallLeftRule to StringFormat[ForallLeftRule] 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[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  27. def getSequentConnector: SequentConnector

    The object connecting the lower and upper sequents.auxFormulas

    The object connecting the lower and upper sequents.auxFormulas

    Definition Classes
    UnaryLKProof
  28. val hashCode: Int
    Definition Classes
    DagProof
  29. def immediateSubProofs: Seq[LKProof]

    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    UnaryLKProofDagProof
  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
    ForallLeftRuleContextRule
  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
    ForallLeftRuleDagProof
  37. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  38. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  39. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  40. def occConnectors: Seq[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
    UnaryLKProof
  42. def premises: Seq[Sequent[Formula]]

    The upper sequents of the rule.

    The upper sequents of the rule.

    Definition Classes
    SequentProof
  43. def stepString(subProofLabels: Map[Any, String]): String
    Attributes
    protected
    Definition Classes
    SequentProofDagProof
  44. val subProof: LKProof

    The immediate subproof of the rule.

    The immediate subproof of the rule.

    Definition Classes
    ForallLeftRuleUnaryLKProof
  45. def subProofAt(pos: List[Int]): LKProof

    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
  46. def subProofs: Set[LKProof]

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

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

    Definition Classes
    DagProof
  47. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  48. val term: Expr
  49. def toString(): String
    Definition Classes
    DagProof → AnyRef → Any
  50. def treeLike: TreeLikeOps[LKProof]

    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. val v: Var
  52. def validateIndices(premise: HOLSequent, antecedentIndices: Seq[SequentIndex], succedentIndices: 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.

    succedentIndices

    Indices that should be in the succedent.

    Attributes
    protected
    Definition Classes
    LKProof
  53. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  54. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  55. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  56. def [B](y: B): (ForallLeftRule, B)
    Implicit
    This member is added by an implicit conversion from ForallLeftRule to ArrowAssoc[ForallLeftRule] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Deprecated Value Members

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

    (Since version ) see corresponding Javadoc for more information.

Inherited from Serializable

Inherited from Serializable

Inherited from CommonRule

Inherited from ContextRule[Formula, LKProof]

Inherited from UnaryLKProof

Inherited from LKProof

Inherited from SequentProof[Formula, LKProof]

Inherited from DagProof[LKProof]

Inherited from Product

Inherited from Equals

Inherited from AnyRef

Inherited from Any

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

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

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

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

Ungrouped