c

gapt.proofs.lk.rules

LogicalAxiom

case class LogicalAxiom(A: Formula) extends InitialSequent with Product with Serializable

An LKProof consisting of a logical axiom:

   --------ax
    A :- A
with A atomic.

A

The atom A.

Source
LogicalAxiom.scala
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. LogicalAxiom
  2. Serializable
  3. InitialSequent
  4. LKProof
  5. SequentProof
  6. DagProof
  7. Product
  8. Equals
  9. AnyRef
  10. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. Protected

Instance Constructors

  1. new LogicalAxiom(A: Formula)

    A

    The atom 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 LogicalAxiom toany2stringadd[LogicalAxiom] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (LogicalAxiom, B)
    Implicit
    This member is added by an implicit conversion from LogicalAxiom toArrowAssoc[LogicalAxiom] 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. 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
  10. def auxIndices: Seq[Nothing]

    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
    InitialSequentSequentProof
  11. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @IntrinsicCandidate()
  12. def conclusion: HOLSequent

    The conclusion of the rule.

    The conclusion of the rule.

    Definition Classes
    LogicalAxiomSequentProof
  13. def dagLike: DagLikeOps[LKProof]

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

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

    Definition Classes
    DagProof
  14. 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
  15. final def endSequent: HOLSequent

    The end-sequent of the rule.

    The end-sequent of the rule.

    Definition Classes
    LKProof
  16. def ensuring(cond: (LogicalAxiom) => Boolean, msg: => Any): LogicalAxiom
    Implicit
    This member is added by an implicit conversion from LogicalAxiom toEnsuring[LogicalAxiom] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  17. def ensuring(cond: (LogicalAxiom) => Boolean): LogicalAxiom
    Implicit
    This member is added by an implicit conversion from LogicalAxiom toEnsuring[LogicalAxiom] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  18. def ensuring(cond: Boolean, msg: => Any): LogicalAxiom
    Implicit
    This member is added by an implicit conversion from LogicalAxiom toEnsuring[LogicalAxiom] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  19. def ensuring(cond: Boolean): LogicalAxiom
    Implicit
    This member is added by an implicit conversion from LogicalAxiom toEnsuring[LogicalAxiom] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  20. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  21. def equals(that: Any): Boolean
    Definition Classes
    DagProof → Equals → AnyRef → Any
  22. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @IntrinsicCandidate()
  23. val hashCode: Int
    Definition Classes
    DagProof
  24. def immediateSubProofs: Seq[Nothing]

    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    InitialSequentDagProof
  25. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  26. def longName: String

    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  27. def mainFormula: Formula
  28. def mainFormulas: Seq[Formula]

    The list of main formulas of the rule.

    The list of main formulas of the rule.

    Definition Classes
    SequentProof
  29. 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
    InitialSequentSequentProof
  30. def name: String

    The name of this rule (in symbols).

    The name of this rule (in symbols).

    Definition Classes
    LogicalAxiomDagProof
  31. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  32. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  33. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  34. def occConnectors: Seq[Nothing]

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

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

    Definition Classes
    InitialSequentSequentProof
  35. def premises: Seq[Sequent[Formula]]

    The upper sequents of the rule.

    The upper sequents of the rule.

    Definition Classes
    SequentProof
  36. def productElementNames: Iterator[String]
    Definition Classes
    Product
  37. def stepString(subProofLabels: Map[Any, String]): String
    Attributes
    protected
    Definition Classes
    SequentProofDagProof
  38. 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
  39. def subProofs: Set[LKProof]

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

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

    Definition Classes
    DagProof
  40. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  41. def toString(): String
    Definition Classes
    DagProof → AnyRef → Any
  42. def treeLike: TreeLikeOps[LKProof]

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

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

    Definition Classes
    DagProof
  43. final 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
  44. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  45. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  46. 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
  2. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from LogicalAxiom toStringFormat[LogicalAxiom] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @deprecated @inline()
    Deprecated

    (Since version 2.12.16) Use formatString.format(value) instead of value.formatted(formatString), or use the f"" string interpolator. In Java 15 and later, formatted resolves to the new method in String which has reversed parameters.

  3. def [B](y: B): (LogicalAxiom, B)
    Implicit
    This member is added by an implicit conversion from LogicalAxiom toArrowAssoc[LogicalAxiom] 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 InitialSequent

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 fromLogicalAxiom to any2stringadd[LogicalAxiom]

Inherited by implicit conversion StringFormat fromLogicalAxiom to StringFormat[LogicalAxiom]

Inherited by implicit conversion Ensuring fromLogicalAxiom to Ensuring[LogicalAxiom]

Inherited by implicit conversion ArrowAssoc fromLogicalAxiom to ArrowAssoc[LogicalAxiom]

Ungrouped