Class

at.logic.gapt.proofs.lk

LogicalAxiom

Related Doc: package lk

Permalink

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

An LKProof consisting of a logical axiom:

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

A

The atom A.

Source
lk.scala
Linear Supertypes
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. LogicalAxiom
  2. Serializable
  3. Serializable
  4. InitialSequent
  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 LogicalAxiom(A: HOLFormula)

    Permalink

    A

    The atom A.

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

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

    Permalink
    Definition Classes
    AnyRef → Any
  6. val A: HOLFormula

    Permalink

    The atom A.

  7. def LKRuleCreationException(message: String): LKRuleCreationException

    Permalink
    Definition Classes
    LKProof
  8. final def asInstanceOf[T0]: T0

    Permalink
    Definition Classes
    Any
  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[Nothing]

    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
    InitialSequentSequentProof
  11. def clone(): AnyRef

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

    Permalink

    The conclusion of the rule.

    The conclusion of the rule.

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

    Permalink

    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
  14. def depth: Int

    Permalink

    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: Sequent[HOLFormula]

    Permalink

    The end-sequent of the rule.

    The end-sequent of the rule.

    Definition Classes
    LKProof
  16. def ensuring(cond: (LogicalAxiom) ⇒ Boolean, msg: ⇒ Any): LogicalAxiom

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

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

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

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

    Permalink
    Definition Classes
    AnyRef
  21. def equals(that: Any): Boolean

    Permalink
    Definition Classes
    DagProof → Equals → AnyRef → Any
  22. def finalize(): Unit

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

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

    Permalink
    Definition Classes
    AnyRef → Any
  25. val hashCode: Int

    Permalink
    Definition Classes
    DagProof → AnyRef → Any
  26. def immediateSubProofs: Seq[Nothing]

    Permalink

    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    InitialSequentDagProof
  27. final def isInstanceOf[T0]: Boolean

    Permalink
    Definition Classes
    Any
  28. def longName: String

    Permalink

    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  29. def mainFormula: HOLFormula

    Permalink
  30. def mainFormulas: Seq[HOLFormula]

    Permalink

    The list of main formulas of the rule.

    The list of main formulas of the rule.

    Definition Classes
    SequentProof
  31. def mainIndices: Seq[SequentIndex]

    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
    InitialSequentSequentProof
  32. def name: String

    Permalink

    The name of this rule (in symbols).

    The name of this rule (in symbols).

    Definition Classes
    InitialSequentDagProof
  33. final def ne(arg0: AnyRef): Boolean

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

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

    Permalink
    Definition Classes
    AnyRef
  36. def occConnectors: Seq[Nothing]

    Permalink

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

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

    Definition Classes
    InitialSequentSequentProof
  37. def premises: Seq[Sequent[HOLFormula]]

    Permalink

    The upper sequents of the rule.

    The upper sequents of the rule.

    Definition Classes
    SequentProof
  38. def stepString(subProofLabels: Map[Any, String]): String

    Permalink
    Attributes
    protected
    Definition Classes
    SequentProofDagProof
  39. def subProofs: Set[LKProof]

    Permalink

    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

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

    Permalink
    Definition Classes
    DagProof → AnyRef → Any
  42. def treeLike: TreeLikeOps[LKProof]

    Permalink

    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
  43. 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
  44. final def wait(): Unit

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

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

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

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

Inherited from Serializable

Inherited from Serializable

Inherited from InitialSequent

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 LogicalAxiom to any2stringadd[LogicalAxiom]

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

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

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

Ungrouped