Packages

case class DefinitionLeftRule(subProof: LKProof, aux: SequentIndex, definition: Definition, replacementContext: Abs) extends DefinitionRule with Product with Serializable

An LKProof ending with a definition on the left:

      (π)
   A[φ], Γ :- Δ
  -----------d:l
   A[c], Γ :- Δ

subProof

The proof π.

aux

The index of A in the antecedent.

definition

The definition c := φ.

replacementContext

A term λx.A[x] that designates the positions for the definition.

Source
lk.scala
Ordering
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  2. By Inheritance
Inherited
  1. DefinitionLeftRule
  2. Serializable
  3. Serializable
  4. DefinitionRule
  5. CommonRule
  6. ContextRule
  7. UnaryLKProof
  8. LKProof
  9. SequentProof
  10. DagProof
  11. Product
  12. Equals
  13. AnyRef
  14. 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 DefinitionLeftRule(subProof: LKProof, aux: SequentIndex, definition: Definition, replacementContext: Abs)

    subProof

    The proof π.

    aux

    The index of A in the antecedent.

    definition

    The definition c := φ.

    replacementContext

    A term λx.A[x] that designates the positions for the definition.

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 DefinitionLeftRule to any2stringadd[DefinitionLeftRule] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (DefinitionLeftRule, B)
    Implicit
    This member is added by an implicit conversion from DefinitionLeftRule to ArrowAssoc[DefinitionLeftRule] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. def LKRuleCreationException(message: String): LKRuleCreationException
    Definition Classes
    LKProof
  7. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  8. val aux: SequentIndex
    Definition Classes
    DefinitionLeftRuleDefinitionRule
  9. val auxFormula_: LambdaExpression
    Definition Classes
    DefinitionRule
  10. def auxFormulas: Seq[Seq[HOLFormula]]

    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
    DefinitionLeftRuleSequentProof
  12. val by: LambdaExpression
    Definition Classes
    DefinitionRule
  13. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  14. lazy val conclusion: Sequent[HOLFormula]

    The conclusion of the rule.

    The conclusion of the rule.

    Definition Classes
    ContextRuleSequentProof
  15. def contexts: Seq[Sequent[HOLFormula]]
    Attributes
    protected
    Definition Classes
    ContextRule
  16. 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
  17. val definition: Definition
    Definition Classes
    DefinitionLeftRuleDefinitionRule
  18. 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
  19. final def endSequent: Sequent[HOLFormula]

    The end-sequent of the rule.

    The end-sequent of the rule.

    Definition Classes
    LKProof
  20. def ensuring(cond: (DefinitionLeftRule) ⇒ Boolean, msg: ⇒ Any): DefinitionLeftRule
    Implicit
    This member is added by an implicit conversion from DefinitionLeftRule to Ensuring[DefinitionLeftRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  21. def ensuring(cond: (DefinitionLeftRule) ⇒ Boolean): DefinitionLeftRule
    Implicit
    This member is added by an implicit conversion from DefinitionLeftRule to Ensuring[DefinitionLeftRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  22. def ensuring(cond: Boolean, msg: ⇒ Any): DefinitionLeftRule
    Implicit
    This member is added by an implicit conversion from DefinitionLeftRule to Ensuring[DefinitionLeftRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  23. def ensuring(cond: Boolean): DefinitionLeftRule
    Implicit
    This member is added by an implicit conversion from DefinitionLeftRule to Ensuring[DefinitionLeftRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  24. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  25. def equals(that: Any): Boolean
    Definition Classes
    DagProof → Equals → AnyRef → Any
  26. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  27. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from DefinitionLeftRule to StringFormat[DefinitionLeftRule] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  28. def formulasToBeDeleted: Seq[Seq[SequentIndex]]
    Attributes
    protected
    Definition Classes
    ContextRule
  29. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
  30. def getOccConnector: OccConnector[HOLFormula]

    The object connecting the lower and upper sequents.auxFormulas

    The object connecting the lower and upper sequents.auxFormulas

    Definition Classes
    UnaryLKProof
  31. val hashCode: Int
    Definition Classes
    DagProof
  32. def immediateSubProofs: Seq[LKProof]

    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    UnaryLKProofDagProof
  33. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  34. def longName: String

    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  35. val mainFormula: HOLFormula
    Definition Classes
    DefinitionRule
  36. def mainFormulaSequent: Sequent[HOLFormula]
    Definition Classes
    DefinitionLeftRuleContextRule
  37. val mainFormula_: LambdaExpression
    Definition Classes
    DefinitionRule
  38. def mainFormulas: Seq[HOLFormula]

    The list of main formulas of the rule.

    The list of main formulas of the rule.

    Definition Classes
    SequentProof
  39. def mainIndices: Seq[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
  40. def name: String

    The name of this rule (in symbols).

    The name of this rule (in symbols).

    Definition Classes
    DefinitionLeftRuleDagProof
  41. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  42. final def notify(): Unit
    Definition Classes
    AnyRef
  43. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  44. def occConnectors: Seq[OccConnector[HOLFormula]]

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

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

    Definition Classes
    ContextRuleSequentProof
  45. def premise: Sequent[HOLFormula]

    The upper sequent of the rule.

    The upper sequent of the rule.

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

    The upper sequents of the rule.

    The upper sequents of the rule.

    Definition Classes
    SequentProof
  47. val replacementContext: Abs
    Definition Classes
    DefinitionLeftRuleDefinitionRule
  48. def stepString(subProofLabels: Map[Any, String]): String
    Attributes
    protected
    Definition Classes
    SequentProofDagProof
  49. val subProof: LKProof
  50. 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
  51. def subProofs: Set[LKProof]

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

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

    Definition Classes
    DagProof
  52. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  53. def toString(): String
    Definition Classes
    DagProof → AnyRef → Any
  54. 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
  55. 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
  56. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  57. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  58. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  59. val what: Const
    Definition Classes
    DefinitionRule
  60. def [B](y: B): (DefinitionLeftRule, B)
    Implicit
    This member is added by an implicit conversion from DefinitionLeftRule to ArrowAssoc[DefinitionLeftRule] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Inherited from Serializable

Inherited from Serializable

Inherited from DefinitionRule

Inherited from CommonRule

Inherited from ContextRule[HOLFormula, LKProof]

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 DefinitionLeftRule to any2stringadd[DefinitionLeftRule]

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

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

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

Ungrouped