Class

at.logic.gapt.proofs.resolution

DefIntro

Related Doc: package resolution

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case class DefIntro(subProof: ResolutionProof, idx: SequentIndex, defAtom: HOLAtom, definition: LambdaExpression) extends PropositionalResolutionRule with Product with Serializable

Definition introduction.

Γ :- Δ, φ(x)
--------
Γ :- Δ, D(x)

This is then used together with Taut in order to use the introduced definitions in other parts of the proof:

------------  Taut
φ(x) :- φ(x)
------------  DefIntro
D(x) :- φ(x)
Source
resolution.scala
Linear Supertypes
Type Hierarchy
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Inherited
  1. DefIntro
  2. Serializable
  3. Serializable
  4. PropositionalResolutionRule
  5. LocalResolutionRule
  6. ContextRule
  7. ResolutionProof
  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 DefIntro(subProof: ResolutionProof, idx: SequentIndex, defAtom: HOLAtom, definition: LambdaExpression)

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Value Members

  1. final def !=(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any
  2. final def ##(): Int

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    Definition Classes
    AnyRef → Any
  3. def +(other: String): String

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    Implicit information
    This member is added by an implicit conversion from DefIntro to any2stringadd[DefIntro] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (DefIntro, B)

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

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

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    Definition Classes
    Any
  7. val assertions: HOLClause

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    Assertions of the proof.

    Assertions of the proof.

    Attention: this is interpreted as assertions.toNegConjunction --> conclusion.toDisjunction

    These assertions indicate the splitting assumptions this proof depends on.

    Definition Classes
    ResolutionProof
  8. def auxFormulas: Seq[Seq[HOLFormula]]

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

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    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
    PropositionalResolutionRuleSequentProof
  10. def clone(): AnyRef

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  11. lazy val conclusion: Sequent[HOLFormula]

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    The conclusion of the rule.

    The conclusion of the rule.

    Definition Classes
    ContextRuleSequentProof
  12. def conclusionString: String

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    Definition Classes
    ResolutionProof
  13. def contexts: Seq[Sequent[HOLFormula]]

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    Attributes
    protected
    Definition Classes
    ContextRule
  14. def dagLike: DagLikeOps[ResolutionProof]

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    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
  15. val defArgs: List[LambdaExpression]

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  16. val defAtom: HOLAtom

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  17. val defConst: HOLAtomConst

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  18. val definition: LambdaExpression

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  19. def definitions: Map[HOLAtomConst, LambdaExpression]

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    All definitions introduced by any subproof.

    All definitions introduced by any subproof.

    Definition Classes
    ResolutionProof
    Exceptions thrown

    Exception if inconsistent definitions are used

  20. def depth: Int

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    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
  21. def ensuring(cond: (DefIntro) ⇒ Boolean, msg: ⇒ Any): DefIntro

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

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

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

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

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

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

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

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    Implicit information
    This member is added by an implicit conversion from DefIntro to StringFormat[DefIntro] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  29. def formulasToBeDeleted: Seq[Seq[SequentIndex]]

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    Attributes
    protected
    Definition Classes
    ContextRule
  30. final def getClass(): Class[_]

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    Definition Classes
    AnyRef → Any
  31. val hashCode: Int

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    Definition Classes
    DagProof → AnyRef → Any
  32. val idx: SequentIndex

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    Definition Classes
    DefIntroPropositionalResolutionRule
  33. def immediateSubProofs: Seq[ResolutionProof]

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    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    PropositionalResolutionRuleDagProof
  34. def introducedDefinitions: Map[HOLAtomConst, LambdaExpression]

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    Definitions introduced by the bottom-most inference rule.

    Definitions introduced by the bottom-most inference rule.

    Definition Classes
    DefIntroResolutionProof
  35. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any
  36. def isProof: Boolean

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    Is this a proof of the empty clause with empty assertions, and consistent definitions?

    Is this a proof of the empty clause with empty assertions, and consistent definitions?

    Definition Classes
    ResolutionProof
  37. def longName: String

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    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  38. def mainFormulaSequent: Sequent[HOLFormula]

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    Definition Classes
    DefIntroContextRule
  39. def mainFormulas: Seq[HOLFormula]

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    The list of main formulas of the rule.

    The list of main formulas of the rule.

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

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    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
  41. def name: String

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    The name of this rule (in symbols).

    The name of this rule (in symbols).

    Definition Classes
    DagProof
  42. final def ne(arg0: AnyRef): Boolean

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    Definition Classes
    AnyRef
  43. final def notify(): Unit

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    Definition Classes
    AnyRef
  44. final def notifyAll(): Unit

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    Definition Classes
    AnyRef
  45. def occConnectors: Seq[OccConnector[HOLFormula]]

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

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

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

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    The upper sequents of the rule.

    The upper sequents of the rule.

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

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    Attributes
    protected
    Definition Classes
    ResolutionProofSequentProofDagProof
  48. val subProof: ResolutionProof

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    Definition Classes
    DefIntroPropositionalResolutionRule
  49. def subProofs: Set[ResolutionProof]

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

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

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

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    Definition Classes
    AnyRef
  51. def toString(): String

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    Definition Classes
    DagProof → AnyRef → Any
  52. def treeLike: TreeLikeOps[ResolutionProof]

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    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
  53. final def wait(): Unit

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

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

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  56. def [B](y: B): (DefIntro, B)

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

Inherited from Serializable

Inherited from Serializable

Inherited from LocalResolutionRule

Inherited from ResolutionProof

Inherited from DagProof[ResolutionProof]

Inherited from Product

Inherited from Equals

Inherited from AnyRef

Inherited from Any

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

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

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

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

Ungrouped