case class Defn(defConst: HOLAtomConst, definition: Expr) extends InitialClause with Product with Serializable

Definition.

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:- ∀x (D(x) <-> φ(x))
Source
resolution.scala
Type Hierarchy
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Inherited
  1. Defn
  2. Serializable
  3. Serializable
  4. InitialClause
  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 Defn(defConst: HOLAtomConst, definition: Expr)

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 Defn to any2stringadd[Defn] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (Defn, B)
    Implicit
    This member is added by an implicit conversion from Defn to ArrowAssoc[Defn] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  7. val assertions: HOLClause

    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[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
  9. 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
    InitialClauseSequentProof
  10. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  11. lazy val conclusion: Sequent[Formula]

    The conclusion of the rule.

    The conclusion of the rule.

    Definition Classes
    ContextRuleSequentProof
  12. def contexts: Seq[Sequent[Formula]]
    Attributes
    protected
    Definition Classes
    ContextRule
  13. def dagLike: DagLikeOps[ResolutionProof]

    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. val defConst: HOLAtomConst
  15. val definition: Expr
  16. val definitionFormula: Formula
  17. def definitions: Map[HOLAtomConst, Expr]

    All definitions introduced by any subproof.

    All definitions introduced by any subproof.

    Definition Classes
    ResolutionProof
    Exceptions thrown

    Exception if inconsistent definitions are used

  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. def ensuring(cond: (Defn) ⇒ Boolean, msg: ⇒ Any): Defn
    Implicit
    This member is added by an implicit conversion from Defn to Ensuring[Defn] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  20. def ensuring(cond: (Defn) ⇒ Boolean): Defn
    Implicit
    This member is added by an implicit conversion from Defn to Ensuring[Defn] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  21. def ensuring(cond: Boolean, msg: ⇒ Any): Defn
    Implicit
    This member is added by an implicit conversion from Defn to Ensuring[Defn] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  22. def ensuring(cond: Boolean): Defn
    Implicit
    This member is added by an implicit conversion from Defn to Ensuring[Defn] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  23. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  24. def equals(that: Any): Boolean
    Definition Classes
    DagProof → Equals → AnyRef → Any
  25. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  26. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from Defn to StringFormat[Defn] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  27. def formulasToBeDeleted: Seq[Seq[SequentIndex]]
    Attributes
    protected
    Definition Classes
    ContextRule
  28. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
  29. val hashCode: Int
    Definition Classes
    DagProof
  30. def immediateSubProofs: Seq[Nothing]

    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    InitialClauseDagProof
  31. def introducedDefinitions: Map[HOLAtomConst, Expr]

    Definitions introduced by the bottom-most inference rule.

    Definitions introduced by the bottom-most inference rule.

    Definition Classes
    DefnResolutionProof
  32. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  33. def isProof: Boolean

    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
  34. def longName: String

    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  35. def mainFormulaSequent: Sequent[Formula]
    Definition Classes
    DefnContextRule
  36. def mainFormulas: Seq[Formula]

    The list of main formulas of the rule.

    The list of main formulas of the rule.

    Definition Classes
    SequentProof
  37. 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
  38. def name: String

    The name of this rule (in symbols).

    The name of this rule (in symbols).

    Definition Classes
    DagProof
  39. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  40. final def notify(): Unit
    Definition Classes
    AnyRef
  41. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  42. 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
  43. def premises: Seq[Sequent[Formula]]

    The upper sequents of the rule.

    The upper sequents of the rule.

    Definition Classes
    SequentProof
  44. def skolemFunctions: SkolemFunctions
    Definition Classes
    ResolutionProof
  45. def stepString(subProofLabels: Map[Any, String]): String
    Attributes
    protected
    Definition Classes
    ResolutionProofSequentProofDagProof
  46. def stringifiedConclusion(implicit sig: BabelSignature): String
    Definition Classes
    ResolutionProof
  47. def subProofAt(pos: List[Int]): ResolutionProof

    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
  48. def subProofs: Set[ResolutionProof]

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

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

    Definition Classes
    DagProof
  49. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  50. def toString(): String
    Definition Classes
    DagProof → AnyRef → Any
  51. def treeLike: TreeLikeOps[ResolutionProof]

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

Inherited from Serializable

Inherited from Serializable

Inherited from InitialClause

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 Defn to any2stringadd[Defn]

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

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

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

Ungrouped