Class/Object

at.logic.gapt.proofs.lk

ForallLeftRule

Related Docs: object ForallLeftRule | package lk

Permalink

case class ForallLeftRule(subProof: LKProof, aux: SequentIndex, A: HOLFormula, term: LambdaExpression, v: Var) extends UnaryLKProof with CommonRule with Product with Serializable

An LKProof ending with a universal quantifier on the left:

           (π)
     A[x\t], Γ :- Δ
    ----------------∀:l
      ∀x.A, Γ :- Δ

subProof

The proof π.

aux

The index of A[x\t].

A

The formula A.

term

The term t.

v

The variable x.

Source
lk.scala
Linear Supertypes
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. ForallLeftRule
  2. Serializable
  3. Serializable
  4. CommonRule
  5. ContextRule
  6. UnaryLKProof
  7. LKProof
  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
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. All

Instance Constructors

  1. new ForallLeftRule(subProof: LKProof, aux: SequentIndex, A: HOLFormula, term: LambdaExpression, v: Var)

    Permalink

    subProof

    The proof π.

    aux

    The index of A[x\t].

    A

    The formula A.

    term

    The term t.

    v

    The variable x.

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

    Permalink
    Implicit information
    This member is added by an implicit conversion from ForallLeftRule to ArrowAssoc[ForallLeftRule] 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 formula A.

  7. def LKRuleCreationException(message: String): LKRuleCreationException

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

    Permalink
    Definition Classes
    Any
  9. val aux: SequentIndex

    Permalink

    The index of A[x\t].

  10. 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
  11. def auxIndices: Seq[Seq[SequentIndex]]

    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
    ForallLeftRuleSequentProof
  12. def clone(): AnyRef

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

    Permalink

    The conclusion of the rule.

    The conclusion of the rule.

    Definition Classes
    ContextRuleSequentProof
  14. def contexts: Seq[Sequent[HOLFormula]]

    Permalink
    Attributes
    protected
    Definition Classes
    ContextRule
  15. 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
  16. 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
  17. final def endSequent: Sequent[HOLFormula]

    Permalink

    The end-sequent of the rule.

    The end-sequent of the rule.

    Definition Classes
    LKProof
  18. def ensuring(cond: (ForallLeftRule) ⇒ Boolean, msg: ⇒ Any): ForallLeftRule

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

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

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

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

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

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

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

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

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

    Permalink
    Definition Classes
    AnyRef → Any
  28. def getOccConnector: OccConnector[HOLFormula]

    Permalink

    The object connecting the lower and upper sequents.auxFormulas

    The object connecting the lower and upper sequents.auxFormulas

    Definition Classes
    UnaryLKProof
  29. val hashCode: Int

    Permalink
    Definition Classes
    DagProof → AnyRef → Any
  30. def immediateSubProofs: Seq[LKProof]

    Permalink

    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    UnaryLKProofDagProof
  31. final def isInstanceOf[T0]: Boolean

    Permalink
    Definition Classes
    Any
  32. def longName: String

    Permalink

    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  33. val mainFormula: HOLFormula

    Permalink
  34. def mainFormulaSequent: Sequent[HOLFormula]

    Permalink
    Definition Classes
    ForallLeftRuleContextRule
  35. def mainFormulas: Seq[HOLFormula]

    Permalink

    The list of main formulas of the rule.

    The list of main formulas of the rule.

    Definition Classes
    SequentProof
  36. 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
    ContextRuleSequentProof
  37. def name: String

    Permalink

    The name of this rule (in symbols).

    The name of this rule (in symbols).

    Definition Classes
    ForallLeftRuleDagProof
  38. final def ne(arg0: AnyRef): Boolean

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

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

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

    Permalink

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

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

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

    Permalink

    The upper sequent of the rule.

    The upper sequent of the rule.

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

    Permalink

    The upper sequents of the rule.

    The upper sequents of the rule.

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

    Permalink
    Attributes
    protected
    Definition Classes
    SequentProofDagProof
  45. val subProof: LKProof

    Permalink

    The proof π.

    The proof π.

    Definition Classes
    ForallLeftRuleUnaryLKProof
  46. def subProofs: Set[LKProof]

    Permalink

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

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

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

    Permalink
    Definition Classes
    AnyRef
  48. val term: LambdaExpression

    Permalink

    The term t.

  49. def toString(): String

    Permalink
    Definition Classes
    DagProof → AnyRef → Any
  50. 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
  51. val v: Var

    Permalink

    The variable x.

  52. 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
  53. final def wait(): Unit

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

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

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

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

Inherited from Serializable

Inherited from Serializable

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 ForallLeftRule to any2stringadd[ForallLeftRule]

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

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

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

Ungrouped