Object

at.logic.gapt.proofs.lk

eliminateTheoryAxioms

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object eliminateTheoryAxioms extends LKVisitor[HOLFormula]

Object for calling the eliminateTheoryAxiom transformation.

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

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  2. final def ##(): Int

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  3. final def ==(arg0: Any): Boolean

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  4. def apply(formula: HOLFormula)(proof: LKProof): LKProof

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    Eliminates some theory axioms from proof, namely those subsumed by formula.

    Eliminates some theory axioms from proof, namely those subsumed by formula.

    formula

    A HOLFormula. Must be of the form ∀x1 ... ∀xn F' with F' quantifier-free.

    proof

    An LKProof.

    returns

    An LKProof proof' with the following properties: Every theory axiom in proof that is subsumed by formula is removed in proof' and formula may occur in the antecedent of the end sequent of proof'.

  5. final def apply(proof: LKProof, otherArg: HOLFormula): LKProof

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    Applies the proof transformation to an LKProof.

    Applies the proof transformation to an LKProof.

    proof

    The input proof.

    returns

    The transformed proof.

    Definition Classes
    LKVisitor
  6. final def asInstanceOf[T0]: T0

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  7. def clone(): AnyRef

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  8. final def eq(arg0: AnyRef): Boolean

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  9. def equals(arg0: Any): Boolean

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  10. def finalize(): Unit

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  11. final def getClass(): Class[_]

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  12. def hashCode(): Int

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  13. final def isInstanceOf[T0]: Boolean

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  14. final def ne(arg0: AnyRef): Boolean

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  15. final def notify(): Unit

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  16. final def notifyAll(): Unit

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  17. def one2one(proof: LKProof, arg: HOLFormula)(func: (Seq[(LKProof, OccConnector[HOLFormula])]) ⇒ LKProof): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  18. def recurse(proof: LKProof, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  19. final def synchronized[T0](arg0: ⇒ T0): T0

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  20. def toString(): String

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  21. def transportToSubProof(arg: HOLFormula, proof: LKProof, subProofIdx: Int): HOLFormula

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    LKVisitor
  22. def visitAndLeft(proof: AndLeftRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  23. def visitAndRight(proof: AndRightRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  24. def visitBottomAxiom(otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  25. def visitContractionLeft(proof: ContractionLeftRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  26. def visitContractionRight(proof: ContractionRightRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  27. def visitCut(proof: CutRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  28. def visitDefinitionLeft(proof: DefinitionLeftRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  29. def visitDefinitionRight(proof: DefinitionRightRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  30. def visitEqualityLeft(proof: EqualityLeftRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  31. def visitEqualityRight(proof: EqualityRightRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  32. def visitExistsLeft(proof: ExistsLeftRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  33. def visitExistsRight(proof: ExistsRightRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  34. def visitExistsSkLeft(proof: ExistsSkLeftRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  35. def visitForallLeft(proof: ForallLeftRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  36. def visitForallRight(proof: ForallRightRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  37. def visitForallSkRight(proof: ForallSkRightRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  38. def visitImpLeft(proof: ImpLeftRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  39. def visitImpRight(proof: ImpRightRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  40. def visitInduction(proof: InductionRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  41. def visitLogicalAxiom(proof: LogicalAxiom, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  42. def visitNegLeft(proof: NegLeftRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  43. def visitNegRight(proof: NegRightRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  44. def visitOpenAssumption(proof: OpenAssumption, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  45. def visitOrLeft(proof: OrLeftRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  46. def visitOrRight(proof: OrRightRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  47. def visitReflexivityAxiom(proof: ReflexivityAxiom, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  48. def visitTheoryAxiom(proof: TheoryAxiom, formula: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    proof

    A theory axiom with sequent A1,...,Ak :- B1,...,:Bn.

    returns

    If A1,...,Ak :- B1,...,:Bn is subsumed by F, returns a proof of F, A1,...,Ak :- B1,...,:Bn. Otherwise the input axiom.

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    protected
    Definition Classes
    eliminateTheoryAxiomsLKVisitor
  49. def visitTopAxiom(otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  50. def visitWeakeningLeft(proof: WeakeningLeftRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  51. def visitWeakeningRight(proof: WeakeningRightRule, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    protected
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    LKVisitor
  52. final def wait(): Unit

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  53. final def wait(arg0: Long, arg1: Int): Unit

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  54. final def wait(arg0: Long): Unit

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  55. def withIdentityOccConnector(proof: LKProof): (LKProof, OccConnector[HOLFormula])

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    LKVisitor
  56. def withOccConnector(formula: HOLFormula)(proof: LKProof): (LKProof, OccConnector[HOLFormula])

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    Eliminates some theory axioms from proof, namely those subsumed by formula.

    Eliminates some theory axioms from proof, namely those subsumed by formula.

    formula

    A HOLFormula. Must be of the form ∀x1 ... ∀xn F' with F' quantifier-free.

    proof

    An LKProof.

    returns

    A pair (proof', conn) with the following properties: Every theory axiom in proof that is subsumed by formula is removed in proof' and formula may occur in the antecedent of the end sequent of proof'; conn is an OccConnector relating proof and proof'.

  57. final def withOccConnector(proof: LKProof, otherArg: HOLFormula): (LKProof, OccConnector[HOLFormula])

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    Applies the proof transformation to an LKProof.

    Applies the proof transformation to an LKProof.

    proof

    The input proof.

    returns

    A pair consisting of the transformed proof and an OccConnector relating the two proofs.

    Definition Classes
    LKVisitor

Inherited from LKVisitor[HOLFormula]

Inherited from AnyRef

Inherited from Any

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