Object

at.logic.gapt.proofs.lk

ParamodulationLeftRule

Related Doc: package lk

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object ParamodulationLeftRule extends ConvenienceConstructor

Source
macroRules.scala
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Type Members

  1. type IndexOrFormula = Either[SequentIndex, HOLFormula]

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    ConvenienceConstructor

Value Members

  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 LKRuleCreationException(text: String): LKRuleCreationException

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    Create an LKRuleCreationException with a message starting with "Cannot create $longName: ..."

    Create an LKRuleCreationException with a message starting with "Cannot create $longName: ..."

    text

    The rest of the message.

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    protected
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    ConvenienceConstructor
  5. def apply(leftSubProof: LKProof, eq: IndexOrFormula, rightSubProof: LKProof, aux: IndexOrFormula, mainFormula: HOLFormula): LKProof

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    Simulates a binary equation rule, aka paramodulation.

    Simulates a binary equation rule, aka paramodulation.

    A binary rule of the form

           (π1)              (π2)
        Γ,Δ :- s = t   A[s], Π :- Λ
      ------------------------------par:l
            A[t], Γ, Π :- Δ, Λ
    
    is expressed as a series of inferences:
                                  (π2)
                            A[s], Π :- Λ
                        --------------------w:l
                        s = t, A[s], Π :- Λ
          (π1)         ---------------------:eq:l
      Γ, Δ :- s = t     A[t], s = t, Π :- Λ
      -------------------------------------cut
               A[t], Γ, Π :- Δ, Λ
    

    Each of the aux formulas can be given as an index or a formula. If it is given as a formula, the constructor will attempt to find an appropriate index on its own.

    leftSubProof

    The left subproof π1.

    eq

    The index of the equation or the equation itself.

    rightSubProof

    The right subproof π2.

    aux

    The index of the aux formula or the aux formula itself.

    mainFormula

    The proposed main formula.

  6. def apply(leftSubProof: LKProof, eq: IndexOrFormula, rightSubProof: LKProof, aux: IndexOrFormula, con: Abs): LKProof

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    Simulates a binary equation rule, aka paramodulation.

    Simulates a binary equation rule, aka paramodulation.

    A binary rule of the form

           (π1)              (π2)
        Γ,Δ :- s = t   A[s], Π :- Λ
      ------------------------------par:l
            A[t], Γ, Π :- Δ, Λ
    
    is expressed as a series of inferences:
                                  (π2)
                            A[s], Π :- Λ
                        --------------------w:l
                        s = t, A[s], Π :- Λ
          (π1)         ---------------------:eq:l
      Γ, Δ :- s = t     A[t], s = t, Π :- Λ
      -------------------------------------cut
               A[t], Γ, Π :- Δ, Λ
    

    Each of the aux formulas can be given as an index or a formula. If it is given as a formula, the constructor will attempt to find an appropriate index on its own.

    leftSubProof

    The left subproof π1.

    eq

    The index of the equation or the equation itself.

    rightSubProof

    The right subproof π2.

    aux

    The index of the aux formula or the aux formula itself.

  7. final def asInstanceOf[T0]: T0

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  8. def clone(): AnyRef

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

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  10. def equals(arg0: Any): Boolean

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  11. def finalize(): Unit

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    @throws( classOf[java.lang.Throwable] )
  12. def findAndValidate(premise: HOLSequent)(antIndicesFormulas: Seq[IndexOrFormula], sucIndicesFormulas: Seq[IndexOrFormula]): (Seq[Int], Seq[Int])

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    Combines findIndicesOrFormulasInPremise and validateIndices.

    Combines findIndicesOrFormulasInPremise and validateIndices. That is, it will return a pair of lists of indices and throw an exception if either list contains a -1.

    premise

    The sequent in question.

    antIndicesFormulas

    The list of indices or formulas in the antecedent.

    sucIndicesFormulas

    The list of indices or formulas in the succedent.

    Attributes
    protected
    Definition Classes
    ConvenienceConstructor
  13. def findIndicesOrFormulasInPremise(premise: HOLSequent)(antIndicesFormulas: Seq[IndexOrFormula], sucIndicesFormulas: Seq[IndexOrFormula]): (Seq[HOLFormula], Seq[Int], Seq[HOLFormula], Seq[Int])

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

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  15. def hashCode(): Int

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  16. final def isInstanceOf[T0]: Boolean

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  17. val longName: String

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    The long name of the rule.

    The long name of the rule.

    Definition Classes
    ConvenienceConstructor
  18. final def ne(arg0: AnyRef): Boolean

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  19. final def notify(): Unit

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  20. final def notifyAll(): Unit

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

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  22. def toString(): String

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  23. def validateIndices(premise: HOLSequent)(antFormulas: Seq[HOLFormula], antIndices: Seq[Int], sucFormulas: Seq[HOLFormula], sucIndices: Seq[Int]): Unit

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    Throws an exception if the output of findFormulasInPremise contains any -1 entries.

    Throws an exception if the output of findFormulasInPremise contains any -1 entries.

    premise

    The sequent in question.

    antFormulas

    The list of formulas in the antecedent.

    antIndices

    The list of indices corresponding to antFormulas.

    sucFormulas

    The list of formulas in the succedent.

    sucIndices

    The list indices corresponding to sucFormulas.

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    protected
    Definition Classes
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  24. final def wait(): Unit

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    @throws( ... )
  25. final def wait(arg0: Long, arg1: Int): Unit

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

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