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gapt.proofs.lk.rules.macros

ParamodulationLeftRule

object ParamodulationLeftRule extends ConvenienceConstructor

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  1. final def !=(arg0: Any): Boolean
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  2. final def ##: Int
    Definition Classes
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  3. final def ==(arg0: Any): Boolean
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  4. final def LKRuleCreationException(text: String): LKRuleCreationException

    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.

    Attributes
    protected
    Definition Classes
    ConvenienceConstructor
  5. def apply(leftSubProof: LKProof, eq: IndexOrFormula, rightSubProof: LKProof, aux: IndexOrFormula, mainFormula: Formula): LKProof

    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

    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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    protected[lang]
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    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @IntrinsicCandidate()
  9. final def eq(arg0: AnyRef): Boolean
    Definition Classes
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  10. def equals(arg0: AnyRef): Boolean
    Definition Classes
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  11. def findAndValidate(premise: HOLSequent)(antIndicesFormulas: Seq[IndexOrFormula], sucIndicesFormulas: Seq[IndexOrFormula]): (Seq[Int], Seq[Int])

    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
  12. def findIndicesOrFormulasInPremise(premise: HOLSequent)(antIndicesFormulas: Seq[IndexOrFormula], sucIndicesFormulas: Seq[IndexOrFormula]): (Seq[Formula], Seq[Int], Seq[Formula], Seq[Int])
    Definition Classes
    ConvenienceConstructor
  13. final def getClass(): Class[_ <: AnyRef]
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    @native() @IntrinsicCandidate()
  14. def hashCode(): Int
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    @native() @IntrinsicCandidate()
  15. final def isInstanceOf[T0]: Boolean
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  16. val longName: String
    Definition Classes
    ConvenienceConstructor
  17. final def ne(arg0: AnyRef): Boolean
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  18. final def notify(): Unit
    Definition Classes
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    @native() @IntrinsicCandidate()
  19. final def notifyAll(): Unit
    Definition Classes
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    @native() @IntrinsicCandidate()
  20. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
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  21. def toString(): String
    Definition Classes
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  22. def validateIndices(premise: HOLSequent)(antFormulas: Seq[Formula], antIndices: Seq[Int], sucFormulas: Seq[Formula], sucIndices: Seq[Int]): Unit

    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.

    Attributes
    protected
    Definition Classes
    ConvenienceConstructor
  23. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
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    @throws(classOf[java.lang.InterruptedException])
  24. final def wait(arg0: Long): Unit
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    @throws(classOf[java.lang.InterruptedException]) @native()
  25. final def wait(): Unit
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    @throws(classOf[java.lang.InterruptedException])

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  1. def finalize(): Unit
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    @throws(classOf[java.lang.Throwable]) @Deprecated
    Deprecated

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