Class/Object

at.logic.gapt.provers.inductionProver

SimpleInductionProof

Related Docs: object SimpleInductionProof | package inductionProver

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class SimpleInductionProof extends AnyRef

Models a simple induction proof.

Source
SIPs.scala
Linear Supertypes
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Inherited
  1. SimpleInductionProof
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Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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Visibility
  1. Public
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Instance Constructors

  1. new SimpleInductionProof(ExpSeq0: ExpansionSequent, ExpSeq1: ExpansionSequent, ExpSeq2: ExpansionSequent, t: List[FOLTerm], u: List[FOLTerm], inductionFormula: HOLFormula = ...)

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    ExpSeq0

    Instances for the induction base.

    ExpSeq1

    Instances for the induction step.

    ExpSeq2

    Instances for the conclusion.

    t

    Terms used in the induction step.

    u

    Terms used in the conclusion

    inductionFormula

    The formula induced over. This argument defaults to X(α, ν, γ) with X a second-order variable, i.e. an unknown induction formula.

Value Members

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

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    Definition Classes
    AnyRef → Any
  2. final def ##(): Int

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    Definition Classes
    AnyRef → Any
  3. def +(other: String): String

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    Implicit information
    This member is added by an implicit conversion from SimpleInductionProof to any2stringadd[SimpleInductionProof] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (SimpleInductionProof, B)

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    Implicit information
    This member is added by an implicit conversion from SimpleInductionProof to ArrowAssoc[SimpleInductionProof] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any
  6. val EndSequent: Sequent[HOLFormula]

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  7. val ExpSeq0: ExpansionSequent

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    Instances for the induction base.

  8. val ExpSeq1: ExpansionSequent

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    Instances for the induction step.

  9. val ExpSeq2: ExpansionSequent

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    Instances for the conclusion.

  10. val Ft: List[HOLFormula]

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  11. val Fu: List[HOLFormula]

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  12. val Gamma0: HOLSequent

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  13. val Gamma1: HOLSequent

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  14. val Gamma2: HOLSequent

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  15. val Sequent0: Sequent[HOLFormula]

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  16. val Sequent1: Sequent[HOLFormula]

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  17. val Sequent2: Sequent[HOLFormula]

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  18. final def asInstanceOf[T0]: T0

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    Definition Classes
    Any
  19. def clone(): AnyRef

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  20. def ensuring(cond: (SimpleInductionProof) ⇒ Boolean, msg: ⇒ Any): SimpleInductionProof

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

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

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

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

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    Definition Classes
    AnyRef
  25. def equals(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any
  26. def finalize(): Unit

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

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    Implicit information
    This member is added by an implicit conversion from SimpleInductionProof to StringFormat[SimpleInductionProof] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  28. final def getClass(): Class[_]

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    Definition Classes
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  29. def hashCode(): Int

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    Definition Classes
    AnyRef → Any
  30. def indFormIsQuantified: Boolean

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    Returns true iff the induction formula needs to be quantified over.

  31. val inductionFormula: HOLFormula

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    The formula induced over.

    The formula induced over. This argument defaults to X(α, ν, γ) with X a second-order variable, i.e. an unknown induction formula.

  32. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any
  33. def isSchematic: Boolean

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    returns

    True if this is a schematic sip, i.e. the induction formula is unknown.

  34. def isSolved: Boolean

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  35. def isSolved(prover: Prover): Boolean

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    returns

    True if the induction formula is in fact a solution.

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

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    Definition Classes
    AnyRef
  37. final def notify(): Unit

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    Definition Classes
    AnyRef
  38. final def notifyAll(): Unit

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    Definition Classes
    AnyRef
  39. def solve(f: FOLFormula): SimpleInductionProof

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    TODO: Find a better name for this

    TODO: Find a better name for this

    f

    A FOLFormula

    returns

    This with the induction formula replaced by f

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

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    Definition Classes
    AnyRef
  41. val t: List[FOLTerm]

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    Terms used in the induction step.

  42. def toInstanceLKProof(n: Int, pi0: LKProof, pi1: LKProof, pi2: LKProof, rename: Boolean): LKProof

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    Computes the nth instance proof, with user-supplied proofs π0, π1, π2.

    Computes the nth instance proof, with user-supplied proofs π0, π1, π2.

    n

    A natural number

    pi0

    Proof of the induction base.

    pi1

    Proof of the induction step.

    pi2

    Proof of the conclusion.

    returns

    The nth instance of this sip.

  43. def toInstanceLKProof(n: Int, prover: Prover, rename: Boolean): LKProof

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    Computes the nth instance proof,

    Computes the nth instance proof,

    n

    A natural number

    prover

    The prover used to generate π0 ,…,π2.

    returns

    The nth instance of this sip.

  44. def toInstanceLKProof(n: Int, rename: Boolean): LKProof

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    Computes the nth instance proof.

    Computes the nth instance proof. Uses prover9 to compute the subproofs.

    n

    A natural number

    returns

    The nth instance of this sip.

  45. def toLKProof: LKProof

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    Converts this into an LKProof, calling prover9 to provide π0, π1, π2.

    Converts this into an LKProof, calling prover9 to provide π0, π1, π2.

    returns

    The LKProof represented by this object

  46. def toLKProof(prover: Prover): LKProof

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    prover

    The prover used to generate π0 ,…,π2.

  47. def toLKProof(pi0: LKProof, pi1: LKProof, pi2: LKProof): LKProof

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    Converts this into an LKProof, with user-supplied proofs π0, π1, π2.

    Converts this into an LKProof, with user-supplied proofs π0, π1, π2.

    pi0

    Proof of the induction base.

    pi1

    Proof of the induction step.

    pi2

    Proof of the conclusion.

    returns

    The LKProof represented by this object.

  48. def toSipGrammar: SipGrammar

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    Extracts a SIP grammar from the SIP according to the paper.

    Extracts a SIP grammar from the SIP according to the paper.

    returns

    The grammar corresponding to the sip.

  49. def toString(): String

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    Definition Classes
    AnyRef → Any
  50. val u: List[FOLTerm]

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    Terms used in the conclusion

  51. final def wait(): Unit

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

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    Definition Classes
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    Annotations
    @throws( ... )
  53. final def wait(arg0: Long): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  54. def [B](y: B): (SimpleInductionProof, B)

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

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd from SimpleInductionProof to any2stringadd[SimpleInductionProof]

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

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

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

Ungrouped