class CERES extends AnyRef

Source
CERES.scala
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  1. CERES
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Instance Constructors

  1. new CERES()

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##: Int
    Definition Classes
    AnyRef → Any
  3. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from CERES toany2stringadd[CERES] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (CERES, B)
    Implicit
    This member is added by an implicit conversion from CERES toArrowAssoc[CERES] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. def apply(endsequent: HOLSequent, projections: Set[LKProof], rp: ResolutionProof): LKProof

    Applies the CERES method to a first order proof with equality.

    Applies the CERES method to a first order proof with equality. Internally this is handled by the ResolutionToLKProof method.

    endsequent

    The end-sequent of the original proof

    projections

    The projections of the original proof

    rp

    A resolution refutation

    returns

    an LK Proof in Atomic Cut Normal Form (ACNF) i.e. without quantified cuts

  7. def apply(p: LKProof, pred: (Formula) => Boolean, prover: ResolutionProver): LKProof
  8. def apply(p: LKProof, pred: (Formula) => Boolean): LKProof

    Applies the CERES method to a first order proof with equality.

    Applies the CERES method to a first order proof with equality. Internally this is handled by the RobinsoToLK method.

    p

    a first-order LKProof without strong quantifiers in the end-sequent (i.e. structural rules, cut, logical rules, equational rules but no definitions, schema,higher order)

    pred

    a predicate to specify which cut formulas to eliminate (e.g. x => containsQuantifiers(x) to keep propositional cuts intact)

    returns

    an LK Proof where all cuts are quantifier-free

  9. def apply(p: LKProof, prover: ResolutionProver): LKProof
  10. def apply(p: LKProof): LKProof

    Applies the CERES method to a first order proof with equality.

    Applies the CERES method to a first order proof with equality. Internally this is handled by the RobinsoToLK method.

    p

    a first-order LKProof (structural rules, cut, logical rules, equational rules but no definitions, schema,higher order) also each formula must be a FOLFormula, since the prover9 interface returns proofs from the FOL layer

    returns

    an LK Proof in Atomic Cut Normal Form (ACNF) i.e. without quantified cuts

  11. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  12. def clone(): AnyRef
    Attributes
    protected[lang]
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    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @IntrinsicCandidate()
  13. def ensuring(cond: (CERES) => Boolean, msg: => Any): CERES
    Implicit
    This member is added by an implicit conversion from CERES toEnsuring[CERES] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  14. def ensuring(cond: (CERES) => Boolean): CERES
    Implicit
    This member is added by an implicit conversion from CERES toEnsuring[CERES] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  15. def ensuring(cond: Boolean, msg: => Any): CERES
    Implicit
    This member is added by an implicit conversion from CERES toEnsuring[CERES] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  16. def ensuring(cond: Boolean): CERES
    Implicit
    This member is added by an implicit conversion from CERES toEnsuring[CERES] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  17. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  18. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  19. def expansionProof(p: LKProof, skip: (Formula) => Boolean = CERES.skipNothing, prover: ResolutionProver = Escargot): ExpansionProof

    Computes the expansion proof of the CERES-normal form using projections and the resolution refutation.

    Computes the expansion proof of the CERES-normal form using projections and the resolution refutation.

    p

    a first-order LKProof without strong quantifiers in the end-sequent (i.e. structural rules, cut, logical rules, equational rules but no definitions, schema,higher order)

    returns

    an expansion proof of the CERES-normal form computed from the projections and the resolution refutation

  20. def findMatchingProjection(endsequent: HOLSequent, projections: Set[LKProof])(input_clause: Input): LKProof

    Finds the matching projection of an input clause in the set of projections.

    Finds the matching projection of an input clause in the set of projections.

    endsequent

    The common end-sequent of all projections.

    projections

    The set of projections.

    input_clause

    The clause we need to project to.

    returns

    An LK proof endsequent x input_clause contained in projections

    Note

    This method is passed to ResolutionToLKProof, which handles the simulation of the reflexivity introduction rule by itself.

  21. def findPartialExpansionSequent(endsequent: HOLSequent, projections: Set[LKProof])(input: Input, set: Set[(Substitution, ExpansionSequent)]): ExpansionSequent

    Computes the partial expansion sequent of the matching projection of an input clause in the set of projections.

    Computes the partial expansion sequent of the matching projection of an input clause in the set of projections.

    endsequent

    The common end-sequent of all projections.

    projections

    The set of projections.

    input

    The clause we need to project to, the expansion sequent we want to modify and a set which we do not change.

    returns

    An expansion sequent of the projection corresponding to the input clause, without the clause part (we compute the expansion trees of all formulas in the end-sequent of the projection except of the formulas corresponding to the input clause).

  22. final def getClass(): Class[_ <: AnyRef]
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    @native() @IntrinsicCandidate()
  23. def hashCode(): Int
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    @native() @IntrinsicCandidate()
  24. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  25. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  26. final def notify(): Unit
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    @native() @IntrinsicCandidate()
  27. final def notifyAll(): Unit
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    @native() @IntrinsicCandidate()
  28. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
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  29. def toString(): String
    Definition Classes
    AnyRef → Any
  30. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
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    @throws(classOf[java.lang.InterruptedException])
  31. final def wait(arg0: Long): Unit
    Definition Classes
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    @throws(classOf[java.lang.InterruptedException]) @native()
  32. final def wait(): Unit
    Definition Classes
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    @throws(classOf[java.lang.InterruptedException])

Deprecated Value Members

  1. def CERESExpansionProof(p: LKProof, prover: ResolutionProver = Escargot): ExpansionProof

    Computes the expansion proof of the CERES-normal form using projections and the resolution refutation.

    Computes the expansion proof of the CERES-normal form using projections and the resolution refutation.

    p

    a first-order LKProof without strong quantifiers in the end-sequent (i.e. structural rules, cut, logical rules, equational rules but no definitions, schema,higher order)

    returns

    an expansion proof of the CERES-normal form computed from the projections and the resolution refutation

    Annotations
    @deprecated
    Deprecated

    (Since version 2.12) Use CERES.expansionProof instead

  2. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.Throwable]) @Deprecated
    Deprecated
  3. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from CERES toStringFormat[CERES] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @deprecated @inline()
    Deprecated

    (Since version 2.12.16) Use formatString.format(value) instead of value.formatted(formatString), or use the f"" string interpolator. In Java 15 and later, formatted resolves to the new method in String which has reversed parameters.

  4. def [B](y: B): (CERES, B)
    Implicit
    This member is added by an implicit conversion from CERES toArrowAssoc[CERES] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @deprecated
    Deprecated

    (Since version 2.13.0) Use -> instead. If you still wish to display it as one character, consider using a font with programming ligatures such as Fira Code.

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromCERES to any2stringadd[CERES]

Inherited by implicit conversion StringFormat fromCERES to StringFormat[CERES]

Inherited by implicit conversion Ensuring fromCERES to Ensuring[CERES]

Inherited by implicit conversion ArrowAssoc fromCERES to ArrowAssoc[CERES]

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