object CERES extends CERES

This implementation of the CERES method does the proof reconstruction via ResolutionToLKProof.

Source
CERES.scala
Linear Supertypes
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. CERES
  2. CERES
  3. AnyRef
  4. Any
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. All

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. 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

    Definition Classes
    CERES
  5. def apply(p: LKProof, pred: (Formula) ⇒ Boolean, prover: ResolutionProver): LKProof
    Definition Classes
    CERES
  6. 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

    Definition Classes
    CERES
  7. def apply(p: LKProof, prover: ResolutionProver): LKProof
    Definition Classes
    CERES
  8. 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

    Definition Classes
    CERES
  9. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  10. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate() @throws( ... )
  11. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  12. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  13. 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

    Definition Classes
    CERES
  14. 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

    Definition Classes
    CERES
    Note

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

  15. 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).

    Definition Classes
    CERES
  16. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  17. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  18. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  19. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  20. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  21. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  22. def skipEquations: (Formula) ⇒ Boolean

    True if the formula is not an equation.

    True if the formula is not an equation. Intended use: predicate argument of CERES. In case the only cuts on equations come from a translation of binary equation rules to unary ones, this should provide the same clause sets and projections as the binary rules.

  23. def skipNothing: (Formula) ⇒ Boolean
  24. def skipPropositional: (Formula) ⇒ Boolean

    True if the formula is propositional and does not contain free variables other than type i.

    True if the formula is propositional and does not contain free variables other than type i. Intended use: predicate argument of CERES. In case the only cuts on equations come from a translation of binary equation rules to unary ones, this should provide the same clause sets and projections as the binary rules.

  25. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  26. def toString(): String
    Definition Classes
    AnyRef → Any
  27. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  28. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  29. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    CERES
    Annotations
    @deprecated
    Deprecated

    (Since version 2.12) Use CERES.expansionProof instead

  2. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @Deprecated @deprecated @throws( classOf[java.lang.Throwable] )
    Deprecated

    (Since version ) see corresponding Javadoc for more information.

Inherited from CERES

Inherited from AnyRef

Inherited from Any

Ungrouped