class CERES extends AnyRef
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- new CERES()
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- 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
- def apply(p: LKProof, pred: (Formula) => Boolean, prover: ResolutionProver): LKProof
- 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
- def apply(p: LKProof, prover: ResolutionProver): LKProof
- 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
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- def ensuring(cond: (CERES) => Boolean, msg: => Any): CERES
- def ensuring(cond: (CERES) => Boolean): CERES
- def ensuring(cond: Boolean, msg: => Any): CERES
- def ensuring(cond: Boolean): CERES
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- 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
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- 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.
- 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).
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Deprecated Value Members
- 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
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- @deprecated
- Deprecated
(Since version 2.12) Use CERES.expansionProof instead
- 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.
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- 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.
This is the API documentation for GAPT.
The main package is gapt.