object CERES extends CERES
This implementation of the CERES method does the proof reconstruction via ResolutionToLKProof.
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- CERES.scala
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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
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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
- Definition Classes
- CERES
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def
apply(p: LKProof, pred: (Formula) ⇒ Boolean, prover: ResolutionProver): LKProof
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- CERES
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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
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def
apply(p: LKProof, prover: ResolutionProver): LKProof
- Definition Classes
- CERES
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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
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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
- Definition Classes
- CERES
- Note
This method is passed to ResolutionToLKProof, which handles the simulation of the reflexivity introduction rule by itself.
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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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- CERES
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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.
- def skipNothing: (Formula) ⇒ Boolean
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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.
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