package reduction
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Type Members
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case class
CombinedReduction
[-P1, P2, +P3, +S1, S2, -S3](red1: Reduction[P1, P2, S1, S2], red2: Reduction[P2, P3, S2, S3]) extends Reduction[P1, P3, S1, S3] with Product with Serializable
Sequential composition of reductions.
Sequential composition of reductions.
This class is not intended to be used directly, but via the Reduction#|> operator.
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case class
HOFunctionReduction
(extraAxioms: Boolean = true) extends OneWayReduction_[HOLSequent] with Product with Serializable
Replaces the use of higher-order functions by fresh function symbols, together with axioms that axiomatize them.
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case class
HOFunctionReductionCNFRes
(extraAxioms: Boolean = true) extends Reduction_[Set[HOLSequent], ResolutionProof] with Product with Serializable
Replaces the use of higher-order functions by fresh function symbols, together with axioms that axiomatize them.
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case class
HOFunctionReductionET
(extraAxioms: Boolean = true) extends Reduction_[HOLSequent, ExpansionProof] with Product with Serializable
Replaces the use of higher-order functions by fresh function symbols, together with axioms that axiomatize them.
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case class
HOFunctionReductionRes
(extraAxioms: Boolean = true) extends Reduction_[HOLSequent, ResolutionProof] with Product with Serializable
Replaces the use of higher-order functions by fresh function symbols, together with axioms that axiomatize them.
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case class
LambdaEliminationReduction
(extraAxioms: Boolean = true) extends OneWayReduction_[HOLSequent] with Product with Serializable
Replaces lambda abstractions by fresh function symbols, together with axioms that axiomatize them.
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case class
LambdaEliminationReductionCNFRes
(extraAxioms: Boolean = true) extends Reduction_[Set[HOLSequent], ResolutionProof] with Product with Serializable
Replaces lambda abstractions by fresh function symbols, together with axioms that axiomatize them.
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case class
LambdaEliminationReductionET
(extraAxioms: Boolean = true) extends Reduction_[HOLSequent, ExpansionProof] with Product with Serializable
Replaces lambda abstractions by fresh function symbols, together with axioms that axiomatize them.
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case class
LambdaEliminationReductionRes
(extraAxioms: Boolean = true) extends Reduction_[HOLSequent, ResolutionProof] with Product with Serializable
Replaces lambda abstractions by fresh function symbols, together with axioms that axiomatize them.
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trait
OneWayReduction_
[P] extends Reduction[P, P, Nothing, Any]
A reduction without back-translation.
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trait
Reduction
[-P1, +P2, +S1, -S2] extends AnyRef
Represents a reduction of a problem together with a back-translation of the solutions.
Represents a reduction of a problem together with a back-translation of the solutions.
A problem P1 is reduced to a problem P2, a solution S2 to the problem P2 can then be translated back to a solution S1 of the problem P1.
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trait
Reduction_
[P, S] extends Reduction[P, P, S, S]
A reduction that does not change the type of the problem.
Value Members
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object
CNFReductionExpRes
extends Reduction[HOLSequent, Set[HOLClause], ExpansionProof, ResolutionProof] with Product with Serializable
Reduces finding an expansion proof for a sequent to finding a resolution proof of a clause set.
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object
CNFReductionLKRes
extends Reduction[HOLSequent, Set[HOLClause], LKProof, ResolutionProof] with Product with Serializable
Reduces finding an LK proof for a sequent to finding a resolution proof of a clause set.
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object
CNFReductionResRes
extends Reduction[HOLSequent, Set[HOLClause], ResolutionProof, ResolutionProof] with Product with Serializable
Reduces finding a resolution proof for a sequent to finding a resolution proof of a clause set.
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object
CNFReductionSequentsResRes
extends Reduction[Set[HOLSequent], Set[HOLClause], ResolutionProof, ResolutionProof] with Product with Serializable
Reduces finding a resolution proof for a sequent set to finding a resolution proof of a clause set.
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object
ErasureReductionCNF
extends Reduction_[Set[HOLClause], ResolutionProof] with Product with Serializable
Reduces finding a resolution proof of a many-sorted clause set to the first-order case.
Reduces finding a resolution proof of a many-sorted clause set to the first-order case.
Sorts are simply ignored and we make a best effort to convert the resolution refutation back.
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object
ErasureReductionET
extends Reduction_[HOLSequent, ExpansionProof] with Product with Serializable
Reduces finding an expansion proof of a many-sorted sequent to the first-order case.
Reduces finding an expansion proof of a many-sorted sequent to the first-order case.
Sorts are simply ignored and we make a best effort to convert the expansion tree.
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object
GroundingReductionET
extends Reduction_[HOLSequent, ExpansionProof] with Product with Serializable
Simplifies the problem by grounding free variables.
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object
PredicateReductionCNF
extends Reduction_[Set[HOLClause], ResolutionProof] with Product with Serializable
Simplifies the problem of finding a resolution refutation of a many-sorted clause set by adding predicates for each of the sorts.
Simplifies the problem of finding a resolution refutation of a many-sorted clause set by adding predicates for each of the sorts. The resulting problem is still many-sorted.
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object
PredicateReductionET
extends Reduction_[HOLSequent, ExpansionProof] with Product with Serializable
Simplifies the problem of finding an expansion proof of a many-sorted sequent by adding predicates for each of the sorts.
Simplifies the problem of finding an expansion proof of a many-sorted sequent by adding predicates for each of the sorts. The resulting problem is still many-sorted.