Object

at.logic.gapt.proofs.lkOld

regularize

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object regularize

An implementation of LK proof regularization. In a regular LK proof, an eigenvariable is globally unique to the proof. E.g. P(u) :- P(u) P(u) :- P(u) ----------------- fa:l ------------------- fa:l \A x:P(x) :- P(u) \A x:P(x) :- P(u) ----------------------- fa:r ------------------- fa:r \A x:P(x) :- \E x:P(x) \A x:P(x) :- \E x: P(x) --------------------------------------------------------- conj:r \A x:P(x), \A x:P(x) :- \E x:P(x) /\ \E x:P(x) --------------------------------------------------------- contr:l \A x:P(x) :- \E x:P(x) /\ \E x:P(x)

is not regular, but P(i) :- P(i) P(u) :- P(u) ----------------- fa:l ------------------- fa:l \A x:P(x) :- P(i) \A x:P(x) :- P(u) ----------------------- fa:r ------------------- fa:r \A x:P(x) :- \E x:P(x) \A x:P(x) :- \E x: P(x) --------------------------------------------------------- conj:r \A x:P(x), \A x:P(x) :- \E x:P(x) /\ \E x:P(x) --------------------------------------------------------- contr:l \A x:P(x) :- \E x:P(x) /\ \E x:P(x)

is.

Source
lk.scala
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  1. final def !=(arg0: Any): Boolean

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  2. final def ##(): Int

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  3. final def ==(arg0: Any): Boolean

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  4. def apply(p: LKProof): LKProof

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    Make the LK proof p regular.

    Make the LK proof p regular.

    p

    An LK proof.

    returns

    The regular version of proof p.

  5. final def asInstanceOf[T0]: T0

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  6. def clone(): AnyRef

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  10. final def getClass(): Class[_]

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  11. def handleBinaryProp(r: base.BinaryLKProof with AuxiliaryFormulas, p1: LKProof, p2: LKProof, a1: FormulaOccurrence, a2: FormulaOccurrence, vars: List[Var], constructor: (LKProof, LKProof, FormulaOccurrence, FormulaOccurrence) ⇒ base.BinaryLKProof with AuxiliaryFormulas): (base.BinaryLKProof with AuxiliaryFormulas, List[Var], Map[FormulaOccurrence, FormulaOccurrence])

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  12. def handleContraction(new_parent: (LKProof, Map[FormulaOccurrence, FormulaOccurrence]), old_parent: LKProof, old_proof: LKProof, a1: FormulaOccurrence, a2: FormulaOccurrence, vars: List[Var], constructor: (LKProof, FormulaOccurrence, FormulaOccurrence) ⇒ LKProof): (LKProof, List[Var], Map[FormulaOccurrence, FormulaOccurrence])

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  13. def handleEquational(r: base.BinaryLKProof with AuxiliaryFormulas, p1: LKProof, p2: LKProof, a1: FormulaOccurrence, a2: FormulaOccurrence, m: HOLFormula, vars: List[Var], constructor: (LKProof, LKProof, FormulaOccurrence, FormulaOccurrence, HOLFormula) ⇒ base.BinaryLKProof with AuxiliaryFormulas): (base.BinaryLKProof with AuxiliaryFormulas, List[Var], Map[FormulaOccurrence, FormulaOccurrence])

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  14. def handleWeakening(new_parent: (LKProof, Map[FormulaOccurrence, FormulaOccurrence]), old_parent: LKProof, old_proof: LKProof, vars: List[Var], constructor: (LKProof, HOLFormula) ⇒ LKProof with PrincipalFormulas, m: FormulaOccurrence): (LKProof with PrincipalFormulas, List[Var], Map[FormulaOccurrence, FormulaOccurrence])

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  15. def hashCode(): Int

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  16. final def isInstanceOf[T0]: Boolean

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  17. final def ne(arg0: AnyRef): Boolean

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  18. final def notify(): Unit

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  19. final def notifyAll(): Unit

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  20. def recApply(proof: LKProof, vars: List[Var]): (LKProof, List[Var], Map[FormulaOccurrence, FormulaOccurrence])

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  21. def recApply(proof: LKProof): (LKProof, List[Var], Map[FormulaOccurrence, FormulaOccurrence])

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  22. final def synchronized[T0](arg0: ⇒ T0): T0

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  26. final def wait(arg0: Long): Unit

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