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at.logic.gapt.proofs.ceres_omega

Projections

Related Doc: package ceres_omega

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object Projections extends Logger

Source
projections.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(proof: LKskProof, cut_ancs: Sequent[Boolean], pred: (HOLFormula) ⇒ Boolean): Set[(LKskProof, Sequent[Boolean])]

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    Given an LKsk proof proof, compute the set of projections for it.

    Given an LKsk proof proof, compute the set of projections for it.

    proof

    The original proof.

    cut_ancs

    A characteristic function indicating which formula occurrences in the conclusion are cut ancestors

    pred

    A predicate deciding if a cut-formula should be included in the projection

    returns

    A set of pairs (projection, cut_ancs) where cut_ancs indicates the cut ancestors of the projection's conclusion

  5. def apply(proof: LKskProof, pred: (HOLFormula) ⇒ Boolean): Set[(LKskProof, Sequent[Boolean])]

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  6. def apply(proof: LKskProof): Set[(LKskProof, Sequent[Boolean])]

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  7. final def asInstanceOf[T0]: T0

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  8. def calculate_child_cut_ecs[T](child: LKskProof, connector1: OccConnector[T], connector2: OccConnector[T], pm1: (LKskProof, Sequent[Boolean]), pm2: (LKskProof, Sequent[Boolean]), default: Boolean): Sequent[Boolean]

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    finds the successor cut-ancestor sequent from two parents

    finds the successor cut-ancestor sequent from two parents

    T

    must be the same as the contents of the conclusion of pm1._1 and pm2._1

    child

    child proof of binary inference with left parent pm1._1 and right parent pm2._1

    connector1

    connector from pm1._1 to child

    connector2

    connector from pm2._1 to child

    pm1

    a pair proof + cut_ancestor sequent

    pm2

    a pair proof + cut_ancestor sequent

    default

    the default to take if a formula has no parent

    returns

    the cut ancestorship sequent for the parent of pm._1

  9. def calculate_child_cut_ecs[T](child: LKskProof, connector: OccConnector[T], pm: (LKskProof, Sequent[Boolean]), default: Boolean): Sequent[Boolean]

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    given an inference from pm._1 to child, infer the child_s cut_anc sequent from pm._2

    given an inference from pm._1 to child, infer the child_s cut_anc sequent from pm._2

    T

    must be the same as the contents of the conclusion of pm._1

    child

    a child proof of pm._1

    connector

    connector from parent child to pm._1

    pm

    a pair proof + cut_ancestor sequent

    default

    the default to take if a formula has no parent

    returns

    the cut ancestorship sequent for the parent of pm._1

  10. def clone(): AnyRef

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  11. def copySetToAncestor(connector: OccConnector[LabelledFormula], s: Sequent[Boolean]): Sequent[Boolean]

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    finds the cut ancestor sequent in the parent connected with the occurrence connector

  12. def debug(msg: ⇒ String): Unit

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  13. final def eq(arg0: AnyRef): Boolean

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  14. def equals(arg0: Any): Boolean

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  15. def error(msg: ⇒ String, e: Throwable): Nothing

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  16. def error(msg: ⇒ String): Unit

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  17. def finalize(): Unit

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

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  19. def getESAncs(proof: LKskProof, cut_ancs: Sequent[Boolean]): LabelledSequent

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  20. def handleBinaryCutAnc(proof: LKskProof, p1: LKskProof, p2: LKskProof, s1: Set[(LKskProof, Sequent[Boolean])], s2: Set[(LKskProof, Sequent[Boolean])], cut_ancs1: Sequent[Boolean], cut_ancs2: Sequent[Boolean]): Set[(LKskProof, Sequent[Boolean])]

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  21. def handleBinaryESAnc[Side1 <: SequentIndex, Side2 <: SequentIndex](proof: LKskProof, parent1: LKskProof, parent2: LKskProof, s1: Set[(LKskProof, Sequent[Boolean])], s2: Set[(LKskProof, Sequent[Boolean])], constructor: (LKskProof, Side1, LKskProof, Side2) ⇒ LKskProof): Set[(LKskProof, Sequent[Boolean])]

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  22. def handleBinaryRule[Side1 <: SequentIndex, Side2 <: SequentIndex](proof: LKskProof, p1: LKskProof, p2: LKskProof, a1: Side1, a2: Side2, constructor: (LKskProof, Side1, LKskProof, Side2) ⇒ LKskProof, pred: (HOLFormula) ⇒ Boolean)(implicit cut_ancs: Sequent[Boolean]): Set[(LKskProof, Sequent[Boolean])]

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  23. def handleContractionRule[Side <: SequentIndex](proof: LKskProof, p: LKskProof, a1: SequentIndex, a2: SequentIndex, constructor: (LKskProof, Side, Side) ⇒ LKskProof, pred: (HOLFormula) ⇒ Boolean)(implicit cut_ancs: Sequent[Boolean]): Set[(LKskProof, Sequent[Boolean])]

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  24. def handleDefRule(proof: LKskProof, p: LKskProof, a: SequentIndex, f: HOLFormula, constructor: (LKskProof, SequentIndex, HOLFormula) ⇒ LKskProof, pred: (HOLFormula) ⇒ Boolean)(implicit cut_ancs: Sequent[Boolean]): Set[(LKskProof, Sequent[Boolean])]

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  25. def handleEqRule(proof: LKskProof, p: LKskProof, e: SequentIndex, a: SequentIndex, flipped: Boolean, con: Abs, pred: (HOLFormula) ⇒ Boolean)(implicit cut_ancs: Sequent[Boolean]): Set[(LKskProof, Sequent[Boolean])]

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  26. def handleNegRule[Side <: SequentIndex](proof: LKskProof, p: LKskProof, a: SequentIndex, constructor: (LKskProof, Side) ⇒ LKskProof, pred: (HOLFormula) ⇒ Boolean)(implicit cut_ancs: Sequent[Boolean]): Set[(LKskProof, Sequent[Boolean])]

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  27. def handleStrongQuantRule[Side <: SequentIndex](proof: LKskProof, p: LKskProof, a: Side, constructor: (LKskProof, Side, HOLFormula, Var) ⇒ LKskProof, pred: (HOLFormula) ⇒ Boolean)(implicit cut_ancs: Sequent[Boolean]): Set[(LKskProof, Sequent[Boolean])]

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  28. def handleStrongSkQuantRule[Side <: SequentIndex](proof: LKskProof, p: LKskProof, a: Side, main: HOLFormula, sk_const: LambdaExpression, sk_def: LambdaExpression, constructor: (LKskProof, Side, HOLFormula, LambdaExpression, LambdaExpression) ⇒ LKskProof, pred: (HOLFormula) ⇒ Boolean)(implicit cut_ancs: Sequent[Boolean]): Set[(LKskProof, Sequent[Boolean])]

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  29. def handleUnaryRule[Side1 <: SequentIndex, Side2 <: SequentIndex](proof: LKskProof, p: LKskProof, a1: Side1, a2: Side2, constructor: (LKskProof, Side1, Side2) ⇒ LKskProof, pred: (HOLFormula) ⇒ Boolean)(implicit cut_ancs: Sequent[Boolean]): Set[(LKskProof, Sequent[Boolean])]

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  30. def handleWeakQuantRule[Side <: SequentIndex](proof: LKskProof, p: LKskProof, a: Side, f: HOLFormula, t: LambdaExpression, constructor: (LKskProof, Side, HOLFormula, LambdaExpression) ⇒ LKskProof, pred: (HOLFormula) ⇒ Boolean)(implicit cut_ancs: Sequent[Boolean]): Set[(LKskProof, Sequent[Boolean])]

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  31. def handleWeakeningRule(proof: LKskProof, p: LKskProof, m: LabelledFormula, constructor: (LKskProof, LabelledFormula) ⇒ LKskProof, pred: (HOLFormula) ⇒ Boolean)(implicit cut_ancs: Sequent[Boolean]): Set[(LKskProof, Sequent[Boolean])]

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  32. def hashCode(): Int

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  33. def info(msg: ⇒ String): Unit

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  34. final def isInstanceOf[T0]: Boolean

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  35. val log: Logger

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  36. def loggerName: String

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

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  38. final def notify(): Unit

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  39. final def notifyAll(): Unit

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  40. def reflexivity_projection(es: LabelledSequent, term: LambdaExpression, label: Label): (LKskProof, Sequent[Boolean])

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

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  42. def toString(): String

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  43. def trace(msg: ⇒ String): Unit

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  44. final def wait(): Unit

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  45. final def wait(arg0: Long, arg1: Int): Unit

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

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  47. def warn(msg: ⇒ String, e: Throwable): Unit

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  48. def warn(msg: ⇒ String): Unit

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  49. def weakenESAncs(esancs: LabelledSequent, s: Set[(LKskProof, Sequent[Boolean])]): Set[(LKskProof, Sequent[Boolean])]

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