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at.logic.gapt.proofs.lk

makeTheoryAxiomsExplicit

object makeTheoryAxiomsExplicit extends LKVisitor[Seq[Formula]]

Given a list of formulas Π, this transforms a proof π of Σ :- Δ into a proof π' of Π, Σ :- Δ.

It replaces theory axioms on sequents S that are subsumed by Π with propositional proofs of Π, S.

Source
makeTheoryAxiomsExplicit.scala
Linear Supertypes
LKVisitor[Seq[Formula]], AnyRef, Any
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  1. makeTheoryAxiomsExplicit
  2. LKVisitor
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Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. def apply(proof: LKProof)(implicit ctx: Context): LKProof
  5. def apply(formulas: Formula*)(proof: LKProof): LKProof

    Eliminates some theory axioms from proof, namely those subsumed by formulas.

    Eliminates some theory axioms from proof, namely those subsumed by formulas.

    formulas

    A list of Formulas. Each must be of the form ∀x1 ... ∀xn F' with F' quantifier-free.

    proof

    An LKProof.

    returns

    An LKProof proof' with the following properties: Every theory axiom in proof that is subsumed by formulas is removed in proof' and elements of formula may occur in the antecedent of the end sequent of proof'.

  6. final def apply(proof: LKProof, otherArg: Seq[Formula]): LKProof

    Applies the proof transformation to an LKProof.

    Applies the proof transformation to an LKProof.

    proof

    The input proof.

    returns

    The transformed proof.

    Definition Classes
    LKVisitor
  7. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  8. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  9. def contractAfter[A](visitingFunction: (LKProof, A) ⇒ (LKProof, SequentConnector)): (LKProof, A) ⇒ (LKProof, SequentConnector)

    Transforms a visiting function by inserting contractions after it.

    Transforms a visiting function by inserting contractions after it. Only formula occurrences that were not in the old proof -- i.e., that have been added by the visitor -- are contracted.

    visitingFunction

    The visiting function after which contractions should be inserted. In most cases, just using recurse here should be fine.

    returns

    A new visiting function that behaves the same as the old one, but contracts all duplicate new formulas at the end.

    Definition Classes
    LKVisitor
  10. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  11. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  12. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  13. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  14. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  15. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  16. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  17. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  18. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  19. def one2one(proof: LKProof, arg: Seq[Formula])(func: (Seq[(LKProof, SequentConnector)]) ⇒ LKProof): (LKProof, SequentConnector)
    Definition Classes
    LKVisitor
  20. def recurse(proof: LKProof, formulas: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    makeTheoryAxiomsExplicit → LKVisitor
  21. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  22. def toString(): String
    Definition Classes
    AnyRef → Any
  23. def transportToSubProof(arg: Seq[Formula], proof: LKProof, subProofIdx: Int): Seq[Formula]
    Definition Classes
    LKVisitor
  24. def visitAndLeft(proof: AndLeftRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  25. def visitAndRight(proof: AndRightRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  26. def visitBottomAxiom(otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  27. def visitContractionLeft(proof: ContractionLeftRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  28. def visitContractionRight(proof: ContractionRightRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  29. def visitCut(proof: CutRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  30. def visitDefinitionLeft(proof: DefinitionLeftRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  31. def visitDefinitionRight(proof: DefinitionRightRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  32. def visitEqualityLeft(proof: EqualityLeftRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  33. def visitEqualityRight(proof: EqualityRightRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  34. def visitExistsLeft(proof: ExistsLeftRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  35. def visitExistsRight(proof: ExistsRightRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  36. def visitExistsSkLeft(proof: ExistsSkLeftRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  37. def visitForallLeft(proof: ForallLeftRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  38. def visitForallRight(proof: ForallRightRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  39. def visitForallSkRight(proof: ForallSkRightRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  40. def visitImpLeft(proof: ImpLeftRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  41. def visitImpRight(proof: ImpRightRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  42. def visitInduction(proof: InductionRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  43. def visitLogicalAxiom(proof: LogicalAxiom, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  44. def visitNegLeft(proof: NegLeftRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  45. def visitNegRight(proof: NegRightRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  46. def visitOpenAssumption(proof: OpenAssumption, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  47. def visitOrLeft(proof: OrLeftRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  48. def visitOrRight(proof: OrRightRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  49. def visitProofLink(proof: ProofLink, formulas: Seq[Formula]): (LKProof, SequentConnector)

    proof

    A theory axiom with sequent A1,...,Ak :- B1,...,:Bn.

    returns

    If A1,...,Ak :- B1,...,:Bn is subsumed by some F in formulas, returns a proof of F, A1,...,Ak :- B1,...,:Bn. Otherwise the input axiom.

    Attributes
    protected
    Definition Classes
    makeTheoryAxiomsExplicit → LKVisitor
  50. def visitReflexivityAxiom(proof: ReflexivityAxiom, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  51. def visitTopAxiom(otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  52. def visitWeakeningLeft(proof: WeakeningLeftRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  53. def visitWeakeningRight(proof: WeakeningRightRule, otherArg: Seq[Formula]): (LKProof, SequentConnector)
    Attributes
    protected
    Definition Classes
    LKVisitor
  54. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  55. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  56. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  57. def withIdentitySequentConnector(proof: LKProof): (LKProof, SequentConnector)
    Definition Classes
    LKVisitor
  58. def withSequentConnector(formulas: Formula*)(proof: LKProof): (LKProof, SequentConnector)

    Eliminates some theory axioms from proof, namely those subsumed by formulas.

    Eliminates some theory axioms from proof, namely those subsumed by formulas.

    formulas

    A list of Formulas. Each must be of the form ∀x1 ... ∀xn F' with F' quantifier-free.

    proof

    An LKProof.

    returns

    A pair (proof', conn) with the following properties: Every theory axiom in proof that is subsumed by formulas is removed in proof' and elements of formulas may occur in the antecedent of the end sequent of proof'; conn is an SequentConnector relating proof and proof'.

  59. final def withSequentConnector(proof: LKProof, otherArg: Seq[Formula]): (LKProof, SequentConnector)

    Applies the proof transformation to an LKProof.

    Applies the proof transformation to an LKProof.

    proof

    The input proof.

    returns

    Transformed proof, and the sequent connector with the new proof as lower sequent and the old proof as upper sequent.

    Definition Classes
    LKVisitor

Inherited from LKVisitor[Seq[Formula]]

Inherited from AnyRef

Inherited from Any

Ungrouped