c

at.logic.gapt.grammars

Pi2PreGrammar

case class Pi2PreGrammar(startSymbol: Var, alpha: Var, betas: Vector[Var], productions: Vector[(Var, Expr)]) extends Product with Serializable

This is a slightly batshit insane and completely wrong formalization of grammars for proofs with a single Π₂-cut. (Should be isomorphic to the usual versions though.)

Say ∀x ∃y φ(x,y) is the cut-formula.

Then the left side of the cut has one strong quantifier inference (with eigenvariable α), and many weak quantifier inferences (with terms t). Each weak quantifier inference is stored as the production α → t (yes, yes, and also, t may contain α).

The right side of the cut has alternating weak and strong quantifier inferences. Say r is the term of the weak quantifier inference, then β is the eigenvariable such that φ(r,β). We store this as the production β → r. Additionally, we require that there is *exactly one* production for each β (this condition is missing from pre-grammars)

Source
pi2.scala
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  1. Pi2PreGrammar
  2. Serializable
  3. Serializable
  4. Product
  5. Equals
  6. AnyRef
  7. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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Instance Constructors

  1. new Pi2PreGrammar(startSymbol: Var, alpha: Var, betas: Vector[Var], productions: Vector[(Var, Expr)])

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from Pi2PreGrammar to any2stringadd[Pi2PreGrammar] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (Pi2PreGrammar, B)
    Implicit
    This member is added by an implicit conversion from Pi2PreGrammar to ArrowAssoc[Pi2PreGrammar] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. val alpha: Var
  7. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  8. val betas: Vector[Var]
  9. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  10. def ensuring(cond: (Pi2PreGrammar) ⇒ Boolean, msg: ⇒ Any): Pi2PreGrammar
    Implicit
    This member is added by an implicit conversion from Pi2PreGrammar to Ensuring[Pi2PreGrammar] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  11. def ensuring(cond: (Pi2PreGrammar) ⇒ Boolean): Pi2PreGrammar
    Implicit
    This member is added by an implicit conversion from Pi2PreGrammar to Ensuring[Pi2PreGrammar] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  12. def ensuring(cond: Boolean, msg: ⇒ Any): Pi2PreGrammar
    Implicit
    This member is added by an implicit conversion from Pi2PreGrammar to Ensuring[Pi2PreGrammar] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  13. def ensuring(cond: Boolean): Pi2PreGrammar
    Implicit
    This member is added by an implicit conversion from Pi2PreGrammar to Ensuring[Pi2PreGrammar] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  14. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  15. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  16. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from Pi2PreGrammar to StringFormat[Pi2PreGrammar] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  17. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  18. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  19. def language: Set[Expr]
  20. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  21. val nonTerminals: Vector[Var]
  22. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  23. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  24. val productions: Vector[(Var, Expr)]
  25. def size: Int
  26. val startSymbol: Var
  27. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  28. def toString(): String
    Definition Classes
    Pi2PreGrammar → AnyRef → Any
  29. def tratg: VTRATG
  30. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  31. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  32. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  33. def [B](y: B): (Pi2PreGrammar, B)
    Implicit
    This member is added by an implicit conversion from Pi2PreGrammar to ArrowAssoc[Pi2PreGrammar] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Inherited from Serializable

Inherited from Serializable

Inherited from Product

Inherited from Equals

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd from Pi2PreGrammar to any2stringadd[Pi2PreGrammar]

Inherited by implicit conversion StringFormat from Pi2PreGrammar to StringFormat[Pi2PreGrammar]

Inherited by implicit conversion Ensuring from Pi2PreGrammar to Ensuring[Pi2PreGrammar]

Inherited by implicit conversion ArrowAssoc from Pi2PreGrammar to ArrowAssoc[Pi2PreGrammar]

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