Packages

case class Sequent[+A](antecedent: Vector[A], succedent: Vector[A]) extends Product with Serializable

A sequent is a pair of sequences of elements of type A, typically written as a1,…,am :- b1,…,bn.

A

The type of the elements of the sequent.

antecedent

The first list.

succedent

The second list.

Source
sequents.scala
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Inherited
  1. Sequent
  2. Serializable
  3. Serializable
  4. Product
  5. Equals
  6. AnyRef
  7. Any
Implicitly
  1. by RichFormulaSequent
  2. by RichFOLSequent
  3. by RichClause
  4. by any2stringadd
  5. by StringFormat
  6. by Ensuring
  7. by ArrowAssoc
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Visibility
  1. Public
  2. All

Instance Constructors

  1. new Sequent(antecedent: Vector[A], succedent: Vector[A])

    antecedent

    The first list.

    succedent

    The second list.

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 Sequent[A] to any2stringadd[Sequent[A]] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ++[B >: A](that: Sequent[B]): Sequent[B]
  5. def ++:[B >: A](es: Traversable[B]): Sequent[B]

    Adds a sequent of elements to the antecedent.

    Adds a sequent of elements to the antecedent. New elements are always outermost, i.e. on the very left.

    es

    A collection of elements of type B > A.

    returns

    The sequent with es added to the antecedent.

  6. def +:[B >: A](e: B): Sequent[B]

    Adds an element to the antecedent.

    Adds an element to the antecedent. New elements are always outermost, i.e. on the very left.

    e

    An element of type B > A

    returns

    The sequent with e added to the antecedent

  7. def ->[B](y: B): (Sequent[A], B)
    Implicit
    This member is added by an implicit conversion from Sequent[A] to ArrowAssoc[Sequent[A]] performed by method ArrowAssoc in scala.Predef. This conversion will take place only if A is a subclass of FOLFormula (A <: FOLFormula).
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  8. def :+[B >: A](e: B): Sequent[B]

    Adds an element to the succedent.

    Adds an element to the succedent. New elements are always outermost, i.e. on the very right.

    e

    An element of type B > A

    returns

    The sequent with e added to the succedent

  9. def :++[B >: A](es: Traversable[B]): Sequent[B]

    Adds a sequence of elements to the succedent.

    Adds a sequence of elements to the succedent. New elements are always outermost, i.e. on the very right.

    es

    A collection of elements of type B > A.

    returns

    The sequent with es added to the succedent.

  10. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  11. val antecedent: Vector[A]
  12. def apply(is: Seq[SequentIndex]): Seq[A]
  13. def apply(i: SequentIndex): A

    Returns the element at some SequentIndex.

    Returns the element at some SequentIndex.

    i

    A SequentIndex, i.e. Ant(k) or Suc(k)

    returns

    The k-th element of the antecedent or succedent, depending on the type of i.

  14. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  15. def cedent(polarity: Polarity): Vector[A]
  16. val clause: Clause[A]
    Implicit
    This member is added by an implicit conversion from Sequent[A] to RichClause[A] performed by method RichClause in at.logic.gapt.proofs.
    Definition Classes
    RichClause
  17. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  18. def collect[B](f: PartialFunction[A, B]): Sequent[B]
  19. def contains[B](el: B, polarity: Polarity): Boolean
  20. def contains[B](el: B): Boolean

    Returns true iff the sequent contains some element in either cedent.

  21. def delete(is: SequentIndex*)(implicit d: DummyImplicit): Sequent[A]
  22. def delete(is: Seq[SequentIndex]): Sequent[A]
  23. def delete(i: SequentIndex): Sequent[A]
  24. def diff[B >: A](other: Sequent[B]): Sequent[A]

    Takes the multiset difference between two sequents, i.e.

    Takes the multiset difference between two sequents, i.e. each side separately.

  25. def distinct: Sequent[A]

    Removes duplicate formulas from both cedents.

  26. def elements: Vector[A]

    Sequence of elements of the sequent.

    Sequence of elements of the sequent.

    returns

    Antecedent concatenated with succedent.

  27. def ensuring(cond: (Sequent[A]) ⇒ Boolean, msg: ⇒ Any): Sequent[A]
    Implicit
    This member is added by an implicit conversion from Sequent[A] to Ensuring[Sequent[A]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  28. def ensuring(cond: (Sequent[A]) ⇒ Boolean): Sequent[A]
    Implicit
    This member is added by an implicit conversion from Sequent[A] to Ensuring[Sequent[A]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  29. def ensuring(cond: Boolean, msg: ⇒ Any): Sequent[A]
    Implicit
    This member is added by an implicit conversion from Sequent[A] to Ensuring[Sequent[A]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  30. def ensuring(cond: Boolean): Sequent[A]
    Implicit
    This member is added by an implicit conversion from Sequent[A] to Ensuring[Sequent[A]] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  31. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  32. def exists(p: (A) ⇒ Boolean): Boolean
  33. def filter(p: (A) ⇒ Boolean): Sequent[A]

    The sub-sequent of elements satisfying some predicate.

    The sub-sequent of elements satisfying some predicate.

    p

    A function of type A => Boolean.

    returns

    The sequent consisting of only those elements satisfying p.

  34. def filterNot(p: (A) ⇒ Boolean): Sequent[A]

    The sub-sequent of elements not satisfying some predicate.

    The sub-sequent of elements not satisfying some predicate.

    p

    A function of type A => Boolean.

    returns

    The sequent consisting of only those elements not satisfying p.

  35. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  36. def find(pred: (A) ⇒ Boolean): Option[SequentIndex]
  37. def flatMap[B](f: (A) ⇒ TraversableOnce[B], g: (A) ⇒ TraversableOnce[B]): Sequent[B]
  38. def flatMap[B](f: (A) ⇒ TraversableOnce[B]): Sequent[B]
  39. def focus(i: SequentIndex): (A, Sequent[A])

    Focuses on one element of the sequent, i.e.

    Focuses on one element of the sequent, i.e. returns element at index and the rest of the sequent.

    i

    A SequentIndex.

    returns

    A pair consisting of this(i) and the rest of this.

  40. def forall(p: (A) ⇒ Boolean): Boolean
  41. def foreach[U](f: (A) ⇒ U): Unit
  42. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from Sequent[A] to StringFormat[Sequent[A]] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  43. def formulas: Vector[Formula]
    Implicit
    This member is added by an implicit conversion from Sequent[A] to RichFormulaSequent performed by method RichFormulaSequent in at.logic.gapt.proofs. This conversion will take place only if A is a subclass of Formula (A <: Formula).
    Definition Classes
    RichFormulaSequent
  44. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  45. def groupBy[B](f: (A) ⇒ B): Sequent[(B, Vector[A])]
  46. def indexOf[B >: A](elem: B, polarity: Polarity): SequentIndex
  47. def indexOf[B >: A](elem: B): SequentIndex
  48. def indexOfInAnt[B >: A](elem: B): SequentIndex
  49. def indexOfInSuc[B >: A](elem: B): SequentIndex
  50. def indexOfOption[B >: A](elem: B, pol: Polarity): Option[SequentIndex]
  51. def indexOfOption[B >: A](elem: B): Option[SequentIndex]
  52. def indices: Vector[SequentIndex]

    Returns the range of indices of the sequent as a sequence.

  53. def indicesSequent: Sequent[SequentIndex]

    Returns the range of indices of the sequent as a sequent.

  54. def indicesWhere(p: (A) ⇒ Boolean): Vector[SequentIndex]

    Returns the list of indices of elements satisfying some predicate.

    Returns the list of indices of elements satisfying some predicate.

    p

    A function of type A => Boolean.

  55. def indicesWherePol(p: (A) ⇒ Boolean, pol: Polarity): Vector[SequentIndex]
  56. def insertAt[B >: A](i: SequentIndex, el: B): Sequent[B]
  57. def intersect[B >: A](other: Sequent[B]): Sequent[A]

    Computes the intersection of two sequents.

  58. def isDefinedAt(i: SequentIndex): Boolean

    Tests whether the sequent is defined at the supplied SequentIndex.

  59. def isEmpty: Boolean

    Returns true iff both cedents are empty.

  60. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  61. def isSubMultisetOf[B >: A](other: Sequent[B]): Boolean
  62. def isSubsetOf[B >: A](other: Sequent[B]): Boolean

    other

    Another Sequent.

    returns

    True iff other contains this pair of sets.

  63. def isTaut: Boolean
  64. def length: Int

    The number of elements in the sequent.

  65. def lengths: (Int, Int)

    A pair consisting of the lengths of the cedents.

  66. def map[B](f: (A) ⇒ B, g: (A) ⇒ B): Sequent[B]

    Maps two functions over the antecedent and succedent, respectively.

    Maps two functions over the antecedent and succedent, respectively.

    B

    The return type of f and g.

    f

    The function to map over the antecedent.

    g

    The function to map over the succedent.

    returns

    The sequent of type B that results from mapping f and g over the antecedent and succedent, respectively.

  67. def map[B](f: (A) ⇒ B): Sequent[B]

    Maps a function over both cedents

    Maps a function over both cedents

    B

    The return type of f

    f

    A function of type A => B

    returns

    The sequent of type B that results from mapping f over both cedents.

  68. def multiSetEquals[B](other: Sequent[B]): Boolean

    Equality treating each side of the sequent as a multiset.

  69. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  70. def negative: Vector[A]
    Implicit
    This member is added by an implicit conversion from Sequent[A] to RichClause[A] performed by method RichClause in at.logic.gapt.proofs.
    Definition Classes
    RichClause
  71. def nonEmpty: Boolean
  72. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  73. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  74. def polarizedElements: Vector[(A, Polarity)]

    Sequence of elements together with polarities of type Boolean signifying whether an element is in the antecedent or succedent.

  75. def positive: Vector[A]
    Implicit
    This member is added by an implicit conversion from Sequent[A] to RichClause[A] performed by method RichClause in at.logic.gapt.proofs.
    Definition Classes
    RichClause
  76. def removeFromAntecedent[B](e: B): Sequent[A]
  77. def removeFromSuccedent[B](e: B): Sequent[A]
  78. def replaceAt[B >: A](i: SequentIndex, el: B): Sequent[B]
  79. def setEquals[B](other: Sequent[B]): Boolean

    Equality treating each side of the sequent as a set.

  80. def size: Int

    Synonym for length.

  81. def sizes: (Int, Int)

    Synonym for lengths.

  82. def sortBy[B](f: (A) ⇒ B)(implicit ord: Ordering[B]): Sequent[A]
  83. def sorted[B >: A](implicit ordering: Ordering[B]): Sequent[A]
  84. val succedent: Vector[A]
  85. def swapped: Sequent[A]
  86. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  87. def toSigRelativeString(implicit sig: BabelSignature): String
  88. def toString(): String
    Definition Classes
    Sequent → AnyRef → Any
  89. def toTuple: (Vector[A], Vector[A])

    returns

    The sequent in tuple form.

  90. def updated[B >: A](index: SequentIndex, elem: B): Sequent[B]
  91. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  92. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  93. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  94. def withFilter(p: (A) ⇒ Boolean): Sequent[A]
  95. def zip[B](that: Sequent[B]): Sequent[(A, B)]
  96. def zipWithIndex: Sequent[(A, SequentIndex)]
  97. def [B](y: B): (Sequent[A], B)
    Implicit
    This member is added by an implicit conversion from Sequent[A] to ArrowAssoc[Sequent[A]] performed by method ArrowAssoc in scala.Predef. This conversion will take place only if A is a subclass of FOLFormula (A <: FOLFormula).
    Definition Classes
    ArrowAssoc

Shadowed Implicit Value Members

  1. val sequent: HOLSequent
    Implicit
    This member is added by an implicit conversion from Sequent[A] to RichFormulaSequent performed by method RichFormulaSequent in at.logic.gapt.proofs. This conversion will take place only if A is a subclass of Formula (A <: Formula).
    Shadowing
    This implicitly inherited member is ambiguous. One or more implicitly inherited members have similar signatures, so calling this member may produce an ambiguous implicit conversion compiler error.
    To access this member you can use a type ascription:
    (sequent: RichFormulaSequent).sequent
    Definition Classes
    RichFormulaSequent
  2. val sequent: FOLSequent
    Implicit
    This member is added by an implicit conversion from Sequent[A] to RichFOLSequent performed by method RichFOLSequent in at.logic.gapt.proofs. This conversion will take place only if A is a subclass of FOLFormula (A <: FOLFormula).
    Shadowing
    This implicitly inherited member is ambiguous. One or more implicitly inherited members have similar signatures, so calling this member may produce an ambiguous implicit conversion compiler error.
    To access this member you can use a type ascription:
    (sequent: RichFOLSequent).sequent
    Definition Classes
    RichFOLSequent
  3. def toConjunction: Formula
    Implicit
    This member is added by an implicit conversion from Sequent[A] to RichFormulaSequent performed by method RichFormulaSequent in at.logic.gapt.proofs. This conversion will take place only if A is a subclass of Formula (A <: Formula).
    Shadowing
    This implicitly inherited member is ambiguous. One or more implicitly inherited members have similar signatures, so calling this member may produce an ambiguous implicit conversion compiler error.
    To access this member you can use a type ascription:
    (sequent: RichFormulaSequent).toConjunction
    Definition Classes
    RichFormulaSequent
  4. def toConjunction: FOLFormula
    Implicit
    This member is added by an implicit conversion from Sequent[A] to RichFOLSequent performed by method RichFOLSequent in at.logic.gapt.proofs. This conversion will take place only if A is a subclass of FOLFormula (A <: FOLFormula).
    Shadowing
    This implicitly inherited member is ambiguous. One or more implicitly inherited members have similar signatures, so calling this member may produce an ambiguous implicit conversion compiler error.
    To access this member you can use a type ascription:
    (sequent: RichFOLSequent).toConjunction
    Definition Classes
    RichFOLSequent
  5. def toDisjunction: Formula
    Implicit
    This member is added by an implicit conversion from Sequent[A] to RichFormulaSequent performed by method RichFormulaSequent in at.logic.gapt.proofs. This conversion will take place only if A is a subclass of Formula (A <: Formula).
    Shadowing
    This implicitly inherited member is ambiguous. One or more implicitly inherited members have similar signatures, so calling this member may produce an ambiguous implicit conversion compiler error.
    To access this member you can use a type ascription:
    (sequent: RichFormulaSequent).toDisjunction
    Definition Classes
    RichFormulaSequent
  6. def toDisjunction: FOLFormula
    Implicit
    This member is added by an implicit conversion from Sequent[A] to RichFOLSequent performed by method RichFOLSequent in at.logic.gapt.proofs. This conversion will take place only if A is a subclass of FOLFormula (A <: FOLFormula).
    Shadowing
    This implicitly inherited member is ambiguous. One or more implicitly inherited members have similar signatures, so calling this member may produce an ambiguous implicit conversion compiler error.
    To access this member you can use a type ascription:
    (sequent: RichFOLSequent).toDisjunction
    Definition Classes
    RichFOLSequent
  7. def toFormula: Formula
    Implicit
    This member is added by an implicit conversion from Sequent[A] to RichFormulaSequent performed by method RichFormulaSequent in at.logic.gapt.proofs. This conversion will take place only if A is a subclass of Formula (A <: Formula).
    Shadowing
    This implicitly inherited member is ambiguous. One or more implicitly inherited members have similar signatures, so calling this member may produce an ambiguous implicit conversion compiler error.
    To access this member you can use a type ascription:
    (sequent: RichFormulaSequent).toFormula
    Definition Classes
    RichFormulaSequent
  8. def toFormula: FOLFormula
    Implicit
    This member is added by an implicit conversion from Sequent[A] to RichFOLSequent performed by method RichFOLSequent in at.logic.gapt.proofs. This conversion will take place only if A is a subclass of FOLFormula (A <: FOLFormula).
    Shadowing
    This implicitly inherited member is ambiguous. One or more implicitly inherited members have similar signatures, so calling this member may produce an ambiguous implicit conversion compiler error.
    To access this member you can use a type ascription:
    (sequent: RichFOLSequent).toFormula
    Definition Classes
    RichFOLSequent
  9. def toImplication: Formula
    Implicit
    This member is added by an implicit conversion from Sequent[A] to RichFormulaSequent performed by method RichFormulaSequent in at.logic.gapt.proofs. This conversion will take place only if A is a subclass of Formula (A <: Formula).
    Shadowing
    This implicitly inherited member is ambiguous. One or more implicitly inherited members have similar signatures, so calling this member may produce an ambiguous implicit conversion compiler error.
    To access this member you can use a type ascription:
    (sequent: RichFormulaSequent).toImplication
    Definition Classes
    RichFormulaSequent
  10. def toImplication: FOLFormula
    Implicit
    This member is added by an implicit conversion from Sequent[A] to RichFOLSequent performed by method RichFOLSequent in at.logic.gapt.proofs. This conversion will take place only if A is a subclass of FOLFormula (A <: FOLFormula).
    Shadowing
    This implicitly inherited member is ambiguous. One or more implicitly inherited members have similar signatures, so calling this member may produce an ambiguous implicit conversion compiler error.
    To access this member you can use a type ascription:
    (sequent: RichFOLSequent).toImplication
    Definition Classes
    RichFOLSequent
  11. def toNegConjunction: Formula
    Implicit
    This member is added by an implicit conversion from Sequent[A] to RichFormulaSequent performed by method RichFormulaSequent in at.logic.gapt.proofs. This conversion will take place only if A is a subclass of Formula (A <: Formula).
    Shadowing
    This implicitly inherited member is ambiguous. One or more implicitly inherited members have similar signatures, so calling this member may produce an ambiguous implicit conversion compiler error.
    To access this member you can use a type ascription:
    (sequent: RichFormulaSequent).toNegConjunction
    Definition Classes
    RichFormulaSequent
  12. def toNegConjunction: FOLFormula
    Implicit
    This member is added by an implicit conversion from Sequent[A] to RichFOLSequent performed by method RichFOLSequent in at.logic.gapt.proofs. This conversion will take place only if A is a subclass of FOLFormula (A <: FOLFormula).
    Shadowing
    This implicitly inherited member is ambiguous. One or more implicitly inherited members have similar signatures, so calling this member may produce an ambiguous implicit conversion compiler error.
    To access this member you can use a type ascription:
    (sequent: RichFOLSequent).toNegConjunction
    Definition Classes
    RichFOLSequent

Deprecated Value Members

  1. def indexOfPol[B >: A](elem: B, polarity: Polarity): SequentIndex
    Annotations
    @deprecated
    Deprecated

    (Since version 2.9) Use indexOf instead.

  2. def indexOfPolOption[B >: A](elem: B, pol: Polarity): Option[SequentIndex]
    Annotations
    @deprecated
    Deprecated

    (Since version 2.9) Use indexOfOption instead.

Inherited from Serializable

Inherited from Serializable

Inherited from Product

Inherited from Equals

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion RichFormulaSequent from Sequent[A] to RichFormulaSequent

Inherited by implicit conversion RichFOLSequent from Sequent[A] to RichFOLSequent

Inherited by implicit conversion RichClause from Sequent[A] to RichClause[A]

Inherited by implicit conversion any2stringadd from Sequent[A] to any2stringadd[Sequent[A]]

Inherited by implicit conversion StringFormat from Sequent[A] to StringFormat[Sequent[A]]

Inherited by implicit conversion Ensuring from Sequent[A] to Ensuring[Sequent[A]]

Inherited by implicit conversion ArrowAssoc from Sequent[A] to ArrowAssoc[Sequent[A]]

Ungrouped