Class/Object

at.logic.gapt.proofs.lk.base

Sequent

Related Docs: object Sequent | package base

Permalink

class Sequent[+A] extends AnyRef

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.

Linear Supertypes
AnyRef, Any
Known Subclasses
Type Hierarchy Learn more about scaladoc diagrams
Ordering
  1. Alphabetic
  2. By inheritance
Inherited
  1. Sequent
  2. AnyRef
  3. Any
Implicitly
  1. by RichOccSequent
  2. by RichFormulaSequent
  3. by any2stringadd
  4. by StringFormat
  5. by Ensuring
  6. by ArrowAssoc
  1. Hide All
  2. Show all
Visibility
  1. Public
  2. All

Instance Constructors

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

    Permalink

    antecedent

    The first list.

    succedent

    The second list.

Value Members

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

    Permalink
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int

    Permalink
    Definition Classes
    AnyRef → Any
  3. def +(other: String): String

    Permalink
    Implicit information
    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]

    Permalink
  5. def ++:[B >: A](es: GenTraversable[B]): Sequent[B]

    Permalink

    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]

    Permalink

    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)

    Permalink
    Implicit information
    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 HOLFormula with FormulaOccurrence (A <: HOLFormula with FormulaOccurrence).
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  8. def :+[B >: A](e: B): Sequent[B]

    Permalink

    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: GenTraversable[B]): Sequent[B]

    Permalink

    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

    Permalink
    Definition Classes
    AnyRef → Any
  11. def =^(o: OccSequent): Boolean

    Permalink
    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichOccSequent performed by method RichOccSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of FormulaOccurrence (A <: FormulaOccurrence).
    Definition Classes
    RichOccSequent
  12. def addToAntecedent[B >: A](e: B): Sequent[B]

    Permalink

    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

  13. def addToSuccedent[B >: A](e: B): Sequent[B]

    Permalink

    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

  14. val antecedent: Seq[A]

    Permalink

    The first list.

  15. def apply(is: Seq[SequentIndex]): Seq[A]

    Permalink
  16. def apply(i: SequentIndex): A

    Permalink

    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.

  17. final def asInstanceOf[T0]: T0

    Permalink
    Definition Classes
    Any
  18. def clone(): AnyRef

    Permalink
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  19. def compose[B >: A](other: Sequent[B]): Sequent[B]

    Permalink
  20. def contains[B](el: B): Boolean

    Permalink

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

  21. def delete(i: SequentIndex): Sequent[A]

    Permalink
  22. def diff[B >: A](other: Sequent[B]): Sequent[A]

    Permalink

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

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

  23. def distinct: Sequent[A]

    Permalink

    Removes duplicate formulas from both cedents.

  24. def elements: Seq[A]

    Permalink

    Sequence of elements of the sequent.

    Sequence of elements of the sequent.

    returns

    Antecedent concatenated with succedent.

  25. def ensuring(cond: (Sequent[A]) ⇒ Boolean, msg: ⇒ Any): Sequent[A]

    Permalink
    Implicit information
    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
  26. def ensuring(cond: (Sequent[A]) ⇒ Boolean): Sequent[A]

    Permalink
    Implicit information
    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
  27. def ensuring(cond: Boolean, msg: ⇒ Any): Sequent[A]

    Permalink
    Implicit information
    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: Boolean): Sequent[A]

    Permalink
    Implicit information
    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. final def eq(arg0: AnyRef): Boolean

    Permalink
    Definition Classes
    AnyRef
  30. def equals(other: Any): Boolean

    Permalink

    Equality treating each side of the sequent as list, i.e.

    Equality treating each side of the sequent as list, i.e. respecting order and multiplicity.

    Definition Classes
    Sequent → AnyRef → Any
  31. def filter(p: (A) ⇒ Boolean): Sequent[A]

    Permalink

    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.

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

    Permalink

    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.

  33. def finalize(): Unit

    Permalink
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  34. def find(pred: (A) ⇒ Boolean): Option[SequentIndex]

    Permalink
  35. def focus(i: SequentIndex): (A, Sequent[A])

    Permalink

    "Focuses on one element of the seuqent, i.e.

    "Focuses on one element of the seuqent, 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.

  36. def formatted(fmtstr: String): String

    Permalink
    Implicit information
    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()
  37. def formulas: Seq[HOLFormula]

    Permalink
    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichFormulaSequent performed by method RichFormulaSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of HOLFormula (A <: HOLFormula).
    Definition Classes
    RichFormulaSequent
  38. def freeVariables: Set[Var]

    Permalink
    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichOccSequent performed by method RichOccSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of FormulaOccurrence (A <: FormulaOccurrence).
    Definition Classes
    RichOccSequent
  39. def getChildOf(ancestor: FormulaOccurrence): Option[FormulaOccurrence]

    Permalink

    Finds the first occurrence in this sequent having the given ancestor.

    Finds the first occurrence in this sequent having the given ancestor.

    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichOccSequent performed by method RichOccSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of FormulaOccurrence (A <: FormulaOccurrence).
    Definition Classes
    RichOccSequent
  40. final def getClass(): Class[_]

    Permalink
    Definition Classes
    AnyRef → Any
  41. def hashCode(): Int

    Permalink
    Definition Classes
    Sequent → AnyRef → Any
  42. def indices: Seq[SequentIndex]

    Permalink

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

  43. def indicesSequent: Sequent[SequentIndex]

    Permalink

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

  44. def indicesWhere(p: (A) ⇒ Boolean): Seq[SequentIndex]

    Permalink

    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.

  45. def intersect[B >: A](other: Sequent[B]): Sequent[A]

    Permalink

    Computes the intersection of two sequents.

  46. def isDefinedAt(i: SequentIndex): Boolean

    Permalink

    Tests whether the sequent is defined at the supplied SequentIndex.

  47. def isEmpty: Boolean

    Permalink

    Returns true iff both cedents are empty.

  48. final def isInstanceOf[T0]: Boolean

    Permalink
    Definition Classes
    Any
  49. def isReflexivity: Boolean

    Permalink

    Is this sequent of the form :- t = t?

    Is this sequent of the form :- t = t?

    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichOccSequent performed by method RichOccSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of FormulaOccurrence (A <: FormulaOccurrence).
    Definition Classes
    RichOccSequent
  50. def isSubMultisetOf[B >: A](other: Sequent[B]): Boolean

    Permalink
  51. def isSubsetOf[B >: A](other: Sequent[B]): Boolean

    Permalink

    other

    Another Sequent.

    returns

    True iff other contains this pair of sets.

  52. def isTaut: Boolean

    Permalink

    Is this sequent of the form F :- F?

    Is this sequent of the form F :- F?

    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichOccSequent performed by method RichOccSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of FormulaOccurrence (A <: FormulaOccurrence).
    Definition Classes
    RichOccSequent
  53. def length: Int

    Permalink

    The number of elements in the sequent.

  54. def lengths: (Int, Int)

    Permalink

    A pair consisting of the lengths of the cedents.

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

    Permalink

    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.

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

    Permalink

    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.

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

    Permalink

    Equality treating each side of the sequent as a multiset.

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

    Permalink
    Definition Classes
    AnyRef
  59. def nonEmpty: Boolean

    Permalink
  60. final def notify(): Unit

    Permalink
    Definition Classes
    AnyRef
  61. final def notifyAll(): Unit

    Permalink
    Definition Classes
    AnyRef
  62. def occurrences: Seq[FormulaOccurrence]

    Permalink

    Occurrences on both sides of the sequent, i.e.

    Occurrences on both sides of the sequent, i.e. the concatenation of antecedent and succedent.

    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichOccSequent performed by method RichOccSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of FormulaOccurrence (A <: FormulaOccurrence).
    Definition Classes
    RichOccSequent
  63. def polarizedElements: Seq[(A, Boolean)]

    Permalink

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

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

    FIXME: Make polarities consistent throughout the system (IMO: false = antecedent, true = succedent)

  64. def polarizedFormulas: Seq[(HOLFormula, Boolean)]

    Permalink
    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichFormulaSequent performed by method RichFormulaSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of HOLFormula (A <: HOLFormula).
    Definition Classes
    RichFormulaSequent
  65. def removeFormulasAtOccurrences(occs: Seq[FormulaOccurrence]): OccSequent

    Permalink

    Removes the specified at.logic.gapt.proofs.occurrences.FormulaOccurrences from each side.

    Removes the specified at.logic.gapt.proofs.occurrences.FormulaOccurrences from each side.

    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichOccSequent performed by method RichOccSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of FormulaOccurrence (A <: FormulaOccurrence).
    Definition Classes
    RichOccSequent
  66. def removeFromAntecedent[B](e: B): Sequent[A]

    Permalink
  67. def removeFromSuccedent[B](e: B): Sequent[A]

    Permalink
  68. def renameSymbols(map: SymbolMap): Sequent[HOLFormula]

    Permalink
    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichFormulaSequent performed by method RichFormulaSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of HOLFormula (A <: HOLFormula).
    Definition Classes
    RichFormulaSequent
  69. def replaceInAntecedent[B, C](from: B, to: C): Sequent[Any]

    Permalink
  70. def replaceInSuccedent[B, C](from: B, to: C): Sequent[Any]

    Permalink
  71. def setEquals[B](other: Sequent[B]): Boolean

    Permalink

    Equality treating each side of the sequent as a set.

  72. def size: Int

    Permalink

    Synonym for length.

  73. def sizes: (Int, Int)

    Permalink

    Synonym for lengths.

  74. def sorted[B >: A](implicit ordering: Ordering[B]): Sequent[A]

    Permalink
  75. val succedent: Seq[A]

    Permalink

    The second list.

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

    Permalink
    Definition Classes
    AnyRef
  77. def syntacticMultisetEquals(o: HOLSequent)(implicit dummy: DummyImplicit): Boolean

    Permalink

    Equality treating each side as a multiset of formulas, ignoring the occurrence.

    Equality treating each side as a multiset of formulas, ignoring the occurrence.

    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichOccSequent performed by method RichOccSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of FormulaOccurrence (A <: FormulaOccurrence).
    Definition Classes
    RichOccSequent
  78. def syntacticMultisetEquals(o: OccSequent): Boolean

    Permalink

    Equality treating each side as a multiset of formulas, ignoring the occurrence.

    Equality treating each side as a multiset of formulas, ignoring the occurrence.

    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichOccSequent performed by method RichOccSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of FormulaOccurrence (A <: FormulaOccurrence).
    Definition Classes
    RichOccSequent
  79. def toHOLSequent: HOLSequent

    Permalink

    Converts to a HOLSequent, ignoring where the formulas occur.

    Converts to a HOLSequent, ignoring where the formulas occur.

    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichOccSequent performed by method RichOccSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of FormulaOccurrence (A <: FormulaOccurrence).
    Definition Classes
    RichOccSequent
  80. def toImplication: HOLFormula

    Permalink
    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichFormulaSequent performed by method RichFormulaSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of HOLFormula (A <: HOLFormula).
    Definition Classes
    RichFormulaSequent
  81. def toNegFormula: HOLFormula

    Permalink
    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichFormulaSequent performed by method RichFormulaSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of HOLFormula (A <: HOLFormula).
    Definition Classes
    RichFormulaSequent
  82. def toString(): String

    Permalink
    Definition Classes
    Sequent → AnyRef → Any
  83. def toTuple: (Seq[A], Seq[A])

    Permalink

    returns

    The sequent in tuple form.

  84. def union[B >: A](other: Sequent[B]): Sequent[B]

    Permalink

    Computes the union of two sequents.

  85. def updated[B >: A](index: SequentIndex, elem: B): Sequent[B]

    Permalink
  86. final def wait(): Unit

    Permalink
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  87. final def wait(arg0: Long, arg1: Int): Unit

    Permalink
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  88. final def wait(arg0: Long): Unit

    Permalink
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  89. def zipWithIndex: Sequent[(A, SequentIndex)]

    Permalink
  90. def [B](y: B): (Sequent[A], B)

    Permalink
    Implicit information
    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 HOLFormula with FormulaOccurrence (A <: HOLFormula with FormulaOccurrence).
    Definition Classes
    ArrowAssoc

Shadowed Implicit Value Members

  1. val sequent: Sequent[FormulaOccurrence]

    Permalink
    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichOccSequent performed by method RichOccSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of FormulaOccurrence (A <: FormulaOccurrence).
    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: RichOccSequent).sequent
    Definition Classes
    RichOccSequent
  2. val sequent: Sequent[HOLFormula]

    Permalink
    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichFormulaSequent performed by method RichFormulaSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of HOLFormula (A <: HOLFormula).
    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
  3. def toFormula: HOLFormula

    Permalink

    Interpretation of the sequent as formula.

    Interpretation of the sequent as formula.

    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichOccSequent performed by method RichOccSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of FormulaOccurrence (A <: FormulaOccurrence).
    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: RichOccSequent).toFormula
    Definition Classes
    RichOccSequent
  4. def toFormula: HOLFormula

    Permalink

    Interpretation of the sequent as a formula.

    Interpretation of the sequent as a formula. Why is this not the definition of a sequent (/\ F -> \/ G)? The current implementation (\/-F \/ G) is only classically equivalent (In IL a -> b :/- -a \/ b).

    Implicit information
    This member is added by an implicit conversion from Sequent[A] to RichFormulaSequent performed by method RichFormulaSequent in at.logic.gapt.proofs.lk.base. This conversion will take place only if A is a subclass of HOLFormula (A <: HOLFormula).
    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

Inherited from AnyRef

Inherited from Any

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

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

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