sbt

# Relation

#### trait Relation[A, B] extends AnyRef

Binary relation between A and B. It is a set of pairs (_1, _2) for _1 in A, _2 in B.

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### Abstract Value Members

1. #### abstract def +(a: A, bs: Traversable[B]): Relation[A, B]

Includes the relations (a, b) for all b in bs.

2. #### abstract def +(a: A, b: B): Relation[A, B]

Includes the relation (a, b).

3. #### abstract def +(pair: (A, B)): Relation[A, B]

Includes the relation given by `pair`.

4. #### abstract def ++(rs: Traversable[(A, B)]): Relation[A, B]

Includes the given relations.

5. #### abstract def ++(r: Relation[A, B]): Relation[A, B]

Returns the union of the relation r with this relation.

6. #### abstract def -(pair: (A, B)): Relation[A, B]

Removes `pair` from this relation.

7. #### abstract def -(_1: A): Relation[A, B]

Removes all pairs (_1, _2) from this relation.

8. #### abstract def --(pairs: TraversableOnce[(A, B)]): Relation[A, B]

Removes all `pairs` from this relation.

9. #### abstract def --(_1s: Traversable[A]): Relation[A, B]

Removes all relations (_1, _2) for all _1 in _1s.

10. #### abstract def _1s: Set[A]

Returns the set of all _1s such that (_1, _2) is in this relation.

11. #### abstract def _2s: Set[B]

Returns the set of all _2s such that (_1, _2) is in this relation.

12. #### abstract def all: Traversable[(A, B)]

Returns all pairs in this relation.

13. #### abstract def contains(a: A, b: B): Boolean

Returns true iff (a,b) is in this relation

14. #### abstract def filter(f: (A, B) ⇒ Boolean): Relation[A, B]

Returns a relation with only pairs (a,b) for which f(a,b) is true.

15. #### abstract def forward(_1: A): Set[B]

Returns the set of all _2s such that (_1, _2) is in this relation.

17. #### abstract def reverse(_2: B): Set[A]

Returns the set of all _1s such that (_1, _2) is in this relation.

19. #### abstract def size: Int

Returns the number of pairs in this relation

### Concrete Value Members

1. #### final def !=(arg0: AnyRef): Boolean

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2. #### final def !=(arg0: Any): Boolean

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3. #### final def ##(): Int

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4. #### final def ==(arg0: AnyRef): Boolean

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5. #### final def ==(arg0: Any): Boolean

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6. #### final def asInstanceOf[T0]: T0

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7. #### def clone(): AnyRef

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8. #### final def eq(arg0: AnyRef): Boolean

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9. #### def equals(arg0: Any): Boolean

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10. #### def finalize(): Unit

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11. #### final def getClass(): java.lang.Class[_]

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12. #### def hashCode(): Int

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13. #### final def isInstanceOf[T0]: Boolean

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14. #### final def ne(arg0: AnyRef): Boolean

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15. #### final def notify(): Unit

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16. #### final def notifyAll(): Unit

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

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18. #### def toString(): String

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19. #### final def wait(): Unit

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

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21. #### final def wait(arg0: Long): Unit

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