Relation

Includes pair in the relation.

Includes (a, b) in the relation.

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

Returns the union of the relation r with this relation.

Includes the given pairs in this relation.

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

Removes pair from this relation.

Removes all elements (_1, _2) for all _1 in _1s from this relation.

Removes all pairs from this relation.

Removes all relations from this relation.

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

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

Returns all pairs in this relation.

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

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

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

Represents this relation as a Map from a _1 to the set of _2s such that (_1, _2) is in this relation.

Specifically, there is one entry for each _1 such that (_1, _2) is in this relation for some _2. The value associated with a given _1 is the set of all _2s such that (_1, _2) is in this relation.

Partitions this relation into a map of relations according to some discriminator function.

Returns a pair of relations: the first contains only pairs (a,b) for which f(a,b) is true and the other only pairs (a,b) for which f(a,b) is false.

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

Represents this relation as a Map from a _2 to the set of _1s such that (_1, _2) is in this relation.

Specifically, there is one entry for each _2 such that (_1, _2) is in this relation for some _1. The value associated with a given _2 is the set of all _1s such that (_1, _2) is in this relation.

Returns the number of pairs in this relation