Name Rascal/Libraries/Prelude/Relation/complement

Synopsis Complement of a relation.

Function

1. rel[&T0, &T1] complement(rel[&T0, &T1] R)
2. rel[&T0, &T1, &T2] complement(rel[&T0, &T1, &T2] R)
3. rel[&T0, &T1, &T2, &T3] complement(rel[&T0, &T1, &T2, &T3] R)
4. rel[&T0, &T1, &T2, &T3, &T4] complement(rel[&T0, &T1, &T2, &T3, &T4] R)

Usage import Relation;

Description Given a relation R a new relation U can be constructed that contains all possible tuples with element values that occur at corresponding tuple positions in R. The function complement returns the complement of R relative to U, in other words: U - R.

Examples

rascal>import Relation;
ok

Declare R and compute corresponding U:

rascal>R = {<1,10>, <2, 20>, <3, 30>};
rel[int,int]: {
  <3,30>,
  <2,20>,
  <1,10>
}
rascal>U = domain(R) * range(R);
rel[int,int]: {
  <3,30>,
  <2,30>,
  <1,30>,
  <1,20>,
  <3,20>,
  <2,20>,
  <3,10>,
  <2,10>,
  <1,10>
}

Here is the complement of R computed in two ways:

rascal>U - R;
rel[int,int]: {
  <2,30>,
  <1,30>,
  <1,20>,
  <3,20>,
  <3,10>,
  <2,10>
}
rascal>complement({<1,10>, <2, 20>, <3, 30>});
rel[int,int]: {
  <2,30>,
  <1,30>,
  <1,20>,
  <3,20>,
  <3,10>,
  <2,10>
}

Questions

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