partial equivalence relation

   (PER) A relation R on a set S where R is symmetric (x R y => y
   R x) and transitive (x R y R z => x R z) and where there may
   exist elements in S for which the relation is not defined.  A
   PER is an equivalence relation on the subset for which it is
   defined, i.e. it is also reflexive (x R x).