  We are motivated by the following question: which data languages admit an
active learning algorithm? This question was left open in previous work by the
authors, and is particularly challenging for languages recognised by
nondeterministic automata. To answer it, we develop the theory of residual
nominal automata, a subclass of nondeterministic nominal automata. We prove
that this class has canonical representatives, which can always be constructed
via a finite number of observations. This property enables active learning
algorithms, and makes up for the fact that residuality -- a semantic property
-- is undecidable for nominal automata. Our construction for canonical residual
automata is based on a machine-independent characterisation of residual
languages, for which we develop new results in nominal lattice theory. Studying
residuality in the context of nominal languages is a step towards a better
understanding of learnability of automata with some sort of nondeterminism.
