  We investigate a class of nominal algebraic Henkin-style models for the
simply typed lambda-calculus in which variables map to names in the denotation
and lambda-abstraction maps to a (non-functional) name-abstraction operation.
The resulting denotations are smaller and better-behaved, in ways we make
precise, than functional valuation-based models.
  Using these new models, we then develop a generalisation of \lambda-term
syntax enriching them with existential meta-variables, thus yielding a theory
of incomplete functions. This incompleteness is orthogonal to the usual notion
of incompleteness given by function abstraction and application, and
corresponds to holes and incomplete objects.
