  We define representations of continuous functions on infinite streams of
discrete values, both in the case of discrete-valued functions, and in the case
of stream-valued functions. We define also an operation on the representations
of two continuous functions between streams that yields a representation of
their composite.
  In the case of discrete-valued functions, the representatives are
well-founded (finite-path) trees of a certain kind. The underlying idea can be
traced back to Brouwer's justification of bar-induction, or to Kreisel and
Troelstra's elimination of choice-sequences. In the case of stream-valued
functions, the representatives are non-wellfounded trees pieced together in a
coinductive fashion from well-founded trees. The definition requires an
alternating fixpoint construction of some ubiquity.
