  Canonical extension of finitary ordered structures such as lattices, posets,
proximity lattices, etc., is a certain completion which entirely describes the
topological dual of the ordered structure and it does so in a purely algebraic
and choice-free way. We adapt the general algebraic technique that constructs
them to the theory of frames.
  As a result, we show that every locally compact frame embeds into a
completely distributive lattice by a construction which generalises, among
others, the canonical extensions for distributive lattices and proximity
lattices. This construction also provides a new description of a construction
by Marcel Ern\'e. Moreover, canonical extensions of frames enable us to
frame-theoretically represent monotone maps with respect to the specialisation
order.
