  We explore the possibility of extending Mardare et al. quantitative algebras
to the structures which naturally emerge from Combinatory Logic and the
lambda-calculus. First of all, we show that the framework is indeed applicable
to those structures, and give soundness and completeness results. Then, we
prove some negative results which clearly delineate to which extent categories
of metric spaces can be models of such theories. We conclude by giving several
examples of non-trivial higher-order quantitative algebras.
