  Weighted automata model quantitative aspects of systems like the consumption
of resources during executions. Traditionally, the weights are assumed to form
the algebraic structure of a semiring, but recently also other weight
computations like average have been considered. Here, we investigate
quantitative context-free languages over very general weight structures
incorporating all semirings, average computations, lattices, and more. In our
main result, we derive the fundamental Chomsky-Sch\"utzenberger theorem for
such quantitative context-free languages, showing that each arises as the image
of a Dyck language and a regular language under a suitable morphism. Moreover,
we show that quantitative context-free language are expressively equivalent to
a model of weighted pushdown automata. This generalizes results previously
known only for semirings. We also investigate when quantitative context-free
languages assume only finitely many values.
