We present a semantics based framework for analysing the quantitative
behaviour of programs with regard to resource usage. We start from an
operational semantics equipped with costs. The dioid structure of the set of
costs allows for defining the quantitative semantics as a linear operator. We
then present an abstraction technique inspired from abstract interpretation in
order to effectively compute global cost information from the program.
Abstraction has to take two distinct notions of order into account: the order
on costs and the order on states. We show that our abstraction technique
provides a correct approximation of the concrete cost computations
