  The aim of this paper is to design a theoretical framework that allows us to
perform the computation of regular expression derivatives through a space of
generic structures. Thanks to this formalism, the main properties of regular
expression derivation, such as the finiteness of the set of derivatives, need
only be stated and proved one time, at the top level. Moreover, it is shown how
to construct an alternating automaton associated with the derivation of a
regular expression in this general framework. Finally, Brzozowski's derivation
and Antimirov's derivation turn out to be a particular case of this general
scheme and it is shown how to construct a DFA, a NFA and an AFA for both of
these derivations.
