The rete algorithm is a well-known algorithm for efficiently addressing the many patterns/many objects match problem, and it has been widely used and implemented in several applications, mainly production systems. But despite of the wide usage of production systems and the rete algorithm, to the best of our knowledge there has been just one proposition for a formal definition of the rete algorithm given by Fages and Lissajoux~\cite{Fages92}, but no attempt to give a formal description of production systems as a whole, giving rise to lots of ambiguities and incompatibilities between the different implementations. Therefore, the need for a formalisation is clear and we present in this report a first approach to it, refining Fages and Lissajoux's approach to fit it in our general model of production systems.