. This work is centred on the specification of partial operations in a system based on a classical logic with total functions. We present a style with pre-conditions: our method enables calculation of the domain of a partial function f independently of calculation of f. We also study the influence of this style upon the proof facility and the later use of the specification. 1 Introduction In this paper we are in the context of a logic which does not incorporate the notion of partiality and where any function is total. This choice is justified by the power of the underlying logic and by the expressive power of the associated languages. In this context, various tricks are used to encode the partiality. In a typed world, a total function of type ! 0 is defined for every value of type . Thus we have to encode a partial function whose arguments and result are respectively of type 1 and 2 into a total function of type ! 0 . Usually 1 and are identical but 2 and 0 are...