Treating Partiality in a Logic of Total Functions

The need to use partial functions arises frequently in formal descriptions of computer systems. However, most proof assistants are based on logics of total functions. One way to address this mismatch is to invent and mechanize a new logic. Another is to develop practical workarounds in existing settings. In this paper we take the latter course : we survey and compare methods used to support partiality in a mechanization of a higher order logic featuring only total functions. The techniques we discuss are generally applicable and are illustrated by relatively large examples.