Isabelle/hol as a Platform for Partiality

In Isabelle, there are several possibilities when one wants to support partial functions. One could put Isabelle to its intended use by directly embedding a logic of partial functions in Isabelle's meta-logic. Alternatively, one could investigate partial functions in one of Isabelle's already well-developed object logics, e.g., ZF or HOL. In this paper we pursue the second approach and describe miscellaneous support for par-tiality found in the HOL instantiation of Isabelle. This support ranges from (1) underspeciication and lifting in a recursive function deenition package, (2) inductive deenitions, to (3) HOLCF, an embedding of domain theory. All approaches are illustrated by relatively large examples.