I have written this <http://hg.gnu.org.ua/hgweb/hol-proofs/file/e6bbb023cfb9/pfunScript.sml> HOL4 theory that introduces a new type for partial (with respect to the universe of the type) functions. The script file is tiny and trivial, but at least it can save the time to type it to somebody else; it can be reused as it is under a free license (GNU GPL 3 or later).

Regards.

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