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Given a type , the partial function classifier is inductively generated by
and the partial order type family is simultaneously inductively generated by
a family of dependent terms
representing that each type is a proposition.
a family of dependent terms
representing the reflexive property of .
a family of dependent terms
representing the transitive property of .
a family of dependent terms
representing the anti-symmetric property of .
a family of dependent terms
representing that is initial in the poset.
a family of dependent terms
a family of dependent terms
representing that denumerable/countable joins exist in the poset.
Partiality, Revisited: The Partiality Monad as a Quotient Inductive-Inductive Type (abs:1610.09254)
Martin Escardó, Cory Knapp, Partial Elements and Recursion via Dominances in Univalent Type Theory (pdf)
Last revised on June 9, 2022 at 23:09:19. See the history of this page for a list of all contributions to it.