Homotopy Type Theory
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< partial function classifier
Definition
Given a type , the partial function classifier is inductively generated by
- a function
- a term
- a function
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.
See also
References
-
Partiality, Revisited: The Partiality Monad as a Quotient Inductive-Inductive Type (abs:1610.09254)
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Martin Escardó, Cory Knapp, Partial Elements and Recursion via Dominances in Univalent Type Theory (pdf)
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