The Coq mailing list

[Thorsten Altenkirch <Thorsten.Altenkirch AT nottingham.ac.uk>]

Nothing to do with canonical objects - Higher Inductive Types comes from
Homotopy Type Theory where we can have not ony constructors for elements
but also constructors for equalities and equalities of equalities and so
on. Basically you view the type and its equalities as one object (actually
an omega groupoid). The best reference is the HoTT book:

https://homotopytypetheory.org/book/

There are some libraries available which allow you to use HITs in Coq via
some hacks using axioms. We are still waiting for a usable implementation
of cubical type theory (there is a prototypical one called ³cubical²)

https://github.com/mortberg/cubicaltt

Cheers,
Thorsten

On 13/12/2016, 06:04, 
"coq-club-request AT inria.fr
 on behalf of Faré"
<coq-club-request AT inria.fr
 on behalf of 
fahree AT gmail.com>
 wrote:

>I'm not sure what you call higher inductive types, but I'm guess it's
>some kind of construction where somehow you manage to get one
>canonical object for each equivalence class up to the system's magic
>implicit equality. I'm not sure how to build such an object.





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