2015-04-25 00:13:08 +00:00
|
|
|
hit
|
|
|
|
===
|
|
|
|
|
2015-05-14 02:01:48 +00:00
|
|
|
Declaration and theorems of higher inductive types in Lean. We take
|
|
|
|
two higher inductive types (hits) as primitive notions in Lean. We
|
|
|
|
define all other hits in terms of these two hits. The hits which are
|
2015-06-04 19:57:00 +00:00
|
|
|
primitive are n-truncation and quotients. These are defined in
|
|
|
|
[init.hit](../init/hit.hlean) and they have definitional computation
|
2015-05-14 02:01:48 +00:00
|
|
|
rules on the point constructors.
|
2015-04-25 00:13:08 +00:00
|
|
|
|
|
|
|
Files in this folder:
|
|
|
|
|
2015-06-04 19:57:00 +00:00
|
|
|
* [quotient](quotient.hlean) (quotients, primitive)
|
2015-04-25 00:13:08 +00:00
|
|
|
* [trunc](trunc.hlean) (truncation, primitive)
|
2015-06-04 19:57:00 +00:00
|
|
|
* [colimit](colimit.hlean) (Colimits of arbitrary diagrams and sequential colimits, defined using quotients)
|
|
|
|
* [pushout](pushout.hlean) (Pushouts, defined using quotients)
|
|
|
|
* [coeq](coeq.hlean) (Co-equalizers, defined using quotients)
|
|
|
|
* [cylinder](cylinder.hlean) (Mapping cylinders, defined using quotients)
|
|
|
|
* [set_quotient](set_quotient.hlean) (Set-quotients, defined using quotients and set-truncation)
|
2015-04-25 00:13:08 +00:00
|
|
|
* [suspension](suspension.hlean) (Suspensions, defined using pushouts)
|
|
|
|
* [sphere](sphere.hlean) (Higher spheres, defined recursively using suspensions)
|
2015-06-04 19:57:00 +00:00
|
|
|
* [circle](circle.hlean) (defined as sphere 1)
|
|
|
|
* [interval](interval.hlean) (defined as the suspension of unit)
|