experiment with HITs and rewritng rules #2098
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Here is an experiment with rewriting rule based HITs. We redefine
ap
andapD
as a symbol with a computation rule inOverture.v
and introduce a new fileInterval2.v
which demonstrates how new HITs can be written. Interval2 seems to be capable of provingfunext
which is quite cool, but it doesn't appear to compute nicely due to how we prove funext.The change to
ap
was a bit more non-trivial than was indicated in #1868 and there are lots and lots of universe issues with the rewrite rules, so I had to come up with some hacky workarounds.This PR isn't intended to be merged, but just to get a feel for what it could be like in the future.