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HoTT / Coq-HoTT

A Coq library for Homotopy Type Theory
http://homotopytypetheory.org/
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Stand-alone? #35

Closed andrejbauer closed 11 years ago

andrejbauer commented 11 years ago

We have now defined our own concat and inverse in Paths.v, even though the equivalent identity_trans and identity_sym exist in the standard library. Would it make sense to just go all independent and define our own identity type? And call it paths? I think the ssreflect library won't be too happy about that.

mikeshulman commented 11 years ago

I vote for continuing to use the standard identity type. (Why have we defined our own 'inverse'?)

On Sun, Dec 16, 2012 at 11:45 PM, Andrej Bauer notifications@github.comwrote:

We have now defined our own concat and inverse in Paths.v, even though the equivalent identity_trans and identity_sym exist in the standard library. Would it make sense to just go all independent and define our own identity type? And call it paths? I think the ssreflect library won't be too happy about that.

— Reply to this email directly or view it on GitHubhttps://github.com/HoTT/HoTT/issues/35.

mikeshulman commented 11 years ago

We're using our own identity type now, defined as paths in Overture.v. I think there was some discussion of this offline that led to that decision; do you remember what it was? The reasoning should perhaps be recorded somewhere.

andrejbauer commented 11 years ago

We wanted more control over transitivity, symmetry and inverse. But we were not allowed to change those for the standard eq/identity type (or its Type-valued version) because it broke various other standard things. And we were not allowed to rename anything, so we used notations, which sort of worked except it did not quite work, etc.

mikeshulman commented 11 years ago

Okay, I added a comment to this effect in Overture.v where we define our identity type.