The Coq mailing list

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

This doesn’t make sense to me whatsoever.

Type theory is based on constructive philosophy and you can’t just “add your semantics”. I have no idea in what sense Type Theory is discrete but this it can be used to reason about continuous and disicrete phenomena. Induction is important but so is coinduction and many other ideas. No it is not based on axioms, things are provable by construction.

Now what the hell is “matching logic”? Not that I really want to know but if somebody could write a paragraph that would be nice. 

Cheers,

Thorsten

From: <coq-club-request AT inria.fr> on behalf of Kenneth Adam Miller <kennethadammiller AT gmail.com>
Reply-To: "coq-club AT inria.fr" <coq-club AT inria.fr>
Date: Tuesday, 31 May 2016 14:55
To: coq-club Club <coq-club AT inria.fr>
Subject: Re: [Coq-Club] Matching logic

Is
 Induction it's own category of semantics? I didn't think so, I thought it was a proof method. But it appears to be the star in Coq. I suppose Coq is actually discrete in that sense; it's a set of type theoretic foundations, and if particular semantics are
 wanted to be modeled or reasoned about, they could be added within the Coq system. Right? I guess that hadn't been answered, although I'm not sure how to ask for what I'm grasping for; how do the different semantics, axiomatic/operational/denotational/<one
 other here> interoperate, or are they discrete because it's a fundamental remaining difficulty with the mathematics that has yet to be reconciled?




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