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[Kenneth Adam Miller <kennethadammiller AT gmail.com>]

| This doesn't...

What specifically doesn't make sense? I'm just trying to learn how the various maths are used and how or if they fit together.

I know, I know about CiC and CoC. I've been reading about them. I just was thinking about different systems for reasoning about programs and algorithms. 

You can't add a semantics for a language built under and by Coq? What about Mezzo, there is a language that was built with Coq. If you're right, then I guess that the mezzo source files just map down to Coq types eventually. 

Matching logic is what appears to me to be a new program verification where operational semantics and axiomatic semantics are one and the same thing. It's wildly different and a totally unique theory, and I probably am not suited to do it justice here, it's best you read about it. I'm pretty sure that this is the seminal paper:

http://fsl.cs.illinois.edu/index.php/From_Hoare_Logic_to_Matching_Logic_Reachability

I didn't mean to set anybody on fire by bringing in a supposed competitor theory. I don't actually think that's what this is. With Coq, you build derive compilable products from within the pristine and perfect system where the program was nutured and perfected. Like Adam said, the Coq is more broad. I'm fascinated with the idea of being able to have a matching logic implemented within Coq. Matching logic is suited only to annotating individual programs after they have been written, and checking that the program fits to the specification. I hope we can all agree that learning is basis of both motivation and spirit in this forum and it ought to be that whatever theory or system that suits a task best is what is used. Formal methods is an incredibly broad category, I wouldn't be surprised if learning several very well would help.

On Tue, May 31, 2016 at 10:57 AM, Thorsten Altenkirch <Thorsten.Altenkirch AT nottingham.ac.uk> wrote:

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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