[Agda] termination by contradiction

[Altenkirch Thorsten]

I am looking for specific examples.

T.

From: Dmytro Starosud <d.starosud at gmail.com<mailto:d.starosud at gmail.com>>
Date: Tuesday, 1 July 2014 17:23
To: Thorsten Altenkirch <psztxa at exmail.nottingham.ac.uk<mailto:psztxa at exmail.nottingham.ac.uk>>
Cc: Sergei Meshveliani <mechvel at botik.ru<mailto:mechvel at botik.ru>>, Agda mailing list <agda at lists.chalmers.se<mailto:agda at lists.chalmers.se>>
Subject: Re: [Agda] termination by contradiction

> What would be a good application of MP in programming?
It will extend the set of positively type-checked programs.
i.e. will decrease amount of first order errors, which in general is very good.


2014-07-01 18:19 GMT+03:00 Altenkirch Thorsten <psztxa at exmail.nottingham.ac.uk<mailto:psztxa at exmail.nottingham.ac.uk>>:
Yes, this is true.

However, it is not clear how to do symbolic evaluation with MP. That is if we have a hypothetical classical proof of termination this doesn’t tell us wether we can partially execute our program.
In the case of a constructive proof this is the case.

We could say that we can run the program if the proof is closed but this seems a bit weird.

What would be a good application of MP in programming?

Cheers,
Thorsten


From: Dmytro Starosud <d.starosud at gmail.com<mailto:d.starosud at gmail.com>>
Date: Tue, 1 Jul 2014 15:19:34 +0100
To: Sergei Meshveliani <mechvel at botik.ru<mailto:mechvel at botik.ru>>
Cc: Agda mailing list <agda at lists.chalmers.se<mailto:agda at lists.chalmers.se>>
Subject: Re: [Agda] termination by contradiction

Markov axiom (for Nat) doesn't leed to a total excluded third.
Constructive logic together with Markov axiom (for Nat) is still constructive.
Here is really nice course<http://scs.hosted.panopto.com/Panopto/Pages/Sessions/List.aspx#folderID=%2207756bb0-b872-4a4a-95b1-b77ad206dab3%22> (and book<http://homotopytypetheory.org/book/>) explaining in very deep details all that stuff with constructive vs classic vs whatever.

Dmytro


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