# [Agda] termination proofs

Altenkirch Thorsten psztxa at exmail.nottingham.ac.uk
Mon Sep 24 21:30:32 CEST 2012

```
On 24/09/2012 19:01, "Serge D. Mechveliani" <mechvel at botik.ru> wrote:

>I thank people for userful responses on my question on termination
>proofs.
>
>Nils Anders Danielsson  writes
>
>On Mon, Sep 24, 2012 at 04:20:58PM +0200, Nils Anders Danielsson wrote:
>> On 2012-09-24 13:36, Serge D. Mechveliani wrote:
>>> Where it is specified in the Language which functions are considered
>>> as provably terminating?
>>
>> A conservative approximation of the criterion used in Agda is described
>> in Section 2.5 of "Subtyping, Declaratively"
>subtyping.html).
>>
>>> Now: how to make a  termination proof  as explicit as possible?
>>
>> You can represent termination proofs explicitly in many different ways.
>> I believe that the paper "Partiality and Recursion in Interactive
>> Theorem Provers ??? An Overview" by Bove, Krauss and Sozeau
>>
>>(http://mattam.org/research/publications/drafts/Partiality_and_Recursion_
>>in_Interactive_Theorem_Provers_-_An_Overview.pdf)
>> lists some of them.
>
>
>I see.
>In my newbie impression, Agda looks very good.
>
>Does there exist an algorithmic map in  Nat -> Nat  for which there
>is not any Agda program with a termination proof accepted by Agda ?

Yes. :-)

Let g : Nat -> Nat -> Nat be the function which to compute g m n
interprets m as the binary encoding of an Agda program and which returns
(f n)+1 if the program type checks and defines a function f : Nat -> Nat
and 0 otherwiseŠ Then define the function f : Nat -> Nat with f x = g x xŠ

Another question: Is there such a program which we can actually write down?

Thorsten

>
>Regards,
>
>------
>Sergei
>
>
>
>_______________________________________________
>Agda mailing list
>Agda at lists.chalmers.se
>https://lists.chalmers.se/mailman/listinfo/agda

This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it.   Please do not use, copy or disclose the information contained in this message or in any attachment.  Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham.

This message has been checked for viruses but the contents of an attachment
may still contain software viruses which could damage your computer system:
you are advised to perform your own checks. Email communications with the
University of Nottingham may be monitored as permitted by UK legislation.
```