[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
>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"
>> (http://www.cse.chalmers.se/~nad/publications/danielsson-altenkirch-
>>> 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
>> 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?


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