[Agda] termination proofs

[Altenkirch Thorsten]

Nice idea. However, I think that termination of Goodstein sequences is
provable in Agda.

We are far beyond Arithmetic. I am sure Anton can give a better answer but
I'd suspect that inductive-recursive definitions give you Pi_1^2-CA. Are
there natural functions which are not provable total in such a theory?

Thorsten

On 24/09/2012 20:42, "Jacques Carette" <carette at mcmaster.ca> wrote:

>On 12-09-24 03:30 PM, Altenkirch Thorsten wrote:
>> Re: Does there exist an algorithmic map in  Nat -> Nat  for which there
>> is not any Agda program with a termination proof accepted by Agda ?
>> [...]
>> Another question: Is there such a program which we can actually write
>>down?
>>
>
>Wouldn't a program based on Goodstein sequences [1] be quite easy to
>write, but with quite a difficult termination proof, at least as far as
>Agda is concerned?
>
>If that's not fast enough, then one can go up the hierarchy [2] (without
>the need to go all Goedelian) of fast growing functions to Friedman's
>TREE function [3] for something quite frightening (although still
>'predicative' in a certain sense).
>
>Jacques
>
>[1] http://en.wikipedia.org/wiki/Goodstein%27s_theorem
>[2] http://en.wikipedia.org/wiki/Fast-growing_hierarchy
>[3] 
>http://en.wikipedia.org/wiki/Kruskal%27s_tree_theorem#Friedman.27s_finite_
>form

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