[Agda] termination proofs

Altenkirch Thorsten psztxa at exmail.nottingham.ac.uk
Tue Sep 25 21:30:15 CEST 2012

The set of Turing machines is countable but we were talking about

The standard proof by diagonalisation that the set of functions from Nat
to Nat is uncountable can be carried out in Agda - this has nothing to do
with being classical.

Assuming that we can find out how a function can be computed (Church's
thesis + choice) is fishy both from a classical and constructive

What is difficult to understand about constructive logic? I am having more
trouble with classical logic. Bool = Prop seems a strange idea.


On 25/09/2012 17:33, "Serge D. Mechveliani" <mechvel at botik.ru> wrote:

>On Tue, Sep 25, 2012 at 05:12:01PM +0100, Peter Hancock wrote:
>>> The countability grounds is not relevant here, because I asked about an
>>> _algorithmic_ map in  Nat -> Nat.
>> For me, a function just *is* an algorithmic map which we can recognise
>>as total.
>> The normal Cantor diagonalisation argument shows that Nat->Nat is
>> I admit, this will seem strange at first, because there are only
>> many Turing machines, and the total ones will be a subset of these.  But
>> the notion of a cardinal is a bit strange constructively.  There are
>> arbitrarily many subsets of a singleton, constructively.  I suggest that
>> this argument is worth a bit more of your attention.
>> (I also admit I am sweeping some subtle points under the carpet.)
>I meant classical mathematics and classical logic. According to them,
>the set of total Tuering machines is countable.
>I try now to imagine many subsets of a singleton. And it comes out that
>there are as many as  2^1  of them, that is  2.
>I like Agda, despite that understand nothing in a non-classical logic.
>So far I, studied only that proofs are build as members of a dependent
>type, and that negation for T is represented as  T -> \bottom
>(if I do not confuse anything).
>Agda mailing list
>Agda at lists.chalmers.se

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