POSTUlATE_TERMINATION --- Was: Re: [Agda] termination by contradiction

[Harley D. Eades III]

On Jul 14, 2014, at 11:54 AM, Wolfram Kahl <kahl at cas.mcmaster.ca> wrote:

> On Fri, Jul 04, 2014 at 08:12:44PM +0200, Ulf Norell wrote:
>> The --no-termination-check flag will still treat functions as terminating.
>> The motivation for the
>> new behaviour (which I honestly thought was the intended behaviour all
>> along) is to let you
>> write possibly non-terminating programs without jeopardising decidability
>> of type checking.
> 
> Perhaps a POSTULATE_TERMINATION pragma might be useful;
> with the intention that this would be used for terminating functions
> that the (current) termination checker does not recognise as such.
> The type checker would trust this just like a postulate;
> this of course means that if the function in question does in fact
> not terminate, the type checker will loop.
> Just like with postulates, *.agdai files should then also be generated.
> Theoretically, the definition could be considered as given via
> Induction.* with postulates for the relevant wellfoundedness properties.
> (``safe'' mode should of course reject it.)

This is a nice idea.  I have always wanted a means to be my own termination
checker.  It would be extremely nice if we could have a pragma like

EXTERNAL_TERM_PROOF 

that takes an argument which is the termination proof.   Then the type 
checker could consider the function terminating with a proof that this is true.  

Sometimes it is easier to prove termination in such a way the termination
checker cannot determine.

Very best regards,
.\ Harley

> 
> 
> Wolfram
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