[Agda] Forget Hurken's Paradox,
Agda has a quicker route to success
Andreas Abel
andreas.abel at ifi.lmu.de
Fri Sep 7 09:31:47 CEST 2012
On 06.09.12 10:52 PM, Andrés Sicard-Ramírez wrote:
> On Thu, Sep 6, 2012 at 12:25 PM, Andreas Abel <andreas.abel at ifi.lmu.de> wrote:
>>
>> I have a fix for this (filed as issue 690), that looks also for occurrences
>> in the indices.
>
> FYI, using that fix the following data type (previously accepted) is
> rejected by Agda (and Coq)
>
> data T : Set → Set where
> c : T (T ℕ)
That seems to be a good thing. Trying to make sense of T in terms of
inductive types, explaining indices via equalities, one arrives at
data T (X : Set) : Set where
c : (X == T N) -> T X
which has a non-positive occurrence of T in (X == T N).
An argument for the existence of T would have to argue for the existence
this least fixed point:
lfp \lambda T X -> (X == T N)
Cheers,
Andreas
--
Andreas Abel <>< Du bist der geliebte Mensch.
Theoretical Computer Science, University of Munich
Oettingenstr. 67, D-80538 Munich, GERMANY
andreas.abel at ifi.lmu.de
http://www2.tcs.ifi.lmu.de/~abel/
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