[Agda] Forget Hurken's Paradox, Agda has a quicker route to success

[Altenkirch Thorsten]

On 16/09/2012 21:09, "Dan Doel" <dan.doel at gmail.com> wrote:

>On Thu, Sep 6, 2012 at 12:47 PM, Nils Anders Danielsson <nad at chalmers.se>
>wrote:
>> On 2012-09-06 17:21, Andreas Abel wrote:
>>>
>>> The problem is that Agda considers
>>>
>>>    F D = \Sigma E : Set. (D ≡ E) * (E → ⊥)
>>>
>>> as strictly positive in D.
>>
>>
>> I'm trying to understand if this is actually a problem. Are there any
>> dire consequences if we stick to predicative types?


I am concerned what happens on the next level, I.e. can we construct a
fixpoint of

F : Set₁ → Set₁
F X = Σ[ E ː Set ] (X ≡ lift E × (E → ⊥))

?

Or alternatively we could use a universe (U : Set, El U -> Set):

F : Set → Set
F X = Σ[ E ː U ] (X ≡ El E × (E → ⊥))


That looks dangerous…

Thorsten


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