[Agda] [newbie] universe levels and BUILTIN EQUALITY

[Thorsten Altenkirch]

At least in the case of equality this can be justified by the HoTT
definition of equality between types at level n to be equivalent to
equivalence (i.e. there exists a function which is an equivalence) which
is at the same level.

Thorsten

On 06/01/2017, 10:25, "Agda on behalf of Andreas Abel"
<agda-bounces at lists.chalmers.se on behalf of andreas.abel at ifi.lmu.de>
wrote:

>Thanks, Roman, for the example.
>
>Indeed, big parameters in small data types are believed to be
>consistent, but I do not know of a worked-out theoretical justification.
>(Maybe someone else has pointers for me?!) This is the same for some
>aspects of induction-recursion, or even very-dependent types.
>
>So, far, Agda gives the benefit of the doubt.
>
>Best,
>Andreas
>
>On 06.01.2017 00:38, Roman wrote:
>> Andreas, it wasn't previously possible to define
>>
>>     data _≡_ {a} {A : Set a} : A → A → Set where
>>       refl : ∀ x → x ≡ x
>>
>> because this requires forcing of `x` to type check. IIRC, it wasn't
>> possible to define
>>
>>     data _≡_ {a} {A : Set a} (x : A) : A → Set where
>>       refl : x ≡ x
>>
>> either (or was it?). Hence I assumed that both the definitons require
>> forcing (which is a poorly documented feature, so I don't really
>> know).
>>
>> But anyway, both the definitions type check currently, so does Agda
>> approve something hazardous that should be rejected instead? But if
>> Agda justifies this, then how many other hazardous definitions pass
>> the type checker as well? Or did I just misunderstand you completely?
>
>
>-- 
>Andreas Abel  <><      Du bist der geliebte Mensch.
>
>Department of Computer Science and Engineering
>Chalmers and Gothenburg University, Sweden
>
>andreas.abel at gu.se
>http://www2.tcs.ifi.lmu.de/~abel/
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