[Agda] Automatic conversion between records and iterated Sigma types

[Thorsten Altenkirch]

I agree you want to do the meta theory using Sigma types but why do you need this during your development. I could also imagine a Agda backend that translate into some combinatory core language but I don’t think we need this within Agda.

Sent from my iPhone

> On 13 Apr 2020, at 20:34, Martin Escardo <m.escardo at cs.bham.ac.uk> wrote:
> 
> Because records are more convenient notationally, but Sigma types are more convenient mathematically, as they allow a uniform treatment. You can prove loads of preservation properties for Sigma formation, and if you use records you have to repeat these proofs. A record *is* the same thing as an iterated Sigma type, and this needs to be made official from a mathematical point of view. This is particularly important in univalent mathematics. The only reason I don't use record types in my developments is this. I would rather use records, but then I would need to reprove everything again, or transport it along equivalences (and none of these two options is attractive). Martin
> 
>> On 13/04/2020 20:25, Thorsten Altenkirch wrote:
>> Why would anybody do something like this?
>> Sent from my iPhone
>>>> On 13 Apr 2020, at 19:48, Martin Escardo <m.escardo at cs.bham.ac.uk> wrote:
>>> 
>>> Is it possible to write a tactic to convert between records and equivalent iterated Sigma types? And, if so, to also produce code to establish their equivalence?
>>> 
>>> Thanks,
>>> Martin
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> -- 
> Martin Escardo
> http://www.cs.bham.ac.uk/~mhe



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