[Agda] A philosophical question on absurd.

[Nicolas Pouillard]

Hi,

One way to understand that you are not cheating when you pass an argument
to *absurd *is to realise that this piece of code is already unreachable.
Syntactically it seems that one could reach this part of the code with
input values. However the whole system is designed such that it is not
possible.

Nicolas

On Fri, Aug 28, 2020 at 3:29 PM Manuel Bärenz <manuel at enigmage.de> wrote:

> Hi,
>
> I'm by no means an expert, but it seems to me that this "computational
> emptyness" of absurd is just corresponding to the fact that in constructive
> logic, you can't have proof by contradiction, only proof of negation. That
> is, at the end absurd will always prove a negation. It has type _|_ -> A
> for some A. You will never be able to construct an A with absurd, only ever
> its negation.
>
> Manuel
> On 28.08.20 15:11, David Banas wrote:
>
> Hi all,
>
> I'm brand new to Agda and the Curry-Howard isomorphism (and really loving
> this new exploration of both!), and I have a *philosophical* objection to
> how the *absurd* function is used to generate whatever we need to
> complete a proof.
>
> I understand how we are able to satisfy the Agda compiler with the
> definition of *absurd*; my objection isn't mechanical/technical.
>
> What bothers me is a feeling that I'm "cheating" when I use this function
> that can never be called, in order to "produce" that which I need to
> complete my proof.
>
> I wonder if someone could offer a different perspective on this, for
> consideration.
>
> Thanks!
> -db
>
>
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