[Agda] Classical Mathematics for a Constructive World
Peter Divianszky
divipp at gmail.com
Sat Jan 12 15:16:57 CET 2013
Right.
I deleted the trivial theorems and uploaded the new version.
Thanks,
Peter
On 12/01/2013 11:16, Andreas Abel wrote:
> Hi, I looked at the updated definition of classical implication as A =>
> B = A -> not not B. There is a slide "Agda demonstration" after that.
> Are not the last two theorems completely trivial (just the identity
> function) with the updated definition? (Also r.a.a. is just the
> definition).
>
> Cheers
> Andreas
>
> On 11.01.13 9:19 PM, Peter Divianszky wrote:
>> > Nice slides, Peter!
>>
>> Thanks!
>>
>> I corrected the slides and I made them available here:
>>
>> http://people.inf.elte.hu/divip/Agda.pdf
>>
>> > If you start with conjunction and negation, should not be classical
>> > implication be defined as
>> >
>> > not (A and not B)
>>
>> Now I define classical connectives on the slides with corresponding
>> constructive connectives and double negation.
>>
>> Cheers,
>> Peter
>>
>>
>> On 17/12/2012 21:13, Andreas Abel wrote:
>>> Nice slides, Peter!
>>>
>>> Here are some remarks that came to me while reading your slides.
>>> Cheers,
>>> Andreas
>>>
>>> slide 21
>>>
>>> It does not make much sense to define a Top-elimination rule. In
>>> natural deduction, there is no such rule; it is an artifact of defining
>>> Top as a data type. The definition as record
>>>
>>> record Top : P where
>>>
>>> clearly does not give an elimination rule. (I understand that you do
>>> not want to go into records in this tutorial, but maybe drop the
>>> Top-elim rule.)
>>>
>>> slide 22
>>>
>>> If you start with conjunction and negation, should not be classical
>>> implication be defined as
>>>
>>> not (A and not B)
>>>
>>> slide 34 3rd bullet
>>>
>>> n * 3 == n + n + n needs induction on n, the wording on the slide is
>>> a bit misleading. Simplification alone does not suffice.
>>>
>>> On 17.12.12 2:53 PM, Peter Divianszky wrote:
>>>> Hi,
>>>>
>>>> I have advertised Agda, I presented the attached slides for approx. 30
>>>> mathematicians in Debrecen, Hungary, 20 of them were students.
>>>> One of my students in Budapest translated the slides to English so I
>>>> can
>>>> present them to you.
>>>>
>>>> Your answers for my questions in this mailing list helped me a lot too,
>>>> thank you very much.
>>>>
>>>> (I hope I didn't claim any false statement about Agda, please tell
>>>> me if
>>>> you find so.)
>>>>
>>>> Cheers,
>>>> Peter
>>>>
>>>>
>>>> _______________________________________________
>>>> Agda mailing list
>>>> Agda at lists.chalmers.se
>>>> https://lists.chalmers.se/mailman/listinfo/agda
>>>>
>>>
>>
>>
>
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