[Agda] using Induction.Nat

[Andreas Abel]

The hard work to show termination is done in Data.Digit, in showing 
that the function that converts a unary into a binary number is 
terminating.  But it seems more principled to do the work there instead 
of the binary exponentiation function, which is best understood as 
structural recursion over binary numbers.

Cheers,
Andreas

On 2013-10-09 23:17, Sergei Meshveliani wrote:
> On Tue, 2013-10-08 at 12:10 +0900, Andreas Abel wrote:
>> Using Data.Bin was also my hunch.  Here is a partial solution to 
>> your
>> problem:
>>
>> [..]
>
>> open import Data.Fin using (zero; suc)
>> open import Data.Bin using (Bin⁺; 0#; _1#; fromℕ)
>>
>> open import Relation.Binary.PropositionalEquality
>>
>> -- Binary exponentiation
>>
>> module Power {A : Set} (_•_ : A → A → A) (x : A) where
>>
>>    binPower : Bin⁺ → A
>>    binPower []       = x
>
>
> Indeed, using the Bin⁺ argument simplifies the proofs greatly.
> Because  (2 *)  converts to  (bit ::),  and termination becomes given
> for free.
> So, my introduction to inductive types is delayed to the first future
> unlucky case.
>
> Thanks to people!
>
> ------
> Sergei

-- 
Andreas Abel  <><     Du bist der geliebte Mensch.

Theoretical Computer Science, University of Munich 
http://www.tcs.informatik.uni-muenchen.de/~abel/