[Haskell-cafe] Re: Implementing fixed-sized vectors (using datatype algebra?)

[Dan Weston]

Brandon S. Allbery KF8NH wrote:
> 
> On Feb 8, 2008, at 11:14 , Stefan Monnier wrote:
> 
>>>>> You seem to write 12 as 1 :+ 2 instead of () :+ 1 :+ 2.  But I 
>>>>> think, the
>>>>> latter representation should probably be prefered.
>>>>> (...)
>> How 'bout treating :+ as similar to `append' rather than similar to 
>> `cons'?
>> Basically treat :+ as taking 2 numbers (rather than a number and
>> a digit).
> 
> Dumb questions department:  why not define e.g. D'0 .. D'9 as () :* 0 .. 
> () :* 9?  Programmers then get D'1 :* 2, but the library sees () :* 1 :* 2.
> 

No, D'0 should be (), not () :* D0. If you allow () :* D0, then you 
introduce redundant types for the same number:

In the first case, D'0 :* D'3 == D'3, and D'0 :* D'0 has no instance. In 
your example, D'3 and D'0 :* D'3 are equivalent, but no longer unify.

Dan