Re: [Caml-list] Dimensional Analysis question

[Octachron <octa@polychoron.fr>]

Le 10/16/14 19:35, Mario Alvarez Picallo wrote:
> Hello Shayne,
>
> I was at first convinced that this could not be done, but you can in 
> fact encode it (in a verbose way) with phantom types,
> using a smart typelevel representation of integers 
> (http://www.kb.ecei.tohoku.ac.jp/ml2008/slides/lindley.pdf).
>
> I've written a small proof of concept that seems to work just fine 
> (but, of course, there may be errors), that you can find
> here: https://gist.github.com/m-alvarez/b1e42b7b42cbeed7d1f0
>
> It seems to be solid enough to pass the tests that Octachron tried, 
> but there probably are some other corner cases for which
> it breaks down. Otherwise, it would be interesting to coalesce both 
> representations, using Octachron's idea of row types instead
> of tuples to have extensible dimensional analysis, where each part of 
> the program can introduce its own dimensions.
>
> Regards,
> Mario A.
>

I forget to add variance annotation in my test so my examples broke down 
due to the presence of monomorphic types. With the right implementation 
(i.e. Mario's),
problems appear within functions. For instance,

let f x = x* x

works only for adimensional variable (i.e f : ('a*'a) t -> ('a*'a) t ) 
which is maybe not surprising.
However, the same thing  also happens to

let f x y = (x+y)*x*y .

because the type of x and y are unified during the addition "x+y".

Regards,
Octachron.