[Aldor-l] rep, per, Rep in SPAD/Aldor

[Ralf Hemmecke]

Gaby,

just a short reply. As I said, I agree that Rep is an important issue. 
It would actually be good to hear what Stephen Watt has to say about 
that issue. I'd like to learn about the original intentions.

> Secondly, what we want to convey with `rep' is not that one can take 
> object foo, restrict its interpretation at type T and then do an 
> `on faith interpretation of its sequence of bytes representation as 
> an object at type U'.   Rather, what we want to say is that object foo 
> at type T is the result of a (hopefully injective) mapping from U and we 
> are interested in its pre-image.  

I don't know that I understand that paragraph. If I understand that 
correctly, then (U = Rep, T = %)

per: Rep -> %     injective map
   In general we have card(Rep)>=card(%). (If this would not always be
   true then I don't know.)

rep: % -> Rep     the "inverse" of per
   If x is from % then rep(x) should be an element from Rep such that
   per(rep x) = x. Since there might be several such elements, rep should
   choose one, and since we want rep to be a function, it should always
   choose the same element from the preimage of per.

Gaby, what you were saying is that Rep and % (in an abstract setting) 
need not be represented by the same string of bytes in memory. That is 
my interpretation of your paragraph. Abstractly seen, this seems to be 
OK, but from an efficiency point of view, it is probably always good if 
rep and per actually do nothing than changing the view on the same 
string of bytes in memory. But, I agree, that decision should be left to 
the compiler.

Ralf