`Covertible' class. Reply.

[S.D.Mechveliani]

Dylan Thurston <dpt@math.harvard.edu>  writes 

> In thinking about various issues with the numeric classes, I came up
> with the following question:  Is there a problem with having a class
> 'Convertible' as follows?
> 
> class Convertible a b where
>    convert :: a -> b
> 
> [..] 


The basic algebra library BAL 
 http://www.botik.ru/pub/local/Mechveliani/basAlgPropos/bal-pre-0.01/
 
suggests             class Cast a b where cast :: a -> b -> a

If  s  is an element of a certain domain, then one can use the
construction  
                     cast s x

to convert various data  x  to corresponding canonical values in the
domain defined by  s.  For example, if  s <- Z[x] 
is a polynomial over Integer, then the expressions

                     cast s 2,  cast s (2,3)

give the constant 2, considered as a polynomial, and a one-term
polynomial equal to  2*x^3. 
Also BAL overloades +, * ... by hiding-reexporting the standard 
Prelude and implements the algebraic categories Group, Ring ...

-----------------
Serge Mechveliani
mechvel@botik.ru