Re: n+k patterns

[haskell-request]

Original-Via: uk.ac.nsf; Wed, 6 Nov 91 20:00:39 GMT
Original-Sender: [EMAIL PROTECTED]


> I would be very much in favour of missing out the >= test in both n+k and
> c*n+k. As Mark says there is no need for a restriction in the latter case.
> In the former, the restriction is only there because of a wish to model
> the Natural Numbers, a data type which is NOT native to Haskell.
> 
> Tony

   May I then propose yet another (sorry :-) arithmetic pattern: -n;
that matches only negative numbers:

                case e0 of {-x -> e; _ -> e';}
                = if e0 < 0 then case -(e0) of {x -> e; _ -> e';} else e'

E.g.
        abs (-n) =  n
        abs   n  =  n

        x ^  (-n)   =  error "x^(-n) is undefined."
        x ^    0    =  1
        x ^    1    =  x
        x ^ (2*n+1) =  x*xn*xn where xn = x^n
        x ^ (2*n)   =    xn*xn where xn = x^n

        x ^^ (-n)  =  1/(x^n)
        x ^^   n   =  x^n

                        /kent k