Revamping the numeric classes

[Peter Douglass]

 I have some questions about how Haskell's numeric classes might be
revamped.

 Is it possible in Haskell to circumscribe the availability of certain
"unsafe" numeric operations such as div, /, mod?  If this is not possible
already, could perhaps a compiler flag "-noUnsafeDivide" could be added to
make such a restriction?

 What I have in mind is to remove division by zero as an untypable
expression.  The idea is to require div, /, mod to take NonZeroNumeric
values in their second argument.  NonZeroNumeric values could be created by
functions of type: 
  Number a => a -> Maybe NonZeroNumeric
or something similar.

  Has this been tried and failed?  I'm curious as to what problems there
might be with such an approach.

--PeterD