[Haskell-cafe] Simple quirk in behavior of `mod`

[Nathan Bloomfield]

Hello haskell-cafe;

I'm fiddling with
this<http://cdsmith.wordpress.com/2009/07/20/calculating-multiplicative-inverses-in-modular-arithmetic/>blog
post about inverting elements of Z/(p), trying to write the inversion
function in pointfree style. This led me to try executing statements like

   n `mod` 0

which in the ring theoretic sense should be n, at least for integers*.
(MathWorld
agrees. <http://mathworld.wolfram.com/Congruence.html>) But Hugs gives a
division by zero error! I'm more of a recreational haskell user and not too
familiar with how the Prelude works. But I dug around a bit and saw
this inGHC.Real: (
link<http://www.haskell.org/ghc/docs/latest/html/libraries/base/src/GHC-Real.html#mod>
)

>  a `mod` b
>   | b == 0                     = divZeroError
>   | a == minBound && b == (-1) = overflowError
>   | otherwise                  =  a `modInt` b

Is there a reason why n `mod` 0 is undefined in Haskell? Maybe this
has already been considered for Haskell' and I'm just unaware.
I did some digging in the archives and this discussion
<http://markmail.org/message/5dmehw4lhu56x4zw#query:haskell%20%22%60mod%60%200%22+page:1+mid:7alg3hdlndapyxg6+state:results>
<http://markmail.org/message/5dmehw4lhu56x4zw> from 2002 is the most
relevant one I could find; it is suggested there that n `mod` 0 should
be an error.

Thanks all-
Nathan Bloomfield

*- The mod function is defined in the Integral class, and I'm not even
sure how to interpret that. It looks kind of like a Euclidean domain.
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