According to the documentation, rem and mod must satisfy the following laws: -- > (x `quot` y)*y + (x `rem` y) == x rem -- > (x `div` y)*y + (x `mod` y) == x mod https://hackage.haskell.org/package/base-4.8.0.0/docs/src/GHC-Real.html Note, however, that there is a case when quot and div result in an arithmetic overflow: Prelude> (minBound :: Int) `quot` (-1) *** Exception: arithmetic overflow Prelude> (minBound :: Int) `div` (-1) *** Exception: arithmetic overflow while rem and mod don't: Prelude> (minBound :: Int) `rem` (-1) 0 Prelude> (minBound :: Int) `mod` (-1) 0 Is this a mistake? For the record, I'm aware of the safeint package, which raises the error for rem and mod, and this ticket: https://ghc.haskell.org/trac/ghc/ticket/8695