Expected behavior of "deriving Ord"?

I have an algebraic data type (not newtype) that derives Ord: data AddBounds a = MinBound | NoBound a | MaxBound deriving (Eq, Ord, Read, Show) I was hoping to get a min method defined in terms of the min method of the type argument (a). Instead, I think GHC is producing something in terms of compare or (<=). Maybe it's defaulting min altogether. What is the expected behavior in (a) the language standard and (b) GHC? The reason I care is that my type parameter a turns out to have partial information, specifically lower bounds. The type of min allows this partial info to be used in producing partial info about the result, while the type of (<=) and compare do not. Thanks, - Conal