Laziness is not always good
Generally, since Haskell is a non-strict language, one should try to make a function least strict.
This is in many cases the best semantics and the most efficient implementation.
However, here is an important exception from the rule:
Monoid instance of the null type
mempty = () mappend _ _ = ()
These functions are least strict, but have a subtle problem:
They do not generally satisfy the monoid laws.
mempty must be the identity element with respect to
forall a. mappend mempty a = a forall a. mappend a mempty = a
You find that it is not
mappend mempty undefined = undefined,
mappend mempty undefined = mempty.
Is this academic nitpicking or practically relevant?
I think it is the latter one, because a
Monoid instance implicitly promises
that monoid laws can be applied in every case.
A programmer expects that every occurence of
mappend mempty a can be safely replaced by
You might even create an optimizer rule doing this.
The above implementation of
mappend however evaluates its operands lazily,
and this gets lost when the optimization is applied.
The solution to this to define
mempty = () mappend () () = () force :: () -> () force _ = ()
mappend (force a) (force b)
mappend a b.
If you find that example too academic, you can choose any other data type with one constructor instead.