You might be interested in another kind of Boolean-like types: Commutative monads. A monad is called commutative if the order of actions does not matter, i.e. if the following always holds. do { x <- mx; y <- my; return f x y} == do {y <- my; x <- mx; return f x y} For example, Maybe is commutative, and [] is up to permutation. For such a monad m consider the type m (). Observe that Maybe () is isomorphic to Bool. Can we derive some operations generically? Indeed,
true = return () (&&) = liftM2 const (||) = mplus false = mzero
I don't think it's by definition yet, but surely by convention, that this is a restricted form of true = pure () (&&) = (<*) (||) = (<|>) false = empty All of these functions require only an Applicative or an Alternative, and except for "true", they're all in the library. Which shows another reason to think twice before using a bool: Applicatives can be a better fit. They can often carry the question behind the bool and the value this question is about in one convenient structure. Cheers, MarLinn