How is this different from the list monad without mzero/[]? - Ryan Ingram

Well, the pointed-set monad is different from the nonempty-set monad, but I guess the pointed-list monad is no different from the nonempty-list monad…

An alternative pointed list monad:

data Pointed a = Pointed { fore::a, back::[a] } deriving (Eq,Show)

instance Functor Pointed where
    fmap f (Pointed a bs) = Pointed (f a) (map f bs)

instance Monad Pointed where
    return a = Pointed a []
    Pointed a bs >>= f = let u = f a in Pointed (fore u) (back u ++ map (fore . f) bs)

test = Pointed 3 [4] >>= \x -> Pointed x [x*10,x*20]

It’s sort of additive where the usual list is multiplicative. It can be used to search trees in which there is a ‘spine’ and you only want to consider leaves a distance of at most one from that spine - if you see what I mean. Like matching strings with up to one error.

– Dan Piponi