# Proposal: Max and Min for Monoid

Conal Elliott conal at conal.net
Thu Sep 23 14:25:50 EDT 2010

```I encountered exactly this issue in my use of the Max & Min monoids in
Reactive.  I wanted to allow already-bounded types to use their own minBound
for Max and maxBound for Min, and also allow unbounded types to be used.
So, rather than entangling bound addition with Max & Min, I defined
AddBounds type wrapper, which is *orthogonal* to Max & Min.  If your type is
already Bounded, then use my simple Max & Min wrappers directly.  If not (as
in Reactive's use), compose Max or Min with AddBounds.

I'm sorry I didn't think to mention this useful composition the Max & Min
trac ticket.

- Conal

On Thu, Sep 23, 2010 at 10:47 AM, Gregory Collins
<greg at gregorycollins.net>wrote:

> Felipe Lessa <felipe.lessa at gmail.com> writes:
> > On Thu, Sep 23, 2010 at 12:58 PM, Jake McArthur <jake.mcarthur at gmail.com>
> wrote:
> >
> >>>    -- | Ordered monoid under 'max'.
> >>>    newtype Max a = Max { getMax :: a }
> >>>            deriving (Eq, Ord, Read, Show, Bounded)
> >>>
> >>>    instance (Ord a, Bounded a) => Monoid (Max a) where
> >>>            mempty = Max minBound
> >>>            Max a `mappend` Max b = Max (a `max` b)
> >
> > Why should we prefer this monoid over
> >
> >> data Max a = Minimum | Max a
> >>              deriving (Eq, Ord, Read, Show)
> >>
> >> instance Ord a => Monoid (Max a) where
> >>   mempty = Minimum
> >>   Minimum `mappend` x   = x
> >>   x `mappend` Minimum   = x
> >>   Max a `mappend` Max b = Max (a `max` b)
>
> You're right, the original wouldn't fly because there are unbounded
> types (like Integer) that you'd like to be able to use with Max/Min.
>
> Rather than your proposal I would suggest that Max/Min mirror
> the existing First/Last, namely:
>
>    newtype Max a = Max { getMax :: Maybe a }
>       deriving (Eq, Ord, Read, Show)
>
>    instance (Ord a) => Monoid (Max a) where
>         mempty  = Max Nothing
>        mappend = max
>
> G
> --
> Gregory Collins <greg at gregorycollins.net>
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