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Conal Elliott | 2 Dec 18:57

Proposal: Max and Min for Monoid (ticket # 1952)

I'd like to add two instances to Data.Monoid, alongside of All/Any, Sum/Product, and First/Last.

Here's a current instance (as a style example):

-- | Boolean monoid under conjunction.
newtype All = All { getAll :: Bool }
deriving (Eq, Ord, Read, Show, Bounded)

instance Monoid All where
mempty = All True
All x `mappend` All y = All (x && y)

My proposed addition:

-- | 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)

-- | Ordered monoid under 'min'.
newtype Min a = Min { getMin :: a }
deriving (Eq, Ord, Read, Show, Bounded)

instance (Ord a, Bounded a) => Monoid (Min a) where
mempty = Min minBound
Min a `mappend` Min b = Min (a `min` b)

I have a niggling uncertainty about the Ord & Bounded instances for Min a? Is there a reason flip the a ordering instead of preserving it?

Suggested review period: two weeks (ending December 16).

Comments?

  - Conal
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Ian Lynagh | 2 Dec 20:26
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Re: Proposal: Max and Min for Monoid (ticket # 1952)

On Sun, Dec 02, 2007 at 09:57:50AM -0800, Conal Elliott wrote:
> 
> instance (Ord a, Bounded a) => Monoid (Min a) where
> 	mempty = Min minBound

I think you mean:

    mempty = Min maxBound

> 	Min a `mappend` Min b = Min (a `min` b)

Thanks
Ian
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Conal Elliott | 2 Dec 21:04

Re: Proposal: Max and Min for Monoid (ticket # 1952)

oops!  copy/paste/edit error.  thanks for catching. 

On Dec 2, 2007 11:26 AM, Ian Lynagh <igloo <at> earth.li> wrote:
On Sun, Dec 02, 2007 at 09:57:50AM -0800, Conal Elliott wrote:
>
> instance (Ord a, Bounded a) => Monoid (Min a) where
>       mempty = Min minBound

I think you mean:

   mempty = Min maxBound

>       Min a `mappend` Min b = Min (a `min` b)


Thanks
Ian

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Ross Paterson | 3 Dec 00:25
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Re: Proposal: Max and Min for Monoid (ticket # 1952)

On Sun, Dec 02, 2007 at 09:57:50AM -0800, Conal Elliott wrote:
> My proposed addition:
> 
> -- | 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)

Funny, I was thinking of proposing a Max type that adjoined a synthetic
identity, as we did in the finger tree paper:

data Max a = NoMax | Max a
	deriving (Eq, Ord, Read, Show)

instance Ord a => Monoid (Max a) where
	mempty = NoMax
	NoMax `mappend` b = b
	a `mappend` NoMax = a
	Max x `mappend` Max y = Max (x `max` y)

and similarly for Min.  One could even define

	getMax :: Bounded a => Max a -> a
	getMax NoMax = minBound
	getMax (Max x) = x
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Isaac Dupree | 3 Dec 17:34

Re: Proposal: Max and Min for Monoid (ticket # 1952)

Ross Paterson wrote:
> Funny, I was thinking of proposing a Max type that adjoined a synthetic
> identity, as we did in the finger tree paper:
> 
> data Max a = NoMax | Max a
> 	deriving (Eq, Ord, Read, Show)
> 
> instance Ord a => Monoid (Max a) where
> 	mempty = NoMax
> 	NoMax `mappend` b = b
> 	a `mappend` NoMax = a
> 	Max x `mappend` Max y = Max (x `max` y)
> 
> and similarly for Min.  One could even define
> 
> 	getMax :: Bounded a => Max a -> a
> 	getMax NoMax = minBound
> 	getMax (Max x) = x

I was thinking you could get that with some version of the (Maybe (Max 
a)) Monoid, but you are right: your version doesn't require (a) to be 
Bounded, thus works with Integers etc.

Isaac
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Isaac Dupree | 3 Dec 17:45

Re: Proposal: Max and Min for Monoid (ticket # 1952)

Ross Paterson wrote:
> data Max a = NoMax | Max a
> 	deriving (Eq, Ord, Read, Show)

> and similarly for Min.

data Min a = Min a | NoMin
so that the deriving Ord works as expected

The newtypes don't add a possible bottom, but data does... should (Max 
undefined) be non-bottom, or should the data types have strictness 
annotations perhaps?

Isaac
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Conal Elliott | 3 Dec 21:38

Re: Proposal: Max and Min for Monoid (ticket # 1952)

Similarly, I'm using the following to get around type parameters that don't provide Bounded:

data AddBounds a = MinBound | NoBound a | MaxBound
  deriving (Eq, Ord, Read, Show)

instance Bounded (AddBounds a) where
  minBound = MinBound
  maxBound = MaxBound


On Dec 2, 2007 3:25 PM, Ross Paterson <ross <at> soi.city.ac.uk> wrote:
On Sun, Dec 02, 2007 at 09:57:50AM -0800, Conal Elliott wrote:
> My proposed addition:
>
> -- | 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)

Funny, I was thinking of proposing a Max type that adjoined a synthetic
identity, as we did in the finger tree paper:

data Max a = NoMax | Max a
       deriving (Eq, Ord, Read, Show)

instance Ord a => Monoid (Max a) where
       mempty = NoMax
       NoMax `mappend` b = b
       a `mappend` NoMax = a
       Max x `mappend` Max y = Max (x `max` y)

and similarly for Min.  One could even define

       getMax :: Bounded a => Max a -> a
       getMax NoMax = minBound
       getMax (Max x) = x
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Gmane