Proposal: Functor and friends for the wrappers in Data.Monoid

[Oleg Grenrus]

And there are the ticket and the patch:

https://ghc.haskell.org/trac/ghc/ticket/10107
https://phabricator.haskell.org/D673


> On 22 Feb 2015, at 12:07, Oleg Grenrus <oleg.grenrus at iki.fi> wrote:
> 
> To clarify the discussion:
> 
> Let's add the following instances:
> 
> A: Functor, Foldable, Traversable to Sum, Product, Dual, First, and Last
> B: Data to everything in Data.Monoid (except Endo): Sum, Product, Dual, First and Last, All, Any, Alt
> C: Applicative, Monad, MonadFix to Sum, Product, Dual, First and Last
> D: Data to Identity
> 
> All seem to agree on A and B, C is "not sure", and D is new item.
> 
> - Oleg
> 
>> On 21 Feb 2015, at 17:34, Oleg Grenrus <oleg.grenrus at iki.fi> wrote:
>> 
>> I propose to add Functor, Applicative, Monad, Foldable, and Traversable and maybe even MonadFix instances to wrapper newtypes in the Data.Monoid module.
>> The same way as in the semigroups package, e.g. https://hackage.haskell.org/package/semigroups-0.16.1/docs/Data-Semigroup.html#t:Min <https://hackage.haskell.org/package/semigroups-0.16.1/docs/Data-Semigroup.html#t:Min>
>> 
>> Basically:
>> 
>> instance Functor Sum where
>> fmap f (Sum x) = Sum (f x)
>> 
>> instance Foldable Sum where
>> foldMap f (Sum a) = f a
>> 
>> instance Traversable Sum where
>> traverse f (Sum a) = Sum <$> f a
>> 
>> instance Applicative Sum where
>> pure = Sum
>> a <* _ = a
>> _ *> a = a
>> Sum f <*> Sum x = Sum (f x)
>> 
>> instance Monad Sum where
>> return = Sum
>> _ >> a = a
>> Sum a >>= f = f a
>> 
>> instance MonadFix Sum where
>> mfix f = fix (f . getSum)
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