[Haskell-cafe] monoids induced by Applicative/Alternative/Monad/MonadPlus?

[Mario Blažević]

On 13-08-22 04:04 PM, Petr Pudlák wrote:
> Or, if there are no such definitions, where would be a good place to add
> them?

	If they are to be added to the base libraries, the Data.Monoid module 
would be my choice.

	I did wish I had the AppMonoid instance on several occasions, when 
using various parser combinator libraries that don't support this 
reasonable instance of Monoid:

 >   numericLiteral = optionalMonoid (string "+" <|> string "-")
 >                    <> some digit
 >                    <> optionalMonoid (string "." <> some digit)


	The problem is, the AppMonoid newtype would not help in that situation 
unless it also implemented Applicative and Alternative class, as well as 
the parsing primitives. Without the latter, the above code would look 
like this:


 >   numericLiteral = optionalMonoid
                         (AppMonoid (string "+" <|> string "-"))
 >                    <> some (AppMonoid digit)
 >                    <> optionalMonoid (AppMonoid (string ".")
 >                                       <> some (AppMonoid digit))


	The point of the above is that I don't think there is enough 
justification for these newtypes. The Applicative and Alternative 
instances are typically used because of the primitives they come with, 
and newtype wrappings like AppMonoid and AltMonoid can't support those 
easily. Unless ekmett adds the appropriate instances to his parsers 
package, they would be too clumsy to use.


>
> Petr
>
> Dne 08/20/2013 06:55 PM, Petr Pudlák napsal(a):
>>
>> Dear Haskellers,
>>
>> are these monoids defined somewhere?
>>
>> |import  Control.Applicative
>> import  Data.Monoid
>>
>> newtype  AppMonoid  m a =AppMonoid  (m  a)
>> instance  (Monoid  a,Applicative  m) =>Monoid  (AppMonoid  m a)where
>>      mempty =AppMonoid  $ pure mempty
>>      mappend (AppMonoid  x) (AppMonoid  y) =AppMonoid  $ mappend <$> x <*> y
>> -- With the () monoid for `a` this becames the monoid of effects.
>>
>> newtype  AltMonoid  m a =AltMonoid  (m  a)
>> instance  Alternative  m =>Monoid  (AltMonoid  m a)where
>>      mempty =AltMonoid  empty
>>      mappend (AltMonoid  x) (AltMonoid  y) =AltMonoid  $ x <|> y|
>>
>> (and similarly for Monad/MonadPlus, until they become subclasses of
>> Applicative?)
>>
>> Best regards,
>> Petr
>>
>
>
>
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