[Haskell-cafe] Does it violate the laws of Alternative/Monoid to implement empty/mempty with mzero from MonadPlus?

[Jaro Reinders]

The 'empty' value should always be the unit of <|>, that is specified in the 
documentation of the Alternative class. The problem starts when you build 
composite parsers. E.g. (char 'a' *> empty) does not need to be a unit of <|>. 
I thought of 'fixing' this by adding another law 'u <*> empty = empty', but 
that disregards all effects that u can have.

On 10/27/20 10:26 AM, YueCompl via Haskell-Cafe wrote:
> In [1], Alternative is said being most commonly considered to form a monoid, so that:
> 
> 
> ```hs
> -- empty is a neutral element
> empty <|> u  =  u
> u <|> empty  =  u
> ```
> 
> In my particular case wrt Megaparsec, when the artifact parser evaluates to `empty` at eof, I suppose the outer `many` should evaluate to whatsoever previously parsed, but current implementation of Megaparsec makes it conditional:
> 
> *) in case the parser hasn't consumed any input, it works the way as expected
> *) incase the parser has consumed some input (whitespaces), the outer `many` throws error
> 
> So can I say this is a violation regarding [1]?
> 
> Best regards,
> Compl
> 
> 
>> On 2020-10-27, at 04:18, Olaf Klinke <olf at aatal-apotheke.de> wrote:
>>
>> I used to think that an Alternative is just an Applicative which is
>> also a Monoid but apparently there is no consensus about this [1,2].
>> Actually it kind of makes sense to make the 'empty' parser fail:
>> Consider the parser combinator
>>
>> choice = Data.Foldable.asum = foldr (<|>) empty
>>
>> which folds over a list of Alternatives. Its semantics can be regarded
>> analogous to 'any' for a list of Booleans, and in the latter the empty
>> list evaluates to False.
>> Put differently: The parser (p <|> q) matches at least as many inputs
>> than either p or q. Hence the neutral element for <|> ought to be the
>> parser that matches the least amount of inputs, but a parser that
>> succeeds on the empty string _does_ match some input. It would be the
>> neutral element for the monoid operation that concatenates parsers.
>>
>> Olaf
>>
>> [1] https://en.wikibooks.org/wiki/Haskell/Alternative_and_MonadPlus
>> [2] https://wiki.haskell.org/MonadPlus
>>
>>
> 
> 
> 
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