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

[YueCompl]

Isn't  'u <*> empty = empty' resembles MonadPlus?

mzero >>= f  =  mzero
v >> mzero   =  mzero

Since ParsecT also has a MonadPlus instance, can we have different implementations of `empty` and `mzero` to have these 2 separate semantics expressible:

*) parse to ignored result from some input
*) un-parsable (input consumed or not is irrelevant as to err out anyway)


parse to no significant result
unparsable
consumed input
empty -> throw ??
mzero -> throw
no input consumed
empty -> nothrow
mzero -> throw

I'd much like the behavior above `empty -> throw ??` changed to `empty -> nothrow` 

> On 2020-10-27, at 17:47, Jaro Reinders <jaro.reinders at gmail.com> wrote:
> 
> 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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