On 2020-10-27, at 17:26, YueCompl via Haskell-Cafe <haskell-cafe@haskell.org> 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@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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