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

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 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