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

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 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:

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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

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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

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