[Haskell-cafe] Re: What are the MonadPlus laws?

Jules Bean jules at jellybean.co.uk
Wed Jan 26 05:56:40 EST 2005

On 26 Jan 2005, at 05:57, David Menendez wrote:
> Philip Wadler listed those as the laws he "would usually insist on" in 
> a
> 1997 message[1].
>     [1] <http://www.dcs.gla.ac.uk/mail-www/haskell/msg00057.html>
> He also mentions two other possible, but problematic, laws:
>     m >>= \x -> mzero           == mzero
>     m >>= \x -> k x `mplus` h x == m >>= k `mplus` m >>= h
> The first doesn't hold when m is bottom. The second doesn't hold for
> lists.

Well I think the issue with bottom is not too upsetting.

The second holds 'up to reordering of the elements', I think?. If you 
consider lists as representing non-deterministic or multiple-valued 
computation, then it is quite natural to feel comfortable ignoring the 
ordering. (In effect, using lists as a model for multi-sets, which form 
a commutative monad?)

But it certainly looks like the IO instance for MonadPlus is badly 

Are there any interesting programming uses of MonadPlus apart from 
'calculations returning multiple values'.. i.e. 


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