[Haskell-cafe] Re: What are the MonadPlus laws?
zednenem at psualum.com
Wed Jan 26 00:57:33 EST 2005
Ashley Yakeley writes:
> In article <F9A40F60-6EFD-11D9-8550-000A95F0ED78 at jellybean.co.uk>,
> Jules Bean <jules at jellybean.co.uk> wrote:
> > So, anyone? What are the laws that MonadPlus is supposed to satisfy?
> These are what I think they should be:
> mplus mzero a = a
> mplus a mzero = a
> mplus (mplus a b) c = mplus a (mplus b c)
> mzero >>= a = mzero
> (mplus a b) >>= c = mplus (a >>= c) (b >>= c)
> These are what is found in Martin and Gibbons paper, even as they're
> wrong that Maybe can follow them.
Philip Wadler listed those as the laws he "would usually insist on" in a
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
David Menendez <zednenem at psualum.com> <http://www.eyrie.org/~zednenem/>
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