[Haskell-cafe] [Haskell] Functor => Applicative => Monad
Brent Yorgey
byorgey at seas.upenn.edu
Wed Dec 15 18:48:54 CET 2010
On Wed, Dec 15, 2010 at 06:25:30PM +0100, Maciej Piechotka wrote:
> On Wed, 2010-12-15 at 13:51 +0200, John Smith wrote:
> > On 15/12/2010 11:39, Lennart Augustsson wrote:
> > > Any refutable pattern match in do would force MonadFail (or MonadPlus if you prefer). So
> > > 1. (MonadFail m) => a -> m a, \ a -> return a
> > > 2. (MonadFail m) => m a, mfail "..."
> > > 3. (MonadFail m) => Maybe a -> m a, \ a -> case a of Nothing -> mfail "..."; Just x -> return x
> > > 4. (Monad m) => a -> b -> m a, \ a b -> return a
> > > 5. (Monad m) => (a, b) -> m a, \ (a, b) -> return a
> > >
> > > As far as type inference and desugaring goes, it seems very little would have to be changed in an implementation.
> >
> > Is there a need for a MonadFail, as distinct from mzero? fail always seems to be defined as error in ordinary monads,
> > and as mzero in MonadPlus (or left at the default error).
>
> Not all types can implement mplus to begin with even if they can have
> 'zero' type. For example technically Maybe breaks the laws while still
> having useful fail:
>
> (guard . even) =<< (Just 1 <|> Just 2)
> (guard . even) =<< Just 1
> guard (even 1)
> guard False
> Nothing
> /=
> Just ()
> Nothing <|> Just ()
> guard False <|> guard True
> (guard (even 1)) <|> (guard (even 2))
> ((guard . even) =<< Just 1) <|> ((guard . even) =<< Just 2)
But that depends on what laws you choose for MonadPlus. See
http://www.haskell.org/haskellwiki/MonadPlus .
-Brent
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