[Haskell-cafe] [Haskell] Functor => Applicative => Monad

[Brent Yorgey]

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