[Haskell-cafe] guards in applicative style

[Brent Yorgey]

Lorenzo is correct, but actually for the wrong reason. =) The *type*
of guard is a historical accident, and the fact that it requires
MonadPlus doesn't really tell us anything.  Let's take a look at its
implementation:

  guard           :: (MonadPlus m) => Bool -> m ()
  guard True      =  return ()
  guard False     =  mzero

'return' is not specific to Monad; we could just as well use 'pure'.
'mzero' is a method of 'MonadPlus' but there is no reason we can't use
'empty' from the 'Alternative' class.  So we could define

  guardA :: Alternative f => Bool -> f ()
  guardA True  = pure ()
  guardA False = empty

(As another example, consider the function 'sequence :: Monad m => [m
a] -> m [a]'.  Actually this function does not need Monad at all, it
only needs Applicative.)

However, guardA is not as useful as guard, and it is not possible to
do the equivalent of the example shown using a list comprehension with
a guard.  The reason is that whereas monadic computations can make use
of intermediate computed values to decide what to do next, Applicative
computations cannot.  So there is no way to generate values for x and
y and then pass them to 'guardA' to do the filtering.  guardA can only
be used to conditionally abort an Applicative computation using
information *external* to the Applicative computation; it cannot
express a condition on the intermediate values computed by the
Applicative computation itself.

-Brent

On Wed, Sep 12, 2012 at 03:52:03PM +0100, Lorenzo Bolla wrote:
> I'm no expert at all, but I would say "no".
> "guard" type is:
> guard :: MonadPlus m => Bool -> m ()
> 
> and "MonadPlus" is a monad "plus" (ehm...) mzero and mplus
> (http://en.wikibooks.org/wiki/Haskell/MonadPlus).
> On the other hand Applicative is "less" than a monad
> (http://www.haskell.org/haskellwiki/Applicative_functor), therefore
> "guard" as is cannot be defined.
> 
> But, in your specific example, with lists, you can always use "filter":
> filter (uncurry somePredicate) ((,) <$> list1 <*> list2 (somePredicate ???))
> 
> hth,
> L.
> 
> 
> On Wed, Sep 12, 2012 at 3:40 PM, felipe zapata <tifonzafel at gmail.com> wrote:
> >
> > Hi Haskellers,
> >
> > Suppose I have two list and I want to calculate
> > the cartesian product between the two of them,
> > constrained to a predicate.
> > In List comprehension notation is just
> >
> > result = [ (x, y) | x <- list1, y <-list2, somePredicate x y ]
> >
> > or in monadic notation
> >
> > result = do
> >  x <- list1
> >  y <- list2
> >  guard (somePredicate x y)
> > return $ (x,y)
> >
> > Then I was wondering if we can do something similar using an applicative style
> >
> > result = (,) <$> list1 <*> list2 (somePredicate ???)
> >
> > The question is then,
> > there is a way for defining a guard in applicative Style?
> >
> > Thanks in advance,
> >
> > Felipe Zapata.
> >
> >
> >
> > _______________________________________________
> > Haskell-Cafe mailing list
> > Haskell-Cafe at haskell.org
> > http://www.haskell.org/mailman/listinfo/haskell-cafe
> >
> 
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