Conor McBride writes:
> Jan-Willem Maessen - Sun Labs East wrote:
> > Tomasz Zielonka wrote:
> >
> >>I found it useful recently, when I needed zip functions for Trees -
> >>this way I didn't have to define functions for 3 trees, 4 trees,
> >>and so on.
> >
> >
> > Note also that:
> >
> > repeat f `zwApply` xs = map f xs
> >
> > When cooking up my own collection-y things (including splittable
> > supplies, for example), I generally provide fmap and an equivalent
> > of zwApply (a generic repeat is not quite so simple or useful).
> > It's a nice little idiom, and a recommend it highly.
> ^^^^^
>
> Funny you should choose that word:
>
> http://www.mail-archive.com/haskell@haskell.org/msg15073.html
>
> saves me banging the same old drum.
Now that I think about it, you can generalize the trick I mentioned
elsewhere to work over any
Idiom/Sequence/more-than-a-functor-not-yet-a-monad thingy.
> class Sequence f where
> unit :: a -> f a
> (<*>) :: f (a -> b) -> f a -> f b
>
> liftN :: Sequence f => (f a -> b) -> a -> b
> liftN d f = d (unit f)
>
> suc :: Sequence f => (f b -> c) -> f (a -> b) -> f a -> c
> suc d f x = d (f <*> x)
>
> zero = id
>
> one :: Sequence f => f (a -> b) -> f a -> f b
> one = suc zero
>
> two :: Sequence f => f (a -> b -> c) -> f a -> f b -> f c
> two = suc one
>
>
> newtype L1 a = L1 { unL1 :: [a] }
> newtype L2 a = L2 { unL2 :: [a] }
>
>
> instance Idiom L1 where
> unit x = L1 [x]
> L1 fs <*> L1 xs = L1 [ f x | f <- fs, x <- xs ]
>
> instance Idiom L2 where
> unit x = L2 (repeat x)
> L2 fs <*> L2 xs = L2 (zipWith ($) fs xs)
*Main> unL1 $ liftN two (,) (L1 [1,2,3]) (L1 "abc")
[(1,'a'),(1,'b'),(1,'c'),(2,'a'),(2,'b'),(2,'c'),(3,'a'),(3,'b'),(3,'c')
]
*Main> unL2 $ liftN two (,) (L2 [1,2,3]) (L2 "abc")
[(1,'a'),(2,'b'),(3,'c')]
--
David Menendez <[EMAIL PROTECTED]> | "In this house, we obey the laws
<http://www.eyrie.org/~zednenem> | of thermodynamics!"
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