I'm glad you liked it!
There's an interesting different way of doing the first half of your
derivation, using a helper function:
> transform t l = FM $ \f -> unFM l (t f)
It transforms the map function passed to foldMap.
The transform function has this property:
> transform a . transform b = transform (b . a)
flatten and fmap can both be written as transformers:
> flatten = transform foldMap
> fmap g = transform (. g)
Now we can derive:
(>>= g)
= flatten . fmap g
= transform foldMap . transform (. g)
= transform ((. g) . foldMap)
= transform (\f -> foldMap f . g)
= FM $ \f -> unFM m (foldMap f . g)
Other examples of transform are:
filter p = transform (\f e -> if p e then f e else mempty)
(<*> xs) = transform (\f g -> unFM xs (f . g))
Unfortunately I couldn't get this code to type-check, so the library
doesn't use transform.
Sjoerd
On Jun 18, 2009, at 11:28 AM, Sebastian Fischer wrote:
On Jun 18, 2009, at 9:57 AM, Sjoerd Visscher wrote:
I am pleased to announce the first release of Data.FMList, lists
represented by their foldMap function: [...]
http://hackage.haskell.org/package/fmlist-0.1
cool!
Just for fun: a derivation translating between different
formulations of monadic bind.
m >>= g
= flatten (fmap g m)
= FM $ \f -> unFM (fmap g m) (foldMap f)
= FM $ \f -> unFM (FM $ \f' -> unFM m (f' . g)) (foldMap f)
= FM $ \f -> (\f' -> unFM m (f' . g)) (foldMap f)
= FM $ \f -> unFM m (folfMap f . g) -- your definition
= FM $ \f -> unFM m (flip unFM f . g)
= FM $ \f -> unFM m (\x -> flip unFM f (g x))
= FM $ \f -> unFM m (\x -> unFM (g x) f) -- like
continuation monad
Cheers,
Sebastian
--
Underestimating the novelty of the future is a time-honored tradition.
(D.G.)
--
Sjoerd Visscher
[email protected]
_______________________________________________
Haskell-Cafe mailing list
[email protected]
http://www.haskell.org/mailman/listinfo/haskell-cafe
