-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 I am wondering if it possible to generalise catMaybes: (Something f, SomethingElse t) => t (f a) -> t a I have being doing some gymnastics with Traversable and Foldable and a couple of other things from category-extras to no avail. Perhaps someone else's brain is molded into an appropriate shape to reveal an answer! - -- Tony Morris http://tmorris.net/ -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.10 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org/ iEYEARECAAYFAk0n0lwACgkQmnpgrYe6r6155gCeLjYizQ/5w1r2qkecbEqiQqq5 ihIAn1bmmK/qNFxM2sSusqjJu/g2/lH7 =+SdM -----END PGP SIGNATURE-----
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 On 1/7/11 21:56 , Tony Morris wrote:
I am wondering if it possible to generalise catMaybes:
(Something f, SomethingElse t) => t (f a) -> t a
I have being doing some gymnastics with Traversable and Foldable and a couple of other things from category-extras to no avail. Perhaps someone else's brain is molded into an appropriate shape to reveal an answer!
Looks to me like you want something like:
mtraverse :: (Traversable t, Monoid m) => t m -> m mtraverse xs = traverse mappend (mempty:xs)
or possibly the same kind of thing using MonadPlus instead of Monoid. _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe - -- brandon s. allbery [linux,solaris,freebsd,perl] allbery@kf8nh.com system administrator [openafs,heimdal,too many hats] allbery@ece.cmu.edu electrical and computer engineering, carnegie mellon university KF8NH -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.11 (Darwin) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org/ iEYEARECAAYFAk0n20AACgkQIn7hlCsL25V0MACeIJjbHmIjnABHxpykeVdcZ62f fS0AoL2xet/PpuvyuioWNvbzCTqWz5Z/ =2HGT -----END PGP SIGNATURE-----
On Fri, 7 Jan 2011, Brandon S Allbery KF8NH wrote:
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1
On 1/7/11 21:56 , Tony Morris wrote:
I am wondering if it possible to generalise catMaybes:
(Something f, SomethingElse t) => t (f a) -> t a
I have being doing some gymnastics with Traversable and Foldable and a couple of other things from category-extras to no avail. Perhaps someone else's brain is molded into an appropriate shape to reveal an answer!
Looks to me like you want something like:
mtraverse :: (Traversable t, Monoid m) => t m -> m mtraverse xs = traverse mappend (mempty:xs)
or possibly the same kind of thing using MonadPlus instead of Monoid.
This is not type-correct, isn't it? Foldable.fold has the type, that you propose. For me, the solutions of Dave Menendez make most sense: Generalize Maybe to Foldable and List to MonadPlus.
On 8 Jan 2011, at 11:14, Henning Thielemann wrote:
For me, the solutions of Dave Menendez make most sense: Generalize Maybe to Foldable and List to MonadPlus.
What has it to do with monads? There's no bind in sight. Alternative is certainly a more general alternative, but then I would say that, wouldn't I? Even that seems a tad too much. Cheers Conor
On Sat, 8 Jan 2011, Conor McBride wrote:
On 8 Jan 2011, at 11:14, Henning Thielemann wrote:
For me, the solutions of Dave Menendez make most sense: Generalize Maybe to Foldable and List to MonadPlus.
What has it to do with monads? There's no bind in sight.
I see a '>>=' in front of each of his expressions.
On 8 Jan 2011, at 15:27, Henning Thielemann wrote:
On Sat, 8 Jan 2011, Conor McBride wrote:
On 8 Jan 2011, at 11:14, Henning Thielemann wrote:
For me, the solutions of Dave Menendez make most sense: Generalize Maybe to Foldable and List to MonadPlus.
What has it to do with monads? There's no bind in sight.
I see a '>>=' in front of each of his expressions.
That'll teach me to wake up first. Sorry. If you have some m (f x), and you make an (m x) from each inner x, then you do need something joiny. Of course, there is an alternative generalisation. [] and Maybe are both Foldable, hence so is their composition. There's got to be a thing of type collapse :: (Foldable f, Alternative a) => f x -> a x which would do the job. Of course, anything which is both foldable and alternative certainly has a function with the type of join. Cheers Conor
On Sat, 8 Jan 2011, Conor McBride wrote:
Of course, there is an alternative generalisation.
[] and Maybe are both Foldable, hence so is their composition.
There's got to be a thing of type
collapse :: (Foldable f, Alternative a) => f x -> a x
which would do the job.
Nice! It would be collapse = Data.Foldable.foldr (\a b -> pure a <|> b) empty and with transformers:Data.Functor.Compose (or the one from TypeCompose) we get catMaybes = collapse . Compose
Of course, anything which is both foldable and alternative certainly has a function with the type of join.
join = collapse . Compose :-)
On Sat, Jan 8, 2011 at 12:05 PM, Conor McBride
On 8 Jan 2011, at 15:27, Henning Thielemann wrote:
On Sat, 8 Jan 2011, Conor McBride wrote:
On 8 Jan 2011, at 11:14, Henning Thielemann wrote:
For me, the solutions of Dave Menendez make most sense: Generalize Maybe to Foldable and List to MonadPlus.
What has it to do with monads? There's no bind in sight.
I see a '>>=' in front of each of his expressions.
That'll teach me to wake up first. Sorry.
If you have some m (f x), and you make an (m x) from each inner x, then you do need something joiny.
Of course, there is an alternative generalisation.
[] and Maybe are both Foldable, hence so is their composition.
There's got to be a thing of type
collapse :: (Foldable f, Alternative a) => f x -> a x
which would do the job.
Something along these lines, I'd imagine. collapse = foldr (\a b -> pure a <|> b) empty Then, to get catMaybes you could either use composition, or just write it out manually: doubleCollapse = foldr (\a b -> foldr (\c d -> pure c <|> d) empty a <|> b) empty :: (Foldable f, Foldable g, Alternative h) => f (g a) -> h a For the generalized catMaybes, f ~ h.
Of course, anything which is both foldable and alternative certainly has a function with the type of join.
Right, that's doubleCollapse when f ~ g ~ h.
Alternative and Foldable are both specified rather loosely, so it's
not clear how closely doubleCollapse approximates join.
In particular, are <|> and empty expected to form a monoid? If not, we
could define a list- or stream-like structure that uses alternation
instead of appending for (<|>). That would not behave at all like
join.
Right now, I suspect any type which has with a monoidal structure,
pure, and a fold that respects the monoid has a join.
That is, if you have:
foldMap f mempty = mempty
foldMap f (a `mappend` b) = foldMap f a `mappend` foldMap f b
then when f = pure you can take a structure apart and put it back
together piece by piece. I think that's enough to get you join.
Naturally, if you also have pure and fmap, you also have a monad.
--
Dave Menendez
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Thanks guys for all the solutions. A slight correction below. On 09/01/11 03:54, David Menendez wrote:
Naturally, if you also have pure and fmap, you also have a monad.
You have a pointed functor but not necessarily a monad. There are many pointed functors that are not monads. The paper, Applicative Programming with Effects (McBride, Paterson) lists a couple. - -- Tony Morris http://tmorris.net/ -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.10 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org/ iEYEARECAAYFAk0o4AgACgkQmnpgrYe6r62z4wCgk4A1njS5lLH3RHtxfnIkVGTL t3sAoKNm7HjVQyk/Gb1AL5LxahRHPmKN =5D4j -----END PGP SIGNATURE-----
On Sat, Jan 8, 2011 at 5:07 PM, Tony Morris
Thanks guys for all the solutions. A slight correction below.
On 09/01/11 03:54, David Menendez wrote:
Naturally, if you also have pure and fmap, you also have a monad.
You have a pointed functor but not necessarily a monad.
You perhaps missed the word "also". If you have join, and you also
have pure and fmap, then you have a monad.
That's admittedly a little fuzzy about what it means to have join,
since the laws join must satisfy are defined in terms of fmap and
pure.
--
Dave Menendez
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 On 1/8/11 07:11 , Conor McBride wrote:
On 8 Jan 2011, at 11:14, Henning Thielemann wrote:
For me, the solutions of Dave Menendez make most sense: Generalize Maybe to Foldable and List to MonadPlus.
What has it to do with monads? There's no bind in sight.
Alternative is certainly a more general alternative, but then I would say that, wouldn't I? Even that seems a tad too much.
That was my thought too, and no, I didn't actually test first, just tried to think out what he was doing. Bad idea when half asleep :/ - -- brandon s. allbery [linux,solaris,freebsd,perl] allbery@kf8nh.com system administrator [openafs,heimdal,too many hats] allbery@ece.cmu.edu electrical and computer engineering, carnegie mellon university KF8NH -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.11 (Darwin) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org/ iEYEARECAAYFAk0oln8ACgkQIn7hlCsL25WL1gCfepiOrw2ptUKah1KNj1vychnZ 1dMAoL2CmnbV2T/ravh6fuc8oyzlncrt =Hx/b -----END PGP SIGNATURE-----
On Fri, Jan 7, 2011 at 9:56 PM, Tony Morris
I am wondering if it possible to generalise catMaybes:
(Something f, SomethingElse t) => t (f a) -> t a
I have being doing some gymnastics with Traversable and Foldable and a couple of other things from category-extras to no avail. Perhaps someone else's brain is molded into an appropriate shape to reveal an answer!
This gets you part of the way there:
(>>= maybe mzero return) :: (MonadPlus m) => m (Maybe a) -> m a
I'm not sure what the SomethingElse should look like. One possibility
would be Foldable.
(>>= Data.Foldable.foldr (mplus . return) mzero)
:: (MonadPlus m, Foldable t) => m (t a) -> m a
I have a MonadPlus-to-Monoid wrapper I call MSum, so I could also write it,
(>>= getMSum . foldMap (MSum . return))
:: (MonadPlus m, Foldable t) => m (t a) -> m a
--
Dave Menendez
* Tony Morris
I am wondering if it possible to generalise catMaybes:
(Something f, SomethingElse t) => t (f a) -> t a
I have being doing some gymnastics with Traversable and Foldable and a couple of other things from category-extras to no avail. Perhaps someone else's brain is molded into an appropriate shape to reveal an answer!
For example, import Control.Applicative import Data.Foldable as F import Control.Monad.Writer cat' :: (Applicative list, Foldable list, Monoid (list a), Foldable maybe) => list (maybe a) -> list a cat' = fold . fmap (execWriter . F.mapM_ (\x -> tell (pure x))) However, this looks rather useless -- there are probably not many containers which can be substituted instead of 'list'. I think catMaybes deserves its own typeclass, which would represent "truncatable" structures: class Truncatable struct where catMaybes :: struct (Maybe a) -> Maybe a This would make perfect sense for Set, Map etc. -- Roman I. Cheplyaka :: http://ro-che.info/ Don't worry what people think, they don't do it very often.
On Sat, 8 Jan 2011, Roman Cheplyaka wrote:
I think catMaybes deserves its own typeclass, which would represent "truncatable" structures:
class Truncatable struct where catMaybes :: struct (Maybe a) -> Maybe a
But catMaybes has the type catMaybes :: struct (Maybe a) -> struct a for struct = []
* Henning Thielemann
On Sat, 8 Jan 2011, Roman Cheplyaka wrote:
I think catMaybes deserves its own typeclass, which would represent "truncatable" structures:
class Truncatable struct where catMaybes :: struct (Maybe a) -> Maybe a
But catMaybes has the type catMaybes :: struct (Maybe a) -> struct a for struct = []
Thanks, that was a typo. -- Roman I. Cheplyaka :: http://ro-che.info/ Don't worry what people think, they don't do it very often.
participants (6)
-
Brandon S Allbery KF8NH -
Conor McBride -
David Menendez -
Henning Thielemann -
Roman Cheplyaka -
Tony Morris