[L06 MoreParser] Questions - SPOILER ALERT

[Riaan Rottier]

Question about Exercise 6

-- Write a function that parses the given string (fails otherwise).

-- ~~~ Use is and mapM ~~~

So I blindly tried the hint and got 

string ::  String  -> Parser String

string = mapM is

Which worked!  Can someone please explain to me why it works.

R

[Tony Morris]

The mapM function is sometimes also called traverse.

It is well described in this paper:
http://www.cs.ox.ac.uk/jeremy.gibbons/publications/iterator.pdf

Or if you prefer Scala:
http://etorreborre.blogspot.com/2011/06/essence-of-iterator-pattern.html‎

--
Tony Morris
http://tmorris.net/

[Tony Morris]

On 30/07/13 20:40, Riaan Rottier wrote:

You might also notice that mapM has the same type as map, but with 'm'
appearing in every return position.

map :: (a -> b) -> [a] -> [b]
mapM :: (a -> m b) -> [a] -> m [b]

This is the same pattern as was seen in earlier functions:

filter :: (a -> Bool) -> [a] -> [a]
filterM :: (a -> m Bool) -> [a] -> m [a]

replicate :: Int -> a -> [a]
reeplicate :: Int -> a -> m [a]

find :: (a -> Bool) -> [a] -> Maybe a
findM :: (a -> m Bool) -> [a] -> m (Maybe a)

[Riaan Rottier]

Thank you, I only followed about 20% of the paper but it seems like we have 

mapM = sequencePaser . fmap f

Am I on the right track?

R

[Tony Morris]

Yes, mapM is indeed fmap then sequence.

Also, sequence is mapM id.

In other words, mapM and sequence have the same power.