[Haskell-beginners] Re: Simplifying code

[Ertugrul Soeylemez]

Patrick LeBoutillier <patrick.leboutillier at gmail.com> wrote:

> > Sure. If you don't mind that the mutations come in a different
> > order, one thing that works wonders is "sequence",
> >
> > sequence :: Monad m => [m a] -> m [a]
> >
> > In particular, for m = [], sequence :: [[a]] -> [[a]]. Then, knowing what
> > sequence does, we can write
> >
> > import Control.Monad (sequence)
> >
> > generateAll :: String -> [String]
> > generateAll word = sequence (map f word)
> >     where
> >     f c = case lookup c leat of
> >                Just r  -> [c,r]
> >                Nothing -> [c]
>
> That's very nice!
>
> One question though: In the docs sequence is described as:
>
>   "Evaluate each action in the sequence from left to right, and
> collect the results."
>
> How is one supposed to deduce what the behavior will be for the list
> monad (besides looking at the source)?

Intuitively it's very easy to understand and makes perfect sense, if you
interpret the list monad as nondeterminism:

  sequence [c1,c2,c3] = do
    x1 <- c1
    x2 <- c2
    x3 <- c3
    return [x1,x2,x3]

  sequence ["ab", "cd", "ef"] = do
    x1 <- "ab"
    x2 <- "cd"
    x3 <- "ef"
    return [x1,x2,x3]
  = ["ace", "acf", "ade", "adf", "bce", "bcf", "bde", "bdf"]

In this code x1 stands for all results of c1, x2 for all results of c2
and x3 for all results of c3.  It's a convenient way of doing list
comprehension without syntactic sugar.  See also mapM and replicateM,
which have interesting behaviours in the list monad.


Greets
Ertugrul


-- 
nightmare = unsafePerformIO (getWrongWife >>= sex)
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