[Haskell-beginners] List Function

[Edward Z. Yang]

Excerpts from Brent Yorgey's message of Wed Apr 29 23:41:03 -0400 2009:
> Others' answers are probably more helpful for learning, but I also
> wanted to point out that there is a Prelude function that does
> something close to this (assuming you meant [4,5,6]), namely,
> 'sequence'.
> 
>   Prelude> sequence [ [1,2,3], [4,5,6] ]
>   [[1,4],[1,5],[1,6],[2,4],[2,5],[2,6],[3,4],[3,5],[3,6]]
>   Prelude> sequence [ [1,2], [3,4,5], [6,7] ]
>  
> [[1,3,6],[1,3,7],[1,4,6],[1,4,7],[1,5,6],[1,5,7],[2,3,6],[2,3,7],[2,4,6],[2,4,7]
> ,[2,5,6],[2,5,7]]
> 
> However, explaining how/why sequence does this requires understanding
> the list monad, which you may or may not want to tackle at this point.

Interesting! According to Hoogle, the sequence function evaluates each
monad and then collects the results. I know evaluating a list monad returns
a list, but what do they mean by "collect"?

> If you import 'Control.Applicative' you can even do exactly what you
> wanted, with pairs and all:
> 
>   Prelude Control.Applicative> liftA2 (,) [1,2,3] [4,5,6]
>   [(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)]
> 
> Here, liftA2 is applying the function (,) to every possible pair of
> values from the two lists.

I'm not even going to try to understand that now.

Cheers,
Edward