Excerpts from Edward Z. Yang's message of Wed Apr 29 22:38:40 -0400 2009:

Excerpts from Nathan Holden's message of Wed Apr 29 22:25:43 -0400 2009:

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Sending two lists, [1,2,3] and [2,3,4] it would return [(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)]. I managed to code my way into returning a list of lists, which works. But it seemed like a very basic list/matrix function, so I honestly believe that the Haskell designers probably would've put it in.

Did you mean [1,2,3] and [4,5,6]?

To elaborate, a list comprehension is what you want, if you want this function to do what I think you want it to do. Prelude> let f as bs = [(a,b) | a <- as, b <- bs] Prelude> f [1,2,3] [4,5,6] [(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)] Cheers, Edward

Occurs to me I said two ways, and only gave one, the one I gave was the tougher way. The easiest way is to use a list comprehension, viz: toPairs xs ys = [(x,y) | x <- xs, y <- ys] This is nice and succint, you can think of it (assuming you're familiar with it) as set-builder notation. The '[' and ']' brackets are the set brackets '{' and '}'. '<-' is roughly like the element symbol. You can even add constraints (called guards), like so: foo xs ys = [x / y | x <- xs, y <- ys, y /= 0] Joe Fredette wrote:

So, two ways you could do it.

I assume your current function looks like:

toPairs :: [a] -> [a] -> [[a]] toPairs [] _ = [] toPairs (x:xs) ls = (zip (\y -> (x,y)) ls) : (toPairs xs ls)

This returns something like:

toPairs [1,2] [3,4] ===> [[(1,3),(1,4)],[(2,3),(2,4)]]

We want a function that takes this list-of-lists to a list. We can certainly see the type as:

foo :: [[a]] -> [a]

`foo` would have to take all the elements of each list, and put it in a new one. We know of a function which combines the elements of two lists, (++) so really, our foo function would do:

foo [] = [] foo (x:xs) = x ++ foo xs

concatenating all of the lists together in order. But this is just a fold, we can call foo:

foo = foldr (++) -- or foldl would work too.

foldr is just the pattern above, abstracted away to a convenient function.

Of course, this function comes up all the time, so we have one in the prelude, it's called. `concat`. and if you look up the source on hoogle, I believe you'll find the above.

Nathan Holden wrote:

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I don't know what you'd call it. Is there a function in any of the basic functions that does this something like this:

Sending two lists, [1,2,3] and [2,3,4] it would return [(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)]. I managed to code my way into returning a list of lists, which works. But it seemed like a very basic list/matrix function, so I honestly believe that the Haskell designers probably would've put it in. ------------------------------------------------------------------------

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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

Edward Z. Yang wrote:

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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"?

There is also sequence_ which does not collect the results, but throws them away. Prelude> sequence_ [ [1,2,3], [4,5,6] ] [(),(),(),(),(),(),(),(),()] (Also, concerning terminology, sequence evaluates each monadic action. You can't evaluate a monad, it's a type constructor, not a function or value.)

...

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.

Also known as liftM2 (,) [1,2,3] [4,5,6] Which is the same as do x <- [1,2,3] y <- [4,5,6] return (x,y) Regards, apfelmus -- http://apfelmus.nfshost.com

On Apr 29, 2009, at 23:57 , Edward Z. Yang wrote:

Excerpts from Brent Yorgey's message of Wed Apr 29 23:41:03 -0400 2009:

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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]]

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"?

In the list monad, "collect" means "concatenate". -- brandon s. allbery [solaris,freebsd,perl,pugs,haskell] allbery@kf8nh.com system administrator [openafs,heimdal,too many hats] allbery@ece.cmu.edu electrical and computer engineering, carnegie mellon university KF8NH