Alson Kemp Alson.Kemp at sloan.mit.edu
Fri Mar 11 15:47:04 EST 2005

```All,
I'm having substantial difficulty understanding Jeff Newbern's Example
7.  Would love some help.
My questions are: How does liftM2 know to lift fn into the _List_ monad?
(Because it's the only possibility?)  After fn is lifted, where is "bind"
used in allCombinations?

Basically, I'd some a detailed explanation of how allCombinations works,
cause I'm not grokking it...

- Alson
---

-- allCombinations returns a list containing the result of

-- folding the binary operator through all combinations

-- of elements of the given lists

-- For example, allCombinations (+) [[0,1],[1,2,3]] would be

--   [0+1,0+2,0+3,1+1,1+2,1+3], or [1,2,3,2,3,4]

-- and allCombinations (*) [[0,1],[1,2],[3,5]] would be

--   [0*1*3,0*1*5,0*2*3,0*2*5,1*1*3,1*1*5,1*2*3,1*2*5], or
[0,0,0,0,3,5,6,10]

allCombinations :: (a -> a -> a) -> [[a]] -> [a]

allCombinations fn []     = []

allCombinations fn (l:ls) = foldl (liftM2 fn) l ls

-- print an example

showExample :: (Show a) => String -> (a -> a -> a) -> [[a]] -> IO ()

showExample opName op ls = do putStrLn \$ "opName over " ++ (show ls) ++ " =
"

putStrLn \$ "  " ++ (show (allCombinations op
ls))

-- shows a few examples of using allCombinations

main :: IO ()

main = do showExample "+" (+)   [[0,1],[1,2,3]]

showExample "*" (*)   [[0,1],[1,2],[3,5]]

showExample "/" div   [[100, 45, 365], [3, 5], [2, 4], [2]]

-------------- next part --------------
An HTML attachment was scrubbed...