[Haskell-cafe] Newbern's Example 7

[Alson Kemp]

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
---
import Monad



-- 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]]
 
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