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]]
