列表monad是否有任何实际用途不仅会滚动到FMAP?您什么时候使用bind bind fim list monad?
例如,您可以做[1,2,3] >>= return . ( + 1)
,但这与(+1) <$> [1,2,3]
相同 - 何时可以使用bind而不返回列表?
使用bint with返回与使用FMAP相当。确实,
fmap f m = m >>= return . f
无法用FMAP复制的绑定的用途正是不涉及返回使用的绑定。要为列表提供一个(希望)有趣的示例,让我们谈谈L系统。
l系统是由Aristid Lindenmeyer在1968年创建的。作为重写系统,它们从一个简单的对象开始,并使用一组重写规则或 Productions 。它们可用于生成分形和其他相似图像。一个无上下文,确定性的L系统(或D0L)由字母,公理和生产规则的集合定义。
对于我们的字母,我们将定义一种类型:
data AB = A | B deriving Show
对于我们的公理或启动状态,我们将使用 [A, B]
一词。
myAxiom = [A, B]
为了我们的规则,我们需要从单个字母到一系列字母的地图。这是AB -> [AB]
类型的函数。让我们使用此规则:
myRule :: AB -> [AB]
myRule A = [A, B]
myRule B = [A]
要应用该规则,我们必须使用其生产规则重写每个字母。我们必须同时对单词中的所有字母执行此操作。方便地,这正是>>=
在列表中所做的:
apply rule axiom = axiom >>= rule
现在,让我们将我们的规则应用于公理,在L系统中生成第一步:
> apply myRule myAxiom
> [A, B, A]
这是Lindenmeyer的原始L系统,用于建模藻类。我们可以迭代看到它的进展:
> mapM_ print . take 7 $ iterate (>>= myRule) myAxiom
[A,B]
[A,B,A]
[A,B,A,A,B]
[A,B,A,A,B,A,B,A]
[A,B,A,A,B,A,B,A,A,B,A,A,B]
[A,B,A,A,B,A,B,A,A,B,A,A,B,A,B,A,A,B,A,B,A]
[A,B,A,A,B,A,B,A,A,B,A,A,B,A,B,A,A,B,A,B,A,A,B,A,A,B,A,B,A,A,B,A,A,B]
通常,列表的绑定为 concatMap
,当您想将映射与串联结合时,可以精确使用它。另一个解释是列表代表非确定性选择,并且通过从列表中选择每种可能性来绑定函数。例如,滚动骰子:
do
d1 <- [1..6]
d2 <- [1..6]
return (d1, d2)
这提供了所有可能的滚动2d6的方法。
factors :: Int -> [Int]
factors n = do
q <- [1..n]
filter ((==n) . (*q)) [1..n]
...或,在删除符号中,
factors n = [1..n] >>= ($[1..n]) . filter . fmap (==n) . (*)
当然这几乎没有效率,但它有效:
*Main> factors 17
[17,1]
*Main> factors 24
[24,12,8,6,4,3,2,1]
*Main> factors 34
[34,17,2,1]
对于不像*
那样简单的操作,因此您无法避免这样的蛮力方法,这实际上可能是一个很好的解决方案。
一方面, concatMap
只是 (=<<)
。和concat
只是join
。我经常在实际代码中使用这两个。
您可以做的另一件事是将功能列表应用于一个值。
λ:> applyList = sequence
λ:> applyList [(2*), (3+)] 4
[8,7]
您还可以生成列表的所有子集的列表
λ:> import Control.Monad
λ:> allSubsets = filterM (const [True, False])
λ:> allSubsets "ego"
["ego","eg","eo","e","go","g","o",""]
,甚至枚举所有可以由字母形成的字符串
λ:> import Data.List
λ:> import Control.Monad
λ:> allStrings = sequence <=< (inits . repeat)
λ:> take 100 $ allStrings ['a'..'z']
["","a","b","c","d","e","f","g","h","i","j","k","l","m","n","o","p","q","r","s","t","u","v","w","x","y","z","aa","ab","ac","ad","ae","af","ag","ah","ai","aj","ak","al","am","an","ao","ap","aq","ar","as","at","au","av","aw","ax","ay","az","ba","bb","bc","bd","be","bf","bg","bh","bi","bj","bk","bl","bm","bn","bo","bp","bq","br","bs","bt","bu","bv","bw","bx","by","bz","ca","cb","cc","cd","ce","cf","cg","ch","ci","cj","ck","cl","cm","cn","co","cp","cq","cr","cs","ct","cu"]
也许更实际,您可以使用应用程序实例将两个列表组合在一起
λ:> zipWith' f xs ys = f <$> xs <*> ys
λ:> zipWith' (+) [1..3] [5..8]
[6,7,8,9,7,8,9,10,8,9,10,11]