重复应用函数直到结果稳定 [英] repeatedly applying a function until the result is stable
问题描述
我想重复应用一个函数 simpl''
,直到结果为stable(即 simplify'(x)== x < code $):
I want to repeatedly apply a function simplify'
until the result is "stable" (i.e. simplify'(x) == x
):
simplify :: Expr -> Expr
simplify expr =
let iterations = iterate simplify' expr
neighbours = zip iterations (tail iterations)
simplified = takeWhile (\(a, b) -> a /= b) neighbours
in snd $ last ((expr, expr) : simplified)
simplify' :: Expr -> Expr
这似乎是我常见的问题。是否有更优雅的解决方案?
This seems to be a common problem to me. Is there a more elegant solution?
更新:我发现了一个更简单的解决方案,但我仍然在寻找更优雅的解决方案:)
Update: I found a much simpler solution, but I'm still looking for a more elegant solution :)
simplify expr =
let next = simplify' expr
in if next == expr
then expr
else simplify next
推荐答案
模式匹配和递归。 converge
通过一个无限列表进行搜索,在一行中查找满足某个谓词的两个元素。然后它返回第二个。
Here's a slight generalization implemented with straightforward pattern matching and recursion. converge
searches through an infinite list, looking for two elements in a row which satisfy some predicate. It then returns the second one.
converge :: (a -> a -> Bool) -> [a] -> a
converge p (x:ys@(y:_))
| p x y = y
| otherwise = converge p ys
simplify = converge (==) . iterate simplify'
这可以很容易地为收敛测试使用近似相等。
This makes it easy to for example use approximate equality for the convergence test.
sqrt x = converge (\x y -> abs (x - y) < 0.001) $ iterate sqrt' x
where sqrt' y = y - (y^2 - x) / (2*y)
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