在Haskell中结合多种过滤功能的绝佳方法 [英] Elegant way to combine multiple filtering functions in Haskell

问题描述

将以下过滤功能用作一元谓词，

 f1 :: Int -> Bool
f1 x = x > 30

f2 :: Int -> Bool
f2 x = x < 60

f3 :: Int -> Bool
f3 x = x `mod` 3 == 0
 

我想过滤所有整数列表.目前，我正在按照以下方式进行操作:

 filtered = filter f1 $ filter f2 $ filter f3 [1..90]
-- [33,36,39,42,45,48,51,54,57]
 

，但几乎没有感觉到这是最优雅的解决方案.特别是我不喜欢filter的多次重复以及缺乏可组合性.

是否有一种方法可以将所有这些谓词组合为一个，我们将其命名为<?>，以便可能的语法类似于以下内容?

 filtered = filter (f1 <?> f2 <?> f3) [1..90]
-- [33,36,39,42,45,48,51,54,57]
 

此假设的<?>运算符的类型签名将为(a -> Bool) -> (a -> Bool) -> (a -> Bool)，但解决方案

这怎么办?

 import Control.Applicative (liftA2)
-- given f1 etc.
filtered = filter (f1 <&&> f2 <&&> f3) [1..90]
  where
    (<&&>) = liftA2 (&&)
 

在这里，将&&提升为Applicative会得到您标记为<?>的内容，即将两个一元谓词的结果组合在一起的和运算符. /p>

(我最初将名称.&&.用作提升后的运算符，但 amalloy 建议<&&>将与其他Functor/Applicative提升的运算符(如<$> )类似，成为更好的名称​​.)

Given the following filtering functions as unary predicates,

f1 :: Int -> Bool
f1 x = x > 30

f2 :: Int -> Bool
f2 x = x < 60

f3 :: Int -> Bool
f3 x = x `mod` 3 == 0

I'd like to filter a list of integers through all of them. Currently I'm doing something along the lines of:

filtered = filter f1 $ filter f2 $ filter f3 [1..90]
-- [33,36,39,42,45,48,51,54,57]

but it hardly feels like this is the most elegant solution possible; especially I don't like the multiple repetitions of filter and the lack of composability.

Would there be a way to compose all these predicates into one, let's name it <?>, so that a possible syntax would resemble something like the following?

filtered = filter (f1 <?> f2 <?> f3) [1..90]
-- [33,36,39,42,45,48,51,54,57]

The type signature of this hypothetical <?> operator would then be (a -> Bool) -> (a -> Bool) -> (a -> Bool) but I wasn't able to find any such thing on Hoogle.

解决方案

What about this?

import Control.Applicative (liftA2)
-- given f1 etc.
filtered = filter (f1 <&&> f2 <&&> f3) [1..90]
  where
    (<&&>) = liftA2 (&&)

Here, lifting && to Applicative gives what you marked as <?>, i.e. an operator to and together the results of two unary predicates.

(I initially used the name .&&. for the lifted operator, but amalloy, suggested that <&&> would be a better name by analogy with the other Functor/Applicative lifted operators like <$>.)

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