我试图了解有关镜头库的更多信息。我已经了解了lens-family包中的镜头及其派生方式,还掌握了Store,Pretext和Bazaar的两个类型参数版本,但是我在理解Control.Lens.Traversal
的 partsOf
, holesOf
和 singular
函数时遇到了麻烦,这些函数是用复杂类型定义的和许多辅助功能。这些功能也可以用一种更简单的学习方式来表达吗?
最佳答案
这是一个相当棘手的问题。我声称我自己并不完全了解holesOf
和partsOf
的工作方式,并且直到几分钟前我也不了解singular
的工作方式,但是我想写下一个可能对您有所帮助的答案。
我想解决一个更普遍的问题:如何阅读lens
源代码。因为如果您牢记几个简化的假设,则通常可以简化一些疯狂的定义,例如
singular :: (Conjoined p, Functor f)
=> Traversing p f s t a a
-> Over p f s t a a
singular l = conjoined
(\afb s -> let b = l sell s in case ins b of
(w:ws) -> unsafeOuts b . (:ws) <$> afb w
[] -> unsafeOuts b . return <$> afb (error "singular: empty traversal"))
(\pafb s -> let b = l sell s in case pins b of
(w:ws) -> unsafeOuts b . (:Prelude.map extract ws) <$> cosieve pafb w
[] -> unsafeOuts b . return <$> cosieve pafb (error "singular: empty traversal"))
unsafeOuts :: (Bizarre p w, Corepresentable p) => w a b t -> [b] -> t
unsafeOuts = evalState `rmap` bazaar (cotabulate (\_ -> state (unconsWithDefault fakeVal)))
where fakeVal = error "unsafePartsOf': not enough elements were supplied"
ins :: Bizarre (->) w => w a b t -> [a]
ins = toListOf (getting bazaar)
unconsWithDefault :: a -> [a] -> (a,[a])
unconsWithDefault d [] = (d,[])
unconsWithDefault _ (x:xs) = (x,xs)
但是我要超越自己
这些是我在阅读
lens
源代码时尝试应用的规则:哑光机
光学通常在整个库中遵循
s-t-a-b
形式,这使您可以修改“目标”的类型(最好是一个重载的单词)。但是,仅使用s
和a
即可实现许多光学功能,并且在您尝试读取定义时,跟踪t
和b
通常没有意义。例如,当我尝试对
singular
进行反向工程时,我在暂存文件中使用了以下类型:{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE NoImplicitPrelude #-}
import BasePrelude hiding (fold)
type Lens big small =
forall f. (Functor f) => (small -> f small) -> (big -> f big)
type Traversal big small =
forall ap. (Applicative ap) => (small -> ap small) -> (big -> ap big)
makeLens :: (big -> small) -> (big -> small -> big) -> Lens big small
makeLens getter setter =
\liftSmall big -> setter big <$> liftSmall (getter big)
组合器看起来像这样:
set :: ((small -> Identity small) -> big -> Identity big) -> small -> big -> big
set setter new big =
runIdentity (setter (\_ -> Identity new) big)
view :: ((small -> Const small small) -> big -> Const small big) -> big -> small
view getter big =
getConst (getter Const big)
离开这里,索引和棱镜
棱镜和分度光学器件作为镜片的消费者非常有用,但它们负责一些令人眼前一亮的代码。为了统一棱镜和分度光学器件,
lens
开发人员使用专业版(例如Choice
和Conjoined
)及其附带的辅助函数(dimap
,rmap
)。当阅读
lens
代码时,我发现每当看到一个profunctor变量时,总是假设p ~ (->)
(函数类型)会很有帮助。这使我可以从上面的代码片段中的签名中删除Representable
,Conjoined
,Bizarre
和Over
类型类。很多类型的孔
借助GHC的类型漏洞,我们可以开始尝试在更简单,更笨拙的类型之上构建自己的
singular
。singular :: Traversal big small -> Lens big small
singular = _
一般的策略称为alluded to briefly on this comonad.com's blog post,它是遍历
big
值以使用[small]
获得小 list (Const
),然后将它们放回使用State
获得它们的位置。遍历以获得列表可以通过重新实现
toListOf
来完成:toListOf :: Traversal big small -> big -> [small]
toListOf traversal = foldrOf traversal (:) []
-- | foldMapOf with mappend/mzero inlined
foldrOf :: Traversal big small -> (small -> r -> r) -> r -> big -> r
foldrOf traversal fold zero =
\big -> appEndo (foldMapOf traversal (Endo . fold) big) zero
-- | Traverses a value of type big, accumulating the result in monoid mon
foldMapOf :: Monoid mon => Traversal big small -> (small -> mon) -> big -> mon
foldMapOf traversal fold =
getConst . traversal (Const . fold)
这里是一个嵌套的monoid玩偶:
Endo
中的Const
中的列表。现在我们有:
singular :: Traversal big small -> Lens big small
singular traversal liftSmall big = do
case toListOf traversal big of
(x:xs) -> _
[] -> _
将值(value)放回去有点曲折。我们一直在避免谈论这种疯狂的功能:
unsafeOuts :: (Bizarre p w, Corepresentable p) => w a b t -> [b] -> t
unsafeOuts = evalState `rmap` bazaar (cotabulate (\_ -> state (unconsWithDefault fakeVal)))
where fakeVal = error "unsafePartsOf': not enough elements were supplied"
在我们简化的宇宙中,
newtype Bazaar' small small' big =
Bazaar { unBazaar :: forall ap. Applicative ap => (small -> ap small') -> ap big }
deriving Functor
instance Applicative (Bazaar' small small') where
pure big =
Bazaar (\_ -> pure big)
Bazaar lhs <*> Bazaar rhs =
Bazaar (\liftSmall -> lhs liftSmall <*> rhs liftSmall)
type Bazaar small big = Bazaar' small small big
gobble :: StateT Identity [a] a
gobble = state (unconsWithDefault (error "empty!"))
unsafeOuts :: Bazaar small big -> [small] -> big
unsafeOuts (Bazaar bazaar) smalls =
evalState (bazaar (\_ -> gobble)) smalls
在这里,我们内联了
rmap = (.)
和cotabulate f = f . Identity
,并且之所以能够这样做是因为我们假设使用p ~ (->)
。搞乱集市的半心半意的尝试
集市很奇怪,似乎没有关于它们的文章。
lens
文档提到它就像遍历一样已经应用到结构上。的确,如果您采用Traversal
类型并将其应用于已经具有的big
值,那么您将获得集市。它也类似于fancy free applicative,但是我不知道这是有用还是有害。
在last comment of this blog post about a seeming unrelated
FunList
datatype上,用户Zemyla计算出data FunList a b t
= Done t
| More a (FunList a b (b -> t))
instance Functor (FunList a b) where ...
instance Applicative (FunList a b) where ...
instance Profunctor (FunList a) where ...
-- example values:
-- * Done (x :: t)
-- * More (a1 :: a) (Done (x :: a -> t))
-- * More (a1 :: a) (More (a2 :: a) (Done (x :: a -> a -> t))
和
lens
集市。我发现这种表示方式对于直觉正在发生的事情会有所帮助。达州立单子(monad)
这里的 gem 是
gobble
,每次运行时都会从状态的顶部弹出列表的头部。我们的bazaar
能够将gobble :: StateT Identity [small] small
值升级为bazaar (\_ -> gobble) :: StateT Identity [small] big
。就像遍历一样,我们能够对小值(value)的一部分采取有效的行动,并将其升级为对整个值(value)起作用的行动。这一切都非常迅速,并且似乎没有足够的代码。有点使我旋转。(可能有帮助的是使用此帮助器功能在GHCi中玩集市:
bazaarOf :: Traversal big small -> big -> Bazaar small big
bazaarOf traversal =
traversal (\small -> Bazaar (\liftSmall -> liftSmall small))
-- See below for `ix`.
λ> unBazaar (bazaarOf (ix 3) [1,2,3,4]) Right
Right [1,2,3,4]
λ> unBazaar (bazaarOf (ix 3) [1,2,3,4]) (\_ -> Right 10)
Right [1,2,3,100]
λ> unBazaar (bazaarOf (ix 1) [1,2,3,4]) Left
Left 2
在简单的情况下,它似乎近似是
traverse
的“延迟”版本。)任何状况之下
unsafeOuts
为我们提供了一种方法,该方法在给定big
值列表和从第一个small
值构造的集市的情况下,检索第二个big
值。现在,我们需要根据传入的原始遍历构造一个集市:singular :: Traversal big small -> Lens big small
singular traversal liftSmall big = do
let bazaar = traversal (\small -> Bazaar ($ small)) big
case toListOf traversal big of
(x:xs) -> _
[] -> _
这里我们做两件事:
Bazaar small small
。由于我们计划遍历big
,因此我们可以获取获得的每个x :: small
值并构造一个Bazaar (\f -> f x) :: Bazaar small small
。这样就够了! Bazaar small small
顺利升级为bazaar :: Bazaar small big
。 原始的
lens
代码使用b = traversal sell big
实例中的sell
与Sellable (->) (Bazaar (->))
一起完成此操作。如果内联该定义,则应该得到相同的结果。在
x:xs
情况下,x
是我们要作用的值。这是我们得到的遍历的第一个目标值,现在成为我们返回的镜头的第一个目标值。我们调用liftSmall x
以获得某些仿函数f small
的f
;然后我们在仿函数内部附加xs
以获得f [small]
;然后我们在仿函数内部调用unsafeOuts bazaar
,将f [small]
重新转换为f big
:singular :: Traversal big small -> Lens big small
singular traversal liftSmall big = do
let bazaar = traversal (\small -> Bazaar ($ small)) big
case toListOf traversal big of
(x:xs) -> fmap (\y -> unsafeOuts bazaar (y:xs)) <$> liftSmall x
[] -> _
在列表为空的情况下,我们将以相同的方式进行操作,只不过在以下内容中填充了一个底值:
singular :: Traversal big small -> Lens big small
singular traversal liftSmall big = do
let bazaar = traversal (\small -> Bazaar ($ small)) big
case toListOf traversal big of
(x:xs) -> fmap (\y -> unsafeOuts bazaar (y:xs)) <$> liftSmall x
[] -> fmap (\y -> unsafeOuts bazaar [y]) <$> liftSmall (error "singularity")
让我们定义一些基本的光学器件,以便我们可以使用我们的定义:
-- | Constructs a Traversal that targets zero or one
makePrism :: (small -> big) -> (big -> Either big small) -> Traversal big small
makePrism constructor getter =
\liftSmall big -> case (fmap liftSmall . getter) big of
Left big' -> pure big'
Right fsmall -> fmap constructor fsmall
_Cons :: Traversal [a] (a, [a])
_Cons = makePrism (uncurry (:)) (\case (x:xs) -> Right (x, xs); [] -> Left [])
_1 :: Lens (a, b) a
_1 = makeLens fst (\(_, b) a' -> (a', b))
_head :: Traversal [a] a
_head = _Cons . _1
ix :: Int -> Traversal [a] a
ix k liftSmall big =
if k < 0 then pure big else go big k
where
go [] _ = pure []
go (x:xs) 0 = (:xs) <$> liftSmall x
go (x:xs) i = (x:) <$> go xs (i - 1)
这些都是从
lens
库中窃取的。不出所料,它可以帮助我们消除烦人的
Monoid
类型类:λ> :t view _head
view _head :: Monoid a => [a] -> a
λ> :t view (singular _head)
view (singular _head) :: [small] -> small
λ> view _head [1,2,3,4]
[snip]
• Ambiguous type variable ‘a0’ arising from a use of ‘print’
prevents the constraint ‘(Show a0)’ from being solved.
[snip]
λ> view (singular _head) [1,2,3,4]
1
并且它没有像预期的那样对setter起作用(因为遍历已经是setter):
λ> set (ix 100) 50 [1,2,3]
[1,2,3]
λ> set (singular (ix 100)) 50 [1,2,3]
[1,2,3]
λ> set _head 50 [1,2,3,4]
[50,2,3,4]
λ> set (singular _head) 50 [1,2,3,4]
[50,2,3,4]
partsOf
和holesOf
-- | A type-restricted version of 'partsOf' that can only be used with a 'Traversal'.
partsOf' :: ATraversal s t a a -> Lens s t [a] [a]
partsOf' l f s = outs b <$> f (ins b) where b = l sell s
纯粹的推测是:据我所知,
partsOf
与singular
极为相似,因为它首先构造了一个集市b
,在集市上调用f (ins b)
,然后“将值放回找到它的位置”。holesOf :: forall p s t a. Conjoined p => Over p (Bazaar p a a) s t a a -> s -> [Pretext p a a t]
holesOf l s = unTagged
( conjoined
(Tagged $ let
f [] _ = []
f (x:xs) g = Pretext (\xfy -> g . (:xs) <$> xfy x) : f xs (g . (x:))
in f (ins b) (unsafeOuts b))
(Tagged $ let
f [] _ = []
f (wx:xs) g = Pretext (\wxfy -> g . (:Prelude.map extract xs) <$> cosieve wxfy wx) : f xs (g . (extract wx:))
in f (pins b) (unsafeOuts b))
:: Tagged (p a b) [Pretext p a a t]
) where b = l sell s
holesOf
也在制作集市(第三次l sell s
!),再次遭受结膜炎的困扰:通过假定p ~ (->)
,您可以删除conjoined
的第二个分支。但是然后您剩下一堆Pretext
和comonads,我不完全确定它们是如何卡在一起的。值得进一步探索!Here is a gist of all the code I had in my scratch file at the time I hit Submit on this wall of text.
关于haskell - Control.Lens.Traversal的partsOf,holesOf和singular的简单定义是什么?,我们在Stack Overflow上找到一个类似的问题:https://stackoverflow.com/questions/44310458/