[英]Why is Haskell monadic bind left-associative?
The >>=
and >>
operators are both infixl 1
. >>=
和>>
运算符都是infixl 1
。 Why the left-associativity? 为什么左关联?
In particular, I observe the equivalences: 特别是,我观察到等价:
(do a; b; c ) == (a >> (b >> c)) -- Do desugaring
(a >> b >> c) == ((a >> b) >> c) -- Fixity definition
So do
is desugared differently to how the fixity definition naturally works, which is surprising. 对于固定性定义如何自然地起作用,这样
do
是不同的,这是令人惊讶的。
>>=
must surely be left-associative. >>=
肯定是左联想的。
Prelude> ["bla","bli di","blub"] >>= words >>= reverse
"albilbidbulb"
Prelude> ["bla","bli di","blub"] >>= (words >>= reverse)
<interactive>:3:30: error:
• Couldn't match expected type ‘[[b0]]’
with actual type ‘String -> [String]’
• Probable cause: ‘words’ is applied to too few arguments
In the first argument of ‘(>>=)’, namely ‘words’
In the second argument of ‘(>>=)’, namely ‘(words >>= reverse)’
In the expression:
["bla", "bli di", "blub"] >>= (words >>= reverse)
And >>
pretty much follows >>=
; 并且
>>
几乎遵循>>=
; if it had another fixity it would not only feel weird as Lennart said, it would also prevent you from using both operators in a chain: 如果它有另一个固定性,它不仅会像Lennart所说的那样感到怪异 ,它还会阻止你在链中使用这两个运算符:
Prelude> ["bla","bli di","blub"] >>= words >> "Ha"
"HaHaHaHa"
Prelude> infixr 1 ⬿≫; (⬿≫) = (>>)
Prelude> ["bla","bli di","blub"] >>= words ⬿≫ "Ha"
<interactive>:6:1: error:
Precedence parsing error
cannot mix ‘>>=’ [infixl 1] and ‘⬿≫’ [infixr 1] in the same infix expression
>>=
is left-associative because it's convenient. >>=
是左关联的,因为它很方便。 We want m >>= f1 >>= f2
to be parsed as (m >>= f1) >>= f2
, not as m >>= (f1 >>= f2)
, which would likely not type check, as pointed out in the comments. 我们希望
m >>= f1 >>= f2
被解析为(m >>= f1) >>= f2
,而不是m >>= (f1 >>= f2)
,这可能不会像指向那样进行类型检查在评论中。
The associativity of >>
however, is simply a mirror of >>=
. 然而,
>>
的相关性只是>>=
的镜像。 This is likely for the sake of consistency, since we can prove that >>
is associative via the third monad law: (m >>= f) >>= g ≡ m >>= ( \\x -> fx >>= g )
. 这可能是为了保持一致,因为我们可以证明
>>
通过第三个monad定律是关联的: (m >>= f) >>= g ≡ m >>= ( \\x -> fx >>= g )
。 That is to say, its associativity doesn't theoretically matter. 也就是说,它的相关性在理论上并不重要。 Here is the proof:
这是证明:
-- Definition:
a >> b ≡ a >>= (\_ -> b)
-- Proof: (a >> b) >> c ≡ a >> (b >> c)
(a >> b) >> c
≡ (a >>= (\_ -> b)) >> c -- [Definition]
≡ (a >>= (\_ -> b)) >>= (\_ -> c) -- [Definition]
≡ a >>= (\x -> (\_ -> b) x >>= (\_ -> c)) -- [Monad law]
≡ a >>= (\_ -> b >>= (\_ -> c)) -- [Beta-reduction]
≡ a >>= (\_ -> b >> c) -- [Definition]
≡ a >> (b >> c) -- [Definition]
∎
do
-notation de-sugars differently because it has a different goal. do
-notation不同,因为它有不同的目标。 Essentially, since do-notation is essentially writing out a lambda, right-association is needed. 从本质上讲,由于do-notation本质上是写出lambda,因此需要正确的关联。 This is because
m >>= (\\v -> (...))
is written as do {v <- m; (...)}
这是因为
m >>= (\\v -> (...))
写成do {v <- m; (...)}
do {v <- m; (...)}
. do {v <- m; (...)}
。 As earlier, the de-sugaring of >>
here seems to follow >>=
for the sake of consistency. 如前所述,为了保持一致性,
>>
的脱糖似乎遵循>>=
。
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