我正在尝试将一个简单的解释器从基于转换器的 monad 堆栈重写为基于 freer 的效果，但是我遇到了将我的意图传达给 GHC 类型系统的困难。
我只使用 State和 Fresh目前的效果。我正在使用两种状态，我的效果运行器如下所示:
runErlish g ls = run . runGlobal g . runGensym 0 . runLexicals ls
where runGlobal = flip runState
runGensym = flip runFresh'
runLexicals = flip runState
最重要的是，我用这种类型定义了一个函数 FindMacro:
findMacro :: Members [State (Global v w), State [Scope v w]] r
=> Arr r Text (Maybe (Macro (Term v w) v w))
到目前为止，所有这些都运行良好。当我尝试写
macroexpand2 时出现问题(好吧，macroexpand1，但我正在简化它，因此问题更容易理解):macroexpand2 s =
do m <- findMacro s
return $ case m of
Just j -> True
Nothing -> False
这会产生以下错误:
Could not deduce (Data.Open.Union.Member'
(State [Scope v0 w0])
r
(Data.Open.Union.FindElem (State [Scope v0 w0]) r))
from the context (Data.Open.Union.Member'
(State [Scope v w])
r
(Data.Open.Union.FindElem (State [Scope v w]) r),
Data.Open.Union.Member'
(State (Global v w))
r
(Data.Open.Union.FindElem (State (Global v w)) r))
bound by the inferred type for `macroexpand2':
(Data.Open.Union.Member'
(State [Scope v w])
r
(Data.Open.Union.FindElem (State [Scope v w]) r),
Data.Open.Union.Member'
(State (Global v w))
r
(Data.Open.Union.FindElem (State (Global v w)) r)) =>
Text -> Eff r Bool
at /tmp/flycheck408QZt/Erlish.hs:(79,1)-(83,23)
The type variables `v0', `w0' are ambiguous
When checking that `macroexpand2' has the inferred type
macroexpand2 :: forall (r :: [* -> *]) v (w :: [* -> *]).
(Data.Open.Union.Member'
(State [Scope v w])
r
(Data.Open.Union.FindElem (State [Scope v w]) r),
Data.Open.Union.Member'
(State (Global v w))
r
(Data.Open.Union.FindElem (State (Global v w)) r)) =>
Text -> Eff r Bool
Probable cause: the inferred type is ambiguous
好的，我可以添加一个
Members类型的注释:macroexpand2 :: Members [State (Global v w), State [Scope v w]] r
=> Text -> Eff r Bool
现在我明白了:
Overlapping instances for Member (State [Scope v0 w0]) r
arising from a use of `findMacro'
Matching instances:
instance Data.Open.Union.Member'
t r (Data.Open.Union.FindElem t r) =>
Member t r
-- Defined in `Data.Open.Union'
There exists a (perhaps superclass) match:
from the context (Members
'[State (Global v w), State [Scope v w]] r)
bound by the type signature for
macroexpand2 :: Members
'[State (Global v w), State [Scope v w]] r =>
Text -> Eff r Bool
at /tmp/flycheck408QnV/Erlish.hs:(79,17)-(80,37)
(The choice depends on the instantiation of `r, v0, w0'
To pick the first instance above, use IncoherentInstances
when compiling the other instance declarations)
In a stmt of a 'do' block: m <- findMacro s
In the expression:
do { m <- findMacro s;
return
$ case m of {
Just j -> True
Nothing -> False } }
In an equation for `macroexpand2':
macroexpand2 s
= do { m <- findMacro s;
return
$ case m of {
Just j -> True
Nothing -> False } }
有人建议我在 irc 上尝试
forall r v w.这没有什么区别。出于好奇，我尝试使用 IncoherentInstances在编译这段代码时(我不喜欢检查 freer 和 play 的分支)，看看它是否会给我一个关于发生了什么的线索。它没:Could not deduce (Data.Open.Union.Member'
(State [Scope v0 w0])
r
(Data.Open.Union.FindElem (State [Scope v0 w0]) r))
arising from a use of `findMacro'
from the context (Members
'[State (Global v w), State [Scope v w]] r)
bound by the type signature for
macroexpand2 :: Members
'[State (Global v w), State [Scope v w]] r =>
Text -> Eff r Bool
at /tmp/flycheck408eru/Erlish.hs:(79,17)-(80,37)
The type variables `v0', `w0' are ambiguous
Relevant bindings include
macroexpand2 :: Text -> Eff r Bool
(bound at /tmp/flycheck408eru/Erlish.hs:81:1)
Note: there are several potential instances:
instance (r ~ (t' : r'), Data.Open.Union.Member' t r' n) =>
Data.Open.Union.Member' t r ('Data.Open.Union.S n)
-- Defined in `Data.Open.Union'
instance (r ~ (t : r')) =>
Data.Open.Union.Member' t r 'Data.Open.Union.Z
-- Defined in `Data.Open.Union'
In a stmt of a 'do' block: m <- findMacro s
In the expression:
do { m <- findMacro s;
return
$ case m of {
Just j -> True
Nothing -> False } }
In an equation for `macroexpand2':
macroexpand2 s
= do { m <- findMacro s;
return
$ case m of {
Just j -> True
Nothing -> False } }
所以，这是我对 freer 内部结构的理解用完的地方，我有问题:
干杯!
最佳答案
可扩展效果的类型推断在历史上一直很糟糕。让我们看一些例子:
{-# language TypeApplications #-}
-- mtl
import qualified Control.Monad.State as M
-- freer
import qualified Control.Monad.Freer as F
import qualified Control.Monad.Freer.State as F
-- mtl works as usual
test1 = M.runState M.get 0
-- this doesn't check
test2 = F.run $ F.runState F.get 0
-- this doesn't check either, although we have a known
-- monomorphic state type
test3 = F.run $ F.runState F.get True
-- this finally checks
test4 = F.run $ F.runState (F.get @Bool) True
-- (the same without TypeApplication)
test5 = F.run $ F.runState (F.get :: F.Eff '[F.State Bool] Bool) True
我将尝试解释一般问题并提供最少的代码说明。代码的独立版本可以是 found here .
在最基本的层面上(不考虑优化的表示)，
Eff定义如下:{-# language
GADTs, DataKinds, TypeOperators, RankNTypes, ScopedTypeVariables,
TypeFamilies, DeriveFunctor, EmptyCase, TypeApplications,
UndecidableInstances, StandaloneDeriving, ConstraintKinds,
MultiParamTypeClasses, FlexibleInstances, FlexibleContexts,
AllowAmbiguousTypes, PolyKinds
#-}
import Control.Monad
data Union (fs :: [* -> *]) (a :: *) where
Here :: f a -> Union (f ': fs) a
There :: Union fs a -> Union (f ': fs) a
data Eff (fs :: [* -> *]) (a :: *) =
Pure a | Free (Union fs (Eff fs a))
deriving instance Functor (Union fs) => Functor (Eff fs)
换句话说，
Eff是一个来自仿函数列表的联合的自由 monad。 Union fs a表现得像一个 n 元 Coproduct .二进制 Coproduct就像 Either对于两个仿函数:data Coproduct f g a = InL (f a) | InR (g a)
相比之下，
Union fs a让我们从仿函数列表中选择一个仿函数:type MyUnion = Union [[], Maybe, (,) Bool] Int
-- choose the first functor, which is []
myUnion1 :: MyUnion
myUnion1 = Here [0..10]
-- choose the second one, which is Maybe
myUnion2 :: MyUnion
myUnion2 = There (Here (Just 0))
-- choose the third one
myUnion3 :: MyUnion
myUnion3 = There (There (Here (False, 0)))
让我们实现
State效果为例。首先，我们需要有一个 Functor Union fs 的实例, 自 Eff只有一个 Monad实例如果 Functor (Union fs) .Functor (Union '[])很简单，因为空联合没有值:instance Functor (Union '[]) where
fmap f fs = case fs of {} -- using EmptyCase
否则，我们在联合前添加一个仿函数:
instance (Functor f, Functor (Union fs)) => Functor (Union (f ': fs)) where
fmap f (Here fa) = Here (fmap f fa)
fmap f (There u) = There (fmap f u)
现在
State定义和运行者:run :: Eff '[] a -> a
run (Pure a) = a
data State s k = Get (s -> k) | Put s k deriving Functor
runState :: forall s fs a. Functor (Union fs) => Eff (State s ': fs) a -> s -> Eff fs (a, s)
runState (Pure a) s = Pure (a, s)
runState (Free (Here (Get k))) s = runState (k s) s
runState (Free (Here (Put s' k))) s = runState k s'
runState (Free (There u)) s = Free (fmap (`runState` s) u)
我们已经可以开始编写和运行我们的
Eff程序，虽然我们缺乏所有的糖和便利:action1 :: Eff '[State Int] Int
action1 =
Free $ Here $ Get $ \s ->
Free $ Here $ Put (s + 10) $
Pure s
-- multiple state
action2 :: Eff '[State Int, State Bool] ()
action2 =
Free $ Here $ Get $ \n -> -- pick the first effect
Free $ There $ Here $ Get $ \b -> -- pick the second effect
Free $ There $ Here $ Put (n < 10) $ -- the second again
Pure ()
现在:
> run $ runState action1 0
(0,10)
> run $ (`runState` False) $ (`runState` 0) action2
(((),0),True)
这里只有两个必不可少的东西。
第一个是
Eff 的 monad 实例这让我们可以使用 do - 符号代替 Free和 Pure ，并且还让我们使用许多多态一元函数。我们将在这里跳过它，因为它写起来很简单。第二个是从效果列表中选择效果的推理/重载。以前我们需要写
Here x为了选择第一个效果，There (Here x)选择第二个，依此类推。相反，我们想在效果列表中编写多态的代码，所以我们必须指定的是一些效果是列表的一个元素，并且一些隐藏的类型类魔法将插入适当数量的 There -s。我们需要一个
Member f fs可以注入(inject)的类 f a -s 进入 Union fs a -s 当 f是 fs 的一个元素.从历史上看，人们以两种方式实现它。一、直接与
OverlappingInstances :class Member (f :: * -> *) (fs :: [* -> *]) where
inj :: f a -> Union fs a
instance Member f (f ': fs) where
inj = Here
instance {-# overlaps #-} Member f fs => Member f (g ': fs) where
inj = There . inj
-- it works
injTest1 :: Union [[], Maybe, (,) Bool] Int
injTest1 = inj [0]
injTest2 :: Union [[], Maybe, (,) Bool] Int
injTest2 = inj (Just 0)
其次，间接地，通过首先计算
f的索引在 fs使用类型系列，然后实现 inj具有非重叠类，由 f 指导-s 计算索引。这通常被认为更好，因为人们往往不喜欢重叠的实例。data Nat = Z | S Nat
type family Lookup f fs where
Lookup f (f ': fs) = Z
Lookup f (g ': fs) = S (Lookup f fs)
class Member' (n :: Nat) (f :: * -> *) (fs :: [* -> *]) where
inj' :: f a -> Union fs a
instance fs ~ (f ': gs) => Member' Z f fs where
inj' = Here
instance (Member' n f gs, fs ~ (g ': gs)) => Member' (S n) f fs where
inj' = There . inj' @n
type Member f fs = Member' (Lookup f fs) f fs
inj :: forall fs f a. Member f fs => f a -> Union fs a
inj = inj' @(Lookup f fs)
-- yay
injTest1 :: Union [[], Maybe, (,) Bool] Int
injTest1 = inj [0]
freer库使用第二种解决方案，而 extensible-effects第一个用于 7.8 之前的 GHC 版本，第二个用于较新的 GHC-s。无论如何，两种解决方案都具有相同的推理限制，即我们几乎总是可以
Lookup只有具体的单态类型，而不是包含类型变量的类型。 ghci 中的示例:> :kind! Lookup Maybe [Maybe, []]
Lookup Maybe [Maybe, []] :: Nat
= 'Z
这是有效的，因为在
Maybe 中都没有类型变量或 [Maybe, []] .> :kind! forall a. Lookup (Either a) [Either Int, Maybe]
forall a. Lookup (Either a) [Either Int, Maybe] :: Nat
= Lookup (Either a) '[Either Int, Maybe]
这个卡住了，因为
a类型变量块减少。> :kind! forall a. Lookup (Maybe a) '[Maybe a]
forall a. Lookup (Maybe a) '[Maybe a] :: Nat
= Z
这是有效的，因为我们对任意类型变量的唯一了解是它们等于自身，并且
a等于 a .通常，类型族缩减会卡在变量上，因为约束求解可能会在以后将它们细化为不同的类型，因此 GHC 无法对它们做出任何假设(除了等于它们自己)。基本上相同的问题出现在
OverlappingInstances 上。实现(尽管没有任何类型系列)。让我们重温
freer鉴于此。import Control.Monad.Freer
import Control.Monad.Freer.State
test1 = run $ runState get 0 -- error
GHC 知道我们有一个单一效果的堆栈，因为
run工作于 Eff '[] a .它也知道那个效果一定是State s .但是当我们写 get ，GHC只知道它有一个State t一些新鲜的效果t变量，以及 Num t必须保持，所以当它试图计算 freer 时相当于 Lookup (State t) '[State s] ，它会卡在类型变量上，并且任何进一步的实例解析都会在卡住的类型系列表达式上绊倒。另一个例子:foo = run $ runState get False -- error
这也失败了，因为 GHC 需要计算
Lookup (State s) '[State Bool] ，虽然我们知道状态必须是 Bool ，这仍然因为 s 卡住了多变的。foo = run $ runState (modify not) False -- this works
这是有效的，因为状态类型为
modify not可以解析到Bool , 和 Lookup (State Bool) '[State Bool]减少。现在，经过这么大的弯路，我将在您的帖子末尾回答您的问题。
Overlapping instances不表示任何可能的解决方案，只是一个类型错误工件。我需要更多的代码上下文来确定它究竟是如何产生的，但我确定它不相关，因为一旦 Lookup卡住了，案子就无望了。 IncoherentInstances也无关紧要，也无济于事。我们需要一个具体的效果位置索引才能为程序生成代码，如果Lookup我们不能凭空拉出一个索引。卡住。 findMacro 的问题是它有State状态内的类型变量的影响。每当您想使用 findMacro你必须确保 v和 w Scope 的参数和 Global是已知的具体类型。您可以通过类型注释来做到这一点，或者更方便的是您可以使用 TypeApplications ，然后写 findMacro @Int @Int用于指定 v = Int和 w = Int .如果您有 findMacro在多态函数中，您需要启用 ScopedTypeVariables , 绑定(bind) v和 w使用 forall v w.该函数的注解，然后写 findMacro @v @w当你使用它时。您还需要启用 {-# language AllowAmbiguousTypes #-}用于多晶v或 w (如评论中所指出的)。我认为虽然在 GHC 8 中启用它是一个合理的扩展，连同 TypeApplications . 附录:
然而，幸运的是，新的 GHC 8 功能让我们修复了可扩展效果的类型推断，我们可以推断出一切
mtl可以，还有一些东西mtl处理不了。新的类型推断对于效果的排序也是不变的。我有一个 minimal implementation here以及一些例子。但是，它尚未在我所知道的任何效果库中使用。我可能会写一篇关于它的文章，并做一个拉取请求以将它添加到
freer .
关于haskell - 如何在 haskell 中组合 'freer' 效果？，我们在Stack Overflow上找到一个类似的问题： https://stackoverflow.com/questions/38993017/