将具有类型类约束的函数转换为采用显式类型类字典的函数 [英] Transform a function with a typeclass constraint into a function taking an explicit typeclass dictionary

问题描述

众所周知，实现Haskell类型类的一种方法是通过类型类字典". (当然，这是在ghc中的实现，尽管我不得不说其他实现也是可能的.)为了解决问题，我将简要描述其工作原理.像

这样的类声明

class (MyClass t) where
  test1 :: t -> t -> t
  test2 :: t -> String
  test3 :: t

可以机械地转换为数据类型的定义，例如:

data MyClass_ t = MyClass_ {
  test1_ :: t -> t -> t,
  test2_ :: t -> String,
  test3_ :: t,
  }

然后，我们可以将每个实例声明机械地转换为该类型的对象；例如:

instance (MyClass Int) where
  test1 = (+)
  test2 = show
  test3 = 3

变成

instance_MyClass_Int :: MyClass_ Int
instance_MyClass_Int =  MyClass_ (+) show 3

以及类似地将具有类型类约束的函数转换为带有额外参数的函数；例如:

my_function :: (MyClass t) => t -> String
my_function val = test2 . test1 test3

变成

my_function_ :: MyClass_ t -> t -> String
my_function_ dict val = (test2_ dict) . (test1_ dict) (test3_ dict)

关键是，只要编译器知道如何填充这些隐藏的参数(这并不简单)，您就可以将使用类和实例的代码转换为仅使用该语言的更多基本功能的代码. /p>

---

在这种背景下，这是我的问题.我有一个模块M，它定义了一堆具有类约束的类和函数. M是'opaque';我可以看到它导出的内容(等效于.hi文件)，也可以从中导入，但是看不到它的源代码.我想构造一个新的模块N，该模块基本上导出相同的内容，但是应用了上面的转换.例如，如果M已导出

class (Foo t) where
  example1 :: t -> t -> t
  example2 :: t             -- note names and type signatures visible here
                            -- because they form part of the interface...

instance (Foo String)       -- details of implementation invisible

instance (Foo Bool)         -- details of implementation invisible

my_fn :: (Foo t) => t -> t  -- exported polymorphic fn with class constraint
                            -- details of implementation invisible

N会像这样

module N where

import M

data Foo_ t = Foo_ {example1_ :: t-> t -> t, example2_ :: t}

instance_Foo_String :: Foo_ String
instance_Foo_String = Foo_ example1 example2
instance_Foo_Bool   :: Foo_ Bool
instance_Foo_Bool   = Foo_ example1 example2

my_fn_ :: Foo_ t -> t -> t
my_fn_ = ???

我的问题是我可以代替??? .换句话说，我该怎么写才能从原始函数中提取功能my_fn的显式类型类"版本?这似乎很棘手，而且令人气愤，因为我们都知道，"M"模块M基本上已经在导出我想要创建的my_fn_之类的东西. (或者至少是在GHC上.)

记录下来，我想我会解释一下我已经知道的"hacky"解决方案.我将主要通过一系列示例进行说明.因此，让我们想象一下，我们正在尝试在以下步骤中对类，实例和函数进行验证(它们主要由漂亮的标准类型类组成，通常在博览会上有所简化):

{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}

module Src where

import Data.List (intercalate)

class SimpleShow a where
  sshow :: a -> String

class SimpleMonoid a where
  mempty  :: a
  mappend :: a -> a -> a

class SimpleFunctor f where
  sfmap :: (a -> b) -> f a -> f b

instance SimpleShow Int where
  sshow = show

instance SimpleMonoid [a] where
  mempty  = []
  mappend = (++)

instance SimpleMonoid ([a], [b]) where
  mempty  = ([], [])
  mappend (a1, b1) (a2, b2) = (a1 ++ a2, b1 ++ b2)

instance SimpleFunctor [] where
  sfmap = map

这些示例中应该有一些一般性:

• 'a'在班级成员中处于积极位置
• 'a'在班级成员中处于负面位置
• 需要灵活实例的实例
• 种类繁多的

我们将多参数类型的家庭留作练习！请注意，我确实相信我所介绍的是一个完全通用的句法程序.我只是认为用示例进行说明比通过正式描述转换要容易.无论如何，让我们假设要处理以下功能:

show_2lists :: (SimpleShow a) => [a] -> [a] -> String
show_2lists as1 as2 = "[" ++ intercalate ", " (map sshow as1) ++ "]/["
                      ++ intercalate ", " (map sshow as2) ++ "]"

mconcat :: (SimpleMonoid a) => [a] -> a
mconcat = foldr mappend mempty

example :: (SimpleMonoid (x, y)) => [(x, y)] -> (x, y)
example = foldr mappend mempty

lift_all :: (SimpleFunctor f) => [a -> b] -> [f a -> f b]
lift_all = map sfmap

然后实际的修改如下:

{-# LANGUAGE PatternGuards #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE EmptyDataDecls #-}
{-# LANGUAGE UndecidableInstances  #-}
{-# LANGUAGE FlexibleInstances #-}

module Main where

import Unsafe.Coerce
import Src

data Proxy k = Proxy

class Reifies s a | s -> a where
  reflect :: proxy s -> a

newtype Magic a r = Magic (forall (s :: *). Reifies s a => Proxy s -> r)

reify :: forall a r. a -> (forall (s :: *). Reifies s a => Proxy s -> r) -> r
reify a k = unsafeCoerce (Magic k :: Magic a r) (const a) Proxy
{-# INLINE reify #-}


data SimpleShow_    a = SimpleShow_    {sshow_  :: a -> String}
data SimpleMonoid_  a = SimpleMonoid_  {mempty_ :: a,
                                        mappend_ :: a -> a -> a}
data SimpleFunctor_ f = SimpleFunctor_ {
  sfmap_  :: forall a b. (a -> b) -> (f a -> f b)
  }

instance_SimpleShow_Int :: SimpleShow_ Int
instance_SimpleShow_Int = SimpleShow_ sshow

instance_SimpleMonoid_lista :: SimpleMonoid_ [a]
instance_SimpleMonoid_lista =  SimpleMonoid_ mempty mappend

instance_SimpleMonoid_listpair :: SimpleMonoid_ ([a], [b])
instance_SimpleMonoid_listpair =  SimpleMonoid_ mempty mappend

instance_SimpleFunctor_list :: SimpleFunctor_ []
instance_SimpleFunctor_list = SimpleFunctor_ sfmap

---------------------------------------------------------------------
--code to reify show_2lists :: (SimpleShow a) => [a] -> [a] -> String

-- for each type variable that occurs in the constraints, we must
-- create a newtype. Here there is only one tpye variable ('a') so we
-- create one newtype.
newtype Wrap_a a s  = Wrap_a { extract_a :: a }

-- for each constraint, we must create an instance of the
-- corresponding typeclass where the instance variables have been
-- replaced by the newtypes we just made, as follows.
instance Reifies s (SimpleShow_ a) => SimpleShow (Wrap_a a s) where
  --sshow :: (Wrap_ a s) -> String
  sshow = unsafeCoerce sshow__
    where sshow__ :: a -> String
          sshow__ = sshow_ $ reflect (undefined :: [] s)

-- now we can reify the main function
show_2lists_ :: forall a. SimpleShow_ a -> [a] -> [a] -> String
show_2lists_ dict = let
  magic :: forall s. ([Wrap_a a s] -> [Wrap_a a s] -> String)
           -> Proxy s -> ([a] -> [a] -> String)
  magic v _ arg1 arg2 = let
    w_arg1 :: [Wrap_a a s]
    w_arg1 =  unsafeCoerce (arg1 :: [a])

    w_arg2 :: [Wrap_a a s]
    w_arg2 =  unsafeCoerce (arg2 :: [a])

    w_ans :: String
    w_ans = v w_arg1 w_arg2

    ans   :: String
    ans   = unsafeCoerce w_ans
    in ans

  in (reify dict $ magic show_2lists)

---------------------------------------------------------------------
--code to reify mconcat :: (SimpleMonoid a) => [a] -> a

-- Here the newtypes begin with Wrap1 to avoid name collisions with
-- the ones above
newtype Wrap1_a a s  = Wrap1_a { extract1_a :: a }
instance Reifies s (SimpleMonoid_ a) => SimpleMonoid (Wrap1_a a s) where
  --mappend :: (Wrap1_a a s) -> (Wrap1_a a s) -> (Wrap1_a a s)
  mappend = unsafeCoerce mappend__
    where mappend__ :: a -> a -> a
          mappend__ =  (mappend_ $ reflect (undefined :: [] s))
  --mempty  :: (Wrap1_a a s)
  mempty = unsafeCoerce mempty__
    where mempty__  :: a
          mempty__  =  (mempty_  $ reflect (undefined :: [] s))

mconcat_ :: forall a. SimpleMonoid_ a -> [a] -> a
mconcat_ dict = let
  magic :: forall s. ([Wrap1_a a s] -> (Wrap1_a a s)) -> Proxy s -> ([a] -> a)
  magic v _ arg1 = let
    w_arg1 :: [Wrap1_a a s]
    w_arg1 =  unsafeCoerce (arg1 :: [a])

    w_ans :: Wrap1_a a s
    w_ans = v w_arg1

    ans   :: a
    ans   = unsafeCoerce w_ans
    in ans

  in (reify dict $ magic mconcat)

---------------------------------------------------------------------
--code to reify example :: (SimpleMonoid (x, y)) => [(x, y)] -> (x, y)

newtype Wrap2_x x s  = Wrap2_x { extract2_x :: x }
newtype Wrap2_y y s  = Wrap2_y { extract2_y :: y }
instance Reifies s (SimpleMonoid_ (x, y))
         => SimpleMonoid (Wrap2_x x s, Wrap2_y y s) where
  --mappend :: (Wrap2_x x s, Wrap2_y y s) -> (Wrap2_x x s, Wrap2_y y s)
  --                 -> (Wrap2_x x s, Wrap2_y y s)
  mappend = unsafeCoerce mappend__
    where mappend__ :: (x, y) -> (x, y) -> (x, y)
          mappend__ =  (mappend_ $ reflect (undefined :: [] s))
  --mempty  :: (Wrap2_x x s, Wrap2_y y s)
  mempty = unsafeCoerce mempty__
    where mempty__  :: (x, y)
          mempty__  =  (mempty_  $ reflect (undefined :: [] s))

example_ :: forall x y. SimpleMonoid_ (x, y) -> [(x, y)] -> (x, y)
example_ dict = let
  magic :: forall s. ([(Wrap2_x x s, Wrap2_y y s)] -> (Wrap2_x x s, Wrap2_y y s))
           -> Proxy s -> ([(x, y)] -> (x, y))
  magic v _ arg1 = let
    w_arg1 :: [(Wrap2_x x s, Wrap2_y y s)]
    w_arg1 =  unsafeCoerce (arg1 :: [(x, y)])

    w_ans :: (Wrap2_x x s, Wrap2_y y s)
    w_ans = v w_arg1

    ans   :: a
    ans   = unsafeCoerce w_ans
    in ans

  in (reify dict $ magic mconcat)

---------------------------------------------------------------------
--code to reify lift_all :: (SimpleFunctor f) => [a -> b] -> [f a -> f b]

newtype Wrap_f f s d = Wrap_f { extract_fd :: f d}
instance Reifies s (SimpleFunctor_ f) => SimpleFunctor (Wrap_f f s) where
  --sfmap :: (a -> b) -> (Wrap_f f s a -> Wrap_f f s b)
  sfmap = unsafeCoerce sfmap__
    where sfmap__ :: (a -> b) -> (f a -> f b)
          sfmap__ = sfmap_ $ reflect (undefined :: [] s)

lift_all_ :: forall a b f. SimpleFunctor_ f -> [a -> b] -> [f a -> f b]
lift_all_ dict = let
  magic :: forall s. ([a -> b] -> [Wrap_f f s a -> Wrap_f f s b])
           -> Proxy s -> ([a -> b] -> [f a -> f b])
  magic v _ arg1 = let
    w_arg1 :: [a -> b]
    w_arg1 =  unsafeCoerce (arg1 :: [a -> b])

    w_ans :: [Wrap_f f s a -> Wrap_f f s b]
    w_ans = v w_arg1

    ans   :: [f a -> f b]
    ans   = unsafeCoerce w_ans
    in ans

  in (reify dict $ magic lift_all)

main :: IO ()
main = do
  print (show_2lists_ instance_SimpleShow_Int     [3, 4] [6, 9])
  print (mconcat_     instance_SimpleMonoid_lista [[1, 2], [3], [4, 5]])
  print (example_     instance_SimpleMonoid_listpair
                                     [([1, 2], ["a", "b"]), ([4], ["q"])])
  let fns' :: [[Int] -> [Int]]
      fns' = lift_all_ instance_SimpleFunctor_list [\ x -> x+1, \x -> x - 1]
  print (map ($ [5, 7]) fns')


{- output:

"[3, 4]/[6, 9]"
[1,2,3,4,5]
([1,2,4],["a","b","q"])
[[6,8],[4,6]]

-}

请注意，我们使用了许多unsafeCoerce，但始终将仅在存在新类型时才有所不同的两种类型相关联.由于运行时表示形式相同，所以可以.

It's well known that one way of implementing Haskell typeclasses is via 'typeclass dictionaries'. (This is of course the implementation in ghc, though I make the obligatory remark that Other Implementations are Possible.) To fix ideas, I'll briefly describe how this works. A class declaration like

class (MyClass t) where
  test1 :: t -> t -> t
  test2 :: t -> String
  test3 :: t

can be mechanically transformed into the definition of a datatype like:

data MyClass_ t = MyClass_ {
  test1_ :: t -> t -> t,
  test2_ :: t -> String,
  test3_ :: t,
  }

Then we can mechanically transform each instance declaration into an object of that type; for instance:

instance (MyClass Int) where
  test1 = (+)
  test2 = show
  test3 = 3

turns into

instance_MyClass_Int :: MyClass_ Int
instance_MyClass_Int =  MyClass_ (+) show 3

and similarly a function which has a typeclass constraint can be turned into a function that takes an extra argument; for instance:

my_function :: (MyClass t) => t -> String
my_function val = test2 . test1 test3

turns into

my_function_ :: MyClass_ t -> t -> String
my_function_ dict val = (test2_ dict) . (test1_ dict) (test3_ dict)

The point is that as long as the compiler knows how to fill in these hidden arguments (which is not totally trivial) then you can translate code that uses classes and instances into code that uses only more basic features of the language.

---

With that background, here's my question. I have a module M which defines a bunch of classes and functions with class constraints. M is 'opaque'; I can see what it exports (the equivalent of the .hi file) and I can import from it but I can't see its source code. I want to construct a new module N which basically exports the same things but with the transformation above applied. So for instance if M exported

class (Foo t) where
  example1 :: t -> t -> t
  example2 :: t             -- note names and type signatures visible here
                            -- because they form part of the interface...

instance (Foo String)       -- details of implementation invisible

instance (Foo Bool)         -- details of implementation invisible

my_fn :: (Foo t) => t -> t  -- exported polymorphic fn with class constraint
                            -- details of implementation invisible

N would start like

module N where

import M

data Foo_ t = Foo_ {example1_ :: t-> t -> t, example2_ :: t}

instance_Foo_String :: Foo_ String
instance_Foo_String = Foo_ example1 example2
instance_Foo_Bool   :: Foo_ Bool
instance_Foo_Bool   = Foo_ example1 example2

my_fn_ :: Foo_ t -> t -> t
my_fn_ = ???

And my question is what on earth I can put in place of the ???. In other words, what can I write to extract the 'explicit typeclass' version of the function my_fn from the original? It seems rather tricky, and it's infuriating because we all know that 'under the hood' the module M is basically already exporting something like the my_fn_ which I want to create. (Or at least, it is on GHC.)

解决方案

For the record, I thought I would explain the 'hacky' solution to this which I already know of. I'll basically illustrate it using a series of examples. So let's imagine we're trying to reify the classes, instances and functions in the following (which consists mostly of pretty standard typeclasses, generally simplified somewhat for the exposition):

{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}

module Src where

import Data.List (intercalate)

class SimpleShow a where
  sshow :: a -> String

class SimpleMonoid a where
  mempty  :: a
  mappend :: a -> a -> a

class SimpleFunctor f where
  sfmap :: (a -> b) -> f a -> f b

instance SimpleShow Int where
  sshow = show

instance SimpleMonoid [a] where
  mempty  = []
  mappend = (++)

instance SimpleMonoid ([a], [b]) where
  mempty  = ([], [])
  mappend (a1, b1) (a2, b2) = (a1 ++ a2, b1 ++ b2)

instance SimpleFunctor [] where
  sfmap = map

There's meant to be some generality in these examples: we have

• 'a' in positive position in the class member
• 'a' in negative position in the class member
• an instance requiring flexible instances
• a higher-kinded type

We leave multi-parameter type families as an exercise! Note that I do believe that what I'm presenting is a completely general, syntactic procedure; I just think it's easier to illustrate with examples than by describing the transformation formally. Anyway, let's suppose we've got the following functions to process:

show_2lists :: (SimpleShow a) => [a] -> [a] -> String
show_2lists as1 as2 = "[" ++ intercalate ", " (map sshow as1) ++ "]/["
                      ++ intercalate ", " (map sshow as2) ++ "]"

mconcat :: (SimpleMonoid a) => [a] -> a
mconcat = foldr mappend mempty

example :: (SimpleMonoid (x, y)) => [(x, y)] -> (x, y)
example = foldr mappend mempty

lift_all :: (SimpleFunctor f) => [a -> b] -> [f a -> f b]
lift_all = map sfmap

Then the actual reification looks like:

{-# LANGUAGE PatternGuards #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE EmptyDataDecls #-}
{-# LANGUAGE UndecidableInstances  #-}
{-# LANGUAGE FlexibleInstances #-}

module Main where

import Unsafe.Coerce
import Src

data Proxy k = Proxy

class Reifies s a | s -> a where
  reflect :: proxy s -> a

newtype Magic a r = Magic (forall (s :: *). Reifies s a => Proxy s -> r)

reify :: forall a r. a -> (forall (s :: *). Reifies s a => Proxy s -> r) -> r
reify a k = unsafeCoerce (Magic k :: Magic a r) (const a) Proxy
{-# INLINE reify #-}


data SimpleShow_    a = SimpleShow_    {sshow_  :: a -> String}
data SimpleMonoid_  a = SimpleMonoid_  {mempty_ :: a,
                                        mappend_ :: a -> a -> a}
data SimpleFunctor_ f = SimpleFunctor_ {
  sfmap_  :: forall a b. (a -> b) -> (f a -> f b)
  }

instance_SimpleShow_Int :: SimpleShow_ Int
instance_SimpleShow_Int = SimpleShow_ sshow

instance_SimpleMonoid_lista :: SimpleMonoid_ [a]
instance_SimpleMonoid_lista =  SimpleMonoid_ mempty mappend

instance_SimpleMonoid_listpair :: SimpleMonoid_ ([a], [b])
instance_SimpleMonoid_listpair =  SimpleMonoid_ mempty mappend

instance_SimpleFunctor_list :: SimpleFunctor_ []
instance_SimpleFunctor_list = SimpleFunctor_ sfmap

---------------------------------------------------------------------
--code to reify show_2lists :: (SimpleShow a) => [a] -> [a] -> String

-- for each type variable that occurs in the constraints, we must
-- create a newtype. Here there is only one tpye variable ('a') so we
-- create one newtype.
newtype Wrap_a a s  = Wrap_a { extract_a :: a }

-- for each constraint, we must create an instance of the
-- corresponding typeclass where the instance variables have been
-- replaced by the newtypes we just made, as follows.
instance Reifies s (SimpleShow_ a) => SimpleShow (Wrap_a a s) where
  --sshow :: (Wrap_ a s) -> String
  sshow = unsafeCoerce sshow__
    where sshow__ :: a -> String
          sshow__ = sshow_ $ reflect (undefined :: [] s)

-- now we can reify the main function
show_2lists_ :: forall a. SimpleShow_ a -> [a] -> [a] -> String
show_2lists_ dict = let
  magic :: forall s. ([Wrap_a a s] -> [Wrap_a a s] -> String)
           -> Proxy s -> ([a] -> [a] -> String)
  magic v _ arg1 arg2 = let
    w_arg1 :: [Wrap_a a s]
    w_arg1 =  unsafeCoerce (arg1 :: [a])

    w_arg2 :: [Wrap_a a s]
    w_arg2 =  unsafeCoerce (arg2 :: [a])

    w_ans :: String
    w_ans = v w_arg1 w_arg2

    ans   :: String
    ans   = unsafeCoerce w_ans
    in ans

  in (reify dict $ magic show_2lists)

---------------------------------------------------------------------
--code to reify mconcat :: (SimpleMonoid a) => [a] -> a

-- Here the newtypes begin with Wrap1 to avoid name collisions with
-- the ones above
newtype Wrap1_a a s  = Wrap1_a { extract1_a :: a }
instance Reifies s (SimpleMonoid_ a) => SimpleMonoid (Wrap1_a a s) where
  --mappend :: (Wrap1_a a s) -> (Wrap1_a a s) -> (Wrap1_a a s)
  mappend = unsafeCoerce mappend__
    where mappend__ :: a -> a -> a
          mappend__ =  (mappend_ $ reflect (undefined :: [] s))
  --mempty  :: (Wrap1_a a s)
  mempty = unsafeCoerce mempty__
    where mempty__  :: a
          mempty__  =  (mempty_  $ reflect (undefined :: [] s))

mconcat_ :: forall a. SimpleMonoid_ a -> [a] -> a
mconcat_ dict = let
  magic :: forall s. ([Wrap1_a a s] -> (Wrap1_a a s)) -> Proxy s -> ([a] -> a)
  magic v _ arg1 = let
    w_arg1 :: [Wrap1_a a s]
    w_arg1 =  unsafeCoerce (arg1 :: [a])

    w_ans :: Wrap1_a a s
    w_ans = v w_arg1

    ans   :: a
    ans   = unsafeCoerce w_ans
    in ans

  in (reify dict $ magic mconcat)

---------------------------------------------------------------------
--code to reify example :: (SimpleMonoid (x, y)) => [(x, y)] -> (x, y)

newtype Wrap2_x x s  = Wrap2_x { extract2_x :: x }
newtype Wrap2_y y s  = Wrap2_y { extract2_y :: y }
instance Reifies s (SimpleMonoid_ (x, y))
         => SimpleMonoid (Wrap2_x x s, Wrap2_y y s) where
  --mappend :: (Wrap2_x x s, Wrap2_y y s) -> (Wrap2_x x s, Wrap2_y y s)
  --                 -> (Wrap2_x x s, Wrap2_y y s)
  mappend = unsafeCoerce mappend__
    where mappend__ :: (x, y) -> (x, y) -> (x, y)
          mappend__ =  (mappend_ $ reflect (undefined :: [] s))
  --mempty  :: (Wrap2_x x s, Wrap2_y y s)
  mempty = unsafeCoerce mempty__
    where mempty__  :: (x, y)
          mempty__  =  (mempty_  $ reflect (undefined :: [] s))

example_ :: forall x y. SimpleMonoid_ (x, y) -> [(x, y)] -> (x, y)
example_ dict = let
  magic :: forall s. ([(Wrap2_x x s, Wrap2_y y s)] -> (Wrap2_x x s, Wrap2_y y s))
           -> Proxy s -> ([(x, y)] -> (x, y))
  magic v _ arg1 = let
    w_arg1 :: [(Wrap2_x x s, Wrap2_y y s)]
    w_arg1 =  unsafeCoerce (arg1 :: [(x, y)])

    w_ans :: (Wrap2_x x s, Wrap2_y y s)
    w_ans = v w_arg1

    ans   :: a
    ans   = unsafeCoerce w_ans
    in ans

  in (reify dict $ magic mconcat)

---------------------------------------------------------------------
--code to reify lift_all :: (SimpleFunctor f) => [a -> b] -> [f a -> f b]

newtype Wrap_f f s d = Wrap_f { extract_fd :: f d}
instance Reifies s (SimpleFunctor_ f) => SimpleFunctor (Wrap_f f s) where
  --sfmap :: (a -> b) -> (Wrap_f f s a -> Wrap_f f s b)
  sfmap = unsafeCoerce sfmap__
    where sfmap__ :: (a -> b) -> (f a -> f b)
          sfmap__ = sfmap_ $ reflect (undefined :: [] s)

lift_all_ :: forall a b f. SimpleFunctor_ f -> [a -> b] -> [f a -> f b]
lift_all_ dict = let
  magic :: forall s. ([a -> b] -> [Wrap_f f s a -> Wrap_f f s b])
           -> Proxy s -> ([a -> b] -> [f a -> f b])
  magic v _ arg1 = let
    w_arg1 :: [a -> b]
    w_arg1 =  unsafeCoerce (arg1 :: [a -> b])

    w_ans :: [Wrap_f f s a -> Wrap_f f s b]
    w_ans = v w_arg1

    ans   :: [f a -> f b]
    ans   = unsafeCoerce w_ans
    in ans

  in (reify dict $ magic lift_all)

main :: IO ()
main = do
  print (show_2lists_ instance_SimpleShow_Int     [3, 4] [6, 9])
  print (mconcat_     instance_SimpleMonoid_lista [[1, 2], [3], [4, 5]])
  print (example_     instance_SimpleMonoid_listpair
                                     [([1, 2], ["a", "b"]), ([4], ["q"])])
  let fns' :: [[Int] -> [Int]]
      fns' = lift_all_ instance_SimpleFunctor_list [\ x -> x+1, \x -> x - 1]
  print (map ($ [5, 7]) fns')


{- output:

"[3, 4]/[6, 9]"
[1,2,3,4,5]
([1,2,4],["a","b","q"])
[[6,8],[4,6]]

-}

Note that we use a lot of unsafeCoerce, but always relating two types that differ only in the presence of a newtype. Since the run time representations are identical, this is ok.

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