Numeric.AD - 類型變量轉義範圍

Question

我試圖在Haskell中使用automatic differentiation來處理非線性控制問題，但在使其運行時遇到一些問題。我基本上有一個cost函數，應該在初始狀態下對其進行優化。該類型是：

data Reference a = Reference a deriving Functor 
data Plant a = Plant a deriving Functor 

optimize :: (RealFloat a) => Reference a -> Plant a -> [a] -> [[a]] 
optimize ref plant initialInputs = gradientDescent (cost ref plant) initialInputs 

cost :: (RealFloat a) => Reference a -> Plant a -> [a] -> a 
cost = ... 

這將導致以下錯誤消息：

Couldn't match expected type `Reference 
           (Numeric.AD.Internal.Reverse.Reverse s a)' 
      with actual type `t' 
    because type variable `s' would escape its scope 
This (rigid, skolem) type variable is bound by 
    a type expected by the context: 
    Data.Reflection.Reifies s Numeric.AD.Internal.Reverse.Tape => 
    [Numeric.AD.Internal.Reverse.Reverse s a] 
    -> Numeric.AD.Internal.Reverse.Reverse s a 
    at test.hs:13:5-50 
Relevant bindings include 
    initialInputs :: [a] (bound at test.hs:12:20) 
    ref :: t (bound at test.hs:12:10) 
    optimize :: t -> t1 -> [a] -> [[a]] (bound at test.hs:12:1) 
In the first argument of `cost', namely `ref' 
In the first argument of `gradientDescent', namely 
    `(cost ref plant)' 

我甚至不知道我是否正確理解錯誤。難道，ref和plant的類型需要訪問s，這是在gradientDescent的第一個參數的範圍內嗎？

是否有可能使這項工作？雖然尋找一個解決方案，我試圖減少問題小例子，發現下面的定義會產生類似的錯誤消息：

optimize f inputs = gradientDescent f inputs 

這似乎有點奇怪，因爲optimize = gradientDescent不會產生任何錯誤。

Answer 1

cost ref plant有型[a] -> a其中a相同a作爲簽名optimize

optimize :: (RealFloat a) => Reference a -> Plant a -> [a] -> [[a]] 
            ^  ^
             |   ------------ 
             ------------------v v 
optimize ref plant initialInputs = gradientDescent (cost ref plant) initialInputs 
                 ^^
            ----------------------- | 
            v   v--------------- 
cost :: (RealFloat a) => Reference a -> Plant a -> [a] -> a 
cost = ... 

但gradientDescent類型是

gradientDescent :: (Traversable f, Fractional a, Ord a) => 
        (forall s. Reifies s Tape => f (Reverse s a) -> Reverse s a) -> 
        f a -> [f a] 

的第一個參數gradientDescent需要能夠（任何s）[Reverse s a]並返回Reverse s a，但cost ref plant只能拿[a]返回a。

由於Reference和Plant都是Functor S，您可以通過fmap荷蘭國際集團auto轉換ref和plant從Reference a和Plant a到Reference (Reverse s a)和Plant (Reverse s a)。

optimize :: (RealFloat a) => Reference a -> Plant a -> [a] -> [[a]] 
optimize ref plant initialInputs = gradientDescent (cost (fmap auto ref) (fmap auto plant)) initialInputs