# [Haskell-cafe] Automated Differentiation Type Question

Dominic Steinitz dominic at steinitz.org
Tue Apr 23 15:00:42 CEST 2013

```Answering my own question, what I needed was:

testGrad2 :: (Fractional a, Num a) =>
(forall s . Mode s => [AD s a]) ->
(forall s . Mode s => [[AD s a]]) ->
[a] -> [a]

On 23 Apr 2013, at 10:44, Dominic Steinitz <dominic at steinitz.org> wrote:

> Can anyone tell me why I get a type error with testGrad2? What are my options? Clearly I would like to be able find the gradient of my cost function for different sets of observations.
>
> Thanks, Dominic.
>
>> {-# LANGUAGE NoMonomorphismRestriction #-}
>>
>>
>> default()
>>
>> costFn :: Floating a => [a] -> [[a]] -> [a] -> a
>> costFn ys xss thetas = (/ (2*m)) \$ sum \$ map (^ (2 :: Int)) \$
>>                       zipWith (\y xs -> costFnAux y xs thetas) ys xss
>>  where
>>    m = fromIntegral \$ length xss
>>    costFnAux :: Floating a => a -> [a] -> [a] -> a
>>    costFnAux y xs thetas = y - head thetas - sum (zipWith (*) xs (tail thetas))
>>
>> ys :: Floating a => [a]
>> ys = [1.0, 2.0, 3.0]
>>
>> xss :: Floating a => [[a]]
>> xss = [[1.0], [2.0], [3.0]]
>>
>> thetas :: Floating a => [a]
>> thetas = [0.0, 1.0]
>>
>> test :: Floating a => a
>> test = costFn ys xss thetas
>>
>>
>> testGrad1 :: Floating a => [a] -> [[a]] -> [a] -> [a]
>> testGrad1 ys xss = grad (costFn (undefined :: Floating a => [a]) (undefined :: Floating a => [[a]]))
>>
>> testGrad2 :: Floating a => [a] -> [[a]] -> [a] -> [a]
>
>> [1 of 1] Compiling Main             ( /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs, interpreted )
>>
>>    from the context (Floating a)
>>      bound by the type signature for
>>                 testGrad2 :: Floating a => [a] -> [[a]] -> [a] -> [a]
>>      bound by a type expected by the context:
>>      `a' is a rigid type variable bound by
>>          the type signature for
>>            testGrad2 :: Floating a => [a] -> [[a]] -> [a] -> [a]
>>      Actual type: [a]
>>    In the first argument of `costFn', namely `ys'
>>    In the first argument of `grad', namely `(costFn ys xss)'
>>    In the expression: grad (costFn ys xss)
>>
>>    from the context (Floating a)
>>      bound by the type signature for
>>                 testGrad2 :: Floating a => [a] -> [[a]] -> [a] -> [a]
>>      bound by a type expected by the context:
>>      `a' is a rigid type variable bound by
>>          the type signature for
>>            testGrad2 :: Floating a => [a] -> [[a]] -> [a] -> [a]