Problem with Numeric.AD and typing

Question

I am trying to work with Numeric.AD and a custom Expr type. I want to calculate the symbolic gradient of a user-entered expression. The first study with constant expression works beautifully:

calcGrad0 :: [Expr Double] calcGrad0 = grad df vars where df [x,y] = eval (env [x,y]) (EVar "x"*EVar "y") env vs = zip varNames vs varNames = ["x","y"] vars = map EVar varNames 

It works:

 >calcGrad0 [Const 0.0 :+ (Const 0.0 :+ (EVar "y" :* Const 1.0)),Const 0.0 :+ (Const 0.0 :+ (EVar "x" :* Const 1.0))] 

However, if you output the expression as a parameter:

 calcGrad1 :: [Expr Double] calcGrad1 = calcGrad1' (EVar "x"*EVar "y") calcGrad1' e = grad df vars where df [x,y] = eval (env [x,y]) e env vs = zip varNames vs varNames = ["x","y"] vars = map EVar varNames 

I get

 Could not deduce (a ~ AD s (Expr a1)) from the context (Num a1, Floating a) bound by the inferred type of calcGrad1' :: (Num a1, Floating a) => Expr a -> [Expr a1] at Symbolics.hs:(60,1)-(65,29) or from (Mode s) bound by a type expected by the context: Mode s => [AD s (Expr a1)] -> AD s (Expr a1) at Symbolics.hs:60:16-27 `a' is a rigid type variable bound by the inferred type of calcGrad1' :: (Num a1, Floating a) => Expr a -> [Expr a1] at Symbolics.hs:60:1 Expected type: [AD s (Expr a1)] -> AD s (Expr a1) Actual type: [a] -> a In the first argument of `grad', namely `df' In the expression: grad df vars 

How do I get ghc to accept this?

Answer 1

I assume that you forget to use lift to convert Expr to AD s Expr .

If you are interested in using the ad package for symbolic differentiation. Lennart Augustsson traced package works well.

Answer 2

When the GHC cannot deduce a type equality signature for a real function, as in your case, the solution should give the function a type signature. I do not know the interface to this library. However, I assume that the correct signature is calcGrad1 :: (Num a, Floating a) => Expr a -> [Expr a] .