Could not deduce (A) from the context (A, ...)

The following code doesn't compile and produces a strange error:

{-# LANGUAGE TypeFamilies, FlexibleContexts #-}

module Numeric.AD.Internal.Tower () where

type family Scalar t

newtype Tower s a = Tower [a]

type instance Scalar (Tower s a) = a

class (Num (Scalar t), Num t) => Mode t where
    (<+>) :: t -> t -> t

instance (Num a) => Mode (Tower s a) where
    Tower as <+> _ = undefined
      where
        _ = (Tower as) <+> (Tower as)

instance Num a => Num (Tower s a) where

src/Numeric/AD/Internal/Tower.hs:17:24:
    Could not deduce (Num (Scalar (Tower s a)))
      arising from a use of `<+>'
    from the context (Num (Scalar (Tower s a)), Num (Tower s a), Num a)
      bound by the instance declaration
      at src/Numeric/AD/Internal/Tower.hs:14:10-36
    Possible fix:
      add an instance declaration for (Num (Scalar (Tower s a)))
    In the expression: (Tower as) <+> (Tower as)
    In a pattern binding: _ = (Tower as) <+> (Tower as)
    In an equation for `<+>':
        (Tower as) <+> _
          = undefined
          where
              _ = (Tower as) <+> (Tower as)

Furthermore, Removing the Num (Scalar t) constraint from the Mode class produces a different strange error:

src/Numeric/AD/Internal/Tower.hs:17:24:
    Overlapping instances for Num (Tower s0 a)
      arising from a use of `<+>'
    Matching givens (or their superclasses):
      (Num (Tower s a))
        bound by the instance declaration
        at src/Numeric/AD/Internal/Tower.hs:14:10-36
    Matching instances:
      instance Num a => Num (Tower s a)
        -- Defined at src/Numeric/AD/Internal/Tower.hs:19:10
    (The choice depends on the instantiation of `a, s0')
    In the expression: (Tower as) <+> (Tower as)
    In a pattern binding: _ = (Tower as) <+> (Tower as)
    In an equation for `<+>':
        (Tower as) <+> _
          = undefined
          where
              _ = (Tower as) <+> (Tower as)

Trac metadata

Trac field	Value
Version	7.6.2
Type	Bug
TypeOfFailure	OtherFailure
Priority	normal
Resolution	Unresolved
Component	Compiler (Type checker)
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