I'm trying to write a determinant function that works on matrices parameterized by their dimensions (Peano naturals). If I declare the following, -- Define a class so that we get a different determinant function -- on the base/recursive cases. class (Eq a, Ring.C a) => Determined m a where determinant :: (m a) -> a -- Base case, 1x1 matrices instance (Eq a, Ring.C a) => Determined (Mat (S Z) (S Z)) a where determinant m = m !!! (0,0) -- Recursive case, (n+2) x (n+2) matrices. instance (Eq a, Ring.C a, Arity n) => Determined (Mat (S (S n)) (S (S n))) a where determinant m = ... -- Recursive algorithm, the i,jth minor has dimension -- (n+1) x (n+1). foo bar (determinant (minor m i j)) I get an error stating that I'm missing an instance: Could not deduce (Determined (Mat (S n) (S n)) a) ... Clearly, I *have* an instance for that case: if n == Z, then it's the base case. If not, it's the recursive case. But GHC can't figure that out. So maybe if I define a dummy instance to make it happy, it won't notice that they overlap? instance (Eq a, Ring.C a) => Determined (Mat m m) a where determinant _ = undefined No such luck:

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let m = fromList [[1,2],[3,4]] :: Mat2 Int determinant m

Overlapping instances for Determined (Mat N2 N2) Int arising from a use of `determinant' Matching instances: instance (Eq a, Ring.C a) => Determined (Mat m m) a -- Defined at Linear/Matrix2.hs:353:10 instance (Eq a, Ring.C a, Arity n) => Determined (Mat (S (S n)) (S (S n))) a ... I even tried generalizing the (Mat m m) instance definition so that OverlappingInstances would pick the one I want, but I can't get that to work either. Is there some way to massage this?