I think the problem in this case is that the author's attempt at generalization went off in the wrong direction.

The fact that fixed-length lists aren't working well as a representation for polynomials is a hint. Polynomials with real coefficients form a vector space [0], so you should really think of them as infinite-dimensional lists of numbers (in which most of the numbers are zero).

Once you know you want to represent an infinite dimensional vector with only a few nonzero entries, you can use a sparse vector. The first library that comes up when you google "Haskell sparse vector" is `Math.LinearAlgebra.Sparse.Vector`, which lets you write something like this (I haven't run this code but it should get the job done):

import Math.LinearAlgebra.Sparse.Vector as V

poly1 = V.sparseList [1, -3, 0, 1]

poly2 = V.sparseList [3, 3]

sumPolys = V.unionVecsWith (+)

So, I read this more as an article about trying to reinvent the wheel in a domain which isn't necessarily simple, which isn't a good idea in any language.

[0]: https://en.wikipedia.org/wiki/Examples_of_vector_spaces#Poly...