Is there an existing typeclass for differences?

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  • linear

    Low-dimensional linear algebra primitives for Haskell.

    That's pretty much exactly the abstraction used in the 'linear' package's Affine class, in which we find points separated by vectors.

  • gdiff

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  • patch

    Data structures for describing changes to other data structures. (by reflex-frp)

    If you want to capture the notion of "changes that can be applied to a structure", then the patch library might be up your alley. but it sounds like you want diffing as well.

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