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Algebraic structures with newtype

Goal: tie implementations of (+), (*) to (<>) and (-), (/) to combination of (<>) and inverse.

  • Data.Group - intermediate module that defines inverse.
  • Data.Semiring - re-uses 2 Monoid instances to get zero, (+), one, (*).
  • Data.Ring and Data.Field - adds Group requirements on top of Semiring to get - and /.

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