Haskell - Implementing Monoid what happens if the operator is not associative
haskell, monoids
Solution
Nothing bad would happen in terms of type safety: Your programs will still not crash.
But a data structure relying on your `Monoid` instance might give unexpected or wrong results.
Consider a tree that is re-balanced upon insertion, and that provides a way to combine its elements using their `Monoid` instance. Then the re-balancing, which is supposed to be an internal operation and not visible to you becomes observable, and referential transparency is “morally broken” – same input (up to supposedly hidden internals), but different output.
Problem
According to the definition or a monoid the binary operator must be associative e.g. `A op (B op C) == (A op B) op C`. The base `mconcat` definition in haskell is: ``` mconcat = foldr mappend mempty ``` Since I know the implementation details of the `mconcat` function, would anything bad happen from defining and using fake monoids where the function isn't associative? Like for example defining instances for subtraction or division. Could this be useful or am I missing the point?