圏論とHaskellが関係あるとか言ってる奴どっちか詳しくねぇだろと思ってる

高速なコードを書くのと可換図式は別ものすぎる

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I get the point -- but I feel like it's to do with way of thinking.

Functional programming style involves shifting the thought process from procedural style (otherwise it'll be forec-fitting same behaviour). And maybe the same sort of thinking is need to understand operations on groups or monoids.

In the end, writing the code like Whitecat-san mentioned is a different skillset