A friend introduced me to Hindley Milner set of equations and the first time (Oct 2019), they looked like arcane maths problems. The looked no different the 7th or 8th time I saw them. I felt the notations were heavily throwing me off. In 2020 I revisited type systems and saw the same equations again.

Luckily this time, I found this stackoverflow thread that resonates with my helplessness of the terminology used. After going through the thread and understanding missing pieces from other sources, here is my take on the equations.

I didn't fully understand this, why is $e_1$ required, it doesn't seem to help proving anything? Let me know in the comments, clearly I am missing something.