Lately I found it's (far) more intriguing to read PhD dissertations compared with other kinds of papers/textbooks. When reading 「A Behavioral Notion of Subtyping」 by Barbara H. Liskov, i derived some interest at subtyping, but wanted to study about it in the functional world intead. Some (re)searches led me to Stephen Dolan's PhD dissertation 「Algebraic Subtyping」. The title immediately illuminated me, since i've been addicted to algebraic stuff (algebraic effects, etc.) but have never actually studied closely about them. This series of pages serve as my interpretation of his complete algebraic subtyping system as well as (some of) the obscure concepts behind.