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So I spent a few days trying to read research papers and even a PhD thesis or two. There are some really great ideas out there. From Algorithm W to Algorithm M to the Generalizing Hindley-Milner Type Inference
Algorithms paper, finally reaching the PhD thesis that Facebook's Flow is based on: Type Inference in the Presence of Subtyping: from Theory to Practice (pdf) and then being pointed to (on the #proglangdesign IRC channel on Freenode) some more recent work in the area, another PhD thesis: Algebraic Subtyping (pdf).
The last two seem particularly relevant to what I'm trying to do, given that Facebook's Flow is solving pretty much the same problem as my type checker/inferencer.
However, the issue with all these papers is that I'm too unfamiliar with the notation and background to understand the ideas presented in them, and I'm not currently willing to spend time on doing the necessary background work. I'm closing this issue as "stalled" as of now. :/
If someone familiar with this stuff or willing to pick up this stuff wants to implement the typechecker, please feel free to announce and reopen! :D