mlstruct

Sum types in the set theoretic approach can be made with `(A & ¬B) | (¬A & B)`, or equivalently `(A | B) & (¬A | ¬B)`. There's no mainstream language with negation types, but a few good research languages with them, eg MLstruct. [MLstruct]:https://github.com/hkust-taco/mlstruct

I recommend anyone interested in this to check the work of Lionel Parreaux, in particular SimpleSub, which is equivalent to MLsub but substantially simpler. As it turns out, Dolan's main contribution wasn't the algorithm (which is overly complex, as proven by Parreaux's simpler implementation), but the type language - the insight that most subtyping constraints can be removed and/or simplified to simple union and intersection types, assuming certain simplifications of the type system (namely: positive/negative types, and distributivity of union/intersection over function types). https://lptk.github.io/programming/2020/03/26/demystifying-m... https://dl.acm.org/doi/10.1145/3409006 Parreaux is continuing to work on this problem, and has since removed one of the assumptions/simplifications (positive/negative types) in his work on MLstruct ht

> I don’t understand why… Because dynamic typing has its own advantages, which are worthy of experimentation even if you perceive absence of static typing as a weakness. Gradual typing can offer us the benefits of both worlds. > inferred typing is nearly as easy to use while being more robust. Implementing type inference can be fairly trivial if your types are all disjoint. Hindley-Milner type inference is well studied and there's plenty of literature. But as soon as you introduce subtyping, the traditional methods are not sufficient. It's only in the past decade that good solutions have been discovered, notably Dolan & Mycroft's MLsub[1], based on Dolan's Algebriac Subtyping thesis[2], and Parreaux & Chau's MLstruct[3], which uses a boolean algebra approach[4]. Type inference with subtyping is not a solved problem - these developments ar

There are fast type inference algorithms available today, such as MLStruct. [0] [0] https://github.com/hkust-taco/mlstruct