types.markdown

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Thanks. Good clean article.

no popular type system can actually express our HighFive type above

data HighFive = Hi | Five

I call bullshit. Unless you have a very interesting definition of “popular” or “types”.

@Profpatsch The constructor Five is not the integer 5. Likewise, the constructor Hi is not the string "hi".

@Profpatsch I would've just given him the type Bool.

@garybernhardt Any singleton is as good as any other. They're isomorphic.

@eduardoleon Integers are a set of values containing 5 and others. Strings are a set of values containing "hi" and others. HighFive is the set of values {5, "hi"}, and each of those values also exists within one of the Integer and String sets. A value taken from HighFive is exactly equal to the same value taken from Integer or String, can be compared against it, etc.

This is not an idea that's directly expressible in Haskell; or, as far as I know, in any actual type system. People have told me that it's expressible in TypeScript, but I'm skeptical.

This example is clearly confusing. But, interestingly, the only people who have objected to it have shown that they know an ML-descended language. I suspect that people with no formalities to fall back on pass right over it without a problem. There are sets of values. Some sets intersect with other sets. It's not a big deal.

Of course, all of this is arguing the color that we should paint a yak at the bottom of a rabbit hole. This is the introductory paragraph of a 3,500-word article; a paragraph that contains no details about any formal mathematical system or software system.

@garybernhardt It should be add instead of f in this Haskell example:

f :: Num a => a -> a -> a
add x y = x + y

@EvgenyOrekhov Nice catch, thanks!

There is Complexity Zoo. Does anybody aware of similar resource for type systems?

Is there a list of languages by type system power like the one at the end of this gist, but then with more languages? There is the Comparison of programming languages by type system on Wikipedia, though this does not have the categorization used in the gist and cannot really be sorted.