types.markdown

This document has moved!

It's now here, in The Programmer's Compendium. The content is the same as before, but being part of the compendium means that it's actively maintained.

@eduardoleon - very much agree with you. One of the goals for me in a type system is to make undesirable or invalid states unrepresentable. The smallest algebra I can implicitly define which represents my desired program and nothing else is the right thing. Thanks for the mention of minimal logic, not something I've looked at in depth before. One for my reading list.

@stereobooster: You can write OO without runtime tagging, but you lose reflection. Haskell also has runtime tagging: that's essentially what that Typeable snippet above is doing.

While program expressions are best typed at their most general, at runtime values can be tagged with their most specific types. It's possible (but not obvious or easy) to have the runtime types be similar or even a subset of the compile time types which creates a strong linkage.

@tiborsaas None of those arguments are really about static vs dynamic types.

1. [Short code] I have found no evidence that static types necessarily causes more code, especially when you have automatic type inference, so you don't actually have to write any type signatures yourself. In some cases you actually need less code since the types carry some of the information needed.
   For example: QuickCheck (an automatic property tester) is a pain to use in Erlang, but it's fully automatic in Haskell, since it can figure out what kind of input to use automatically from the types.
   Furthermore, you'll usually need more unit tests to compensate for the lack of types, which is usually a lot less compact than the corresponding type annotations.
2. [Javascript example] You can just as easily have automatic coercion (aka. "Weak types") in a statically typed language as in a dynamic one. That is a completely different question.

See also, the blog post about common fallacies in the dynamic vs static types debate, that was quoted in the article: https://cdsmith.wordpress.com/2011/01/09/an-old-article-i-wrote/

@yogthos No one is forcing you to prove anything just because you are using a static language. If anything, the compiler relieves you of the burden of proof, by doing the heavy lifting for you.

If you want to, you can encode many complex properties in the types and have the compiler verify them for you. This is obviously more difficult the more complex properties you try to enforce.

If you don't want to do that, just write code similar/identical to what you would have written in a dynamically typed language and get some simple proofs (compatible types, no missing methods, etc.) for free.

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.