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> But that's a modularity issue, has nothing to do with exhaustiveness, and can also go the other way (as pattern matching makes it hard to add new variants to an ADT in a modular fashion).

I would disagree on this point. With exhaustiveness checks you get at least errors in every place you match against a data type you just extended with a new variant. So your compiler can point you to the places you have to edit after adding new variants to your ADT. That's a helpful feature.

Note that I talked about doing it in a modular fashion. With an ADT, you have to rewrite every single pattern match in your code to support the new variant. (And you don't even get warnings if you have a general fallback case that matches everything.)

In an OO language, the equivalent to simple pattern matching would be to dispatch on an abstract method of a shared supertype. If you add a new type and forget to implement the abstract method, you get a compiler error. There's your exhaustiveness checking and it's entirely modular as you don't have to touch your original code.

As I said, that's one side of the expression problem. OO languages conversely have a problem (unless they support multiple dispatch or methods external to a class) when they have to add new actions. With ADTs, that's just a new function. With inheritance, you have to add a new method to every single class that implements a variant.

The expression problem has two sides, right. I don't advocated that pattern matching on ADTs is "the better" solution. Neither the OO approach is.

There isn't usually a 100% modular solution, because you want to stay flexible respectively in either dimension, to some extend. You have to chose between trade-off (as always).

That's way I like hybrid languages like Scala where I can actually make an informed choice whether it's more likely to add new variants or more functionality in the future. But when I have to do the thing I didn't anticipate in the first place I want help from the compiler to avoid errors. That's way an exhaustiveness checker for pattern matching is a very welcomed and neat feature.

> There isn't usually a 100% modular solution, because you want to stay flexible respectively in either dimension, to some extend. You have to chose between trade-off (as always).

There are actually language mechanisms that can get you both. multimethods, for example, or their ultimate generalization, predicate dispatch. Few languages support them, though, because they are overkill for most application domains (though there are some, such as computer algebra, where they can be very useful).

Note also that while many OO languages constrain you in having methods only occur within a class definition, this is not a requirement. Multimethods invariably need to be more flexible (because there's no privileged "self" object), but the multimethod approach can also be applied to single dispatch. See also partial classes and related techniques.

Also, ADTs in their basic form are still a very specialized, limited form of sum types. Even if you want sum types, better extensibility is often needed (though ADTs remain a very useful special case), as well as the ability to actually describe subtypes of a sum type.

See how OCaml ended up with having polymorphic variants and extensible variant types and Scala with case classes, for example.

it is well known the expression problem is trivial in dynamic (untyped) languages—however, static type safety is a requirement of the problem definition of the expression problem.

I didn't mention dynamic typing anywhere?

no, but multi-methods are 99% of the time found in dynamic languages, right?

1. Multimethods simply are a rare feature in general.

2. Multiple dispatch and static typing are completely orthogonal features.

3. Strictly speaking, you don't even need multiple dispatch. The key feature of multimethods that you need is the ability to add a method outside the class body.

under definition 3 then extension methods are also multi-methods - doesn't seem right. even c# has extension methods

Extension methods do not support dynamic dispatch and hence are not proper instance methods. Try MultiJava's open classes for an approach that works.

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