Well, programming languages do have a prescriptive aspect. Arrays in C# 1.0 were more fundamental than List whereas the situation in F# 1.0 was the reverse, and F# doesn't really want you to use arrays as much as it wants you to use list.
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Personally, I always mark my classes as either sealed or abstract. In OO terms, I only care about extending the Shape class, not the individual subclasses because those themselves are are already extensions... of the Shape class. If I did want to extend, say, the Circle class, I would probably make a new abstract class called Ellipse that derived from Shape and then derive Circle from Ellipse.
But, I don't really think in strict OO terms any more. C# has a decent type system (despite what my fellow ML programmers might say), but one of the mistakes of the language (i.e. the spec) is that it conflates types with classes. Those are different things. You may see three classes, but I see one type. In this case it's a sum type called Shape that ranges over Circle and Square. A sum type , as you may know, is just the type-theoretic version of logical OR.
Indeed, it wasn't until I learned about sum types that I finally understood why you would use an abstract class as opposed to an interface: abstract classes are for when you want to say that a Foo is a Bar OR a Baz OR a Biz whereas interfaces are for when you want to say that Foo is a Bar AND a Baz, AND a Biz.
You would have to modify the code, and as I mentioned, it can be pretty painful in F# and other ML languages if you already have a bunch of functions that apply to Shape.
Subclassing is a good and useful tool that simply works better in C# than F#. But, just as importantly, class hierarchies are often a poor way to model a problem.
It just occurred to me that you may have been asking about extending Shape in the C# example. In that case, you'd just subclass Shape as normal[1]. Some people argue that sum types shouldn't be extended, but I never really understood that. Basically, C# lets you define unbounded sum types (in the form of subclassing) whereas idiomatic F# more or less demands that you know up front how many variants you're going to need.
[1] Although, sometimes I do define my classes to prevent this by marking the constructor(s) of the abstract base class as private, and then writing the derived class definitions within the body of the base class.
I have seen opinions that C# is good for architecture and F# is good for implementation of components. I might opt for such an approach. Really wish I had a default non-null immutability in C# though.
Well, programming languages do have a prescriptive aspect. Arrays in C# 1.0 were more fundamental than List whereas the situation in F# 1.0 was the reverse, and F# doesn't really want you to use arrays as much as it wants you to use list.
...
Personally, I always mark my classes as either sealed or abstract. In OO terms, I only care about extending the Shape class, not the individual subclasses because those themselves are are already extensions... of the Shape class. If I did want to extend, say, the Circle class, I would probably make a new abstract class called Ellipse that derived from Shape and then derive Circle from Ellipse.
But, I don't really think in strict OO terms any more. C# has a decent type system (despite what my fellow ML programmers might say), but one of the mistakes of the language (i.e. the spec) is that it conflates types with classes. Those are different things. You may see three classes, but I see one type. In this case it's a sum type called Shape that ranges over Circle and Square. A sum type , as you may know, is just the type-theoretic version of logical OR.
Indeed, it wasn't until I learned about sum types that I finally understood why you would use an abstract class as opposed to an interface: abstract classes are for when you want to say that a Foo is a Bar OR a Baz OR a Biz whereas interfaces are for when you want to say that Foo is a Bar AND a Baz, AND a Biz.