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In a language like Python you can consider there to be one type called, say, ThePythonType, or which all types are a variant. Then all objects have type ThePyth

In a language like Python you can consider there to be one type called, say, ThePythonType, or which all types are a variant. Then all objects have type ThePythonType. A more useful type system would have "union types". They differ from sum types in that you can construct a union type from existing types in an ad-hoc manner. For example, if you have a function that returns a string or nil you can construct a union type "Union of string or nil". To do this with a sum type you'd have to have a common super type of string and nil and no other types. There are also intersection types, about which I know very little.

seanmcdirmid 12y ago
> In a language like Python you can consider there to be one type called, say, ThePythonType, or which all types are a variant. Then all objects have type ThePythonType. This is only if you reject the notion of a dynamic type (as most type theorists do, but programmers do not). Otherwise, Python has a rich type system that is checked at run-time. It lacks sum types, but we could easily imagine a dynamically checked realization.
- jlouis 12y ago
  A good way of getting at this is to call things at runtime "classes" or "tags" to make it apparent that their discrimination happens at runtime, not compile-time. The problem is that if you call both things types, you quickly run into a situation where you are essentially talking about different concepts entirely. Note that most sum-types are implemented by having a runtime tag on which you can discriminate.
  - seanmcdirmid 12y ago
    Classes exist statically also. Tags are meaningless outside of implementation discussions.
- tel 12y ago
  I don't think type theorists reject that at all. They just don't call them "types". Which I don't know why anyone would care in the context of a technical argument. If an "average programmer" here and a type theorist spent 1 minute at the beginning of the conversation normalizing terms then nobody would have any argument here. I don't think anyone tries to claim that "types" and "static types" (or, in the type theorist's parlance, "tags" and "types") are the same... they just try to argue whether or not it's "right" to call one or the other by the name "type".
  - seanmcdirmid 12y ago
    Most type theorists reject that dynamic typing is meaningful and not a misnomer, hence Noel Welsh's assertion that Python has only one type. It doesn't start the conversation off very well.
    - dllthomas 12y ago
      Did you mean that to be a restatement of what tel said? It seems to be.
      - seanmcdirmid 12y ago
        All but the "if we just listened to each other, we'd understand each other." The type theorist's and programmer's different perspective s means basically that we'd fight over the meaning of type for our entire conversation.
        dllthomas 12y ago
        It wasn't "if we listened", but "if we normalized terms". I agree that getting people to normalize terms with the aim of successfully communicating can be difficult...
    - tel 12y ago
      I don't think anyone argues that Python has more than one (static) type. It however has a dynamic type system. Significantly, static types and dynamic types do not behave the same way and their corresponding theories have somewhat minor overlap. In particular, many things I can state about static types do not carry over to dynamic types and visa versa. I believe many conversations get derailed early because among static type researchers, static types are known merely as "types" and dynamic types as "tags" or "classes". There are meaningful ways to compare these two kinds of things but somehow or another they ought to have different words since confusing the concepts will inhibit understanding quite severely.
dllthomas 12y ago
"To do this with a sum type you'd have to have a common super type of string and nil and no other types." This seems wrong. You can make a new type that simply contains one of those, right? In a sense that's what you're doing with a sum type in Haskell, though there you get to produce new types automatically from higher kinded types.
theseoafs 12y ago
> To do this with a sum type you'd have to have a common super type of string and nil and no other types. I'm not sure you understand sum types. Sum types subsume normal unions; sum types and unions are essentially the same thing and capturing this kind of return type in Haskell or ML is extremely easy. "Supertypes" are completely unrelated and subtyping is not actually needed in languages with sum types (for example Haskell has sum types but doesn't have any real form of subtyping). For example in Haskell you'd use the `Maybe` type constructor. If your type returns a `Maybe String` that means it either returns a string or nothing.
- dllthomas 12y ago
  You can implement a (open) sum type with supertypes, though, can't you?
  - theseoafs 12y ago
    Sort of. You can effectively do so in a language like Java, which allows you to inspect the types of objects at runtime. For example if you have a class `Foo` with two subclasses `SubA` and `SubB` you could do something like this: public static void test(Foo f) { if (f isinstanceof SubA) { SubA a = (SubA)f; /* ... */ } else if (f isinstanceof SubB) { SubB b = (SubB)f; } } This works okay but you have to implement all the machinery yourself, and for a statically typed language Java is notoriously type-unsafe so if you make a mistake with your casts you're basically not going to find out until you get an exception at runtime. And of course there might be other existing subclasses of `Foo` which means that you get no compile-time guarantee that you didn't miss a possible case. Standard ML approaches subtyping in a very different way that renders this kind of approach impossible. It gives you less freedom in that it eliminates downcasting, but that ultimately results in a safer language. Of course Standard ML has proper sum types with all of their compile-time guarantees so there's little reason for it anyway.
    - deleted 12y ago
      [deleted]

seanmcdirmid 12y ago

> In a language like Python you can consider there to be one type called, say, ThePythonType, or which all types are a variant. Then all objects have type ThePythonType. This is only if you reject the notion of a dynamic type (as most type theorists do, but programmers do not). Otherwise, Python has a rich type system that is checked at run-time. It lacks sum types, but we could easily imagine a dynamically checked realization.

jlouis 12y ago
A good way of getting at this is to call things at runtime "classes" or "tags" to make it apparent that their discrimination happens at runtime, not compile-time. The problem is that if you call both things types, you quickly run into a situation where you are essentially talking about different concepts entirely. Note that most sum-types are implemented by having a runtime tag on which you can discriminate.
- seanmcdirmid 12y ago
  Classes exist statically also. Tags are meaningless outside of implementation discussions.
tel 12y ago
I don't think type theorists reject that at all. They just don't call them "types". Which I don't know why anyone would care in the context of a technical argument. If an "average programmer" here and a type theorist spent 1 minute at the beginning of the conversation normalizing terms then nobody would have any argument here. I don't think anyone tries to claim that "types" and "static types" (or, in the type theorist's parlance, "tags" and "types") are the same... they just try to argue whether or not it's "right" to call one or the other by the name "type".
- seanmcdirmid 12y ago
  Most type theorists reject that dynamic typing is meaningful and not a misnomer, hence Noel Welsh's assertion that Python has only one type. It doesn't start the conversation off very well.
  - dllthomas 12y ago
    Did you mean that to be a restatement of what tel said? It seems to be.
    - seanmcdirmid 12y ago
      All but the "if we just listened to each other, we'd understand each other." The type theorist's and programmer's different perspective s means basically that we'd fight over the meaning of type for our entire conversation.
      - dllthomas 12y ago
        It wasn't "if we listened", but "if we normalized terms". I agree that getting people to normalize terms with the aim of successfully communicating can be difficult...
  - tel 12y ago
    I don't think anyone argues that Python has more than one (static) type. It however has a dynamic type system. Significantly, static types and dynamic types do not behave the same way and their corresponding theories have somewhat minor overlap. In particular, many things I can state about static types do not carry over to dynamic types and visa versa. I believe many conversations get derailed early because among static type researchers, static types are known merely as "types" and dynamic types as "tags" or "classes". There are meaningful ways to compare these two kinds of things but somehow or another they ought to have different words since confusing the concepts will inhibit understanding quite severely.

dllthomas 12y ago

"To do this with a sum type you'd have to have a common super type of string and nil and no other types." This seems wrong. You can make a new type that simply contains one of those, right? In a sense that's what you're doing with a sum type in Haskell, though there you get to produce new types automatically from higher kinded types.

theseoafs 12y ago

> To do this with a sum type you'd have to have a common super type of string and nil and no other types. I'm not sure you understand sum types. Sum types subsume normal unions; sum types and unions are essentially the same thing and capturing this kind of return type in Haskell or ML is extremely easy. "Supertypes" are completely unrelated and subtyping is not actually needed in languages with sum types (for example Haskell has sum types but doesn't have any real form of subtyping). For example in Haskell you'd use the `Maybe` type constructor. If your type returns a `Maybe String` that means it either returns a string or nothing.

dllthomas 12y ago
You can implement a (open) sum type with supertypes, though, can't you?
- theseoafs 12y ago
  Sort of. You can effectively do so in a language like Java, which allows you to inspect the types of objects at runtime. For example if you have a class `Foo` with two subclasses `SubA` and `SubB` you could do something like this: public static void test(Foo f) { if (f isinstanceof SubA) { SubA a = (SubA)f; /* ... */ } else if (f isinstanceof SubB) { SubB b = (SubB)f; } } This works okay but you have to implement all the machinery yourself, and for a statically typed language Java is notoriously type-unsafe so if you make a mistake with your casts you're basically not going to find out until you get an exception at runtime. And of course there might be other existing subclasses of `Foo` which means that you get no compile-time guarantee that you didn't miss a possible case. Standard ML approaches subtyping in a very different way that renders this kind of approach impossible. It gives you less freedom in that it eliminates downcasting, but that ultimately results in a safer language. Of course Standard ML has proper sum types with all of their compile-time guarantees so there's little reason for it anyway.
  - deleted 12y ago
    [deleted]