How does Haskell know whether a data type declaration is a variable or a named type?

Question

Take a data type declaration like

data myType = Null | Container TypeA v 

As I understand it, Haskell would read this as myType coming in two different flavors. One of them is Null which Haskell interprets just as some name of a ... I guess you'd call it an instance of the type? Or a subtype? Factor? Level? Anyway, if we changed Null to Nubb it would behave in basically the same way--Haskell doesn't really know anything about null values.

The other flavor is Container and I would expect Haskell to read this as saying that the Container flavor takes two fields, TypeA and v. I expect this is because, when making this type definition, the first word is always read as the name of the flavor and everything that follows is another field.

My question (besides: did I get any of that wrong?) is, how does Haskell know that TypeA is a specific named type rather than an un-typed variable? Am I wrong to assume that it reads v as an un-typed variable, and if that's right, is it because of the lower-case initial letter?

By un-typed I mean how the types appear in the following type-declaration for a function:

func :: a -> a 
func a = a

Answer 1

First of all, terminology: "flavors" are called "cases" or "constructors". Your type has two cases - Null and Container.

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Second, what you call "untyped" is not really "untyped". That's not the right way to think about it. The a in declaration func :: a -> a does not mean "untyped" the same way variables are "untyped" in JavaScript or Python (though even that is not really true), but rather "whoever calls this function chooses the type". So if I call func "abc", then I have chosen a to be String, and now the compiler knows that the result of this call must also be String, since that's what the func's signature says - "I take any type you choose, and I return the same type". The proper term for this is "generic".

The difference between "untyped" and "generic" is that "untyped" is free-for-all, the type will only be known at runtime, no guarantees whatsoever; whereas generic types, even though not precisely known yet, still have some sort of relationship between them. For example, your func says that it returns the same type it takes, and not something random. Or for another example:

mkList :: a -> [a]
mkList a = [a]

This function says "I take some type that you choose, and I will return a list of that same type - never a list of something else".

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Finally, your myType declaration is actually illegal. In Haskell, concrete types have to be Capitalized, while values and type variables are javaCase. So first, you have to change the name of the type to satisfy this:

data MyType = Null | Container TypeA v

If you try to compile this now, you'll still get an error saying that "Type variable v is unknown". See, Haskell has decided that v must be a type variable, and not a concrete type, because it's lower case. That simple.

If you want to use a type variable, you have to declare it somewhere. In function declaration, type variables can just sort of "appear" out of nowhere, and the compiler will consider them "declared". But in a type declaration you have to declare your type variables explicitly, e.g.:

data MyType v = Null | Container TypeA v

This requirement exist to avoid confusion and ambiguity in cases where you have several type variables, or when type variables come from another context, such as a type class instance.

Declared this way, you'll have to specify something in place of v every time you use MyType, for example:

n :: MyType Int
n = Null

mkStringContainer :: TypeA -> String -> MyType String
mkStringContainer ta s = Container ta s

-- Or make the function generic
mkContainer :: TypeA -> a -> MyType a
mkContainer ta a = Container ta a

Answer 2

Haskell uses a critically important distinction between variables and constructors. Variables begin with a lower-case letter; constructors begin with an upper-case letter¹.

So data myType = Null | Container TypeA v is actually incorrect; the first symbol after the data keyword is the name of the new type constructor you're introducing, so it must start with a capital letter.

Assuming you've fixed that to data MyType = Null | Container TypeA v, then each of the alternatives separated by | is required to consist of a data constructor name (here you've chosen Null and Container) followed by a type expression for each of the fields of that constructor.

The Null constructor has no fields. The Container constructor has two fields:

1. TypeA, which starts with a capital letter so it must be a type constructor; therefore the field is of that concrete type.
2. v, which starts with a lowercase letter and is therefore a type variable. Normally this variable would be defined as a type parameter on the MyType type being defined, like data MyType v = Null | Container TypeA v. You cannot normally use free variables, so this was another error in your original example.²

Your data declaration showed how the distinction between constructors and variables matters at the type level. This distinction between variables and constructors is also present at the value level. It's how the compiler can tell (when you're writing pattern matches) which terms are patterns it should be checking the data against, and which terms are variables that should be bound to whatever the data contains. For example:

lookAtMaybe :: Show a => Maybe a -> String
lookAtMaybe Nothing = "Nothing to see here"
lookAtMaybe (Just x) = "I found: " ++ show x

If Haskell didn't have the first-letter rule, then there would be two possible interpretations of the first clause of the function:

1. Nothing could be a reference to the externally-defined Nothing constructor, saying I want this function rule to apply when the argument matches that constructor. This is the interpretation the first-letter rule mandates.
2. Nothing could be a definition of an (unused) variable, representing the function's argument. This would be the equivalent of lookAtMaybe x = "Nothing to see here"

Both of those interpretations are valid Haskell code producing different behaviour (try changing the capital N to a lower case n and see what the function does). So Haskell needs a rule to choose between them. The designers chose the first-letter rule as a way of simply disambiguating constructors from variables (that is simple to both the compiler and to human readers) without requiring any additional syntactic noise.

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¹ The rule about the case of the first letter applies to alphanumeric names, which can only consist of letters, numbers, and underscores. Haskell also has symbolic names, which consists only of symbol characters like +, *, :, etc. For these, the rule is that names beginning with the : character are constructors, while names beginning with another character are variables. This is how the list constructor : is distinguished from a function name like +.

² With the ExistentialQuantification extension turned on it is possible to write data MyType = Null | forall v. Container TypeA v, so that the the constructor has a field with a variable type and the variable does not appear as a parameter to the overall type. I'm not going to explain how this works here; it's generally considered an advanced feature, and isn't part of standard Haskell code (which is why it requires an extension)