What Is First Class Label?

In languages with first-class labels, labels are treated as first-class values that can be passed as arguments. I’ll use Javascript to explain how it differs from our familiar ones.

const person = {
  name: "john",
  age: 50,
};

static_access = person.age;
dyn_label = "age";
dynamic_access = person[dyn_label];

In normal record calculi, labels are part of syntax and always statically known, as static_access. Thus, age is not a first-class label.

Javascript also supports a computed field access which allows you to give a variable which value can be assigned in runtime, then compute the result. And dyn_label is a first-class label.

Why bother?

While the behavior of dynamic semantics is straightforward, designing the corresponding type system is a challenge. For the purpose of this demonstration, I will be using” qualified type system:

In expression person.age, _.age is a operator that access constant label age, so its type can be

(_.age) :: ∀ r a. (r\age) => {age :: a | r} -> a

_age indicates that given a record containing label age, return the term with the type associated with label age.

In expression person["age"], since "age" can be given in runtime, _._ become a operator and its type is

(_[_]) ::∀ r l a. (r\l) => {l :: a | r} -> Lab l -> a

Though "age" is a string, we view it as a Lab type. The type of _[_] means given a record containing a arbitrary label l, and a label l, return the term with the type associated with label l.