I feel like you're using "mutable" too narrowly, as it's used colloquially in some programming languages. E.g. in JS, MDN itself talks about "reassignment"[0] and not "mutability" even though people often use "mutability" as a word to refer to the distinction between `const` and `let`. The only mention of mutability there is:

> Others may prefer `let` for non-primitives that are mutated

I.e. explicitly using `let` for mutated arrays, even if not reassigned, to make the signal mutability (which JS cannot express).

Note that you used "reassignment" which is the specific word for "mutating a binding", but the article is not referring to bindings at all.

[0] https://developer.mozilla.org/en-US/docs/Web/JavaScript/Refe...

Whether or not something belongs into a type system is ultimately determined by the type system. We can choose whether or not mutability is considered a part of a type.

> When we speak of "type of a variable", we mean this variable can only be assigned (bound to) values of certain type. This has nothing to do with whether it can be reassigned (i.e. mutability).

This is a bit too simplistic IMO. You're talking about name bindings, the article is talking more about things like interior mutability.

Rebinding a name is ... generally not a type system concern by my understanding.

Variables can be described by types. That is, a mutable slot referencing a value can be a value itself (a reference to a reference) and we can use subtype relationships to describe it. Variables are covariant when used as inputs (i.e code reads from the variable) and contravariant when used as outputs, and invariant when used as both. You can logically supply a Box<Cat> to a vet(in Box<Animal>) routine, and supply Box<Animal> to catchAndStore(out Box<Cat>). Substitute `ref X` for `Box<X>` when using a language that can pass variables by reference.

In statically typed languages, variables and expressions have a compile-time type and values have a run-time type.

> Mutability is a property of variable, not of a value.

In which languages?

In D, mutability is a property of a type. And variables and expressions have a compile-time type and values have a run-time type, so mutability is also a property of variables, expressions, and values.

(Immutability is also transitive in D, so an immutable value cannot have mutable parts, including mutable references, and a variable with an immutable type cannot contain a value or reference with any mutable parts.)

I'm currently being annoyed by python's type hinting system, which has exactly this sort of hierarchy for containers, but there's nothing stopping a caller/callee from using type-narrowing to "discover" that the underlying type is actually e.g. a (mutable) list, and then modifying it without any complaints from the type checker. The only way to enforce this would be to actually convert to an immutable implementation type, involving unnecessary copying.