Other comments are saying non-capturing closures are not closures. If we want to have this pedantic argument of definitions: proto_lambda is actually right, with Rust's definition of closures.

According to the Rust reference:

Closure types > > A closure expression produces a closure value with a unique, anonymous type that cannot be written out.

https://doc.rust-lang.org/reference/types/closure.html

Even a non-capturing closure is written using a closure expression and produces a unique, anonymous type.