Anyway, if you would be allowed to reimplement a built-in operator, then from then on you would be using the new operator and you would be limited to its syntax.
Common Lisp OTOH provides namespaces (called "package") and there is a pre-defined namespace "COMMON-LISP" for the core language.
This hasn't been a problem in this thread thus far, but to be explicit, this seems like a good definition: https://en.wikipedia.org/wiki/Lisp_%28programming_language%2...
Given that definition, we can see that there are many actual standards for programming languages with specifications under the name "Lisp". Scheme - as was mentioned in this thread, is one such standard, along with Common Lisp.
> Anyway, if you would be allowed to reimplement a built-in operator, then from then on you would be using the new operator and you would be limited to its syntax.
I think you're arguing the merits of doing something like redefining define here, which is not the subject of this comment chain. Of course such behavior is questionable at best. The comment chain is discussing if such a thing would be valid in Lisp - and, in some dialects (such as Scheme) it is.
Scheme also has a feature called "libraries" which makes such behavior more feasible, as you could still have access to the shadowed primitive. Consider:
gosh[r7rs.user]$ (import (prefix (scheme base) base:))
gosh[r7rs.user]$ (define (define x) 5)
define
gosh[r7rs.user]$ (base:define x (+ (define define) (define define)))
x
gosh[r7rs.user]$ x
10
Then see the Scheme standards. They include a syntax definition.
> The comment chain is discussing if such a thing would be valid in Lisp - and, in some dialects (such as Scheme) it is.
Lisp is not a defined language, thus you can assume anything.
My point is: Lisp dialects have syntax. This syntax is usually defined on top of s-expressions. S-expressions also have a syntax, but this syntax usually (there are exceptions) describes only data types (lists, conses, numbers, strings, symbols, arrays, records/structures, bit vectors, pathnames, ...) and not the actual programming language with its operators (functions, macros, special operators) & their way to define and invoke them.
Example: The LET operator in various Lisp dialects there have a specific syntax. This syntax is not the syntax of simple function calls like (operator arg0 ... args).
R7RS small defines this syntax (and also calls it syntax):
(let ⟨bindings⟩ ⟨body⟩)
(let ⟨variable⟩ (⟨binding spec⟩*) ⟨tail body⟩)
⟨Bindings⟩ has the form ((⟨variable1⟩ ⟨init1⟩) ...)