Lisp is based on lambda calculus which has no tools to modify programs written in itself, this is apparently a useful feature, so there are many lisp-like languages with added macros as such there are many different implementations of these features. Even something as prevalent in lisp-likes as eval isn't part of lambda calculus, which only has abstraction application and variables (no env). If the notion of reflection is well defined and if tree calculus is reflective then it's definitely not just lisp (certainly not forth) with a different syntax

I'm no expert so take this post with a mountain of salt. Without confusing the issue: In practice it's just a slow lisp, in theory it's different from lambda calculus and can be used to implement that slow lisp-like in a simpler way.

If it doesn't have mandatory parentheses around and indentation sensitivity, that's already a huge plus for people with my taste.

It's fine other people have different tastes really. I'm just sad that homoiconicity is mostly trapped within lisp dialects.