"The problem is that it's trying to fulfill two different purposes at the same time (addition and concatenation), so there's inconsistencies with regard to numbers."
If your numbers were Church encoded, then I guess there wouldn't be a difference between addition and concatenation. XD (This is given that concatenating functions is the same as composing them.)
Yeah, sure, and let's just use lambdas for everything:
(def cons (x y) (fn (f) (f x y)))
(def car (x) (x (fn (a b) a)))
(def cdr (x) (x (fn (a b) b)))
(car (cons 'a nil)) -> a
:P
On a semi-related note, I had an interest a while back for implementing a Lisp interpreter using only lambda-calculus. I'm still not sure if it's possible or not, but I wanted to give it a try.
