Lambda (Functions)

(lambda (x y) (+ x y))

Creates an ANONYMOUS function. Equivalent to Python's lambda x, y: x + y.

((lambda (x y) (+ x y)) 3 4)   -> 7
(define add (lambda (x y) (+ x y)))
(add 3 4)                       -> 7

Implementation:

The KEY insight: the procedure captures env. Later when called, the new environment has env as parent — so the function can access variables that existed when it was DEFINED.

This is lexical scoping + closures — the foundation of Lisp.

Common shorthand: (define (add x y) (+ x y)) is sugar for (define add (lambda (x y) (+ x y))).

In Scheme, named functions are just lambdas bound to names. There's no special "function definition" syntax.