A let
is a lambda
.
E.g.
(let ((x 1))
body)
can be translated into
((lambda (x) body) 1)
Furthermore, in Scheme all control and environment structures can be represented by lambda expressions and applications of lambdas.
So, lambda
is strictly more powerful than let
and forms the basis of many of the interesting constructs found in Scheme.
Concerning define
and lambda
, a top-level define
adds a binding to the top-level environment.
When you write
(define (f x)
body)
you are really saying
(define f (lambda (x) body))
Nested defines are translated into letrec
, which can be rewritten using lambdas as well.
So, again, a lot of Scheme constructs can be translated into something using lambda
, and therefore it is really worthwile that you understand lambda
well.