avatar Kisaragi Hiu

A newbie’s attempt to explain lambdas

A lambda is a function.

A function is an ordinary value, just like numbers, lists, and characters.

Just like how a list can be created with (list 'item 'item 'item), a function can be created with (lambda (input) body-expr).

(lambda (x y) (+ x y)) produces a function that takes two arguments and sends them to the + function. In a typical environment:

((lambda (x y) (+ x y)) 2 3)
; => 5


The way the argument list is given depends on the language. In Scheme-based languages, the first argument to lambda is:

  • a list, each element in the list is bound to a local variable: (lambda (x y) (+ x y))

  • an “improper list” (like (a b . c)) behaves like the above, but the last element is the rest argument, bound to a list containing arguments not bound by the positional arguments: (lambda (a b . c) (string-append a b (string-join c)))

  • a symbol; it becomes the rest argument: (lambda input (string-join input))

Binding to an identifier

define is used to assign an identifier to a value: (define x 9) binds x to 9. In the same way, (define my-add (lambda (x y z) (+ x y z))) binds my-add to the value (lambda (x y z) (+ x y z)). Now my-add can be used like the lambda itself.

((lambda (x y z) (+ x y z)) 1 2 3)
; => 6

(define my-add
  (lambda (x y z) (+ x y z)))
(my-add 1 2 3)
; => 6

Shorthand for defining functions

define has a shorthand for creating functions:

(define my-add (lambda (x y) (+ x y)))

can be written as:

(define (my-add x y) (+ x y))