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An attempt to explain function values (lambdas)


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A lambda is simply a function.

Functions do not have to be named. Consider the fact that in English, “function” is also a noun. It 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

How to read this:

  1. The expression is a list of three values: (lambda …), 2, and 3.

  2. The first expression is evaluated first, resulting in a function value.

  3. The second and third values are evaluated in turn. Numbers evaluate to be themselves.

  4. The function value receives the second and third values as arguments and performs the calculation.

  5. The result of that calculation becomes the value of the whole expression after being evaluated.

Arguments

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))