## A newbie's attempt to explain lambdas

2017/12/22

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
```

## 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: ```
racket
(define my-add (lambda (x y) (+ x y)))
```

can be written as: ```
racket
(define (my-add x y) (+ x y))
```