On this page:
4.5.1 Function Shorthand
4.5.2 Curried Function Shorthand
4.5.3 Multiple Values and define-values
4.5.4 Internal Definitions

4.5 Definitions: define

A basic definition has the form

(define id expr)

in which case id is bound to the result of expr.

(define salutation (list-ref '("Hi" "Hello") (random 2)))
> salutation


4.5.1 Function Shorthand

The define form also supports a shorthand for function definitions:

(define (id arg ...) body ...+)

which is a shorthand for

(define id (lambda (arg ...) body ...+))

(define (greet name)
  (string-append salutation ", " name))
> (greet "John")

"Hello, John"

(define (greet first [surname "Smith"] #:hi [hi salutation])
  (string-append hi ", " first " " surname))


> (greet "John")

"Hello, John Smith"

> (greet "John" #:hi "Hey")

"Hey, John Smith"

> (greet "John" "Doe")

"Hello, John Doe"

The function shorthand via define also supports a rest argument (i.e., a final argument to collect extra arguments in a list):

(define (id arg ... . rest-id) body ...+)

which is a shorthand

(define id (lambda (arg ... . rest-id) body ...+))

(define (avg . l)
  (/ (apply + l) (length l)))
> (avg 1 2 3)


4.5.2 Curried Function Shorthand

Consider the following make-add-suffix function that takes a string and returns another function that takes a string:

(define make-add-suffix
  (lambda (s2)
    (lambda (s) (string-append s s2))))


Although it’s not common, result of make-add-suffix could be called directly, like this:

> ((make-add-suffix "!") "hello")


In a sense, make-add-suffix is a function that takes two arguments, but it takes them one at a time. A function that takes some of its arguments and returns a function to consume more is sometimes called a curried function.

Using the function-shorthand form of define, make-add-suffix can be written equivalently as

(define (make-add-suffix s2)
  (lambda (s) (string-append s s2)))

This shorthand reflects the shape of the function call (make-add-suffix "!"). The define form further supports a shorthand for defining curried functions that reflects nested function calls:

(define ((make-add-suffix s2) s)
  (string-append s s2))


> ((make-add-suffix "!") "hello")


(define louder (make-add-suffix "!"))
(define less-sure (make-add-suffix "?"))


> (less-sure "really")


> (louder "really")


The full syntax of the function shorthand for define is as follows:

(define (head args) body ...+)
head = id
  | (head args)
args = arg ...
  | arg ... . rest-id

The expansion of this shorthand has one nested lambda form for each head in the definition, where the innermost head corresponds to the outermost lambda.

4.5.3 Multiple Values and define-values

A Racket expression normally produces a single result, but some expressions can produce multiple results. For example, quotient and remainder each produce a single value, but quotient/remainder produces the same two values at once:

> (quotient 13 3)


> (remainder 13 3)


> (quotient/remainder 13 3)



As shown above, the REPL prints each result value on its own line.

Multiple-valued functions can be implemented in terms of the values function, which takes any number of values and returns them as the results:

> (values 1 2 3)




(define (split-name name)
  (let ([parts (regexp-split " " name)])
    (if (= (length parts) 2)
        (values (list-ref parts 0) (list-ref parts 1))
        (error "not a <first> <last> name"))))


> (split-name "Adam Smith")



The define-values form binds multiple identifiers at once to multiple results produced from a single expression:

(define-values (id ...) expr)

The number of results produced by the expr must match the number of ids.

(define-values (given surname) (split-name "Adam Smith"))
> given


> surname


A define form (that is not a function shorthand) is equivalent to a define-values form with a single id.

+Definitions: define, define-syntax, ... in The Racket Reference provides more on definitions.

4.5.4 Internal Definitions

When the grammar for a syntactic form specifies body, then the corresponding form can be either a definition or an expression. A definition as a body is an internal definition.

Expressions and internal definitions in a body sequence can be mixed, as long as the last body is an expression.

For example, the syntax of lambda is

(lambda gen-formals
  body ...+)

so the following are valid instances of the grammar:

(lambda (f)                ; no definitions
  (printf "running\n")
  (f 0))
(lambda (f)                ; one definition
  (define (log-it what)
    (printf "~a\n" what))
  (log-it "running")
  (f 0)
  (log-it "done"))
(lambda (f n)              ; two definitions
  (define (call n)
    (if (zero? n)
        (log-it "done")
          (log-it "running")
          (f n)
          (call (- n 1)))))
  (define (log-it what)
    (printf "~a\n" what))
  (call n))

Internal definitions in a particular body sequence are mutually recursive; that is, any definition can refer to any other definition—as long as the reference isn’t actually evaluated before its definition takes place. If a definition is referenced too early, an error occurs.

(define (weird)
  (define x x)
> (weird)

x: undefined;

 cannot use before initialization

A sequence of internal definitions using just define is easily translated to an equivalent letrec form (as introduced in the next section). However, other definition forms can appear as a body, including define-values, struct (see Programmer-Defined Datatypes) or define-syntax (see Macros).

+Internal Definitions in The Racket Reference documents the fine points of internal definitions.