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# Definitions: `define`
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A basic definition has the form
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```racket
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(define id expr)
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```
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in which case `id` is bound to the result of `expr`.
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Examples:
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```racket
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(define salutation (list-ref '("Hi" "Hello") (random 2)))
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> salutation
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"Hi"
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```
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## 1. Function Shorthand
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The `define` form also supports a shorthand for function definitions:
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```racket
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(define (id arg ...) body ...+)
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```
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which is a shorthand for
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`(define` `id` `(lambda` `(arg` `...)` `body` `...+))`
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Examples:
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```racket
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(define (greet name)
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(string-append salutation ", " name))
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> (greet "John")
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"Hi, John"
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```
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```racket
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(define (greet first [surname "Smith"] #:hi [hi salutation])
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(string-append hi ", " first " " surname))
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```
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```racket
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> (greet "John")
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"Hi, John Smith"
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> (greet "John" #:hi "Hey")
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"Hey, John Smith"
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> (greet "John" "Doe")
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"Hi, John Doe"
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```
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The function shorthand via `define` also supports a rest argument
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\(i.e., a final argument to collect extra arguments in a list\):
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```racket
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(define (id arg ... . rest-id) body ...+)
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```
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which is a shorthand
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`(define` `id` `(lambda` `(arg` `...` `. rest-id)` `body` `...+))`
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Examples:
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```racket
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(define (avg . l)
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(/ (apply + l) (length l)))
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> (avg 1 2 3)
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2
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```
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## 2. Curried Function Shorthand
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Consider the following `make-add-suffix` function that takes a string
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and returns another function that takes a string:
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```racket
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(define make-add-suffix
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(lambda (s2)
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(lambda (s) (string-append s s2))))
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```
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Although it’s not common, result of `make-add-suffix` could be called
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directly, like this:
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```racket
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> ((make-add-suffix "!") "hello")
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"hello!"
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```
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In a sense, `make-add-suffix` is a function takes two arguments, but it
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takes them one at a time. A function that takes some of its arguments
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and returns a function to consume more is sometimes called a _curried
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function_.
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Using the function-shorthand form of `define`, `make-add-suffix` can be
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written equivalently as
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```racket
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(define (make-add-suffix s2)
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(lambda (s) (string-append s s2)))
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```
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This shorthand reflects the shape of the function call `(make-add-suffix
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"!")`. The `define` form further supports a shorthand for defining
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curried functions that reflects nested function calls:
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```racket
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(define ((make-add-suffix s2) s)
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(string-append s s2))
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```
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```racket
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> ((make-add-suffix "!") "hello")
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"hello!"
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```
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```racket
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(define louder (make-add-suffix "!"))
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(define less-sure (make-add-suffix "?"))
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```
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```racket
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> (less-sure "really")
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"really?"
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> (louder "really")
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"really!"
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```
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The full syntax of the function shorthand for `define` is as follows:
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```racket
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(define (head args) body ...+)
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head = id
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args = arg ...
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| arg ... . rest-id
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```
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The expansion of this shorthand has one nested `lambda` form for each
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`head` in the definition, where the innermost `head` corresponds to the
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outermost `lambda`.
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## 3. Multiple Values and `define-values`
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A Racket expression normally produces a single result, but some
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expressions can produce multiple results. For example, `quotient` and
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`remainder` each produce a single value, but `quotient/remainder`
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produces the same two values at once:
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```racket
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> (quotient 13 3)
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4
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> (remainder 13 3)
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1
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> (quotient/remainder 13 3)
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4
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1
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```
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As shown above, the REPL prints each result value on its own line.
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Multiple-valued functions can be implemented in terms of the `values`
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function, which takes any number of values and returns them as the
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results:
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```racket
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> (values 1 2 3)
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1
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2
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3
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```
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```racket
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(define (split-name name)
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(let ([parts (regexp-split " " name)])
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(if (= (length parts) 2)
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(values (list-ref parts 0) (list-ref parts 1))
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(error "not a <first> <last> name"))))
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```
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```racket
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> (split-name "Adam Smith")
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"Adam"
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"Smith"
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```
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The `define-values` form binds multiple identifiers at once to multiple
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results produced from a single expression:
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```racket
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(define-values (id ...) expr)
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```
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The number of results produced by the `expr` must match the number of
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`id`s.
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Examples:
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```racket
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(define-values (given surname) (split-name "Adam Smith"))
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> given
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"Adam"
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> surname
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"Smith"
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```
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A `define` form \(that is not a function shorthand\) is equivalent to a
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`define-values` form with a single `id`.
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> +\[missing\] in \[missing\] provides more on definitions.
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## 4. Internal Definitions
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When the grammar for a syntactic form specifies `body`, then the
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corresponding form can be either a definition or an expression. A
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definition as a `body` is an _internal definition_.
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Expressions and internal definitions in a `body` sequence can be mixed,
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as long as the last `body` is an expression.
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For example, the syntax of `lambda` is
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```racket
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(lambda gen-formals
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body ...+)
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```
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so the following are valid instances of the grammar:
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```racket
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(lambda (f) ; no definitions
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(printf "running\n")
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(f 0))
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(lambda (f) ; one definition
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(define (log-it what)
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(printf "~a\n" what))
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(log-it "running")
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(f 0)
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(log-it "done"))
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(lambda (f n) ; two definitions
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(define (call n)
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(if (zero? n)
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(log-it "done")
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(begin
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(log-it "running")
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(f n)
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(call (- n 1)))))
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(define (log-it what)
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(printf "~a\n" what))
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(call n))
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```
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Internal definitions in a particular `body` sequence are mutually
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recursive; that is, any definition can refer to any other definition—as
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long as the reference isn’t actually evaluated before its definition
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takes place. If a definition is referenced too early, an error occurs.
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Examples:
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```racket
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(define (weird)
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(define x x)
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x)
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> (weird)
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x: undefined;
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cannot use before initialization
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```
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A sequence of internal definitions using just `define` is easily
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translated to an equivalent `letrec` form \(as introduced in the next
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section\). However, other definition forms can appear as a `body`,
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including `define-values`, `struct` \(see \[missing\]\) or
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`define-syntax` \(see \[missing\]\).
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> +\[missing\] in \[missing\] documents the fine points of internal
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> definitions.
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