4.5 Definitions: define

A basic definition has the form

(define id expr)

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

Examples:

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

> salutation

"Hi"

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 ...+))

Examples:

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

> (greet "John")

"Hi, John"

(define (greet first [surname "Smith"] #:hi [hi salutation])

(string-append hi ", " first " " surname))

> (greet "John")

"Hi, John Smith"

> (greet "John" #:hi "Hey")

"Hey, John Smith"

> (greet "John" "Doe")

"Hi, 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 ...+))

Examples:

(define (avg . l)     (/ (apply + l) (length l)))

> (avg 1 2 3)

2

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")

"hello!"

In a sense, make-add-suffix is a function 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")

"hello!"

(define louder (make-add-suffix "!"))

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

> (less-sure "really")

"really?"

> (louder "really")

"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 Scheme 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)

4

> (remainder 13 3)

1

> (quotient/remainder 13 3)

4

1

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)

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")

"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.

Examples:

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

> given

"Adam"

> surname

"Smith"

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 Reference: PLT Scheme 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.

All internal definitions in a body sequence must appear before any expression, and the last body must be 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"))

(log-it "running")

(f 0)

(log-it "done"))

(lambda (f n)              ; two definitions

(define (call n)

(if (zero? n)

(log-it "done")

(begin

(log-it "running")

(f 0)

(call (- n 1)))))

(define (log-it what)

(printf "~a\n"))

(call f 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, the result is a special value #<undefined>.

Examples:

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

> (weird)

#<undefined>

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, define-struct (see Programmer-Defined Datatypes) or define-syntax (see Macros).

Internal Definitions in Reference: PLT Scheme documents the fine points of internal definitions.