4.4 Functions (Procedures): lambda

A lambda expression creates a function. In the simplest case, a lambda expression has the form

(lambda (arg-id ...)   body ...+)

A lambda form with n arg-ids accepts n arguments:

> ((lambda (x) x)      1)

1

> ((lambda (x y) (+ x y))      1 2)

3

> ((lambda (x y) (+ x y))      1)

#<procedure>: expects 2 arguments, given 1: 1

4.4.1 Declaring a Rest Argument

A lambda expression can also have the form

(lambda rest-id   body ...+)

That is, a lambda expression can have a single rest-id that is not surrounded by parentheses. The resulting function accepts any number of arguments, and the arguments are put into a list bound to rest-id.

Examples:

> ((lambda x x)      1 2 3)

'(1 2 3)

> ((lambda x x))

'()

> ((lambda x (car x))      1 2 3)

1

Functions with a rest-id often use apply to call another function that accepts any number of arguments.

The apply Function describes apply.

Examples:

(define max-mag     (lambda nums       (apply max (map magnitude nums))))

> (max 1 -2 0)

1

> (max-mag 1 -2 0)

2

The lambda form also supports required arguments combined with a rest-id:

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

The result of this form is a function that requires at least as many arguments as arg-ids, and also accepts any number of additional arguments.

Examples:

(define max-mag     (lambda (num . nums)       (apply max (map magnitude (cons num nums)))))

> (max-mag 1 -2 0)

2

> (max-mag)

procedure max-mag: expects at least 1 argument, given 0

A rest-id variable is sometimes called a rest argument, because it accepts the “rest” of the function arguments.

4.4.2 Declaring Optional Arguments

Instead of just an identifier, an argument (other than a rest argument) in a lambda form can be specified with an identifier and a default value:

(lambda gen-formals   body ...+)

gen-formals   =   (arg ...)     |   rest-id     |   (arg ...+ . rest-id)           arg   =   arg-id     |   [arg-id default-expr]

A argument of the form [arg-id default-expr] is optional. When the argument is not supplied in an application, default-expr produces the default value. The default-expr can refer to any preceding arg-id, and every following arg-id must have a default as well.

Examples:

(define greet     (lambda (given [surname "Smith"])       (string-append "Hello, " given " " surname)))

> (greet "John")

"Hello, John Smith"

> (greet "John" "Doe")

"Hello, John Doe"

(define greet     (lambda (given [surname (if (equal? given "John")                                 "Doe"                                 "Smith")])       (string-append "Hello, " given " " surname)))

> (greet "John")   "Hello, John Doe"   > (greet "Adam")   "Hello, Adam Smith"

4.4.3 Declaring Keyword Arguments

A lambda form can declare an argument to be passed by keyword, instead of position. Keyword arguments can be mixed with by-position arguments, and default-value expressions can be supplied for either kind of argument:

Keyword Arguments introduces function calls with keywords.

(lambda gen-formals   body ...+)

gen-formals   =   (arg ...)     |   rest-id     |   (arg ...+ . rest-id)           arg   =   arg-id     |   [arg-id default-expr]     |   arg-keyword arg-id     |   arg-keyword [arg-id default-expr]

An argument specified as arg-keyword arg-id is supplied by an application using the same arg-keyword. The position of the keyword–identifier pair in the argument list does not matter for matching with arguments in an application, because it will be matched to an argument value by keyword instead of by position.

(define greet     (lambda (given #:last surname)       (string-append "Hello, " given " " surname)))

> (greet "John" #:last "Smith")   "Hello, John Smith"   > (greet #:last "Doe" "John")   "Hello, John Doe"

An arg-keyword [arg-id default-expr] argument specifies a keyword-based argument with a default value.

Examples:

(define greet     (lambda (#:hi [hi "Hello"] given #:last [surname "Smith"])       (string-append hi ", " given " " surname)))

> (greet "John")

"Hello, John Smith"

> (greet "Karl" #:last "Marx")

"Hello, Karl Marx"

> (greet "John" #:hi "Howdy")

"Howdy, John Smith"

> (greet "Karl" #:last "Marx" #:hi "Guten Tag")

"Guten Tag, Karl Marx"

The lambda form does not directly support the creation of a function that accepts “rest” keywords. To construct a function that accepts all keyword arguments, use make-keyword-procedure. The function supplied to make-keyword-procedure receives keyword arguments through parallel lists in the first two (by-position) arguments, and then all by-position arguments from an application as the remaining by-position arguments.

The apply Function introduces keyword-apply.

Examples:

(define (trace-wrap f)     (make-keyword-procedure      (lambda (kws kw-args . rest)        (printf "Called with ~s ~s ~s\n" kws kw-args rest)        (keyword-apply f kws kw-args rest))))

> ((trace-wrap greet) "John" #:hi "Howdy")

Called with (#:hi) ("Howdy") ("John")

"Howdy, John Smith"

Procedure Expressions: lambda and case-lambda in Reference: Racket provides more on function expressions.

4.4.4 Arity-Sensitive Functions: case-lambda

The case-lambda form creates a function that can have completely different behaviors depending on the number of arguments that are supplied. A case-lambda expression has the form

(case-lambda   [formals body ...+]   ...)

formals   =   (arg-id ...)     |   rest-id     |   (arg-id ...+ . rest-id)

where each [formals body ...+] is analogous to (lambda formals body ...+). Applying a function produced by case-lambda is like applying a lambda for the first case that matches the number of given arguments.

Examples:

(define greet     (case-lambda       [(name) (string-append "Hello, " name)]       [(given surname) (string-append "Hello, " given " " surname)]))

> (greet "John")

"Hello, John"

> (greet "John" "Smith")

"Hello, John Smith"

> (greet)

procedure greet: no clause matching 0 arguments

A case-lambda function cannot directly support optional or keyword arguments.