#lang scribble/doc
@(require scribble/manual
          scribble/eval
          "guide-utils.ss")

@(define greet-eval (make-base-eval))

@title[#:tag "lambda"]{Functions@aux-elem{ (Procedures)}: @racket[lambda]}

A @racket[lambda] expression creates a function. In the simplest
case, a @racket[lambda] expression has the form

@specform[
(lambda (arg-id ...)
  body ...+)
]

A @racket[lambda] form with @math{n} @racket[_arg-id]s accepts
@math{n} arguments:

@interaction[
((lambda (x) x)
 1)
((lambda (x y) (+ x y))
 1 2)
((lambda (x y) (+ x y))
 1)
]

@;------------------------------------------------------------------------
@section[#:tag "rest-args"]{Declaring a Rest Argument}

A @racket[lambda] expression can also have the form

@specform[
(lambda rest-id
  body ...+)
]

That is, a @racket[lambda] expression can have a single
@racket[_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 @racket[_rest-id].

@examples[
((lambda x x)
 1 2 3)
((lambda x x))
((lambda x (car x))
 1 2 3)
]

Functions with a @racket[_rest-id] often use @racket[apply] to call
another function that accepts any number of arguments.

@guideother{@secref["apply"] describes @racket[apply].}

@defexamples[
(define max-mag
  (lambda nums
    (apply max (map magnitude nums))))

(max 1 -2 0)
(max-mag 1 -2 0)
]

The @racket[lambda] form also supports required arguments combined
with a @racket[_rest-id]:

@specform[
(lambda (arg-id ...+ . rest-id)
  body ...+)
]

The result of this form is a function that requires at least as many
arguments as @racket[_arg-id]s, and also accepts any number of
additional arguments.

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

(max-mag 1 -2 0)
(max-mag)
]

A @racket[_rest-id] variable is sometimes called a @defterm{rest
argument}, because it accepts the ``rest'' of the function arguments.

@;------------------------------------------------------------------------
@section{Declaring Optional Arguments}

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

@specform/subs[
(lambda gen-formals
  body ...+)
([gen-formals (arg ...)
              rest-id
              (arg ...+ . rest-id)]
 [arg arg-id
      [arg-id default-expr]])
]{}

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

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

(greet "John")
(greet "John" "Doe")
]

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

(greet "John")
(greet "Adam")
]

@section[#:tag "lambda-keywords"]{Declaring Keyword Arguments}

A @racket[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:

@guideother{@secref["keyword-args"] introduces function
calls with keywords.}

@specform/subs[
(lambda gen-formals
  body ...+)
([gen-formals (arg ...)
              rest-id
              (arg ...+ . rest-id)]
 [arg arg-id
      [arg-id default-expr]
      (code:line arg-keyword arg-id)
      (code:line arg-keyword [arg-id default-expr])])
]{}

An argument specified as @racket[(code:line _arg-keyword _arg-id)] is
supplied by an application using the same @racket[_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.

@def+int[
(define greet
  (lambda (given #:last surname)
    (string-append "Hello, " given " " surname)))

(greet "John" #:last "Smith")
(greet #:last "Doe" "John")
]

An @racket[(code:line _arg-keyword [_arg-id _default-expr])] argument
specifies a keyword-based argument with a default value.

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

(greet "John")
(greet "Karl" #:last "Marx")
(greet "John" #:hi "Howdy")
(greet "Karl" #:last "Marx" #:hi "Guten Tag")
]

The @racket[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
@racket[make-keyword-procedure]. The function supplied to
@racket[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.

@guideother{@secref["apply"] introduces @racket[keyword-apply].}

@defexamples[
#:eval greet-eval
(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")
]

@refdetails["lambda"]{function expressions}

@;------------------------------------------------------------------------
@section[#:tag "case-lambda"]{Arity-Sensitive Functions: @racket[case-lambda]}

The @racket[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

@specform/subs[
(case-lambda
  [formals body ...+]
  ...)
([formals (arg-id ...)
          rest-id
          (arg-id ...+ . rest-id)])
]

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

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

(greet "John")
(greet "John" "Smith")
(greet)
]

A @racket[case-lambda] function cannot directly support optional or
keyword arguments.

@; ----------------------------------------------------------------------

@close-eval[greet-eval]
