@c This file is part of the MIT/GNU Scheme Reference Manual.
@c $Id: special-forms.texi,v 1.4 2007/01/05 21:48:32 cph Exp $

@c Copyright (C) 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994,
@c     1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004,
@c     2005, 2006, 2007 Massachusetts Institute of Technology
@c See file scheme.texinfo for copying conditions.

@node Special Forms, Equivalence Predicates, Overview, Top
@chapter Special Forms

@cindex special form
A special form is an expression that follows special evaluation rules.
This chapter describes the basic Scheme special forms.

@menu
* Lambda Expressions::          
* Lexical Binding::             
* Dynamic Binding::             
* Definitions::                 
* Assignments::                 
* Quoting::                     
* Conditionals::                
* Sequencing::                  
* Iteration::                   
* Structure Definitions::       
* Macros::                      
* SRFI syntax::                 
@end menu

@node Lambda Expressions, Lexical Binding, Special Forms, Special Forms
@section Lambda Expressions

@deffn {special form} lambda formals expression expression @dots{}
@cindex lambda expression (defn)
@cindex procedure, construction
@cindex procedure, closing environment (defn)
@cindex procedure, invocation environment (defn)
@cindex construction, of procedure
@cindex closing environment, of procedure (defn)
@cindex invocation environment, of procedure (defn)
@cindex environment, of procedure
@cindex environment, procedure closing (defn)
@cindex environment, procedure invocation (defn)
A @code{lambda} expression evaluates to a procedure.  The environment in
effect when the @code{lambda} expression is evaluated is remembered as
part of the procedure; it is called the @dfn{closing environment}.  When
the procedure is later called with some arguments, the closing
environment is extended by binding the variables in the formal parameter
list to fresh locations, and the locations are filled with the arguments
according to rules about to be given.  The new environment created by
this process is referred to as the @dfn{invocation environment}.

@cindex region of variable binding, lambda
@cindex variable binding, lambda
Once the invocation environment has been constructed, the
@var{expression}s in the body of the @code{lambda} expression are
evaluated sequentially in it.  This means that the region of the
variables bound by the @code{lambda} expression is all of the
@var{expression}s in the body.  The result of evaluating the last
@var{expression} in the body is returned as the result of the procedure
call.

@cindex lambda list (defn)
@cindex parameter list, of lambda (defn)
@cindex formal parameter list, of lambda (defn)
@var{Formals}, the formal parameter list, is often referred to as a
@dfn{lambda list}.

The process of matching up formal parameters with arguments is somewhat
involved.  There are three types of parameters, and the matching treats
each in sequence:

@need 1000
@table @asis
@item Required
All of the @dfn{required} parameters are matched against the arguments
first.  If there are fewer arguments than required parameters, an error
of type @code{condition-type:wrong-number-of-arguments} is signalled;
this error is also signalled if there are more arguments than required
parameters and there are no further parameters.
@cindex required parameter (defn)
@cindex parameter, required (defn)
@findex condition-type:wrong-number-of-arguments

@item Optional
Once the required parameters have all been matched, the @dfn{optional}
parameters are matched against the remaining arguments.  If there are
fewer arguments than optional parameters, the unmatched parameters are
bound to special objects called @dfn{default objects}.  If there are
more arguments than optional parameters, and there are no further
parameters, an error of type
@code{condition-type:wrong-number-of-arguments} is signalled.
@cindex optional parameter (defn)
@cindex parameter, optional (defn)
@cindex default object (defn)
@findex condition-type:wrong-number-of-arguments

@findex default-object?
The predicate @code{default-object?}, which is true only of default
objects, can be used to determine which optional parameters were
supplied, and which were defaulted.

@item Rest
Finally, if there is a @dfn{rest} parameter (there can only be one), any
remaining arguments are made into a list, and the list is bound to the
rest parameter.  (If there are no remaining arguments, the rest
parameter is bound to the empty list.)
@cindex rest parameter (defn)
@cindex parameter, rest (defn)

In Scheme, unlike some other Lisp implementations, the list to which a
rest parameter is bound is always freshly allocated.  It has infinite
extent and may be modified without affecting the procedure's caller.
@end table

@findex #!optional
@findex #!rest
Specially recognized keywords divide the @var{formals} parameters into
these three classes.  The keywords used here are @samp{#!optional},
@samp{.}, and @samp{#!rest}.  Note that only @samp{.} is defined by
standard Scheme --- the other keywords are MIT/GNU Scheme extensions.
@samp{#!rest} has the same meaning as @samp{.} in @var{formals}.

The use of these keywords is best explained by means of examples.  The
following are typical lambda lists, followed by descriptions of which
parameters are required, optional, and rest.  We will use @samp{#!rest}
in these examples, but anywhere it appears @samp{.} could be used
instead.

@table @code
@item (a b c)
@code{a}, @code{b}, and @code{c} are all required.  The procedure must
be passed exactly three arguments.

@item (a b #!optional c)
@code{a} and @code{b} are required, @code{c} is optional.  The procedure
may be passed either two or three arguments.

@item (#!optional a b c)
@code{a}, @code{b}, and @code{c} are all optional.  The procedure may be
passed any number of arguments between zero and three, inclusive.

@item a
@itemx (#!rest a)
These two examples are equivalent.  @code{a} is a rest parameter.  The
procedure may be passed any number of arguments.  Note: this is the only
case in which @samp{.} cannot be used in place of @samp{#!rest}.

@item (a b #!optional c d #!rest e)
@code{a} and @code{b} are required, @code{c} and @code{d} are optional,
and @code{e} is rest.  The procedure may be passed two or more
arguments.
@end table

Some examples of @code{lambda} expressions:

@example
@group
(lambda (x) (+ x x))            @result{}  #[compound-procedure 53]

((lambda (x) (+ x x)) 4)                @result{}  8

(define reverse-subtract
  (lambda (x y)
    (- y x)))
(reverse-subtract 7 10)                 @result{}  3

(define foo
  (let ((x 4))
    (lambda (y) (+ x y))))
(foo 6)                                 @result{}  10
@end group
@end example
@end deffn

@deffn {special form} named-lambda formals expression expression @dots{}
@cindex named lambda (defn)
The @code{named-lambda} special form is similar to @code{lambda}, except
that the first ``required parameter'' in @var{formals} is not a
parameter but the @dfn{name} of the resulting procedure; thus
@var{formals} must have at least one required parameter.  This name has
no semantic meaning, but is included in the external representation of
the procedure, making it useful for debugging.  In MIT/GNU Scheme,
@code{lambda} is implemented as @code{named-lambda}, with a special name
that means ``unnamed''.

@example
@group
(named-lambda (f x) (+ x x))    @result{}  #[compound-procedure 53 f]
((named-lambda (f x) (+ x x)) 4)        @result{}  8
@end group
@end example
@end deffn

@node Lexical Binding, Dynamic Binding, Lambda Expressions, Special Forms
@section Lexical Binding

@cindex lexical binding expression
@cindex binding expression, lexical
@cindex block structure
The three binding constructs @code{let}, @code{let*}, and @code{letrec},
give Scheme block structure.  The syntax of the three constructs is
identical, but they differ in the regions they establish for their
variable bindings.  In a @code{let} expression, the initial values are
computed before any of the variables become bound.  In a @code{let*}
expression, the evaluations and bindings are sequentially interleaved.
And in a @code{letrec} expression, all the bindings are in effect while
the initial values are being computed (thus allowing mutually recursive
definitions).

@deffn {special form} let ((@var{variable} @var{init}) @dots{}) expression expression @dots{}
@cindex region of variable binding, let
@cindex variable binding, let
The @var{init}s are evaluated in the current environment (in some
unspecified order), the @var{variable}s are bound to fresh locations
holding the results, the @var{expression}s are evaluated sequentially in
the extended environment, and the value of the last @var{expression} is
returned.  Each binding of a @var{variable} has the @var{expression}s as
its region.

MIT/GNU Scheme allows any of the @var{init}s to be omitted, in which
case the corresponding @var{variable}s are unassigned.

@cindex lambda, implicit in let
Note that the following are equivalent:

@example
@group
(let ((@var{variable} @var{init}) @dots{}) @var{expression} @var{expression} @dots{})
((lambda (@var{variable} @dots{}) @var{expression} @var{expression} @dots{}) @var{init} @dots{})
@end group
@end example

Some examples:

@example
@group
(let ((x 2) (y 3))
  (* x y))                              @result{}  6
@end group

@group
(let ((x 2) (y 3))
  (let ((foo (lambda (z) (+ x y z)))
        (x 7))
    (foo 4)))                           @result{}  9
@end group
@end example

@xref{Iteration}, for information on ``named @code{let}''.
@end deffn

@deffn {special form} let* ((@var{variable} @var{init}) @dots{}) expression expression @dots{}
@cindex region of variable binding, let*
@cindex variable binding, let*
@code{let*} is similar to @code{let}, but the bindings are performed
sequentially from left to right, and the region of a binding is that
part of the @code{let*} expression to the right of the binding.  Thus
the second binding is done in an environment in which the first binding
is visible, and so on.

Note that the following are equivalent:

@example
@group
(let* ((@var{variable1} @var{init1})
       (@var{variable2} @var{init2})
       @dots{}
       (@var{variableN} @var{initN}))
   @var{expression}
   @var{expression} @dots{})
@end group

@group
(let ((@var{variable1} @var{init1}))
  (let ((@var{variable2} @var{init2}))
    @dots{}
      (let ((@var{variableN} @var{initN}))
        @var{expression}
        @var{expression} @dots{})
    @dots{}))
@end group
@end example

An example:

@example
@group
(let ((x 2) (y 3))
  (let* ((x 7)
         (z (+ x y)))
    (* z x)))                           @result{}  70
@end group
@end example
@end deffn

@deffn {special form} letrec ((@var{variable} @var{init}) @dots{}) expression expression @dots{}
@cindex region of variable binding, letrec
@cindex variable binding, letrec
The @var{variable}s are bound to fresh locations holding unassigned
values, the @var{init}s are evaluated in the extended environment (in
some unspecified order), each @var{variable} is assigned to the result
of the corresponding @var{init}, the @var{expression}s are evaluated
sequentially in the extended environment, and the value of the last
@var{expression} is returned.  Each binding of a @var{variable} has the
entire @code{letrec} expression as its region, making it possible to
define mutually recursive procedures.

MIT/GNU Scheme allows any of the @var{init}s to be omitted, in which
case the corresponding @var{variable}s are unassigned.

@example
@group
(letrec ((even?
          (lambda (n)
            (if (zero? n)
                #t
                (odd? (- n 1)))))
         (odd?
          (lambda (n)
            (if (zero? n)
                #f
                (even? (- n 1))))))
  (even? 88))                           @result{}  #t
@end group
@end example

@findex lambda
@findex delay
One restriction on @code{letrec} is very important: it shall be possible
to evaluated each @var{init} without assigning or referring to the value
of any @var{variable}.  If this restriction is violated, then it is an
error.  The restriction is necessary because Scheme passes arguments by
value rather than by name.  In the most common uses of @code{letrec},
all the @var{init}s are @code{lambda} or @code{delay} expressions and
the restriction is satisfied automatically.
@end deffn

@node Dynamic Binding, Definitions, Lexical Binding, Special Forms
@section Dynamic Binding

@deffn {special form} fluid-let ((@var{variable} @var{init}) @dots{}) expression expression @dots{}
@cindex binding expression, dynamic (or fluid)
@cindex fluid binding
@cindex dynamic binding
@cindex variable binding, fluid-let
The @var{init}s are evaluated in the current environment (in some
unspecified order), the current values of the @var{variable}s are saved,
the results are assigned to the @var{variable}s, the @var{expression}s
are evaluated sequentially in the current environment, the
@var{variable}s are restored to their original values, and the value of
the last @var{expression} is returned.

@findex let
The syntax of this special form is similar to that of @code{let}, but
@code{fluid-let} temporarily rebinds existing variables.  Unlike
@code{let}, @code{fluid-let} creates no new bindings; instead it
@emph{assigns} the value of each @var{init} to the binding (determined
by the rules of lexical scoping) of its corresponding @var{variable}.

@cindex unassigned variable, and dynamic bindings
MIT/GNU Scheme allows any of the @var{init}s to be omitted, in which
case the corresponding @var{variable}s are temporarily unassigned.

An error of type @code{condition-type:unbound-variable} is signalled if
any of the @var{variable}s are unbound.  However, because
@code{fluid-let} operates by means of side effects, it is valid for any
@var{variable} to be unassigned when the form is entered.
@findex condition-type:unbound-variable

Here is an example showing the difference between @code{fluid-let} and
@code{let}.  First see how @code{let} affects the binding of a variable:

@example
@group
(define variable #t)
(define (access-variable) variable)
variable                                @result{}  #t
(let ((variable #f))
  (access-variable))                    @result{}  #t
variable                                @result{}  #t
@end group
@end example

@code{access-variable} returns @code{#t} in this case because it
is defined in an environment with @code{variable} bound to
@code{#t}.  @code{fluid-let}, on the other hand, temporarily reuses an
existing variable:

@example
@group
variable                                @result{}  #t
(fluid-let ((variable #f))              @r{;reuses old binding}
  (access-variable))                    @result{}  #f
variable                                @result{}  #t
@end group
@end example

@cindex extent, of dynamic binding (defn)
The @dfn{extent} of a dynamic binding is defined to be the time period
during which the variable contains the new value.  Normally this time
period begins when the body is entered and ends when it is exited; on a
sequential machine it is normally a contiguous time period.  However,
because Scheme has first-class continuations, it is possible to leave
the body and then reenter it, as many times as desired.  In this
situation, the extent becomes non-contiguous.

@cindex dynamic binding, and continuations
@cindex continuation, and dynamic binding
When the body is exited by invoking a continuation, the new value is
saved, and the variable is set to the old value.  Then, if the body is
reentered by invoking a continuation, the old value is saved, and the
variable is set to the new value.  In addition, side effects to the
variable that occur both inside and outside of body are preserved, even
if continuations are used to jump in and out of body repeatedly.
@end deffn

Here is a complicated example that shows the interaction between dynamic
binding and continuations:

@example
@group
(define (complicated-dynamic-binding)
  (let ((variable 1)
        (inside-continuation))
    (write-line variable)
    (call-with-current-continuation
     (lambda (outside-continuation)
       (fluid-let ((variable 2))
         (write-line variable)
         (set! variable 3)
         (call-with-current-continuation
          (lambda (k)
            (set! inside-continuation k)
            (outside-continuation #t)))
         (write-line variable)
         (set! inside-continuation #f))))
    (write-line variable)
    (if inside-continuation
        (begin
          (set! variable 4)
          (inside-continuation #f)))))
@end group
@end example

@noindent
Evaluating @samp{(complicated-dynamic-binding)} writes the following on
the console:

@example
@group
1
2
1
3
4
@end group
@end example

@noindent
Commentary: the first two values written are the initial binding of
@code{variable} and its new binding after the @code{fluid-let}'s body is
entered.  Immediately after they are written, @code{variable} is set to
@samp{3}, and then @code{outside-continuation} is invoked, causing us to
exit the body.  At this point, @samp{1} is written, demonstrating that
the original value of @code{variable} has been restored, because we have
left the body.  Then we set @code{variable} to @samp{4} and reenter the
body by invoking @code{inside-continuation}.  At this point, @samp{3} is
written, indicating that the side effect that previously occurred within
the body has been preserved.  Finally, we exit body normally, and write
@samp{4}, demonstrating that the side effect that occurred outside of
the body was also preserved.

@node Definitions, Assignments, Dynamic Binding, Special Forms
@section Definitions
@cindex definition

@deffn {special form} define variable [expression]
@deffnx {special form} define @var{formals} expression expression @dots{}
@cindex variable, adding to environment
@cindex definition, top-level (defn)
@cindex definition, internal (defn)
@cindex top-level definition (defn)
@cindex internal definition (defn)
@findex lambda
@findex let
@findex let*
@findex letrec
@findex fluid-let
Definitions are valid in some but not all contexts where expressions are
allowed.  Definitions may only occur at the top level of a program and
at the beginning of a lambda body (that is, the body of a @code{lambda},
@code{let}, @code{let*}, @code{letrec}, @code{fluid-let}, or ``procedure
@code{define}'' expression).  A definition that occurs at the top level
of a program is called a @dfn{top-level definition}, and a definition
that occurs at the beginning of a body is called an @dfn{internal
definition}.

@cindex lambda, implicit in define
@cindex procedure define (defn)
@cindex define, procedure (defn)
@findex named-lambda
In the second form of @code{define} (called ``@dfn{procedure
@code{define}}''), the component @var{formals} is identical to the
component of the same name in a @code{named-lambda} expression.  In
fact, these two expressions are equivalent:

@example
@group
(define (@var{name1} @var{name2} @dots{})
  @var{expression}
  @var{expression} @dots{})
@end group

@group
(define @var{name1}
  (named-lambda (@var{name1} @var{name2} @dots{})
    @var{expression}
    @var{expression} @dots{}))
@end group
@end example
@end deffn

@menu
* Top-Level Definitions::       
* Internal Definitions::        
@end menu

@node Top-Level Definitions, Internal Definitions, Definitions, Definitions
@subsection Top-Level Definitions
@cindex top-level definition
@cindex definition, top-level

@cindex variable binding, top-level definition
A top-level definition,

@example
(define @var{variable} @var{expression})
@end example

@noindent
has essentially the same effect as this assignment expression, if
@var{variable} is bound:

@example
(set! @var{variable} @var{expression})
@end example

@cindex unassigned variable, and definition
@findex set!
If @var{variable} is not bound, however, @code{define} binds
@var{variable} to a new location in the current environment before
performing the assignment (it is an error to perform a @code{set!} on an
unbound variable).  If you omit @var{expression}, the variable becomes
unassigned; an attempt to reference such a variable is an error.

@example
@group
(define add3
   (lambda (x) (+ x 3)))                @result{}  @r{unspecified}
(add3 3)                                @result{}  6

(define first car)                      @result{}  @r{unspecified}
(first '(1 2))                          @result{}  1

(define bar)                            @result{}  @r{unspecified}
bar                                     @error{} Unassigned variable
@end group
@end example

@node Internal Definitions,  , Top-Level Definitions, Definitions
@subsection Internal Definitions

@cindex internal definition
@cindex definition, internal
@cindex region of variable binding, internal definition
@cindex variable binding, internal definition
@findex lambda
@findex let
@findex let*
@findex letrec
@findex fluid-let
@findex define
An @dfn{internal definition} is a definition that occurs at the
beginning of a @var{body} (that is, the body of a @code{lambda},
@code{let}, @code{let*}, @code{letrec}, @code{fluid-let}, or ``procedure
@code{define}'' expression), rather than at the top level of a program.
The variable defined by an internal definition is local to the
@var{body}.  That is, @var{variable} is bound rather than assigned, and
the region of the binding is the entire @var{body}.  For example,

@example
@group
(let ((x 5))
  (define foo (lambda (y) (bar x y)))
  (define bar (lambda (a b) (+ (* a b) a)))
  (foo (+ x 3)))                        @result{}  45
@end group
@end example

@findex letrec
A @var{body} containing internal definitions can always be converted
into a completely equivalent @code{letrec} expression.  For example, the
@code{let} expression in the above example is equivalent to

@cindex letrec, implicit in define
@example
@group
(let ((x 5))
  (letrec ((foo (lambda (y) (bar x y)))
           (bar (lambda (a b) (+ (* a b) a))))
    (foo (+ x 3))))
@end group
@end example

@need 1000
@node Assignments, Quoting, Definitions, Special Forms
@section Assignments
@cindex assignment

@deffn {special form} set! variable [expression]
@cindex variable, assigning values to
@cindex unassigned variable, and assignment
If @var{expression} is specified, evaluates @var{expression} and stores
the resulting value in the location to which @var{variable} is bound.
If @var{expression} is omitted, @var{variable} is altered to be
unassigned; a subsequent reference to such a @var{variable} is an error.
In either case, the value of the @code{set!} expression is unspecified.

@var{Variable} must be bound either in some region enclosing the
@code{set!} expression, or at the top level.  However, @var{variable} is
permitted to be unassigned when the @code{set!} form is entered.

@example
@group
(define x 2)                            @result{}  @r{unspecified}
(+ x 1)                                 @result{}  3
(set! x 4)                              @result{}  @r{unspecified}
(+ x 1)                                 @result{}  5
@end group
@end example

@cindex access, used with set!
@findex access
@var{Variable} may be an @code{access} expression
(@pxref{Environments}).  This allows you to assign variables in an
arbitrary environment.  For example,

@example
@group
(define x (let ((y 0)) (the-environment)))
(define y 'a)
y                                       @result{}  a
(access y x)                            @result{}  0
(set! (access y x) 1)                   @result{}  @r{unspecified}
y                                       @result{}  a
(access y x)                            @result{}  1
@end group
@end example
@end deffn

@node Quoting, Conditionals, Assignments, Special Forms
@section Quoting
@cindex quoting

This section describes the expressions that are used to modify or
prevent the evaluation of objects.

@deffn {special form} quote datum
@cindex external representation, and quote
@cindex literal, and quote
@cindex constant, and quote
@code{(quote @var{datum})} evaluates to @var{datum}.  @var{Datum} may be
any external representation of a Scheme object
(@pxref{External Representations}).
Use @code{quote} to include literal constants in
Scheme code.

@example
@group
(quote a)                               @result{}  a
(quote #(a b c))                        @result{}  #(a b c)
(quote (+ 1 2))                         @result{}  (+ 1 2)
@end group
@end example

@cindex ' as external representation
@cindex apostrophe, as external representation
@cindex quote, as external representation
@findex '
@code{(quote @var{datum})} may be abbreviated as @code{'@var{datum}}.
The two notations are equivalent in all respects.

@example
@group
'a                                      @result{}  a
'#(a b c)                               @result{}  #(a b c)
'(+ 1 2)                                @result{}  (+ 1 2)
'(quote a)                              @result{}  (quote a)
''a                                     @result{}  (quote a)
@end group
@end example

Numeric constants, string constants, character constants, and boolean
constants evaluate to themselves, so they don't need to be quoted.

@example
@group
'"abc"                                  @result{}  "abc"
"abc"                                   @result{}  "abc"
'145932                                 @result{}  145932
145932                                  @result{}  145932
'#t                                     @result{}  #t
#t                                      @result{}  #t
'#\a                                    @result{}  #\a
#\a                                     @result{}  #\a
@end group
@end example
@end deffn

@deffn {special form} quasiquote template
@cindex external representation, and quasiquote
@cindex literal, and quasiquote
@cindex constant, and quasiquote
@findex equal?
``Backquote'' or ``quasiquote'' expressions are useful for constructing
a list or vector structure when most but not all of the desired
structure is known in advance.  If no commas appear within the
@var{template}, the result of evaluating @code{`@var{template}} is
equivalent (in the sense of @code{equal?}) to the result of evaluating
@code{'@var{template}}.  If a comma appears within the @var{template},
however, the expression following the comma is evaluated (``unquoted'')
and its result is inserted into the structure instead of the comma and
the expression.  If a comma appears followed immediately by an at-sign
(@@), then the following expression shall evaluate to a list; the
opening and closing parentheses of the list are then ``stripped away''
and the elements of the list are inserted in place of the comma at-sign
expression sequence.

@example
@group
`(list ,(+ 1 2) 4)                       @result{}  (list 3 4)

(let ((name 'a)) `(list ,name ',name))   @result{}  (list a 'a)

`(a ,(+ 1 2) ,@@(map abs '(4 -5 6)) b)    @result{}  (a 3 4 5 6 b)

`((foo ,(- 10 3)) ,@@(cdr '(c)) . ,(car '(cons)))
                                         @result{}  ((foo 7) . cons)

`#(10 5 ,(sqrt 4) ,@@(map sqrt '(16 9)) 8)
                                         @result{}  #(10 5 2 4 3 8)

`,(+ 2 3)                                @result{}  5
@end group
@end example

@cindex nesting, of quasiquote expressions
Quasiquote forms may be nested.  Substitutions are made only for
unquoted components appearing at the same nesting level as the outermost
backquote.  The nesting level increases by one inside each successive
quasiquotation, and decreases by one inside each unquotation.

@example
@group
`(a `(b ,(+ 1 2) ,(foo ,(+ 1 3) d) e) f)
     @result{}  (a `(b ,(+ 1 2) ,(foo 4 d) e) f)

(let ((name1 'x)
      (name2 'y))
   `(a `(b ,,name1 ,',name2 d) e))
     @result{}  (a `(b ,x ,'y d) e)
@end group
@end example

@cindex backquote, as external representation
@cindex ` as external representation
@cindex comma, as external representation
@cindex , as external representation
@cindex ,@@ as external representation
@findex unquote
@findex unquote-splicing
@findex `
@findex ,
@findex ,@@
The notations @code{`@var{template}} and (@code{quasiquote
@var{template}}) are identical in all respects.
@code{,@var{expression}} is identical to @code{(unquote
@var{expression})} and @code{,@@@var{expression}} is identical to
@code{(unquote-splicing @var{expression})}.

@example
@group
(quasiquote (list (unquote (+ 1 2)) 4))
     @result{}  (list 3 4)

'(quasiquote (list (unquote (+ 1 2)) 4))
     @result{}  `(list ,(+ 1 2) 4)
     @emph{i.e.,} (quasiquote (list (unquote (+ 1 2)) 4))
@end group
@end example

Unpredictable behavior can result if any of the symbols
@code{quasiquote}, @code{unquote}, or @code{unquote-splicing} appear in
a @var{template} in ways otherwise than as described above.
@end deffn

@node Conditionals, Sequencing, Quoting, Special Forms
@section Conditionals

@cindex expression, conditional (defn)
@cindex conditional expression (defn)
@cindex true, in conditional expression (defn)
@cindex false, in conditional expression (defn)
@findex #f
@findex #t
The behavior of the @dfn{conditional expressions} is determined by
whether objects are true or false.  The conditional expressions count
only @code{#f} as false.  They count everything else, including
@code{#t}, pairs, symbols, numbers, strings, vectors, and procedures as
true (but @pxref{True and False}).

In the descriptions that follow, we say that an object has ``a true
value'' or ``is true'' when the conditional expressions treat it as
true, and we say that an object has ``a false value'' or ``is false''
when the conditional expressions treat it as false.

@deffn {special form} if predicate consequent [alternative]
@var{Predicate}, @var{consequent}, and @var{alternative} are
expressions.  An @code{if} expression is evaluated as follows: first,
@var{predicate} is evaluated.  If it yields a true value, then
@var{consequent} is evaluated and its value is returned.  Otherwise
@var{alternative} is evaluated and its value is returned.  If
@var{predicate} yields a false value and no @var{alternative} is
specified, then the result of the expression is unspecified.

An @code{if} expression evaluates either @var{consequent} or
@var{alternative}, never both.  Programs should not depend on the value
of an @code{if} expression that has no @var{alternative}.

@example
@group
(if (> 3 2) 'yes 'no)                   @result{}  yes
(if (> 2 3) 'yes 'no)                   @result{}  no
(if (> 3 2)
    (- 3 2)
    (+ 3 2))                            @result{}  1
@end group
@end example
@end deffn

@deffn {special form} cond clause clause @dots{}
@cindex cond clause
@cindex clause, of cond expression
Each @var{clause} has this form:

@example
(@var{predicate} @var{expression} @dots{})
@end example

@noindent
@cindex else clause, of cond expression (defn)
@findex else
where @var{predicate} is any expression.  The last @var{clause} may be
an @dfn{@code{else} clause}, which has the form:

@example
(else @var{expression} @var{expression} @dots{})
@end example

A @code{cond} expression does the following:

@enumerate
@item
Evaluates the @var{predicate} expressions of successive @var{clause}s in
order, until one of the @var{predicate}s evaluates to a true
value.

@item
When a @var{predicate} evaluates to a true value, @code{cond} evaluates
the @var{expression}s in the associated @var{clause} in left to right
order, and returns the result of evaluating the last @var{expression} in
the @var{clause} as the result of the entire @code{cond} expression.

If the selected @var{clause} contains only the @var{predicate} and no
@var{expression}s, @code{cond} returns the value of the @var{predicate}
as the result.

@item
If all @var{predicate}s evaluate to false values, and there is no
@code{else} clause, the result of the conditional expression is
unspecified; if there is an @code{else} clause, @code{cond} evaluates
its @var{expression}s (left to right) and returns the value of the last
one.
@end enumerate

@example
@group
(cond ((> 3 2) 'greater)
      ((< 3 2) 'less))                  @result{}  greater

(cond ((> 3 3) 'greater)
      ((< 3 3) 'less)
      (else 'equal))                    @result{}  equal
@end group
@end example

Normally, programs should not depend on the value of a @code{cond}
expression that has no @code{else} clause.  However, some Scheme
programmers prefer to write @code{cond} expressions in which at least
one of the @var{predicate}s is always true.  In this style, the final
@var{clause} is equivalent to an @code{else} clause.

@cindex => in cond clause
@findex =>
Scheme supports an alternative @var{clause} syntax:

@example
(@var{predicate} => @var{recipient})
@end example

@noindent
where @var{recipient} is an expression.  If @var{predicate} evaluates to
a true value, then @var{recipient} is evaluated.  Its value must be a
procedure of one argument; this procedure is then invoked on the value
of the @var{predicate}.

@example
@group
(cond ((assv 'b '((a 1) (b 2))) => cadr)
      (else #f))                        @result{}  2
@end group
@end example
@end deffn

@deffn {special form} case key clause clause @dots{}
@cindex case clause
@cindex clause, of case expression
@var{Key} may be any expression.  Each @var{clause} has this
form:

@example
((@var{object} @dots{}) @var{expression} @var{expression} @dots{})
@end example

@cindex else clause, of case expression (defn)
@findex else
No @var{object} is evaluated, and all the @var{object}s must be
distinct.  The last @var{clause} may be an @dfn{@code{else} clause},
which has the form:

@example
(else @var{expression} @var{expression} @dots{})
@end example

A @code{case} expression does the following:

@enumerate
@item
Evaluates @var{key} and compares the result with each
@var{object}.

@item
If the result of evaluating @var{key} is equivalent (in the sense of
@code{eqv?}; @pxref{Equivalence Predicates}) to an @var{object},
@code{case} evaluates the @var{expression}s in the corresponding
@var{clause} from left to right and returns the result of evaluating the
last @var{expression} in the @var{clause} as the result of the
@code{case} expression.
@findex eqv?

@item
If the result of evaluating @var{key} is different from every
@var{object}, and if there's an @code{else} clause, @code{case}
evaluates its @var{expression}s and returns the result of the last one
as the result of the @code{case} expression.  If there's no @code{else}
clause, @code{case} returns an unspecified result.  Programs should not
depend on the value of a @code{case} expression that has no @code{else}
clause.
@end enumerate

For example,

@example
@group
(case (* 2 3)
   ((2 3 5 7) 'prime)
   ((1 4 6 8 9) 'composite))            @result{}  composite

(case (car '(c d))
   ((a) 'a)
   ((b) 'b))                            @result{}  @r{unspecified}

(case (car '(c d))
   ((a e i o u) 'vowel)
   ((w y) 'semivowel)
   (else 'consonant))                   @result{}  consonant
@end group
@end example
@end deffn

@deffn {special form} and expression @dots{}
The @var{expression}s are evaluated from left to right, and the value of
the first @var{expression} that evaluates to a false value is returned.
Any remaining @var{expression}s are not evaluated.  If all the
@var{expression}s evaluate to true values, the value of the last
@var{expression} is returned.  If there are no @var{expression}s then
@code{#t} is returned.

@example
@group
(and (= 2 2) (> 2 1))                   @result{}  #t
(and (= 2 2) (< 2 1))                   @result{}  #f
(and 1 2 'c '(f g))                     @result{}  (f g)
(and)                                   @result{}  #t
@end group
@end example
@end deffn

@deffn {special form} or expression @dots{}
The @var{expression}s are evaluated from left to right, and the value of
the first @var{expression} that evaluates to a true value is returned.
Any remaining @var{expression}s are not evaluated.  If all
@var{expression}s evaluate to false values, the value of the last
@var{expression} is returned.  If there are no @var{expression}s then
@code{#f} is returned.

@example
@group
(or (= 2 2) (> 2 1))                    @result{}  #t
(or (= 2 2) (< 2 1))                    @result{}  #t
(or #f #f #f)                           @result{}  #f
(or (memq 'b '(a b c)) (/ 3 0))         @result{}  (b c)
@end group
@end example
@end deffn

@node Sequencing, Iteration, Conditionals, Special Forms
@section Sequencing
@cindex sequencing expressions

The @code{begin} special form is used to evaluate expressions in a
particular order.

@deffn {special form} begin expression expression @dots{}
The @var{expression}s are evaluated sequentially from left to right, and
the value of the last @var{expression} is returned.  This expression
type is used to sequence side effects such as input and output.

@example
@group
(define x 0)
(begin (set! x 5)
       (+ x 1))                 @result{}  6

(begin (display "4 plus 1 equals ")
       (display (+ 4 1)))
                                @print{}  4 plus 1 equals 5
                                @result{}  @r{unspecified}
@end group
@end example

@cindex implicit begin
Often the use of @code{begin} is unnecessary, because many special forms
already support sequences of expressions (that is, they have an implicit
@code{begin}).  Some of these special forms are:

@example
@group
case
cond
define          @r{;``procedure @code{define}'' only}
do
fluid-let
lambda
let
let*
letrec
named-lambda
@end group
@end example
@findex case
@findex cond
@findex define
@findex do
@findex fluid-let
@findex lambda
@findex let
@findex let*
@findex letrec
@findex named-lambda

@findex sequence
The obsolete special form @code{sequence} is identical to @code{begin}.
It should not be used in new code.
@end deffn

@node Iteration, Structure Definitions, Sequencing, Special Forms
@section Iteration

@cindex expression, iteration (defn)
@cindex iteration expression (defn)
@cindex looping (see iteration expressions)
@cindex tail recursion, vs. iteration expression
The @dfn{iteration expressions} are: ``named @code{let}'' and @code{do}.
They are also binding expressions, but are more commonly referred to as
iteration expressions.  Because Scheme is properly tail-recursive, you
don't need to use these special forms to express iteration; you can
simply use appropriately written ``recursive'' procedure calls.

@deffn {special form} let name ((@var{variable} @var{init}) @dots{}) expression expression @dots{}
@cindex named let (defn)
MIT/GNU Scheme permits a variant on the syntax of @code{let} called
``named @code{let}'' which provides a more general looping construct
than @code{do}, and may also be used to express recursions.

Named @code{let} has the same syntax and semantics as ordinary
@code{let} except that @var{name} is bound within the @var{expression}s
to a procedure whose formal arguments are the @var{variable}s and whose
body is the @var{expression}s.  Thus the execution of the
@var{expression}s may be repeated by invoking the procedure named by
@var{name}.

@cindex unassigned variable, and named let
MIT/GNU Scheme allows any of the @var{init}s to be omitted, in which
case the corresponding @var{variable}s are unassigned.

Note: the following expressions are equivalent:

@example
@group
(let @var{name} ((@var{variable} @var{init}) @dots{})
  @var{expression}
  @var{expression} @dots{})

((letrec ((@var{name}
           (named-lambda (@var{name} @var{variable} @dots{})
             @var{expression}
             @var{expression} @dots{})))
   @var{name})
 @var{init} @dots{})
@end group
@end example

Here is an example:

@example
@group
(let loop
     ((numbers '(3 -2 1 6 -5))
      (nonneg '())
      (neg '()))
  (cond ((null? numbers)
         (list nonneg neg))
        ((>= (car numbers) 0)
         (loop (cdr numbers)
               (cons (car numbers) nonneg)
               neg))
        (else
         (loop (cdr numbers)
               nonneg
               (cons (car numbers) neg)))))

     @result{}  ((6 1 3) (-5 -2))
@end group
@end example
@end deffn

@deffn {special form} do ((@var{variable} @var{init} @var{step}) @dots{}) (@var{test} @var{expression} @dots{}) command @dots{}
@code{do} is an iteration construct.  It specifies a set of variables to
be bound, how they are to be initialized at the start, and how they are
to be updated on each iteration.  When a termination condition is met,
the loop exits with a specified result value.

@code{do} expressions are evaluated as follows: The @var{init}
expressions are evaluated (in some unspecified order), the
@var{variable}s are bound to fresh locations, the results of the
@var{init} expressions are stored in the bindings of the
@var{variable}s, and then the iteration phase begins.

Each iteration begins by evaluating @var{test}; if the result is false,
then the @var{command} expressions are evaluated in order for effect,
the @var{step} expressions are evaluated in some unspecified order, the
@var{variable}s are bound to fresh locations, the results of the
@var{step}s are stored in the bindings of the @var{variable}s, and the
next iteration begins.

If @var{test} evaluates to a true value, then the @var{expression}s are
evaluated from left to right and the value of the last @var{expression}
is returned as the value of the @code{do} expression.  If no
@var{expression}s are present, then the value of the @code{do}
expression is unspecified in standard Scheme; in MIT/GNU Scheme, the
value of @var{test} is returned.

@cindex region of variable binding, do
@cindex variable binding, do
The region of the binding of a @var{variable} consists of the entire
@code{do} expression except for the @var{init}s.  It is an error for a
@var{variable} to appear more than once in the list of @code{do}
variables.

A @var{step} may be omitted, in which case the effect is the same as if
@code{(@var{variable} @var{init} @var{variable})} had been written
instead of @code{(@var{variable} @var{init})}.

@example
@group
(do ((vec (make-vector 5))
      (i 0 (+ i 1)))
    ((= i 5) vec)
   (vector-set! vec i i))               @result{}  #(0 1 2 3 4)
@end group

@group
(let ((x '(1 3 5 7 9)))
   (do ((x x (cdr x))
        (sum 0 (+ sum (car x))))
       ((null? x) sum)))                @result{}  25
@end group
@end example
@end deffn

@node Structure Definitions, Macros, Iteration, Special Forms
@section Structure Definitions

This section provides examples and describes the options and syntax of
@code{define-structure}, an MIT/GNU Scheme macro that is very similar to
@code{defstruct} in Common Lisp.  The differences between them are
summarized at the end of this section.  For more information, see
Steele's Common Lisp book.

@deffn {special form} define-structure (name structure-option @dots{}) slot-description @dots{}
Each @var{slot-description} takes one of the following forms:

@example
@group
@var{slot-name}
(@var{slot-name} @var{default-init} [@var{slot-option} @var{value}]*)
@end group
@end example

@cindex keyword constructor
@cindex BOA constructor
The fields @var{name} and @var{slot-name} must both be symbols.  The
field @var{default-init} is an expression for the initial value of the
slot.  It is evaluated each time a new instance is constructed.  If it
is not specified, the initial content of the slot is undefined.  Default
values are only useful with a @sc{boa} constructor with argument list or
a keyword constructor (see below).

Evaluation of a @code{define-structure} expression defines a structure
descriptor and a set of procedures to manipulate instances of the
structure.  These instances are represented as records by default
(@pxref{Records}) but may alternately be lists or vectors.  The
accessors and modifiers are marked with compiler declarations so that
calls to them are automatically transformed into appropriate references.
Often, no options are required, so a simple call to
@code{define-structure} looks like:

@example
(define-structure foo a b c)
@end example

This defines a type descriptor @code{rtd:foo}, a constructor
@code{make-foo}, a predicate @code{foo?}, accessors @code{foo-a},
@code{foo-b}, and @code{foo-c}, and modifiers @code{set-foo-a!},
@code{set-foo-b!}, and @code{set-foo-c!}.

In general, if no options are specified, @code{define-structure} defines
the following (using the simple call above as an example):

@table @asis
@item type descriptor
The name of the type descriptor is @code{"rtd:"} followed by the name of
the structure, e.g.@: @samp{rtd:foo}.  The type descriptor satisfies the
predicate @code{record-type?}.

@item constructor
The name of the constructor is @code{"make-"} followed by the name of
the structure, e.g.@: @samp{make-foo}.  The number of arguments accepted
by the constructor is the same as the number of slots; the arguments are
the initial values for the slots, and the order of the arguments matches
the order of the slot definitions.

@item predicate
The name of the predicate is the name of the structure followed by
@code{"?"}, e.g.@: @samp{foo?}.  The predicate is a procedure of one
argument, which returns @code{#t} if its argument is a record of the
type defined by this structure definition, and @code{#f} otherwise.

@item accessors
For each slot, an accessor is defined.  The name of the accessor is
formed by appending the name of the structure, a hyphen, and the name of
the slot, e.g.@: @samp{foo-a}.  The accessor is a procedure of one
argument, which must be a record of the type defined by this structure
definition.  The accessor extracts the contents of the corresponding
slot in that record and returns it.

@item modifiers
For each slot, a modifier is defined.  The name of the modifier is
formed by appending @code{"set-"}, the name of the accessor, and
@code{"!"}, e.g.@: @samp{set-foo-a!}.  The modifier is a procedure of
two arguments, the first of which must be a record of the type defined
by this structure definition, and the second of which may be any object.
The modifier modifies the contents of the corresponding slot in that
record to be that object, and returns an unspecified value.
@end table

When options are not supplied, @code{(@var{name})} may be abbreviated to
@var{name}.  This convention holds equally for @var{structure-options}
and @var{slot-options}.  Hence, these are equivalent:

@example
@group
(define-structure foo a b c)
(define-structure (foo) (a) b (c))
@end group
@end example

@noindent
as are

@example
@group
(define-structure (foo keyword-constructor) a b c)
(define-structure (foo (keyword-constructor)) a b c)
@end group
@end example

When specified as option values, @code{false} and @code{nil} are
equivalent to @code{#f}, and @code{true} and @code{t} are equivalent to
@code{#t}.
@end deffn

Possible @var{slot-options} are:

@deffn {slot option} read-only value
When given a @var{value} other than @code{#f}, this specifies that no
modifier should be created for the slot.
@end deffn

@deffn {slot option} type type-descriptor
This is accepted but not presently used.
@end deffn

Possible @var{structure-options} are:

@deffn {structure option} predicate [name]
This option controls the definition of a predicate procedure for the
structure.  If @var{name} is not given, the predicate is defined with
the default name (see above).  If @var{name} is @code{#f}, the predicate
is not defined at all.  Otherwise, @var{name} must be a symbol, and
the predicate is defined with that symbol as its name.
@end deffn

@deffn {structure option} copier [name]
This option controls the definition of a procedure to copy instances of
the structure.  This is a procedure of one argument, a structure
instance, that makes a newly allocated copy of the structure and returns
it.  If @var{name} is not given, the copier is defined, and the name
of the copier is @code{"copy-"} followed by the structure name (e.g.@:
@samp{copy-foo}).  If @var{name} is @code{#f}, the copier is not
defined.  Otherwise, @var{name} must be a symbol, and the copier is
defined with that symbol as its name.
@end deffn

@deffn {structure option} print-procedure expression
Evaluating @var{expression} must yield a procedure of two arguments,
which is used to print instances of the structure.  The procedure is an
@dfn{unparser method} (@pxref{Custom Output}).  If the structure
instances are records, this option has the same effect as calling
@code{set-record-type-unparser-method!}.
@findex set-record-type-unparser-method!
@end deffn

@deffn {structure option} constructor [name [argument-list]]
@cindex BOA constructor (defn)
This option controls the definition of constructor procedures.  These
constructor procedures are called ``@sc{boa} constructors'', for ``By
Order of Arguments'', because the arguments to the constructor specify
the initial contents of the structure's slots by the order in which they
are given.  This is as opposed to ``keyword constructors'', which
specify the initial contents using keywords, and in which the order of
arguments is irrelevant.

If @var{name} is not given, a constructor is defined with the default
name and arguments (see above).  If @var{name} is @code{#f}, no
constructor is defined; @var{argument-list} may not be specified in this
case.  Otherwise, @var{name} must be a symbol, and a constructor is
defined with that symbol as its name.  If @var{name} is a symbol,
@var{argument-list} is optionally allowed; if it is omitted, the
constructor accepts one argument for each slot in the structure
definition, in the same order in which the slots appear in the
definition.  Otherwise, @var{argument-list} must be a lambda list
(@pxref{Lambda Expressions}), and each of the parameters of the lambda
list must be the name of a slot in the structure.  The arguments
accepted by the constructor are defined by this lambda list.  Any slot
that is not specified by the lambda list is initialized to the
@var{default-init} as specified above; likewise for any slot specified
as an optional parameter when the corresponding argument is not
supplied.

If the @code{constructor} option is specified, the default constructor
is not defined.  Additionally, the @code{constructor} option may be
specified multiple times to define multiple constructors with
different names and argument lists.

@example
@group
(define-structure (foo
                   (constructor make-foo (#!optional a b)))
  (a 6 read-only #t)
  (b 9))
@end group
@end example
@end deffn

@deffn {structure option} keyword-constructor [name]
@cindex keyword constructor (defn)
This option controls the definition of keyword constructor procedures.
A @dfn{keyword constructor} is a procedure that accepts arguments that
are alternating slot names and values.  If @var{name} is omitted, a
keyword constructor is defined, and the name of the constructor is
@code{"make-"} followed by the name of the structure (e.g.@:
@samp{make-foo}).  Otherwise, @var{name} must be a symbol, and a keyword
constructor is defined with this symbol as its name.

If the @code{keyword-constructor} option is specified, the default
constructor is not defined.  Additionally, the
@code{keyword-constructor} option may be specified multiple times to
define multiple keyword constructors; this is usually not done since
such constructors would all be equivalent.

@example
@group
(define-structure (foo (keyword-constructor make-bar)) a b)
(foo-a (make-bar 'b 20 'a 19))         @result{} 19
@end group
@end example
@end deffn

@deffn {structure option} type-descriptor name
This option cannot be used with the @code{type} or @code{named} options.

By default, structures are implemented as records.  The name of the
structure is defined to hold the type descriptor of the record defined
by the structure.  The @code{type-descriptor} option specifies a
different name to hold the type descriptor.

@example
@group
(define-structure foo a b)
foo             @result{} #[record-type 18]

(define-structure (bar (type-descriptor <bar>)) a b)
bar             @error{} Unbound variable: bar
<bar>         @result{} #[record-type 19]
@end group
@end example
@end deffn

@deffn {structure option} conc-name [name]
By default, the prefix for naming accessors and modifiers is the name of
the structure followed by a hyphen.  The @code{conc-name} option can be
used to specify an alternative.  If @var{name} is not given, the prefix
is the name of the structure followed by a hyphen (the default).  If
@var{name} is @code{#f}, the slot names are used directly, without
prefix.  Otherwise, @var{name} must a symbol, and that symbol is used as
the prefix.

@example
@code{(define-structure (foo (conc-name moby/)) a b)}
@end example

@noindent
defines accessors @code{moby/a} and @code{moby/b}, and modifiers
@code{set-moby/a!} and @code{set-moby/b!}.

@example
@code{(define-structure (foo (conc-name #f)) a b)}
@end example

@noindent
defines accessors @code{a} and @code{b}, and modifiers @code{set-a!} and
@code{set-b!}.
@end deffn

@deffn {structure option} type representation-type
This option cannot be used with the @code{type-descriptor} option.

By default, structures are implemented as records.  The @code{type}
option overrides this default, allowing the programmer to specify that
the structure be implemented using another data type.  The option value
@var{representation-type} specifies the alternate data type; it is
allowed to be one of the symbols @code{vector} or @code{list}, and the
data type used is the one corresponding to the symbol.

If this option is given, and the @code{named} option is not specified,
the representation will not be tagged, and neither a predicate nor a
type descriptor will be defined; also, the @code{print-procedure}
option may not be given.

@example
@group
(define-structure (foo (type list)) a b) 
(make-foo 1 2)                          @result{} (1 2)
@end group
@end example
@end deffn

@deffn {structure option} named [expression]
This is valid only in conjunction with the @code{type} option and
specifies that the structure instances be tagged to make them
identifiable as instances of this structure type.  This option cannot be
used with the @code{type-descriptor} option.

In the usual case, where @var{expression} is not given, the @code{named}
option causes a type descriptor and predicate to be defined for the
structure (recall that the @code{type} option without @code{named}
suppresses their definition), and also defines a default unparser method
for the structure instances (which can be overridden by the
@code{print-procedure} option).  If the default unparser method is not
wanted then the @code{print-procedure} option should be specified as
@code{#F}.  This causes the structure to be printed in its native
representation, as a list or vector, which includes the type descriptor.
The type descriptor is a unique object, @emph{not} a record type, that
describes the structure instances and is additionally stored in the
structure instances to identify them: if the representation type is
@code{vector}, the type descriptor is stored in the zero-th slot of the
vector, and if the representation type is @code{list}, it is stored as
the first element of the list.


@example
@group
(define-structure (foo (type vector) named) a b c)
(vector-ref (make-foo 1 2 3) 0) @result{} #[structure-type 52]
@end group
@end example

If @var{expression} is specified, it is an expression that is evaluated
to yield a tag object.  The @var{expression} is evaluated once when the
structure definition is evaluated (to specify the unparser method), and
again whenever a predicate or constructor is called.  Because of this,
@var{expression} is normally a variable reference or a constant.  The
value yielded by @var{expression} may be any object at all.  That object
is stored in the structure instances in the same place that the type
descriptor is normally stored, as described above.  If @var{expression}
is specified, no type descriptor is defined, only a predicate.

@example
@group
(define-structure (foo (type vector) (named 'foo)) a b c)
(vector-ref (make-foo 1 2 3) 0) @result{} foo
@end group
@end example
@end deffn

@deffn {structure option} safe-accessors [boolean]
This option allows the programmer to have some control over the safety
of the slot accessors (and modifiers) generated by
@code{define-structure}.  If @code{safe-accessors} is not specified, or
if @var{boolean} is @code{#f}, then the accessors are optimized for
speed at the expense of safety; when compiled, the accessors will turn
into very fast inline sequences, usually one to three machine
instructions in length.  However, if @code{safe-accessors} is specified
and @var{boolean} is either omitted or @code{#t}, then the accessors are
optimized for safety, will check the type and structure of their
argument, and will be close-coded.

@example
@group
(define-structure (foo safe-accessors) a b c)
@end group
@end example
@end deffn

@deffn {structure option} initial-offset offset
This is valid only in conjunction with the @code{type} option.
@var{Offset} must be an exact non-negative integer and specifies the
number of slots to leave open at the beginning of the structure instance
before the specified slots are allocated.  Specifying an @var{offset} of
zero is equivalent to omitting the @code{initial-offset} option.

If the @code{named} option is specified, the structure tag appears in
the first slot, followed by the ``offset'' slots, and then the regular
slots.  Otherwise, the ``offset'' slots come first, followed by the
regular slots.

@example
@group
(define-structure (foo (type vector) (initial-offset 3))
  a b c)
(make-foo 1 2 3)                @result{} #(() () () 1 2 3)
@end group
@end example
@end deffn

The essential differences between MIT/GNU Scheme's @code{define-structure}
and Common Lisp's @code{defstruct} are:

@itemize @bullet
@item
The default constructor procedure takes positional arguments, in the
same order as specified in the definition of the structure.  A keyword
constructor may be specified by giving the option
@code{keyword-constructor}.

@item
@sc{boa} constructors are described using Scheme lambda lists.  Since there
is nothing corresponding to @code{&aux} in Scheme lambda lists, this
functionality is not implemented.

@item
By default, no @code{copier} procedure is defined.

@item
The side-effect procedure corresponding to the accessor @code{foo} is
given the name @code{set-foo!}.

@item
Keywords are ordinary symbols -- use @code{foo} instead of @code{:foo}.

@item
The option values @code{false}, @code{nil}, @code{true}, and @code{t}
are treated as if the appropriate boolean constant had been specified
instead.

@item
The @code{print-function} option is named @code{print-procedure}.  Its
argument is a procedure of two arguments (the unparser state and the
structure instance) rather than three as in Common Lisp.

@item
By default, named structures are tagged with a unique object of some
kind.  In Common Lisp, the structures are tagged with symbols.  This
depends on the Common Lisp package system to help generate unique tags;
MIT/GNU Scheme has no such way to generate unique symbols.

@item
The @code{named} option may optionally take an argument, which is
normally the name of a variable (any expression may be used, but it is
evaluated whenever the tag name is needed).  If used, structure
instances will be tagged with that variable's value.  The variable must
be defined when @code{define-structure} is evaluated.

@item
The @code{type} option is restricted to the values @code{vector} and
@code{list}.

@item
The @code{include} option is not implemented.
@end itemize

@node Macros, SRFI syntax, Structure Definitions, Special Forms
@section Macros

(This section is largely taken from the @cite{Revised^4 Report on the
Algorithmic Language Scheme}.  The section on Syntactic Closures is
derived from a document written by Chris Hanson.  The section on
Explicit Renaming is derived from a document written by William
Clinger.)

@cindex macro
Scheme programs can define and use new derived expression types, called
@dfn{macros}.  Program-defined expression types have the syntax

@example
(@var{keyword} @var{datum} @dots{})
@end example

@noindent
@cindex syntactic keyword
@cindex keyword
@cindex macro keyword
where @var{keyword} is an identifier that uniquely determines the
expression type.  This identifier is called the @dfn{syntactic keyword},
or simply @dfn{keyword}, of the macro.  The number of the @var{datum}s,
and their syntax, depends on the expression type.

@cindex macro use
@cindex macro transformer
Each instance of a macro is called a @dfn{use} of the macro.  The set of
rules that specifies how a use of a macro is transcribed into a more
primitive expression is called the @dfn{transformer} of the macro.

@cindex anonymous syntactic keyword
MIT/GNU Scheme also supports @dfn{anonymous syntactic keywords}.  This means
that it's not necessary to bind a macro transformer to a syntactic
keyword before it is used.  Instead, any macro-transformer expression
can appear as the first element of a form, and the form will be expanded
by the transformer.

The macro definition facility consists of these parts:

@itemize @bullet
@item
A set of expressions used to establish that certain identifiers are
macro keywords, associate them with macro transformers, and control the
scope within which a macro is defined.

@item
A standard high-level pattern language for specifying macro
transformers, introduced by the @code{syntax-rules} special form.

@item
Two non-standard low-level languages for specifying macro transformers,
@dfn{syntactic closures} and @dfn{explicit renaming}.
@end itemize

@cindex hygienic
@cindex referentially transparent
The syntactic keyword of a macro may shadow variable bindings, and local
variable bindings may shadow keyword bindings.  All macros defined using
the pattern language are ``hygienic'' and ``referentially transparent''
and thus preserve Scheme's lexical scoping:

@itemize @bullet
@item
If a macro transformer inserts a binding for an identifier (variable or
keyword), the identifier will in effect be renamed throughout its scope
to avoid conflicts with other identifiers.

@item
If a macro transformer inserts a free reference to an identifier, the
reference refers to the binding that was visible where the transformer
was specified, regardless of any local bindings that may surround the
use of the macro.
@end itemize

@menu
* Syntactic Binding Constructs::  
* Pattern Language::            
* Syntactic Closures::          
* Explicit Renaming::           
@end menu

@node Syntactic Binding Constructs, Pattern Language, Macros, Macros
@subsection Binding Constructs for Syntactic Keywords

@code{let-syntax}, @code{letrec-syntax}, @code{let*-syntax} and
@code{define-syntax} are analogous to @code{let}, @code{letrec},
@code{let*} and @code{define}, but they bind syntactic keywords to macro
transformers instead of binding variables to locations that contain
values.

Any argument named @var{transformer-spec} must be a macro-transformer
expression, which is one of the following:

@itemize @bullet
@item
A macro transformer defined by the pattern language and denoted by the
syntactic keyword @code{syntax-rules}.

@item
A macro transformer defined by one of the low-level mechanisms and
denoted by one of the syntactic keywords @code{sc-macro-transformer},
@code{rsc-macro-transformer}, or @code{er-macro-transformer}.

@item
A syntactic keyword bound in the enclosing environment.  This is used
to bind another name to an existing macro transformer.
@end itemize

@deffn {special form} let-syntax bindings expression expression @dots{}
@var{Bindings} should have the form

@example
((@var{keyword} @var{transformer-spec}) @dots{})
@end example

@noindent
Each @var{keyword} is an identifier, each @var{transformer-spec} is a
a macro-transformer expression, and the body is a sequence of
one or more expressions.  It is an error for a @var{keyword} to appear
more than once in the list of keywords being bound.

The @var{expression}s are expanded in the syntactic environment obtained
by extending the syntactic environment of the @code{let-syntax}
expression with macros whose keywords are the @var{keyword}s, bound to
the specified transformers.  Each binding of a @var{keyword} has the
@var{expression}s as its region.

@example
@group
(let-syntax ((when (syntax-rules ()
                     ((when test stmt1 stmt2 ...)
                      (if test
                          (begin stmt1
                                 stmt2 ...))))))
  (let ((if #t))
    (when if (set! if 'now))
    if))                           @result{}  now

(let ((x 'outer))
  (let-syntax ((m (syntax-rules () ((m) x))))
    (let ((x 'inner))
      (m))))                       @result{}  outer
@end group
@end example
@end deffn

@deffn {special form} letrec-syntax bindings expression expression @dots{}
The syntax of @code{letrec-syntax} is the same as for @code{let-syntax}.

The @var{expression}s are expanded in the syntactic environment obtained
by extending the syntactic environment of the @code{letrec-syntax}
expression with macros whose keywords are the @var{keyword}s, bound to
the specified transformers.  Each binding of a @var{keyword} has the
@var{bindings} as well as the @var{expression}s within its region, so
the transformers can transcribe expressions into uses of the macros
introduced by the @code{letrec-syntax} expression.

@example
@group
(letrec-syntax
  ((my-or (syntax-rules ()
            ((my-or) #f)
            ((my-or e) e)
            ((my-or e1 e2 ...)
             (let ((temp e1))
               (if temp
                   temp
                   (my-or e2 ...)))))))
  (let ((x #f)
        (y 7)
        (temp 8)
        (let odd?)
        (if even?))
    (my-or x
           (let temp)
           (if y)
           y)))        @result{}  7
@end group
@end example
@end deffn

@deffn {special form} let*-syntax bindings expression expression @dots{}
The syntax of @code{let*-syntax} is the same as for @code{let-syntax}.

The @var{expression}s are expanded in the syntactic environment obtained
by extending the syntactic environment of the @code{letrec-syntax}
expression with macros whose keywords are the @var{keyword}s, bound to
the specified transformers.  Each binding of a @var{keyword} has the
subsequent @var{bindings} as well as the @var{expression}s within its
region.  Thus

@example
@group
(let*-syntax
   ((a (syntax-rules @dots{}))
    (b (syntax-rules @dots{})))
  @dots{})
@end group
@end example

@noindent
is equivalent to

@example
@group
(let-syntax ((a (syntax-rules @dots{})))
  (let-syntax ((b (syntax-rules @dots{})))
    @dots{}))
@end group
@end example
@end deffn

@deffn {special form} define-syntax keyword transformer-spec
@var{Keyword} is an identifier, and @var{transformer-spec} is a macro
transformer expression.  The syntactic environment is extended by
binding the @var{keyword} to the specified transformer.

The region of the binding introduced by @code{define-syntax} is the
entire block in which it appears.  However, the @var{keyword} may only
be used after it has been defined.

MIT/GNU Scheme permits @code{define-syntax} to appear both at top level and
within @code{lambda} bodies.  The Revised^4 Report permits only
top-level uses of @code{define-syntax}.

When compiling a program, a top-level instance of @code{define-syntax}
both defines the syntactic keyword and generates code that will redefine
the keyword when the program is loaded.  This means that the same syntax
can be used for defining macros that will be used during compilation
and for defining macros to be used at run time.

Although macros may expand into definitions and syntax definitions in
any context that permits them, it is an error for a definition or syntax
definition to shadow a syntactic keyword whose meaning is needed to
determine whether some form in the group of forms that contains the
shadowing definition is in fact a definition, or, for internal definitions,
is needed to determine the boundary between the group and the expressions
that follow the group.  For example, the following are errors:

@example
(define define 3)

(begin (define begin list))

(let-syntax
  ((foo (syntax-rules ()
          ((foo (proc args ...) body ...)
           (define proc
             (lambda (args ...)
               body ...))))))
  (let ((x 3))
    (foo (plus x y) (+ x y))
    (define foo x)
    (plus foo x)))
@end example
@end deffn

@node Pattern Language, Syntactic Closures, Syntactic Binding Constructs, Macros
@subsection Pattern Language

MIT/GNU Scheme supports a high-level pattern language for specifying macro
transformers.  This pattern language is defined by the Revised^4 Report
and is portable to other conforming Scheme implementations.  To use the
pattern language, specify a @var{transformer-spec} as a
@code{syntax-rules} form:

@deffn {special form} syntax-rules literals syntax-rule @dots{}
@var{Literals} is a list of identifiers and each @var{syntax-rule}
should be of the form

@example
(@var{pattern} @var{template})
@end example

The @var{pattern} in a @var{syntax-rule} is a list @var{pattern} that
begins with the keyword for the macro.

A @var{pattern} is either an identifier, a constant, or one of the
following

@example
(@var{pattern} @dots{})
(@var{pattern} @var{pattern} @dots{} . @var{pattern})
(@var{pattern} @dots{} @var{pattern} @var{ellipsis})
@end example

@noindent
and a template is either an identifier, a constant, or one of the
following

@example
(@var{element} @dots{})
(@var{element} @var{element} @dots{} . @var{template})
@end example

@vindex ...
where an @var{element} is a @var{template} optionally followed by an
@var{ellipsis} and an @var{ellipsis} is the identifier @samp{...} (which
cannot be used as an identifier in either a template or a pattern).

An instance of @code{syntax-rules} produces a new macro transformer by
specifying a sequence of hygienic rewrite rules.  A use of a macro whose
keyword is associated with a transformer specified by
@code{syntax-rules} is matched against the patterns contained in the
@var{syntax-rule}s, beginning with the leftmost @var{syntax-rule}.  When
a match is found, the macro use is transcribed hygienically according to
the template.

An identifier that appears in the pattern of a @var{syntax-rule} is a
@dfn{pattern-variable}, unless it is the keyword that begins the
pattern, is listed in @var{literals}, or is the identifier @samp{...}.
Pattern variables match arbitrary input elements and are used to refer
to elements of the input in the template.  It is an error for the same
pattern variable to appear more than once in a @var{pattern}.

The keyword at the beginning of the pattern in a @var{syntax-rule} is
not involved in the matching and is not considered a pattern variable or
literal identifier.

Identifiers that appear in @var{literals} are interpreted as literal
identifiers to be matched against corresponding subforms of the input.
A subform in the input matches a literal identifier if and only if it is
an identifier and either both its occurrence in the macro expression and
its occurrence in the macro definition have the same lexical binding, or
the two identifiers are equal and both have no lexical binding.

A subpattern followed by @samp{...} can match zero or more elements of
the input.  It is an error for @samp{...} to appear in @var{literals}.
Within a pattern the identifier @samp{...} must follow the last element
of a nonempty sequence of subpatterns.

More formally, an input form @var{F} matches a pattern @var{P} if and
only if:

@itemize @bullet
@item
@var{P} is a non-literal identifier; or

@item
@var{P} is a literal identifier and @var{F} is an identifier with the
same binding; or

@item
@var{P} is a list @code{(@var{P_1} @dots{} @var{P_n})} and @var{F} is a
list of @var{n} forms that match @var{P_1} through @var{P_n},
respectively; or

@item
@var{P} is an improper list @code{(@var{P_1} @var{P_2} @dots{} @var{P_n}
. @var{P_n+1})} and @var{F} is a list or improper list of @var{n} or
more forms that match @var{P_1} through @var{P_n}, respectively, and
whose @var{n}th ``cdr'' matches @var{P_n+1}; or

@item
@var{P} is of the form @code{(@var{P_1} @dots{} @var{P_n} @var{P_n+1}
@var{ellipsis})} where @var{ellipsis} is the identifier @samp{...} and
@var{F} is a proper list of at least @var{n} forms, the first @var{n} of
which match @var{P_1} through @var{P_n}, respectively, and each
remaining element of @var{F} matches @var{P_n+1}; or

@item
@var{P} is a datum and @var{F} is equal to @var{P} in the sense of the
@code{equal?} procedure.
@end itemize

It is an error to use a macro keyword, within the scope of its
binding, in an expression that does not match any of the patterns.

When a macro use is transcribed according to the template of the
matching @var{syntax rule}, pattern variables that occur in the template
are replaced by the subforms they match in the input.  Pattern variables
that occur in subpatterns followed by one or more instances of the
identifier @samp{...} are allowed only in subtemplates that are followed
by as many instances of @samp{...}.  They are replaced in the output by
all of the subforms they match in the input, distributed as indicated.
It is an error if the output cannot be built up as specified.

Identifiers that appear in the template but are not pattern variables or
the identifier @samp{...} are inserted into the output as literal
identifiers.  If a literal identifier is inserted as a free identifier
then it refers to the binding of that identifier within whose scope the
instance of @code{syntax-rules} appears.  If a literal identifier is
inserted as a bound identifier then it is in effect renamed to prevent
inadvertent captures of free identifiers.

@example
@group
(let ((=> #f))
  (cond (#t => 'ok)))           @result{} ok
@end group
@end example

The macro transformer for @code{cond} recognizes @code{=>}
as a local variable, and hence an expression, and not as the
top-level identifier @code{=>}, which the macro transformer treats
as a syntactic keyword.  Thus the example expands into

@example
@group
(let ((=> #f))
  (if #t (begin => 'ok)))
@end group
@end example

instead of

@example
@group
(let ((=> #f))
  (let ((temp #t))
    (if temp 
        ('ok temp))))
@end group
@end example

which would result in an invalid procedure call.
@end deffn

@node Syntactic Closures, Explicit Renaming, Pattern Language, Macros
@subsection Syntactic Closures

@cindex syntactic closures
MIT/GNU Scheme's syntax-transformation engine is an implementation of
@dfn{syntactic closures}, a mechanism invented by Alan Bawden and
Jonathan Rees.  The main feature of the syntactic-closures mechanism is
its simplicity and its close relationship to the environment models
commonly used with Scheme.  Using the mechanism to write macro
transformers is somewhat cumbersome and can be confusing for the newly
initiated, but it is easily mastered.

@menu
* Syntax Terminology::          
* SC Transformer Definition::   
* SC Identifiers::              
@end menu

@node Syntax Terminology, SC Transformer Definition, Syntactic Closures, Syntactic Closures
@subsubsection Syntax Terminology

This section defines the concepts and data types used by the syntactic
closures facility.

@itemize @bullet
@item
@cindex form
@dfn{Forms} are the syntactic entities out of which programs are
recursively constructed.  A form is any expression, any definition, any
syntactic keyword, or any syntactic closure.  The variable name that
appears in a @code{set!} special form is also a form.  Examples of
forms:

@example
@group
17
#t
car
(+ x 4)
(lambda (x) x)
(define pi 3.14159)
if
define
@end group
@end example

@item
@cindex alias
@cindex identifier
@cindex synthetic identifier
An @dfn{alias} is an alternate name for a given symbol.  It can appear
anywhere in a form that the symbol could be used, and when quoted it is
replaced by the symbol; however, it does not satisfy the predicate
@code{symbol?}.  Macro transformers rarely distinguish symbols from
aliases, referring to both as @dfn{identifiers}.  Another name for an
alias is @dfn{synthetic identifier}; this document uses both names.

@item
@cindex syntactic environment
A @dfn{syntactic environment} maps identifiers to their meanings.  More
precisely, it determines whether an identifier is a syntactic keyword
or a variable.  If it is a keyword, the meaning is an interpretation
for the form in which that keyword appears.  If it is a variable, the
meaning identifies which binding of that variable is referenced.  In
short, syntactic environments contain all of the contextual information
necessary for interpreting the meaning of a particular form.

@item
@cindex syntactic closure
A @dfn{syntactic closure} consists of a form, a syntactic environment,
and a list of identifiers.  All identifiers in the form take their
meaning from the syntactic environment, except those in the given list.
The identifiers in the list are to have their meanings determined
later.

A syntactic closure may be used in any context in which its form could
have been used.  Since a syntactic closure is also a form, it may not
be used in contexts where a form would be illegal.  For example, a form
may not appear as a clause in the @code{cond} special form.

A syntactic closure appearing in a quoted structure is replaced by its
form.
@end itemize

@node SC Transformer Definition, SC Identifiers, Syntax Terminology, Syntactic Closures
@subsubsection Transformer Definition

This section describes the special forms for defining syntactic-closures
macro transformers, and the associated procedures for manipulating
syntactic closures and syntactic environments.

@deffn {special form} sc-macro-transformer expression
The @var{expression} is expanded in the syntactic environment of the
@code{sc-macro-transformer} expression, and the expanded expression is
evaluated in the transformer environment to yield a macro transformer as
described below.  This macro transformer is bound to a macro keyword by
the special form in which the @code{transformer} expression appears (for
example, @code{let-syntax}).

@cindex macro transformer
@cindex input form
@cindex usage environment
@cindex output form
@cindex transformer environment
In the syntactic closures facility, a @dfn{macro transformer} is a
procedure that takes two arguments, a form and a syntactic environment,
and returns a new form.  The first argument, the @dfn{input form}, is
the form in which the macro keyword occurred.  The second argument, the
@dfn{usage environment}, is the syntactic environment in which the input
form occurred.  The result of the transformer, the @dfn{output form}, is
automatically closed in the @dfn{transformer environment}, which is the
syntactic environment in which the @code{transformer} expression
occurred.

For example, here is a definition of a @code{push} macro using
@code{syntax-rules}:

@example
@group
(define-syntax push
  (syntax-rules ()
    ((push item list)
     (set! list (cons item list)))))
@end group
@end example

@noindent
Here is an equivalent definition using @code{sc-macro-transformer}:

@example
@group
(define-syntax push
  (sc-macro-transformer
   (lambda (exp env)
     (let ((item (make-syntactic-closure env '() (cadr exp)))
           (list (make-syntactic-closure env '() (caddr exp))))
       `(set! ,list (cons ,item ,list))))))
@end group
@end example

@noindent
In this example, the identifiers @code{set!} and @code{cons} are closed
in the transformer environment, and thus will not be affected by the
meanings of those identifiers in the usage environment @code{env}.

Some macros may be non-hygienic by design.  For example, the following
defines a @code{loop} macro that implicitly binds @code{exit} to an
escape procedure.  The binding of @code{exit} is intended to capture
free references to @code{exit} in the body of the loop, so @code{exit}
must be left free when the body is closed:

@example
@group
(define-syntax loop
  (sc-macro-transformer
   (lambda (exp env)
     (let ((body (cdr exp)))
       `(call-with-current-continuation
         (lambda (exit)
           (let f ()
             ,@@(map (lambda (exp)
                      (make-syntactic-closure env '(exit)
                        exp))
                    body)
             (f))))))))
@end group
@end example
@end deffn

@deffn {special form} rsc-macro-transformer expression
This form is an alternative way to define a syntactic-closures macro
transformer.  Its syntax and usage are identical to
@code{sc-macro-transformer}, except that the roles of the usage
environment and transformer environment are reversed.  (Hence
@acronym{RSC} stands for @dfn{Reversed Syntactic Closures}.)  In other
words, the procedure specified by @var{expression} still accepts two
arguments, but its second argument will be the transformer environment
rather than the usage environment, and the returned expression is closed
in the usage environment rather than the transformer environment.

The advantage of this arrangement is that it allows a simpler definition
style in some situations.  For example, here is the @code{push} macro
from above, rewritten in this style:

@example
@group
(define-syntax push
  (rsc-macro-transformer
   (lambda (exp env)
     `(,(make-syntactic-closure env '() 'SET!)
       ,(caddr exp)
       (,(make-syntactic-closure env '() 'CONS)
        ,(cadr exp)
        ,(caddr exp))))))
@end group
@end example

@noindent
In this style only the introduced keywords are closed, while everything
else remains open.

Note that @code{rsc-macro-transformer} and @code{sc-macro-transformer}
are easily interchangeable.  Here is how to emulate
@code{rsc-macro-transformer} using @code{sc-macro-transformer}.  (This
technique can be used to effect the opposite emulation as well.)

@example
@group
(define-syntax push
  (sc-macro-transformer
   (lambda (exp usage-env)
     (capture-syntactic-environment
      (lambda (env)
        (make-syntactic-closure usage-env '()
          `(,(make-syntactic-closure env '() 'SET!)
            ,(caddr exp)
            (,(make-syntactic-closure env '() 'CONS)
             ,(cadr exp)
             ,(caddr exp)))))))))
@end group
@end example
@end deffn

To assign meanings to the identifiers in a form, use
@code{make-syntactic-closure} to close the form in a syntactic
environment.

@deffn procedure make-syntactic-closure environment free-names form
@var{Environment} must be a syntactic environment, @var{free-names}
must be a list of identifiers, and @var{form} must be a form.
@code{make-syntactic-closure} constructs and returns a syntactic
closure of @var{form} in @var{environment}, which can be used anywhere
that @var{form} could have been used.  All the identifiers used in
@var{form}, except those explicitly excepted by @var{free-names},
obtain their meanings from @var{environment}.

Here is an example where @var{free-names} is something other than the
empty list.  It is instructive to compare the use of @var{free-names}
in this example with its use in the @code{loop} example above: the
examples are similar except for the source of the identifier being left
free.

@example
@group
(define-syntax let1
  (sc-macro-transformer
   (lambda (exp env)
     (let ((id (cadr exp))
           (init (caddr exp))
           (exp (cadddr exp)))
       `((lambda (,id)
           ,(make-syntactic-closure env (list id) exp))
         ,(make-syntactic-closure env '() init))))))
@end group
@end example

@noindent
@code{let1} is a simplified version of @code{let} that only binds a
single identifier, and whose body consists of a single expression.
When the body expression is syntactically closed in its original
syntactic environment, the identifier that is to be bound by
@code{let1} must be left free, so that it can be properly captured by
the @code{lambda} in the output form.
@end deffn

In most situations, the @var{free-names} argument to
@code{make-syntactic-closure} is the empty list.  In those cases, the
more succinct @code{close-syntax} can be used:

@deffn procedure close-syntax form environment
@var{Environment} must be a syntactic environment and @var{form} must be
a form.  Returns a new syntactic closure of @var{form} in
@var{environment}, with no free names.  Entirely equivalent to

@example
(make-syntactic-closure @var{environment} '() @var{form})
@end example
@end deffn

To obtain a syntactic environment other than the usage environment,
use @code{capture-syntactic-environment}.

@deffn procedure capture-syntactic-environment procedure
@code{capture-syntactic-environment} returns a form that will, when
transformed, call @var{procedure} on the current syntactic environment.
@var{Procedure} should compute and return a new form to be transformed,
in that same syntactic environment, in place of the form.

An example will make this clear.  Suppose we wanted to define a simple
@code{loop-until} keyword equivalent to

@example
@group
(define-syntax loop-until
  (syntax-rules ()
    ((loop-until id init test return step)
     (letrec ((loop
               (lambda (id)
                 (if test return (loop step)))))
       (loop init)))))
@end group
@end example

@noindent
The following attempt at defining @code{loop-until} has a subtle
bug:

@example
@group
(define-syntax loop-until
  (sc-macro-transformer
   (lambda (exp env)
     (let ((id (cadr exp))
           (init (caddr exp))
           (test (cadddr exp))
           (return (cadddr (cdr exp)))
           (step (cadddr (cddr exp)))
           (close
            (lambda (exp free)
              (make-syntactic-closure env free exp))))
       `(letrec ((loop
                  (lambda (,id)
                    (if ,(close test (list id))
                        ,(close return (list id))
                        (loop ,(close step (list id)))))))
          (loop ,(close init '())))))))
@end group
@end example

@noindent
This definition appears to take all of the proper precautions to
prevent unintended captures.  It carefully closes the subexpressions in
their original syntactic environment and it leaves the @code{id}
identifier free in the @code{test}, @code{return}, and @code{step}
expressions, so that it will be captured by the binding introduced by
the @code{lambda} expression.  Unfortunately it uses the identifiers
@code{if} and @code{loop} @emph{within} that @code{lambda} expression,
so if the user of @code{loop-until} just happens to use, say, @code{if}
for the identifier, it will be inadvertently captured.

The syntactic environment that @code{if} and @code{loop} want to be
exposed to is the one just outside the @code{lambda} expression: before
the user's identifier is added to the syntactic environment, but after
the identifier @code{loop} has been added.
@code{capture-syntactic-environment} captures exactly that environment
as follows:

@example
@group
(define-syntax loop-until
  (sc-macro-transformer
   (lambda (exp env)
     (let ((id (cadr exp))
           (init (caddr exp))
           (test (cadddr exp))
           (return (cadddr (cdr exp)))
           (step (cadddr (cddr exp)))
           (close
            (lambda (exp free)
              (make-syntactic-closure env free exp))))
       `(letrec ((loop
                  ,(capture-syntactic-environment
                    (lambda (env)
                      `(lambda (,id)
                         (,(make-syntactic-closure env '() `if)
                          ,(close test (list id))
                          ,(close return (list id))
                          (,(make-syntactic-closure env '() `loop)
                           ,(close step (list id)))))))))
          (loop ,(close init '())))))))
@end group
@end example

@noindent
In this case, having captured the desired syntactic environment, it is
convenient to construct syntactic closures of the identifiers @code{if}
and the @code{loop} and use them in the body of the
@code{lambda}.

A common use of @code{capture-syntactic-environment} is to get the
transformer environment of a macro transformer:

@example
@group
(sc-macro-transformer
 (lambda (exp env)
   (capture-syntactic-environment
    (lambda (transformer-env)
      @dots{}))))
@end group
@end example
@end deffn

@node SC Identifiers,  , SC Transformer Definition, Syntactic Closures
@subsubsection Identifiers

This section describes the procedures that create and manipulate
identifiers.  The identifier data type extends the syntactic closures
facility to be compatible with the high-level @code{syntax-rules}
facility.

@cindex alias
As discussed earlier, an identifier is either a symbol or an
@dfn{alias}.  An alias is implemented as a syntactic closure whose
@var{form} is an identifier:

@example
@group
(make-syntactic-closure env '() 'a) @result{} @r{an alias}
@end group
@end example

@noindent
Aliases are implemented as syntactic closures because they behave just
like syntactic closures most of the time.  The difference is that an
alias may be bound to a new value (for example by @code{lambda} or
@code{let-syntax}); other syntactic closures may not be used this way.
If an alias is bound, then within the scope of that binding it is looked
up in the syntactic environment just like any other identifier.

Aliases are used in the implementation of the high-level facility
@code{syntax-rules}.  A macro transformer created by @code{syntax-rules}
uses a template to generate its output form, substituting subforms of
the input form into the template.  In a syntactic closures
implementation, all of the symbols in the template are replaced by
aliases closed in the transformer environment, while the output form
itself is closed in the usage environment.  This guarantees that the
macro transformation is hygienic, without requiring the transformer to
know the syntactic roles of the substituted input subforms.

@deffn procedure identifier? object
Returns @code{#t} if @var{object} is an identifier, otherwise returns
@code{#f}.  Examples:

@example
@group
(identifier? 'a)        @result{} #t
(identifier? (make-syntactic-closure env '() 'a))
                        @result{} #t

(identifier? "a")       @result{} #f
(identifier? #\a)       @result{} #f
(identifier? 97)        @result{} #f
(identifier? #f)        @result{} #f
(identifier? '(a))      @result{} #f
(identifier? '#(a))     @result{} #f
@end group
@end example
@end deffn

The predicate @code{eq?} is used to determine if two identifers are
``the same''.  Thus @code{eq?} can be used to compare identifiers
exactly as it would be used to compare symbols.  Often, though, it is
useful to know whether two identifiers ``mean the same thing''.  For
example, the @code{cond} macro uses the symbol @code{else} to identify
the final clause in the conditional.  A macro transformer for
@code{cond} cannot just look for the symbol @code{else}, because the
@code{cond} form might be the output of another macro transformer that
replaced the symbol @code{else} with an alias.  Instead the transformer
must look for an identifier that ``means the same thing'' in the usage
environment as the symbol @code{else} means in the transformer
environment.

@deffn procedure identifier=? environment1 identifier1 environment2 identifier2
@var{Environment1} and @var{environment2} must be syntactic
environments, and @var{identifier1} and @var{identifier2} must be
identifiers.  @code{identifier=?} returns @code{#t} if the meaning of
@var{identifier1} in @var{environment1} is the same as that of
@var{identifier2} in @var{environment2}, otherwise it returns @code{#f}.
Examples:

@example
@group
(let-syntax
    ((foo
      (sc-macro-transformer
       (lambda (form env)
         (capture-syntactic-environment
          (lambda (transformer-env)
            (identifier=? transformer-env 'x env 'x)))))))
  (list (foo)
        (let ((x 3))
          (foo))))
                        @result{} (#t #f)
@end group

@group
(let-syntax ((bar foo))
  (let-syntax
      ((foo
        (sc-macro-transformer
         (lambda (form env)
           (capture-syntactic-environment
            (lambda (transformer-env)
              (identifier=? transformer-env 'foo
                            env (cadr form))))))))
    (list (foo foo)
          (foo bar))))
                        @result{} (#f #t)
@end group
@end example
@end deffn

Sometimes it is useful to be able to introduce a new identifier that is
guaranteed to be different from any existing identifier, similarly to
the way that @code{generate-uninterned-symbol} is used. 

@deffn procedure make-synthetic-identifier identifier
Creates and returns and new synthetic identifier (alias) that is
guaranteed to be different from all existing identifiers.
@var{Identifier} is any existing identifier, which is used in deriving
the name of the new identifier.

This is implemented by syntactically closing @var{identifier} in a
special empty environment.
@end deffn

@node Explicit Renaming,  , Syntactic Closures, Macros
@subsection Explicit Renaming

@cindex explicit renaming
@dfn{Explicit renaming} is an alternative facility for defining macro
transformers.  In the MIT/GNU Scheme implementation, explicit-renaming
transformers are implemented as an abstraction layer on top of syntactic
closures.  An explicit-renaming macro transformer is defined by an
instance of the @code{er-macro-transformer} keyword:

@deffn {special form} er-macro-transformer expression
The @var{expression} is expanded in the syntactic environment of the
@code{er-macro-transformer} expression, and the expanded expression is
evaluated in the transformer environment to yield a macro transformer as
described below.  This macro transformer is bound to a macro keyword by
the special form in which the @code{transformer} expression appears (for
example, @code{let-syntax}).

@cindex macro transformer
@cindex input form, to macro
In the explicit-renaming facility, a @dfn{macro transformer} is a
procedure that takes three arguments, a form, a renaming procedure, and
a comparison predicate, and returns a new form.  The first argument, the
@dfn{input form}, is the form in which the macro keyword occurred.

@cindex renaming procedure
The second argument to a transformation procedure is a @dfn{renaming
procedure} that takes the representation of an identifier as its
argument and returns the representation of a fresh identifier that
occurs nowhere else in the program.  For example, the transformation
procedure for a simplified version of the @code{let} macro might be
written as

@example
@group
(lambda (exp rename compare)
  (let ((vars (map car (cadr exp)))
        (inits (map cadr (cadr exp)))
        (body (cddr exp)))
    `((lambda ,vars ,@@body)
      ,@@inits)))
@end group
@end example

@noindent
This would not be hygienic, however.  A hygienic @code{let} macro must
rename the identifier @code{lambda} to protect it from being captured by
a local binding.  The renaming effectively creates an fresh alias for
@code{lambda}, one that cannot be captured by any subsequent binding:

@example
@group
(lambda (exp rename compare)
  (let ((vars (map car (cadr exp)))
        (inits (map cadr (cadr exp)))
        (body (cddr exp)))
    `((,(rename 'lambda) ,vars ,@@body)
      ,@@inits)))
@end group
@end example

The expression returned by the transformation procedure will be expanded
in the syntactic environment obtained from the syntactic environment of
the macro application by binding any fresh identifiers generated by the
renaming procedure to the denotations of the original identifiers in the
syntactic environment in which the macro was defined.  This means that a
renamed identifier will denote the same thing as the original identifier
unless the transformation procedure that renamed the identifier placed
an occurrence of it in a binding position.

The renaming procedure acts as a mathematical function in the sense that
the identifiers obtained from any two calls with the same argument will
be the same in the sense of @code{eqv?}.  It is an error if the renaming
procedure is called after the transformation procedure has returned.

@cindex comparison predicate
The third argument to a transformation procedure is a @dfn{comparison
predicate} that takes the representations of two identifiers as its
arguments and returns true if and only if they denote the same thing in
the syntactic environment that will be used to expand the transformed
macro application.  For example, the transformation procedure for a
simplified version of the @code{cond} macro can be written as

@example
@group
(lambda (exp rename compare)
  (let ((clauses (cdr exp)))
    (if (null? clauses)
        `(,(rename 'quote) unspecified)
        (let* ((first (car clauses))
               (rest (cdr clauses))
               (test (car first)))
          (cond ((and (identifier? test)
                      (compare test (rename 'else)))
                 `(,(rename 'begin) ,@@(cdr first)))
                (else `(,(rename 'if)
                        ,test
                         (,(rename 'begin) ,@@(cdr first))
                         (cond ,@@rest))))))))))
@end group
@end example

@noindent
In this example the identifier @code{else} is renamed before being passed
to the comparison predicate, so the comparison will be true if and
only if the test expression is an identifier that denotes the same
thing in the syntactic environment of the expression being transformed
as @code{else} denotes in the syntactic environment in which the @code{cond}
macro was defined.  If @code{else} were not renamed before being passed to
the comparison predicate, then it would match a local variable that
happened to be named @code{else}, and the macro would not be hygienic.

Some macros are non-hygienic by design.  For example, the following
defines a @code{loop} macro that implicitly binds @code{exit} to an
escape procedure.  The binding of @code{exit} is intended to capture
free references to @code{exit} in the body of the loop, so @code{exit}
is not renamed.

@example
@group
(define-syntax loop
  (er-macro-transformer
   (lambda (x r c)
     (let ((body (cdr x)))
       `(,(r 'call-with-current-continuation)
         (,(r 'lambda) (exit)
          (,(r 'let) ,(r 'f) () ,@@body (,(r 'f)))))))))
@end group
@end example

Suppose a @code{while} macro is implemented using @code{loop}, with the
intent that @code{exit} may be used to escape from the @code{while}
loop.  The @code{while} macro cannot be written as

@example
@group
(define-syntax while
  (syntax-rules ()
    ((while test body ...)
     (loop (if (not test) (exit #f))
           body ...))))
@end group
@end example

@noindent
because the reference to @code{exit} that is inserted by the
@code{while} macro is intended to be captured by the binding of
@code{exit} that will be inserted by the @code{loop} macro.  In other
words, this @code{while} macro is not hygienic.  Like @code{loop}, it
must be written using the @code{er-macro-transformer} syntax:

@example
@group
(define-syntax while
  (er-macro-transformer
   (lambda (x r c)
     (let ((test (cadr x))
           (body (cddr x)))
       `(,(r 'loop)
         (,(r 'if) (,(r 'not) ,test) (exit #f))
         ,@@body)))))
@end group
@end example
@end deffn

@node SRFI syntax,  , Macros, Special Forms
@section SRFI syntax

@cindex SRFI syntax
Several special forms have been introduced to support some of the
@uref{http://srfi.schemers.org/,Scheme Requests for Implementation}
(@acronym{SRFI}).  Note that MIT/GNU Scheme has for some time supported
@uref{http://srfi.schemers.org/srfi-23/srfi-23.html,@acronym{SRFI} 23}
(error-reporting mechanism) and
@uref{http://srfi.schemers.org/srfi-30/srfi-30.html,@acronym{SRFI} 30}
(nested multi-line comments), since these @acronym{SRFI}s reflect
existing practice rather than introducing new functionality.

@menu
* cond-expand (SRFI 0)::        
* receive (SRFI 8)::            
* and-let* (SRFI 2)::
* define-record-type (SRFI 9)::  
@end menu

@node cond-expand (SRFI 0), receive (SRFI 8), SRFI syntax, SRFI syntax
@subsection cond-expand (SRFI 0)

@cindex SRFI 0
@uref{http://srfi.schemers.org/srfi-0/srfi-0.html,@acronym{SRFI} 0}
is a mechanism for portably determining the availability of
@uref{http://srfi.schemers.org/,@acronym{SRFI}} @dfn{features}.
The @code{cond-expand} special form conditionally expands according to
the features available.

@deffn {special form} cond-expand clause clause dots{}
Each @var{clause} has the form

@example
(@var{feature-requirement} @var{expression} @dots{})
@end example

where @var{feature-requirement} can have one of the following forms:

@example
@group
@var{feature-identifier}
(and @var{feature-requirement} @dots{})
(or @var{feature-requirement} @dots{})
(not @var{feature-requirement})
else
@end group
@end example

(Note that at most one @code{else} clause may be present, and it must
always be the last clause.)

The @code{cond-expand} special form tests for the existence of features
at macro-expansion time.  It either expands into the body of one of its
@var{clause}s or signals an error during syntactic processing.
@code{cond-expand} expands into the body of the first @var{clause} whose
@var{feature-requirement} is currently satisfied (an @code{else}
@var{clause}, if present, is selected if none of the previous
@var{clauses} is selected).

A @var{feature-requirement} has an obvious interpretation as a logical
formula, where the @var{feature-identifier} variables have meaning true
if the feature corresponding to the @var{feature-identifier}, as
specified in the @acronym{SRFI} registry, is in effect at the location
of the @code{cond-expand} form, and false otherwise.  A
@var{feature-requirement} is satisfied if its formula is true under this
interpretation.

@example
@group
(cond-expand
  ((and srfi-1 srfi-10)
   (write 1))
  ((or srfi-1 srfi-10)
   (write 2))
  (else))

(cond-expand
  (command-line
   (define (program-name) (car (argv)))))
@end group
@end example

The second example assumes that @code{command-line} is an alias for some
feature which gives access to command line arguments.  Note that an
error will be signaled at macro-expansion time if this feature is not
present.

Note that MIT/GNU Scheme allows @code{cond-expand} in any context where a
special form is allowed.  This is an extension of the semantics defined
by @acronym{SRFI 0}, which only allows @code{cond-expand} at top level.
@end deffn

@node receive (SRFI 8), and-let* (SRFI 2), cond-expand (SRFI 0), SRFI syntax
@subsection receive (SRFI 8)

@cindex SRFI 8
@uref{http://srfi.schemers.org/srfi-8/srfi-8.html,@acronym{SRFI} 8}
defines a convenient syntax to bind an identifier to each of the values
of a multiple-valued expression and then evaluate an expression in the
scope of the bindings.  As an instance of this pattern, consider the
following excerpt from a @samp{quicksort} procedure:

@example
@group
(call-with-values
  (lambda ()
    (partition (precedes pivot) others))
  (lambda (fore aft)
    (append (qsort fore) (cons pivot (qsort aft)))))
@end group
@end example

Here @samp{partition} is a multiple-valued procedure that takes two
arguments, a predicate and a list, and returns two lists, one comprising
the list elements that satisfy the predicate, the other those that do
not.  The purpose of the expression shown is to partition the list
@samp{others}, sort each of the sublists, and recombine the results into
a sorted list.

For our purposes, the important step is the binding of the identifiers
@samp{fore} and @samp{aft} to the values returned by @samp{partition}.
Expressing the construction and use of these bindings with the
call-by-values primitive is cumbersome: One must explicitly embed the
expression that provides the values for the bindings in a parameterless
procedure, and one must explicitly embed the expression to be evaluated
in the scope of those bindings in another procedure, writing as its
parameters the identifiers that are to be bound to the values received.

These embeddings are boilerplate, exposing the underlying binding
mechanism but not revealing anything relevant to the particular program
in which it occurs.  So the use of a syntactic abstraction that exposes
only the interesting parts -- the identifiers to be bound, the
multiple-valued expression that supplies the values, and the body of the
receiving procedure -- makes the code more concise and more readable:

@example
@group
(receive (fore aft) (partition (precedes pivot) others)
  (append (qsort fore) (cons pivot (qsort aft))))
@end group
@end example

The advantages are similar to those of a @samp{let} expression over a
procedure call with a @samp{lambda} expression as its operator.  In both
cases, cleanly separating a ``header'' in which the bindings are
established from a ``body'' in which they are used makes it easier to
follow the code.

@deffn {special form} receive formals expression body
@var{Formals} and @var{body} are defined as for @samp{lambda}
(@pxref{Lambda Expressions}).  Specifically, @var{formals} can have the
following forms (the use of @samp{#!optional} and @samp{#!rest} is also
allowed in @var{formals} but is omitted for brevity):

@table @samp
@item (@var{ident1} @dots{} @var{identN})
The environment in which the @samp{receive} expression is evaluated is
extended by binding @var{ident1}, @dots{}, @var{identN} to fresh
locations.  The @var{expression} is evaluated, and its values are stored
into those locations.  (It is an error if @var{expression} does not have
exactly @var{N} values.)

@item @var{ident}
The environment in which the @samp{receive} expression is evaluated is
extended by binding @var{ident} to a fresh location.  The
@var{expression} is evaluated, its values are converted into a newly
allocated list, and the list is stored in the location bound to
@var{ident}.

@item (@var{ident1} @dots{} @var{identN} . @var{identN+1})
The environment in which the @samp{receive} expression is evaluated is
extended by binding @var{ident1}, @dots{}, @var{identN+1} to fresh
locations.  The @var{expression} is evaluated.  Its first @var{N} values
are stored into the locations bound to @var{ident1} @dots{} @var{identN}.
Any remaining values are converted into a newly allocated list, which is
stored into the location bound to @var{identN+1}.  (It is an error if
@var{expression} does not have at least @var{N} values.)
@end table

In any case, the expressions in @var{body} are evaluated sequentially in
the extended environment.  The results of the last expression in the
body are the values of the @samp{receive} expression.
@end deffn

@node and-let* (SRFI 2), define-record-type (SRFI 9), receive (SRFI 8), SRFI syntax
@subsection and-let* (SRFI 2)

@cindex SRFI 2
@uref{http://srfi.schemers.org/srfi-2/srfi-2.html,@acronym{SRFI} 2}
provides a form that combines @samp{and} and @samp{let*} for a
logically short-circuiting sequential binding operator.

@deffn {special form} and-let* (clause @dots{}) body
Runs through each of the clauses left-to-right, short-circuiting like
@samp{and} in that the first false clause will result in the whole
@samp{and-let*} form returning false.  If a body is supplied, and all
of the clauses evaluate true, then the body is evaluated sequentially
as if in a @samp{begin} form, and the value of the @samp{and-let*}
expression is the value of the last body form, evaluated in a tail
position with respect to the @samp{and-let*} expression.  If no body
is supplied, the value of the last clause, also evaluated in a tail
position with respect to the @samp{and-let*} expression, is used
instead.

Each @var{clause} should have one of the following forms:

@table @samp
@item @var{identifier}
in which case @var{identifier}'s value is tested.

@item (@var{expression})
in which case the value of @var{expression} is tested.

@item (@var{identifier} @var{expression})
in which case @var{expression} is evaluated, and, if its value is not
false, @var{identifier} is bound to that value for the remainder of
the clauses and the optional body.
@end table
@end deffn

@comment More examples, please!

Example:

@example
@group
(and-let* ((list (compute-list))
           ((pair? list))
           (item (car list))
           ((integer? item)))
  (sqrt item))
@end group
@end example

@node define-record-type (SRFI 9),  , and-let* (SRFI 2), SRFI syntax
@subsection define-record-type (SRFI 9)

@cindex SRFI 9
The @samp{define-record-type} syntax described in
@uref{http://srfi.schemers.org/srfi-9/srfi-9.html,@acronym{SRFI} 9} is a
slight simplification of one written for Scheme 48 by Jonathan Rees.
Unlike many record-defining special forms, it does not create any new
identifiers.  Instead, the names of the record type, predicate,
constructor, and so on are all listed explicitly in the source.  This
has the following advantages:

@itemize @bullet
@item
It can be defined using a simple macro in Scheme implementations that
provide a procedural interface for creating record types.

@item
It does not restrict users to a particular naming convention.

@item
Tools like @command{grep} and the GNU Emacs tag facility will see the
defining occurance of each identifier.
@end itemize

@deffn {special form} define-record-type type-name (constructor-name field-tag @dots{}) predicate-name field-spec @dots{}
@var{Type-name}, @var{contructor-name}, @var{field-tag}, and
@var{predicate-name} are identifiers.  @var{Field-spec} has one of these
two forms:

@example
@group
(@var{field-tag} @var{accessor-name})
(@var{field-tag} @var{accessor-name} @var{modifier-name})
@end group
@end example

@noindent
where @var{field-tag}, @var{accessor-name}, and @var{modifier-name} are
each identifiers.

@code{define-record-type} is generative: each use creates a new record
type that is distinct from all existing types, including other record
types and Scheme's predefined types.  Record-type definitions may only
occur at top-level (there are two possible semantics for ``internal''
record-type definitions, generative and nongenerative, and no consensus
as to which is better).

An instance of @code{define-record-type} is equivalent to the following
definitions:

@itemize @bullet
@item
@var{Type-name} is bound to a representation of the record type itself.
Operations on record types, such as defining print methods, reflection,
etc.@: are left to other SRFIs.

@item
@var{constructor-name} is bound to a procedure that takes as many
arguments as there are @var{field-tag}s in the (@var{constructor-name}
@dots{}) subform and returns a new @var{type-name} record.  Fields whose
tags are listed with @var{constructor-name} have the corresponding
argument as their initial value.  The initial values of all other fields
are unspecified.

@item
@var{predicate-name} is a predicate that returns @code{#t} when given a
value returned by @var{constructor-name} and @code{#f} for everything
else.

@item
Each @var{accessor-name} is a procedure that takes a record of type
@var{type-name} and returns the current value of the corresponding
field.  It is an error to pass an accessor a value which is not a record
of the appropriate type.

@item
Each @var{modifier-name} is a procedure that takes a record of type
@var{type-name} and a value which becomes the new value of the
corresponding field; an unspecified value is returned.  It is an error
to pass a modifier a first argument which is not a record of the
appropriate type.
@end itemize

Assigning the value of any of these identifiers has no effect on the
behavior of any of their original values.
@end deffn

The following

@example
@group
(define-record-type :pare
  (kons x y)
  pare?
  (x kar set-kar!)
  (y kdr))
@end group
@end example

@noindent
defines @samp{kons} to be a constructor, @samp{kar} and @samp{kdr} to be
accessors, @samp{set-kar!} to be a modifier, and @samp{pare?} to be a
predicate for objects of type @samp{:pare}.

@example
@group
(pare? (kons 1 2))        @result{} #t
(pare? (cons 1 2))        @result{} #f
(kar (kons 1 2))          @result{} 1
(kdr (kons 1 2))          @result{} 2
(let ((k (kons 1 2)))
  (set-kar! k 3)
  (kar k))                @result{} 3
@end group
@end example
