Expression types are categorized as primitive or derived. Primitive expression types include variables and procedure calls. Derived expression types are not semantically primitive, but can instead be defined as macros. With the exception of quasiquote, whose macro definition is complex, the derived expressions are classified as library features. Suitable definitions are given in section 7.3.
An expression consisting of a variable (section 3.1) is a variable reference. The value of the variable reference is the value stored in the location to which the variable is bound. It is an error to reference an unbound variable.
(define x 28)
x ===> 28
(quote <datum>) evaluates to <datum>. <Datum> may be any external representation of a Scheme object (see section 3.3). This notation is used to include literal constants in Scheme code.
(quote a) ===> a
(quote #(a b c)) ===> #(a b c)
(quote (+ 1 2)) ===> (+ 1 2)
(quote <datum>) may be abbreviated as '<datum>. The two notations are equivalent in all respects.
'a ===> a
'#(a b c) ===> #(a b c)
'() ===> ()
'(+ 1 2) ===> (+ 1 2)
'(quote a) ===> (quote a)
''a ===> (quote a)
Numerical constants, string constants, character constants, and boolean constants evaluate ``to themselves''; they need not be quoted.
'"abc" ===> "abc"
"abc" ===> "abc"
'145932 ===> 145932
145932 ===> 145932
'#t ===> #t
#t ===> #t
As noted in section 3.4, it is an error to alter a constant (i.e. the value of a literal expression) using a mutation procedure like set-car! or string-set!.
A procedure call is written by simply enclosing in parentheses
expressions for the procedure to be called and the arguments to be
passed to it. The operator and operand expressions are evaluated (in an
unspecified order) and the resulting procedure is passed the resulting
arguments.
(+ 3 4) ===> 7
((if #f + *) 3 4) ===> 12
A number of procedures are available as the values of variables in the initial environment; for example, the addition and multiplication procedures in the above examples are the values of the variables + and *. New procedures are created by evaluating lambda expressions (see section 4.1.4). Procedure calls may return any number of values (see values in section 6.4). With the exception of values the procedures available in the initial environment return one value or, for procedures such as apply, pass on the values returned by a call to one of their arguments.
Procedure calls are also called combinations.
Note: In contrast to other dialects of Lisp, the order of evaluation is unspecified, and the operator expression and the operand expressions are always evaluated with the same evaluation rules.
Note: Although the order of evaluation is otherwise unspecified, the effect of any concurrent evaluation of the operator and operand expressions is constrained to be consistent with some sequential order of evaluation. The order of evaluation may be chosen differently for each procedure call.
Note: In many dialects of Lisp, the empty combination, (), is a legitimate expression. In Scheme, combinations must have at least one subexpression, so () is not a syntactically valid expression.
Syntax: <Formals> should be a formal arguments list as described below, and <body> should be a sequence of one or more expressions.
Semantics: A lambda expression evaluates to a procedure. The environment in effect when the lambda expression was evaluated is remembered as part of the procedure. When the procedure is later called with some actual arguments, the environment in which the lambda expression was evaluated will be extended by binding the variables in the formal argument list to fresh locations, the corresponding actual argument values will be stored in those locations, and the expressions in the body of the lambda expression will be evaluated sequentially in the extended environment. The result(s) of the last expression in the body will be returned as the result(s) of the procedure call.
(lambda (x) (+ x x)) ===> a procedure
((lambda (x) (+ x x)) 4) ===> 8
(define reverse-subtract
(lambda (x y) (- y x)))
(reverse-subtract 7 10) ===> 3
(define add4
(let ((x 4))
(lambda (y) (+ x y))))
(add4 6) ===> 10
<Formals> should have one of the following forms:
(<variable1> ...): The procedure takes a fixed number of arguments; when the procedure is called, the arguments will be stored in the bindings of the corresponding variables.
<variable>: The procedure takes any number of arguments; when the procedure is called, the sequence of actual arguments is converted into a newly allocated list, and the list is stored in the binding of the <variable>.
(<variable1> ... <variablen> . <variablen+1>): If a space-delimited period precedes the last variable, then the procedure takes n or more arguments, where n is the number of formal arguments before the period (there must be at least one). The value stored in the binding of the last variable will be a newly allocated list of the actual arguments left over after all the other actual arguments have been matched up against the other formal arguments.
It is an error for a <variable> to appear more than once in <formals>.
((lambda x x) 3 4 5 6) ===> (3 4 5 6)
((lambda (x y . z) z)
3 4 5 6) ===> (5 6)
Each procedure created as the result of evaluating a lambda expression is (conceptually) tagged with a storage location, in order to make eqv? and eq? work on procedures (see section 6.1).
Syntax: <Test>, <consequent>, and <alternate> may be arbitrary expressions.
Semantics: An if expression is evaluated as follows: first, <test> is evaluated. If it yields a true value (see section 6.3.1), then <consequent> is evaluated and its value(s) is(are) returned. Otherwise <alternate> is evaluated and its value(s) is(are) returned. If <test> yields a false value and no <alternate> is specified, then the result of the expression is unspecified.
(if (> 3 2) 'yes 'no) ===> yes
(if (> 2 3) 'yes 'no) ===> no
(if (> 3 2)
(- 3 2)
(+ 3 2)) ===> 1
<Expression> is evaluated, and the resulting value is stored in the location to which <variable> is bound. <Variable> must be bound either in some region enclosing the set! expression or at top level. The result of the set! expression is unspecified.
(define x 2)
(+ x 1) ===> 3
(set! x 4) ===> unspecified
(+ x 1) ===> 5
The constructs in this section are hygienic, as discussed in section 4.3. For reference purposes, section 7.3 gives macro definitions that will convert most of the constructs described in this section into the primitive constructs described in the previous section.
Syntax: Each <clause> should be of the form (<test> <expression1> ...)
where <test> is any expression. Alternatively, a <clause> may be of the form (<test> => <expression>) The last <clause> may be an ``else clause,'' which has the form (else <expression1> <expression2> ...).Semantics: A cond expression is evaluated by evaluating the <test> expressions of successive <clause>s in order until one of them evaluates to a true value (see section 6.3.1). When a <test> evaluates to a true value, then the remaining <expression>s in its <clause> are evaluated in order, and the result(s) of the last <expression> in the <clause> is(are) returned as the result(s) of the entire cond expression. If the selected <clause> contains only the <test> and no <expression>s, then the value of the <test> is returned as the result. If the selected <clause> uses the => alternate form, then the <expression> is evaluated. Its value must be a procedure that accepts one argument; this procedure is then called on the value of the <test> and the value(s) returned by this procedure is(are) returned by the cond expression. If all <test>s evaluate to false values, and there is no else clause, then the result of the conditional expression is unspecified; if there is an else clause, then its <expression>s are evaluated, and the value(s) of the last one is(are) returned.
(cond ((> 3 2) 'greater)
((< 3 2) 'less)) ===> greater
(cond ((> 3 3) 'greater)
((< 3 3) 'less)
(else 'equal)) ===> equal
(cond ((assv 'b '((a 1) (b 2))) => cadr)
(else #f)) ===> 2
Syntax: <Key> may be any expression. Each <clause> should have the form ((<datum1> ...) <expression1> <expression2> ...),
where each <datum> is an external representation of some object. All the <datum>s must be distinct. The last <clause> may be an ``else clause,'' which has the form (else <expression1> <expression2> ...).Semantics: A case expression is evaluated as follows. <Key> is evaluated and its result is compared against each <datum>. If the result of evaluating <key> is equivalent (in the sense of eqv?; see section 6.1) to a <datum>, then the expressions in the corresponding <clause> are evaluated from left to right and the result(s) of the last expression in the <clause> is(are) returned as the result(s) of the case expression. If the result of evaluating <key> is different from every <datum>, then if there is an else clause its expressions are evaluated and the result(s) of the last is(are) the result(s) of the case expression; otherwise the result of the case expression is unspecified.
(case (* 2 3)
((2 3 5 7) 'prime)
((1 4 6 8 9) 'composite)) ===> composite
(case (car '(c d))
((a) 'a)
((b) 'b)) ===> unspecified
(case (car '(c d))
((a e i o u) 'vowel)
((w y) 'semivowel)
(else 'consonant)) ===> consonant
The <test> expressions are evaluated from left to right, and the value of the first expression that evaluates to a false value (see section 6.3.1) is returned. Any remaining expressions are not evaluated. If all the expressions evaluate to true values, the value of the last expression is returned. If there are no expressions then #t is returned.
(and (= 2 2) (> 2 1)) ===> #t
(and (= 2 2) (< 2 1)) ===> #f
(and 1 2 'c '(f g)) ===> (f g)
(and) ===> #t
The <test> expressions are evaluated from left to right, and the value of the first expression that evaluates to a true value (see section 6.3.1) is returned. Any remaining expressions are not evaluated. If all expressions evaluate to false values, the value of the last expression is returned. If there are no expressions then #f is returned.
(or (= 2 2) (> 2 1)) ===> #t
(or (= 2 2) (< 2 1)) ===> #t
(or #f #f #f) ===> #f
(or (memq 'b '(a b c))
(/ 3 0)) ===> (b c)
The three binding constructs let, let*, and letrec give Scheme a block structure, like Algol 60. The syntax of the three constructs is identical, but they differ in the regions they establish for their variable bindings. In a let expression, the initial values are computed before any of the variables become bound; in a let* expression, the bindings and evaluations are performed sequentially; while in a letrec expression, all the bindings are in effect while their initial values are being computed, thus allowing mutually recursive definitions.
Syntax: <Bindings> should have the form ((<variable1> <init1>) ...),
where each <init> is an expression, and <body> should be a sequence of one or more expressions. It is an error for a <variable> to appear more than once in the list of variables being bound.Semantics: The <init>s are evaluated in the current environment (in some unspecified order), the <variable>s are bound to fresh locations holding the results, the <body> is evaluated in the extended environment, and the value(s) of the last expression of <body> is(are) returned. Each binding of a <variable> has <body> as its region.
(let ((x 2) (y 3))
(* x y)) ===> 6
(let ((x 2) (y 3))
(let ((x 7)
(z (+ x y)))
(* z x))) ===> 35
See also named let, section 4.2.4.
Syntax: <Bindings> should have the form ((<variable1> <init1>) ...),
and <body> should be a sequence of one or more expressions.Semantics: Let* is similar to let, but the bindings are performed sequentially from left to right, and the region of a binding indicated by (<variable> <init>) is that part of the 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.
(let ((x 2) (y 3))
(let* ((x 7)
(z (+ x y)))
(* z x))) ===> 70
Syntax: <Bindings> should have the form ((<variable1> <init1>) ...),
and <body> should be a sequence of one or more expressions. It is an error for a <variable> to appear more than once in the list of variables being bound.Semantics: The <variable>s are bound to fresh locations holding undefined values, the <init>s are evaluated in the resulting environment (in some unspecified order), each <variable> is assigned to the result of the corresponding <init>, the <body> is evaluated in the resulting environment, and the value(s) of the last expression in <body> is(are) returned. Each binding of a <variable> has the entire letrec expression as its region, making it possible to define mutually recursive procedures.
(letrec ((even?
(lambda (n)
(if (zero? n)
#t
(odd? (- n 1)))))
(odd?
(lambda (n)
(if (zero? n)
#f
(even? (- n 1))))))
(even? 88))
===> #t
One restriction on letrec is very important: it must be possible to evaluate each <init> without assigning or referring to the value of any <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 letrec, all the <init>s are lambda expressions and the restriction is satisfied automatically.
The <expression>s are evaluated sequentially from left to right, and the value(s) of the last <expression> is(are) returned. This expression type is used to sequence side effects such as input and output.
(define x 0)
(begin (set! x 5)
(+ x 1)) ===> 6
(begin (display "4 plus 1 equals ")
(display (+ 4 1))) ===> unspecified
and prints 4 plus 1 equals 5
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 after evaluating the <expression>s.
Do expressions are evaluated as follows: The <init> expressions are evaluated (in some unspecified order), the <variable>s are bound to fresh locations, the results of the <init> expressions are stored in the bindings of the <variable>s, and then the iteration phase begins.
Each iteration begins by evaluating <test>; if the result is false (see section 6.3.1), then the <command> expressions are evaluated in order for effect, the <step> expressions are evaluated in some unspecified order, the <variable>s are bound to fresh locations, the results of the <step>s are stored in the bindings of the <variable>s, and the next iteration begins.
If <test> evaluates to a true value, then the <expression>s are evaluated from left to right and the value(s) of the last <expression> is(are) returned. If no <expression>s are present, then the value of the do expression is unspecified.
The region of the binding of a <variable> consists of the entire do expression except for the <init>s. It is an error for a <variable> to appear more than once in the list of do variables.
A <step> may be omitted, in which case the effect is the same as if (<variable> <init> <variable>) had been written instead of (<variable> <init>).
(do ((vec (make-vector 5))
(i 0 (+ i 1)))
((= i 5) vec)
(vector-set! vec i i)) ===> #(0 1 2 3 4)
(let ((x '(1 3 5 7 9)))
(do ((x x (cdr x))
(sum 0 (+ sum (car x))))
((null? x) sum))) ===> 25
``Named let'' is a variant on the syntax of let which provides a more general looping construct than do and may also be used to express recursions. It has the same syntax and semantics as ordinary let except that <variable> is bound within <body> to a procedure whose formal arguments are the bound variables and whose body is <body>. Thus the execution of <body> may be repeated by invoking the procedure named by <variable>.
(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))
((< (car numbers) 0)
(loop (cdr numbers)
nonneg
(cons (car numbers) neg)))))
===> ((6 1 3) (-5 -2))
The delay construct is used together with the procedure force to implement lazy evaluation or call by need. (delay <expression>) returns an object called a promise which at some point in the future may be asked (by the force procedure) to evaluate <expression>, and deliver the resulting value. The effect of <expression> returning multiple values is unspecified.
See the description of force (section 6.4) for a more complete description of delay.
``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 <qq template>, the result of evaluating `<qq template> is equivalent to the result of evaluating '<qq template>. If a comma appears within the <qq 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 must 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. A comma at-sign should only appear within a list or vector <qq template>.
`(list ,(+ 1 2) 4) ===> (list 3 4)
(let ((name 'a)) `(list ,name ',name))
===> (list a (quote a))
`(a ,(+ 1 2) ,@(map abs '(4 -5 6)) b)
===> (a 3 4 5 6 b)
`(( foo ,(- 10 3)) ,@(cdr '(c)) . ,(car '(cons)))
===> ((foo 7) . cons)
`#(10 5 ,(sqrt 4) ,@(map sqrt '(16 9)) 8)
===> #(10 5 2 4 3 8)
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.
`(a `(b ,(+ 1 2) ,(foo ,(+ 1 3) d) e) f)
===> (a `(b ,(+ 1 2) ,(foo 4 d) e) f)
(let ((name1 'x)
(name2 'y))
`(a `(b ,,name1 ,',name2 d) e))
===> (a `(b ,x ,'y d) e)
The two notations `<qq template> and (quasiquote <qq template>) are identical in all respects. ,<expression> is identical to (unquote <expression>), and ,@<expression> is identical to (unquote-splicing <expression>). The external syntax generated by write for two-element lists whose car is one of these symbols may vary between implementations.
(quasiquote (list (unquote (+ 1 2)) 4))
===> (list 3 4)
'(quasiquote (list (unquote (+ 1 2)) 4))
===> `(list ,(+ 1 2) 4)
i.e., (quasiquote (list (unquote (+ 1 2)) 4))
Unpredictable behavior can result if any of the symbols quasiquote, unquote, or unquote-splicing appear in positions within a <qq template> otherwise than as described above.
Scheme programs can define and use new derived expression types, called macros. Program-defined expression types have the syntax (<keyword> <datum> ...)
where <keyword> is an identifier that uniquely determines the expression type. This identifier is called the syntactic keyword, or simply keyword, of the macro. The number of the <datum>s, and their syntax, depends on the expression type.Each instance of a macro is called a 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 transformer of the macro.
The macro definition facility consists of two parts:
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, and
a pattern language for specifying macro transformers.
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 [14, 15, 2, 7, 9]:
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. Note that a define at top level may or may not introduce a binding; see section 5.2.
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.
Let-syntax and letrec-syntax are analogous to let and letrec, but they bind syntactic keywords to macro transformers instead of binding variables to locations that contain values. Syntactic keywords may also be bound at top level; see section 5.3.
Syntax: <Bindings> should have the form ((<keyword> <transformer spec>) ...)
Each <keyword> is an identifier, each <transformer spec> is an instance of syntax-rules, and <body> should be a sequence of one or more expressions. It is an error for a <keyword> to appear more than once in the list of keywords being bound.Semantics: The <body> is expanded in the syntactic environment obtained by extending the syntactic environment of the let-syntax expression with macros whose keywords are the <keyword>s, bound to the specified transformers. Each binding of a <keyword> has <body> as its region.
(let-syntax ((when (syntax-rules ()
((when test stmt1 stmt2 ...)
(if test
(begin stmt1
stmt2 ...))))))
(let ((if #t))
(when if (set! if 'now))
if)) ===> now
(let ((x 'outer))
(let-syntax ((m (syntax-rules () ((m) x))))
(let ((x 'inner))
(m)))) ===> outer
Syntax: Same as for let-syntax.
Semantics: The <body> is expanded in the syntactic environment obtained by extending the syntactic environment of the letrec-syntax expression with macros whose keywords are the <keyword>s, bound to the specified transformers. Each binding of a <keyword> has the <bindings> as well as the <body> within its region, so the transformers can transcribe expressions into uses of the macros introduced by the letrec-syntax expression.
(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))) ===> 7
A <transformer spec> has the following form:
Syntax: <Literals> is a list of identifiers and each <syntax rule> should be of the form (<pattern> <template>)
The <pattern> in a <syntax rule> is a list <pattern> that begins with the keyword for the macro.
A <pattern> is either an identifier, a constant, or one of the
following
(<pattern> ...)
(<pattern> <pattern> ... . <pattern>)
(<pattern> ... <pattern> <ellipsis>)
#(<pattern> ...)
#(<pattern> ... <pattern> <ellipsis>)
Semantics: An instance of 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 syntax-rules is matched against the patterns contained in the <syntax rule>s, beginning with the leftmost <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 <syntax rule> is a pattern variable, unless it is the keyword that begins the pattern, is listed in <literals>, or is the identifier ``...''. 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 <pattern>.
The keyword at the beginning of the pattern in a <syntax rule> is not involved in the matching and is not considered a pattern variable or literal identifier.
Rationale: The scope of the keyword is determined by the expression or syntax definition that binds it to the associated macro transformer. If the keyword were a pattern variable or literal identifier, then the template that follows the pattern would be within its scope regardless of whether the keyword were bound by let-syntax or by letrec-syntax.
Identifiers that appear in <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 ... can match zero or more elements of the input. It is an error for ... to appear in <literals>. Within a pattern the identifier ... must follow the last element of a nonempty sequence of subpatterns.
More formally, an input form F matches a pattern P if and only if:
P is a non-literal identifier; or
P is a literal identifier and F is an identifier with the same binding; or
P is a list (P1 ... Pn) and F is a list of n forms that match P1 through Pn, respectively; or
P is an improper list (P1 P2 ... Pn . Pn+1) and F is a list or improper list of n or more forms that match P1 through Pn, respectively, and whose nth ``cdr'' matches Pn+1; or
P is of the form (P1 ... Pn Pn+1 <ellipsis>) where <ellipsis> is the identifier ... and F is a proper list of at least n forms, the first n of which match P1 through Pn, respectively, and each remaining element of F matches Pn+1; or
P is a vector of the form #(P1 ... Pn) and F is a vector of n forms that match P1 through Pn; or
P is of the form #(P1 ... Pn Pn+1 <ellipsis>) where <ellipsis> is the identifier ... and F is a vector of n or more forms the first n of which match P1 through Pn, respectively, and each remaining element of F matches Pn+1; or
P is a datum and F is equal to P in the sense of the equal? procedure.
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 <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 ... are allowed only in subtemplates that are followed by as many instances of .... 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 ... 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 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.
As an example, if let and cond are defined as in section 7.3 then they are hygienic (as required) and the following is not an error.
(let ((=> #f))
(cond (#t => 'ok))) ===> ok
The macro transformer for cond recognizes => as a local variable, and hence an expression, and not as the top-level identifier =>, which the macro transformer treats as a syntactic keyword. Thus the example expands into
(let ((=> #f))
(if #t (begin => 'ok)))
instead of
(let ((=> #f))
(let ((temp #t))
(if temp ('ok temp))))
which would result in an invalid procedure call.