A Scheme expression is a construct that returns a value, such as a variable reference, literal, procedure call, or conditional.
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 explained in terms of the primitive constructs as in section section Derived expression types. They are redundant in the strict sense of the word, but they capture common patterns of usage, and are therefore provided as convenient abbreviations.
An expression consisting of a variable (section see section Variables and regions) 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 see section External representations). 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)
Numeric 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
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 indeterminate 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 see section lambda expressions).
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: 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 of the last expression in the body will be returned as the result 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 foo
(let ((x 4))
(lambda (y) (+ x y))))
(foo 6) ==> 10
<Formals> should have one of the following forms:
((lambda x x) 3 4 5 6) ==> (3 4 5 6) ((lambda (x y . z) z) 3 4 5 6) ==> (5 6)
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 see section Booleans), then <consequent> is evaluated and
its value is returned. Otherwise <alternate> is evaluated and its
value is 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
For reference purposes, section section Derived expression types gives rewrite rules that will convert constructs described in this section into the primitive constructs described in the previous section.
Syntax: Each <clause> should be of the form
(<test> <expression> ...,)
where <test> is any 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 see section Booleans). When a <test> evaluates to a true
value, then the remaining <expression>s in its <clause> are
evaluated in order, and the result of the last <expression> in the
<clause> is returned as the result 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 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 of
the last one is returned.
(cond ((> 3 2) 'greater)
((< 3 2) 'less)) ==> greater
(cond ((> 3 3) 'greater)
((< 3 3) 'less)
(else 'equal)) ==> equal
Some implementations support an alternative <clause> syntax, (<test> => <recipient>), where <recipient> is an expression. If <test> evaluates to a true value, then <recipient> is evaluated. Its value must be a procedure of one argument; this procedure is then invoked on the value of the <test>.
(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 see section Equivalence predicates) to a <datum>, then the
expressions in the corresponding <clause> are evaluated from left
to right and the result of the last expression in the <clause> is
returned as the result 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 of the last is the result 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 see section Booleans) 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 see section Booleans) 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, 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.
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 of the last expression of <body> is 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 ((foo (lambda (z) (+ x y z)))
(x 7))
(foo 4))) ==> 9
See also named let, section section Iteration.
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 1) (y (+ x 1))) y) ==> 2
Syntax: <Bindings> should have the form
((<variable1> <init1>) ...,),
and <body> should be a sequence of one or more expressions.
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 of the last expression in
<body> is 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 referring to the value of any
<variable>. If this restriction is violated, then the effect is
undefined, and an error may be signalled during evaluation of the
<init>s. 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 of the last <expression> is returned. This expression type is used to sequence side effects such as input and output.
(begin (set! x 5)
(+ x 1)) ==> 6
(begin (display "4 plus 1 equals ")
(display (+ 4 1))) ==> unspecified
and prints 4 plus 1 equals 5
Note: [SICP] uses the keyword
sequenceinstead ofbegin.
...,) (<test> <expression> ...,) <command> ...,)
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.
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 see section Booleans), 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 of
the last <expression> is returned as the value of the do
expression. 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.
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
Some implementations of Scheme permit a variant on the syntax of
let called "named let" which provides a more general
looping construct than do, and may also be used to express
recursions.
Named let 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.
See the description of force (section see section Control features) for a
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 <template>, the result of evaluating `<template> is equivalent to the result of evaluating '<template>. If a comma appears within the <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.
`(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 notations
`<template> and (quasiquote <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 <template> otherwise than as described above.
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