This document describes Chicken's R5RS support, with a heavy emphasis on syntax and procedures. It is based directly on the Revised^5 Report on the Algorithmic Language Scheme.

Overview of Scheme

Lexical conventions

Basic concepts

Expressions


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.

Primitive expression types


Variable references




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

Literal expressions


(quote )
'


(quote ) evaluates to . 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 ) may be abbreviated as '. 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!.

Procedure calls


( ...)

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.

Procedures


(lambda )

Syntax: should be a formal arguments list as described below, and 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

should have one of the following forms:
  • ( ...): 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.
  • : 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 .
  • ( ... . ): 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 to appear more than once in .
 ((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).

Conditionals


(if )
(if )

Syntax: , , and may be arbitrary expressions.
Semantics: An if expression is evaluated as follows: first, is evaluated. If it yields a true value (see section 6.3.1), then is evaluated and its value(s) is(are) returned. Otherwise is evaluated and its value(s) is(are) returned. If yields a false value and no 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

Assignments


(set! )

is evaluated, and the resulting value is stored in the location to which is bound. 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

Derived expression types


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.

Conditionals


(cond ...)

Syntax: Each should be of the form
 (<test> <expression[1]> ...)

where is any expression. Alternatively, a may be of the form
 (<test> => <expression>)

The last may be an "else clause," which has the form
 (else <expression[1]> <expression[2]> ...).

Semantics: A cond expression is evaluated by evaluating the expressions of successive s in order until one of them evaluates to a true value (see section 6.3.1). When a evaluates to a true value, then the remaining s in its are evaluated in order, and the result(s) of the last in the is(are) returned as the result(s) of the entire cond expression. If the selected contains only the and no s, then the value of the is returned as the result. If the selected uses the => alternate form, then the is evaluated. Its value must be a procedure that accepts one argument; this procedure is then called on the value of the and the value(s) returned by this procedure is(are) returned by the cond expression. If all 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 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

(case ...)

Syntax: may be any expression. Each should have the form
 ((<datum[1]> ...) <expression[1]> <expression[2]> ...),

where each is an external representation of some object. All the s must be distinct. The last may be an "else clause," which has the form
 (else <expression[1]> <expression[2]> ...).

Semantics: A case expression is evaluated as follows. is evaluated and its result is compared against each . If the result of evaluating is equivalent (in the sense of eqv?; see section 6.1) to a , then the expressions in the corresponding are evaluated from left to right and the result(s) of the last expression in the is(are) returned as the result(s) of the case expression. If the result of evaluating is different from every , 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

(and ...)

The 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

(or ...)

The 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)

Binding constructs


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.
(let )

Syntax: should have the form
 ((<variable[1]> <init[1]>) ...),

where each is an expression, and should be a sequence of one or more expressions. It is an error for a to appear more than once in the list of variables being bound.
Semantics: The s are evaluated in the current environment (in some unspecified order), the s are bound to fresh locations holding the results, the is evaluated in the extended environment, and the value(s) of the last expression of is(are) returned. Each binding of a has 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.
(let* )

Syntax: should have the form
 ((<variable[1]> <init[1]>) ...),

and 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 ( ) 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

(letrec )

Syntax: should have the form
 ((<variable[1]> <init[1]>) ...),

and should be a sequence of one or more expressions. It is an error for a to appear more than once in the list of variables being bound.
Semantics: The s are bound to fresh locations holding undefined values, the s are evaluated in the resulting environment (in some unspecified order), each is assigned to the result of the corresponding , the is evaluated in the resulting environment, and the value(s) of the last expression in is(are) returned. Each binding of a 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 without assigning or referring to the value of any . 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 s are lambda expressions and the restriction is satisfied automatically.

Sequencing


(begin ...)

The s are evaluated sequentially from left to right, and the value(s) of the last 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

Iteration


(do (( ) ...) ( ...) ...)

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 s.
Do expressions are evaluated as follows: The expressions are evaluated (in some unspecified order), the s are bound to fresh locations, the results of the expressions are stored in the bindings of the s, and then the iteration phase begins.
Each iteration begins by evaluating ; if the result is false (see section 6.3.1), then the expressions are evaluated in order for effect, the expressions are evaluated in some unspecified order, the s are bound to fresh locations, the results of the s are stored in the bindings of the s, and the next iteration begins.
If evaluates to a true value, then the s are evaluated from left to right and the value(s) of the last is(are) returned. If no s are present, then the value of the do expression is unspecified.
The region of the binding of a consists of the entire do expression except for the s. It is an error for a to appear more than once in the list of do variables.
A may be omitted, in which case the effect is the same as if ( ) had been written instead of ( ).
 (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

(let )

"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 is bound within to a procedure whose formal arguments are the bound variables and whose body is . Thus the execution of may be repeated by invoking the procedure named by .
 (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))

Delayed evaluation


(delay )

The delay construct is used together with the procedure force to implement lazy evaluation or call by need. (delay ) returns an object called a promise which at some point in the future may be asked (by the force procedure) to evaluate , and deliver the resulting value. The effect of returning multiple values is unspecified.
See the description of force (section 6.4) for a more complete description of delay.

Quasiquotation


(quasiquote )
`

"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 , the result of evaluating ` is equivalent to the result of evaluating '. If a comma appears within the , 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 .
 `(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 ` and (quasiquote ) are identical in all respects. , is identical to (unquote ), and ,@ is identical to (unquote-splicing ). 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 otherwise than as described above.

Macros


Scheme programs can define and use new derived expression types, called macros. Program-defined expression types have the syntax
 (<keyword> <datum> ...)

where 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 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:
  • 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.

Binding constructs for syntactic keywords


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.
(let-syntax )

Syntax: should have the form
 ((<keyword> <transformer spec>) ...)

Each is an identifier, each is an instance of syntax-rules, and should be a sequence of one or more expressions. It is an error for a to appear more than once in the list of keywords being bound.
Semantics: The is expanded in the syntactic environment obtained by extending the syntactic environment of the let-syntax expression with macros whose keywords are the s, bound to the specified transformers. Each binding of a has 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

(letrec-syntax )

Syntax: Same as for let-syntax.
Semantics: The is expanded in the syntactic environment obtained by extending the syntactic environment of the letrec-syntax expression with macros whose keywords are the s, bound to the specified transformers. Each binding of a has the as well as the 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

Pattern language


A has the following form:
 (syntax-rules <literals> <syntax rule> ...)

Syntax: is a list of identifiers and each should be of the form
 (<pattern> <template>)

The in a is a list that begins with the keyword for the macro.
A is either an identifier, a constant, or one of the following
 (<pattern> ...)
 (<pattern> <pattern> ... . <pattern>)
 (<pattern> ... <pattern> <ellipsis>)
 #(<pattern> ...)
 #(<pattern> ... <pattern> <ellipsis>)

and a template is either an identifier, a constant, or one of the following
 (<element> ...)
 (<element> <element> ... . <template>)
 #(<element> ...)

where an is a