2 @c This is part of the GNU Guile Reference Manual.
3 @c Copyright (C) 1996, 1997, 2000, 2001, 2002, 2003, 2004, 2005
4 @c Free Software Foundation, Inc.
5 @c See the file guile.texi for copying conditions.
8 @section Basic Ideas in Scheme
10 In this chapter, we introduce the basic concepts that underpin the
11 elegance and power of the Scheme language.
13 Readers who already possess a background knowledge of Scheme may happily
14 skip this chapter. For the reader who is new to the language, however,
15 the following discussions on data, procedures, expressions and closure
16 are designed to provide a minimum level of Scheme understanding that is
17 more or less assumed by the reference chapters that follow.
19 The style of this introductory material aims about halfway between the
20 terse precision of R5RS and the discursive randomness of a Scheme
24 * About Data:: Latent typing, types, values and variables.
25 * About Procedures:: The representation and use of procedures.
26 * About Expressions:: All kinds of expressions and their meaning.
27 * About Closure:: Closure, scoping and environments.
32 @subsection Data Types, Values and Variables
34 This section discusses the representation of data types and values, what
35 it means for Scheme to be a @dfn{latently typed} language, and the role
36 of variables. We conclude by introducing the Scheme syntaxes for
37 defining a new variable, and for changing the value of an existing
41 * Latent Typing:: Scheme as a "latently typed" language.
42 * Values and Variables:: About data types, values and variables.
43 * Definition:: Defining variables and setting their values.
48 @subsubsection Latent Typing
50 The term @dfn{latent typing} is used to describe a computer language,
51 such as Scheme, for which you cannot, @emph{in general}, simply look at
52 a program's source code and determine what type of data will be
53 associated with a particular variable, or with the result of a
54 particular expression.
56 Sometimes, of course, you @emph{can} tell from the code what the type of
57 an expression will be. If you have a line in your program that sets the
58 variable @code{x} to the numeric value 1, you can be certain that,
59 immediately after that line has executed (and in the absence of multiple
60 threads), @code{x} has the numeric value 1. Or if you write a procedure
61 that is designed to concatenate two strings, it is likely that the rest
62 of your application will always invoke this procedure with two string
63 parameters, and quite probable that the procedure would go wrong in some
64 way if it was ever invoked with parameters that were not both strings.
66 Nevertheless, the point is that there is nothing in Scheme which
67 requires the procedure parameters always to be strings, or @code{x}
68 always to hold a numeric value, and there is no way of declaring in your
69 program that such constraints should always be obeyed. In the same
70 vein, there is no way to declare the expected type of a procedure's
73 Instead, the types of variables and expressions are only known -- in
74 general -- at run time. If you @emph{need} to check at some point that
75 a value has the expected type, Scheme provides run time procedures that
76 you can invoke to do so. But equally, it can be perfectly valid for two
77 separate invocations of the same procedure to specify arguments with
78 different types, and to return values with different types.
80 The next subsection explains what this means in practice, for the ways
81 that Scheme programs use data types, values and variables.
84 @node Values and Variables
85 @subsubsection Values and Variables
87 Scheme provides many data types that you can use to represent your data.
88 Primitive types include characters, strings, numbers and procedures.
89 Compound types, which allow a group of primitive and compound values to
90 be stored together, include lists, pairs, vectors and multi-dimensional
91 arrays. In addition, Guile allows applications to define their own data
92 types, with the same status as the built-in standard Scheme types.
94 As a Scheme program runs, values of all types pop in and out of
95 existence. Sometimes values are stored in variables, but more commonly
96 they pass seamlessly from being the result of one computation to being
97 one of the parameters for the next.
99 Consider an example. A string value is created because the interpreter
100 reads in a literal string from your program's source code. Then a
101 numeric value is created as the result of calculating the length of the
102 string. A second numeric value is created by doubling the calculated
103 length. Finally the program creates a list with two elements -- the
104 doubled length and the original string itself -- and stores this list in
107 All of the values involved here -- in fact, all values in Scheme --
108 carry their type with them. In other words, every value ``knows,'' at
109 runtime, what kind of value it is. A number, a string, a list,
112 A variable, on the other hand, has no fixed type. A variable --
113 @code{x}, say -- is simply the name of a location -- a box -- in which
114 you can store any kind of Scheme value. So the same variable in a
115 program may hold a number at one moment, a list of procedures the next,
116 and later a pair of strings. The ``type'' of a variable -- insofar as
117 the idea is meaningful at all -- is simply the type of whatever value
118 the variable happens to be storing at a particular moment.
122 @subsubsection Defining and Setting Variables
124 To define a new variable, you use Scheme's @code{define} syntax like
128 (define @var{variable-name} @var{value})
131 This makes a new variable called @var{variable-name} and stores
132 @var{value} in it as the variable's initial value. For example:
135 ;; Make a variable `x' with initial numeric value 1.
138 ;; Make a variable `organization' with an initial string value.
139 (define organization "Free Software Foundation")
142 (In Scheme, a semicolon marks the beginning of a comment that continues
143 until the end of the line. So the lines beginning @code{;;} are
146 Changing the value of an already existing variable is very similar,
147 except that @code{define} is replaced by the Scheme syntax @code{set!},
151 (set! @var{variable-name} @var{new-value})
154 Remember that variables do not have fixed types, so @var{new-value} may
155 have a completely different type from whatever was previously stored in
156 the location named by @var{variable-name}. Both of the following
157 examples are therefore correct.
160 ;; Change the value of `x' to 5.
163 ;; Change the value of `organization' to the FSF's street number.
164 (set! organization 545)
167 In these examples, @var{value} and @var{new-value} are literal numeric
168 or string values. In general, however, @var{value} and @var{new-value}
169 can be any Scheme expression. Even though we have not yet covered the
170 forms that Scheme expressions can take (@pxref{About Expressions}), you
171 can probably guess what the following @code{set!} example does@dots{}
177 (Note: this is not a complete description of @code{define} and
178 @code{set!}, because we need to introduce some other aspects of Scheme
179 before the missing pieces can be filled in. If, however, you are
180 already familiar with the structure of Scheme, you may like to read
181 about those missing pieces immediately by jumping ahead to the following
186 @ref{Lambda Alternatives}, to read about an alternative form of the
187 @code{define} syntax that can be used when defining new procedures.
190 @ref{Procedures with Setters}, to read about an alternative form of the
191 @code{set!} syntax that helps with changing a single value in the depths
192 of a compound data structure.)
195 @xref{Internal Definitions}, to read about using @code{define} other
196 than at top level in a Scheme program, including a discussion of when it
197 works to use @code{define} rather than @code{set!} to change the value
198 of an existing variable.
202 @node About Procedures
203 @subsection The Representation and Use of Procedures
205 This section introduces the basics of using and creating Scheme
206 procedures. It discusses the representation of procedures as just
207 another kind of Scheme value, and shows how procedure invocation
208 expressions are constructed. We then explain how @code{lambda} is used
209 to create new procedures, and conclude by presenting the various
210 shorthand forms of @code{define} that can be used instead of writing an
211 explicit @code{lambda} expression.
214 * Procedures as Values:: Procedures are values like everything else.
215 * Simple Invocation:: How to write a simple procedure invocation.
216 * Creating a Procedure:: How to create your own procedures.
217 * Lambda Alternatives:: Other ways of writing procedure definitions.
221 @node Procedures as Values
222 @subsubsection Procedures as Values
224 One of the great simplifications of Scheme is that a procedure is just
225 another type of value, and that procedure values can be passed around
226 and stored in variables in exactly the same way as, for example, strings
227 and lists. When we talk about a built-in standard Scheme procedure such
228 as @code{open-input-file}, what we actually mean is that there is a
229 pre-defined top level variable called @code{open-input-file}, whose
230 value is a procedure that implements what R5RS says that
231 @code{open-input-file} should do.
233 Note that this is quite different from many dialects of Lisp ---
234 including Emacs Lisp --- in which a program can use the same name with
235 two quite separate meanings: one meaning identifies a Lisp function,
236 while the other meaning identifies a Lisp variable, whose value need
237 have nothing to do with the function that is associated with the first
238 meaning. In these dialects, functions and variables are said to live in
239 different @dfn{namespaces}.
241 In Scheme, on the other hand, all names belong to a single unified
242 namespace, and the variables that these names identify can hold any kind
243 of Scheme value, including procedure values.
245 One consequence of the ``procedures as values'' idea is that, if you
246 don't happen to like the standard name for a Scheme procedure, you can
249 For example, @code{call-with-current-continuation} is a very important
250 standard Scheme procedure, but it also has a very long name! So, many
251 programmers use the following definition to assign the same procedure
252 value to the more convenient name @code{call/cc}.
255 (define call/cc call-with-current-continuation)
258 Let's understand exactly how this works. The definition creates a new
259 variable @code{call/cc}, and then sets its value to the value of the
260 variable @code{call-with-current-continuation}; the latter value is a
261 procedure that implements the behaviour that R5RS specifies under the
262 name ``call-with-current-continuation''. So @code{call/cc} ends up
263 holding this value as well.
265 Now that @code{call/cc} holds the required procedure value, you could
266 choose to use @code{call-with-current-continuation} for a completely
267 different purpose, or just change its value so that you will get an
268 error if you accidentally use @code{call-with-current-continuation} as a
269 procedure in your program rather than @code{call/cc}. For example:
272 (set! call-with-current-continuation "Not a procedure any more!")
275 Or you could just leave @code{call-with-current-continuation} as it was.
276 It's perfectly fine for more than one variable to hold the same
280 @node Simple Invocation
281 @subsubsection Simple Procedure Invocation
283 A procedure invocation in Scheme is written like this:
286 (@var{procedure} [@var{arg1} [@var{arg2} @dots{}]])
289 In this expression, @var{procedure} can be any Scheme expression whose
290 value is a procedure. Most commonly, however, @var{procedure} is simply
291 the name of a variable whose value is a procedure.
293 For example, @code{string-append} is a standard Scheme procedure whose
294 behaviour is to concatenate together all the arguments, which are
295 expected to be strings, that it is given. So the expression
298 (string-append "/home" "/" "andrew")
302 is a procedure invocation whose result is the string value
303 @code{"/home/andrew"}.
305 Similarly, @code{string-length} is a standard Scheme procedure that
306 returns the length of a single string argument, so
309 (string-length "abc")
313 is a procedure invocation whose result is the numeric value 3.
315 Each of the parameters in a procedure invocation can itself be any
316 Scheme expression. Since a procedure invocation is itself a type of
317 expression, we can put these two examples together to get
320 (string-length (string-append "/home" "/" "andrew"))
324 --- a procedure invocation whose result is the numeric value 12.
326 (You may be wondering what happens if the two examples are combined the
327 other way round. If we do this, we can make a procedure invocation
328 expression that is @emph{syntactically} correct:
331 (string-append "/home" (string-length "abc"))
335 but when this expression is executed, it will cause an error, because
336 the result of @code{(string-length "abc")} is a numeric value, and
337 @code{string-append} is not designed to accept a numeric value as one of
341 @node Creating a Procedure
342 @subsubsection Creating and Using a New Procedure
344 Scheme has lots of standard procedures, and Guile provides all of these
345 via predefined top level variables. All of these standard procedures
346 are documented in the later chapters of this reference manual.
348 Before very long, though, you will want to create new procedures that
349 encapsulate aspects of your own applications' functionality. To do
350 this, you can use the famous @code{lambda} syntax.
352 For example, the value of the following Scheme expression
355 (lambda (name address) @var{expression} @dots{})
359 is a newly created procedure that takes two arguments:
360 @code{name} and @code{address}. The behaviour of the
361 new procedure is determined by the sequence of @var{expression}s in the
362 @dfn{body} of the procedure definition. (Typically, these
363 @var{expression}s would use the arguments in some way, or else there
364 wouldn't be any point in giving them to the procedure.) When invoked,
365 the new procedure returns a value that is the value of the last
366 @var{expression} in the procedure body.
368 To make things more concrete, let's suppose that the two arguments are
369 both strings, and that the purpose of this procedure is to form a
370 combined string that includes these arguments. Then the full lambda
371 expression might look like this:
374 (lambda (name address)
375 (string-append "Name=" name ":Address=" address))
378 We noted in the previous subsection that the @var{procedure} part of a
379 procedure invocation expression can be any Scheme expression whose value
380 is a procedure. But that's exactly what a lambda expression is! So we
381 can use a lambda expression directly in a procedure invocation, like
385 ((lambda (name address)
386 (string-append "Name=" name ":Address=" address))
392 This is a valid procedure invocation expression, and its result is the
396 "Name=FSF:Address=Cambridge"
399 It is more common, though, to store the procedure value in a variable ---
402 (define make-combined-string
403 (lambda (name address)
404 (string-append "Name=" name ":Address=" address)))
408 --- and then to use the variable name in the procedure invocation:
411 (make-combined-string "FSF" "Cambridge")
415 Which has exactly the same result.
417 It's important to note that procedures created using @code{lambda} have
418 exactly the same status as the standard built in Scheme procedures, and
419 can be invoked, passed around, and stored in variables in exactly the
423 @node Lambda Alternatives
424 @subsubsection Lambda Alternatives
426 Since it is so common in Scheme programs to want to create a procedure
427 and then store it in a variable, there is an alternative form of the
428 @code{define} syntax that allows you to do just that.
430 A @code{define} expression of the form
433 (define (@var{name} [@var{arg1} [@var{arg2} @dots{}]])
434 @var{expression} @dots{})
438 is exactly equivalent to the longer form
442 (lambda ([@var{arg1} [@var{arg2} @dots{}]])
443 @var{expression} @dots{}))
446 So, for example, the definition of @code{make-combined-string} in the
447 previous subsection could equally be written:
450 (define (make-combined-string name address)
451 (string-append "Name=" name ":Address=" address))
454 This kind of procedure definition creates a procedure that requires
455 exactly the expected number of arguments. There are two further forms
456 of the @code{lambda} expression, which create a procedure that can
457 accept a variable number of arguments:
460 (lambda (@var{arg1} @dots{} . @var{args}) @var{expression} @dots{})
462 (lambda @var{args} @var{expression} @dots{})
466 The corresponding forms of the alternative @code{define} syntax are:
469 (define (@var{name} @var{arg1} @dots{} . @var{args}) @var{expression} @dots{})
471 (define (@var{name} . @var{args}) @var{expression} @dots{})
475 For details on how these forms work, see @xref{Lambda}.
477 (It could be argued that the alternative @code{define} forms are rather
478 confusing, especially for newcomers to the Scheme language, as they hide
479 both the role of @code{lambda} and the fact that procedures are values
480 that are stored in variables in the some way as any other kind of value.
481 On the other hand, they are very convenient, and they are also a good
482 example of another of Scheme's powerful features: the ability to specify
483 arbitrary syntactic transformations at run time, which can be applied to
484 subsequently read input.)
487 @node About Expressions
488 @subsection Expressions and Evaluation
490 So far, we have met expressions that @emph{do} things, such as the
491 @code{define} expressions that create and initialize new variables, and
492 we have also talked about expressions that have @emph{values}, for
493 example the value of the procedure invocation expression:
496 (string-append "/home" "/" "andrew")
500 but we haven't yet been precise about what causes an expression like
501 this procedure invocation to be reduced to its ``value'', or how the
502 processing of such expressions relates to the execution of a Scheme
505 This section clarifies what we mean by an expression's value, by
506 introducing the idea of @dfn{evaluation}. It discusses the side effects
507 that evaluation can have, explains how each of the various types of
508 Scheme expression is evaluated, and describes the behaviour and use of
509 the Guile REPL as a mechanism for exploring evaluation. The section
510 concludes with a very brief summary of Scheme's common syntactic
514 * Evaluating:: How a Scheme program is executed.
515 * Tail Calls:: Space-safe recursion.
516 * The REPL:: Interacting with the Guile interpreter.
517 * Syntax Summary:: Common syntactic expressions -- in brief.
522 @subsubsection Evaluating Expressions and Executing Programs
524 In Scheme, the process of executing an expression is known as
525 @dfn{evaluation}. Evaluation has two kinds of result:
529 the @dfn{value} of the evaluated expression
532 the @dfn{side effects} of the evaluation, which consist of any effects of
533 evaluating the expression that are not represented by the value.
536 Of the expressions that we have met so far, @code{define} and
537 @code{set!} expressions have side effects --- the creation or
538 modification of a variable --- but no value; @code{lambda} expressions
539 have values --- the newly constructed procedures --- but no side
540 effects; and procedure invocation expressions, in general, have either
541 values, or side effects, or both.
543 It is tempting to try to define more intuitively what we mean by
544 ``value'' and ``side effects'', and what the difference between them is.
545 In general, though, this is extremely difficult. It is also
546 unnecessary; instead, we can quite happily define the behaviour of a
547 Scheme program by specifying how Scheme executes a program as a whole,
548 and then by describing the value and side effects of evaluation for each
549 type of expression individually.
552 So, some@footnote{These definitions are approximate. For the whole and
553 detailed truth, see @xref{Formal syntax and semantics,R5RS
554 syntax,,r5rs}.} definitions@dots{}
559 A Scheme program consists of a sequence of expressions.
562 A Scheme interpreter executes the program by evaluating these
563 expressions in order, one by one.
570 a piece of literal data, such as a number @code{2.3} or a string
571 @code{"Hello world!"}
575 a procedure invocation expression
577 one of Scheme's special syntactic expressions.
582 The following subsections describe how each of these types of expression
586 @c * Eval Literal:: Evaluating literal data.
587 @c * Eval Variable:: Evaluating variable references.
588 @c * Eval Procedure:: Evaluating procedure invocation expressions.
589 @c * Eval Special:: Evaluating special syntactic expressions.
592 @c @node Eval Literal
594 @subsubheading Evaluating Literal Data
596 When a literal data expression is evaluated, the value of the expression
597 is simply the value that the expression describes. The evaluation of a
598 literal data expression has no side effects.
605 the value of the expression @code{"abc"} is the string value
609 the value of the expression @code{3+4i} is the complex number 3 + 4i
612 the value of the expression @code{#(1 2 3)} is a three-element vector
613 containing the numeric values 1, 2 and 3.
616 For any data type which can be expressed literally like this, the syntax
617 of the literal data expression for that data type --- in other words,
618 what you need to write in your code to indicate a literal value of that
619 type --- is known as the data type's @dfn{read syntax}. This manual
620 specifies the read syntax for each such data type in the section that
621 describes that data type.
623 Some data types do not have a read syntax. Procedures, for example,
624 cannot be expressed as literal data; they must be created using a
625 @code{lambda} expression (@pxref{Creating a Procedure}) or implicitly
626 using the shorthand form of @code{define} (@pxref{Lambda Alternatives}).
629 @c @node Eval Variable
630 @subsubheading Evaluating a Variable Reference
632 When an expression that consists simply of a variable name is evaluated,
633 the value of the expression is the value of the named variable. The
634 evaluation of a variable reference expression has no side effects.
639 (define key "Paul Evans")
643 the value of the expression @code{key} is the string value @code{"Paul
644 Evans"}. If @var{key} is then modified by
651 the value of the expression @code{key} is the numeric value 3.74.
653 If there is no variable with the specified name, evaluation of the
654 variable reference expression signals an error.
657 @c @node Eval Procedure
658 @subsubheading Evaluating a Procedure Invocation Expression
660 This is where evaluation starts getting interesting! As already noted,
661 a procedure invocation expression has the form
664 (@var{procedure} [@var{arg1} [@var{arg2} @dots{}]])
668 where @var{procedure} must be an expression whose value, when evaluated,
671 The evaluation of a procedure invocation expression like this proceeds
676 evaluating individually the expressions @var{procedure}, @var{arg1},
677 @var{arg2}, and so on
680 calling the procedure that is the value of the @var{procedure}
681 expression with the list of values obtained from the evaluations of
682 @var{arg1}, @var{arg2} etc. as its parameters.
685 For a procedure defined in Scheme, ``calling the procedure with the list
686 of values as its parameters'' means binding the values to the
687 procedure's formal parameters and then evaluating the sequence of
688 expressions that make up the body of the procedure definition. The
689 value of the procedure invocation expression is the value of the last
690 evaluated expression in the procedure body. The side effects of calling
691 the procedure are the combination of the side effects of the sequence of
692 evaluations of expressions in the procedure body.
694 For a built-in procedure, the value and side-effects of calling the
695 procedure are best described by that procedure's documentation.
697 Note that the complete side effects of evaluating a procedure invocation
698 expression consist not only of the side effects of the procedure call,
699 but also of any side effects of the preceding evaluation of the
700 expressions @var{procedure}, @var{arg1}, @var{arg2}, and so on.
702 To illustrate this, let's look again at the procedure invocation
706 (string-length (string-append "/home" "/" "andrew"))
709 In the outermost expression, @var{procedure} is @code{string-length} and
710 @var{arg1} is @code{(string-append "/home" "/" "andrew")}.
714 Evaluation of @code{string-length}, which is a variable, gives a
715 procedure value that implements the expected behaviour for
719 Evaluation of @code{(string-append "/home" "/" "andrew")}, which is
720 another procedure invocation expression, means evaluating each of
724 @code{string-append}, which gives a procedure value that implements the
725 expected behaviour for ``string-append''
728 @code{"/home"}, which gives the string value @code{"/home"}
731 @code{"/"}, which gives the string value @code{"/"}
734 @code{"andrew"}, which gives the string value @code{"andrew"}
737 and then invoking the procedure value with this list of string values as
738 its arguments. The resulting value is a single string value that is the
739 concatenation of all the arguments, namely @code{"/home/andrew"}.
742 In the evaluation of the outermost expression, the interpreter can now
743 invoke the procedure value obtained from @var{procedure} with the value
744 obtained from @var{arg1} as its arguments. The resulting value is a
745 numeric value that is the length of the argument string, which is 12.
748 @c @node Eval Special
749 @subsubheading Evaluating Special Syntactic Expressions
751 When a procedure invocation expression is evaluated, the procedure and
752 @emph{all} the argument expressions must be evaluated before the
753 procedure can be invoked. Special syntactic expressions are special
754 because they are able to manipulate their arguments in an unevaluated
755 form, and can choose whether to evaluate any or all of the argument
758 Why is this needed? Consider a program fragment that asks the user
759 whether or not to delete a file, and then deletes the file if the user
763 (if (string=? (read-answer "Should I delete this file?")
768 If the outermost @code{(if @dots{})} expression here was a procedure
769 invocation expression, the expression @code{(delete-file file)}, whose
770 side effect is to actually delete a file, would already have been
771 evaluated before the @code{if} procedure even got invoked! Clearly this
772 is no use --- the whole point of an @code{if} expression is that the
773 @dfn{consequent} expression is only evaluated if the condition of the
774 @code{if} expression is ``true''.
776 Therefore @code{if} must be special syntax, not a procedure. Other
777 special syntaxes that we have already met are @code{define}, @code{set!}
778 and @code{lambda}. @code{define} and @code{set!} are syntax because
779 they need to know the variable @emph{name} that is given as the first
780 argument in a @code{define} or @code{set!} expression, not that
781 variable's value. @code{lambda} is syntax because it does not
782 immediately evaluate the expressions that define the procedure body;
783 instead it creates a procedure object that incorporates these
784 expressions so that they can be evaluated in the future, when that
785 procedure is invoked.
787 The rules for evaluating each special syntactic expression are specified
788 individually for each special syntax. For a summary of standard special
789 syntax, see @xref{Syntax Summary}.
793 @subsubsection Tail calls
797 Scheme is ``properly tail recursive'', meaning that tail calls or
798 recursions from certain contexts do not consume stack space or other
799 resources and can therefore be used on arbitrarily large data or for
800 an arbitrarily long calculation. Consider for example,
816 @code{foo} prints numbers infinitely, starting from the given @var{n}.
817 It's implemented by printing @var{n} then recursing to itself to print
818 @math{@var{n}+1} and so on. This recursion is a tail call, it's the
819 last thing done, and in Scheme such tail calls can be made without
822 Or consider a case where a value is returned, a version of the SRFI-1
823 @code{last} function (@pxref{SRFI-1 Selectors}) returning the last
827 (define (my-last lst)
828 (if (null? (cdr lst))
830 (my-last (cdr lst))))
832 (my-last '(1 2 3)) @result{} 3
835 If the list has more than one element, @code{my-last} applies itself
836 to the @code{cdr}. This recursion is a tail call, there's no code
837 after it, and the return value is the return value from that call. In
838 Scheme this can be used on an arbitrarily long list argument.
841 A proper tail call is only available from certain contexts, namely the
842 following special form positions,
846 @code{and} --- last expression
849 @code{begin} --- last expression
852 @code{case} --- last expression in each clause
855 @code{cond} --- last expression in each clause, and the call to a
856 @code{=>} procedure is a tail call
859 @code{do} --- last result expression
862 @code{if} --- ``true'' and ``false'' leg expressions
865 @code{lambda} --- last expression in body
868 @code{let}, @code{let*}, @code{letrec}, @code{let-syntax},
869 @code{letrec-syntax} --- last expression in body
872 @code{or} --- last expression
876 The following core functions make tail calls,
880 @code{apply} --- tail call to given procedure
883 @code{call-with-current-continuation} --- tail call to the procedure
884 receiving the new continuation
887 @code{call-with-values} --- tail call to the values-receiving
891 @code{eval} --- tail call to evaluate the form
894 @code{string-any}, @code{string-every} --- tail call to predicate on
895 the last character (if that point is reached)
899 The above are just core functions and special forms. Tail calls in
900 other modules are described with the relevant documentation, for
901 example SRFI-1 @code{any} and @code{every} (@pxref{SRFI-1 Searching}).
903 It will be noted there are a lot of places which could potentially be
904 tail calls, for instance the last call in a @code{for-each}, but only
905 those explicitly described are guaranteed.
909 @subsubsection Using the Guile REPL
911 If you start Guile without specifying a particular program for it to
912 execute, Guile enters its standard Read Evaluate Print Loop --- or
913 @dfn{REPL} for short. In this mode, Guile repeatedly reads in the next
914 Scheme expression that the user types, evaluates it, and prints the
917 The REPL is a useful mechanism for exploring the evaluation behaviour
918 described in the previous subsection. If you type @code{string-append},
919 for example, the REPL replies @code{#<primitive-procedure
920 string-append>}, illustrating the relationship between the variable
921 @code{string-append} and the procedure value stored in that variable.
923 In this manual, the notation @result{} is used to mean ``evaluates
924 to''. Wherever you see an example of the form
933 feel free to try it out yourself by typing @var{expression} into the
934 REPL and checking that it gives the expected @var{result}.
938 @subsubsection Summary of Common Syntax
940 This subsection lists the most commonly used Scheme syntactic
941 expressions, simply so that you will recognize common special syntax
942 when you see it. For a full description of each of these syntaxes,
943 follow the appropriate reference.
945 @code{lambda} (@pxref{Lambda}) is used to construct procedure objects.
947 @code{define} (@pxref{Top Level}) is used to create a new variable and
948 set its initial value.
950 @code{set!} (@pxref{Top Level}) is used to modify an existing variable's
953 @code{let}, @code{let*} and @code{letrec} (@pxref{Local Bindings})
954 create an inner lexical environment for the evaluation of a sequence of
955 expressions, in which a specified set of local variables is bound to the
956 values of a corresponding set of expressions. For an introduction to
957 environments, see @xref{About Closure}.
959 @code{begin} (@pxref{begin}) executes a sequence of expressions in order
960 and returns the value of the last expression. Note that this is not the
961 same as a procedure which returns its last argument, because the
962 evaluation of a procedure invocation expression does not guarantee to
963 evaluate the arguments in order.
965 @code{if} and @code{cond} (@pxref{if cond case}) provide conditional
966 evaluation of argument expressions depending on whether one or more
967 conditions evaluate to ``true'' or ``false''.
969 @code{case} (@pxref{if cond case}) provides conditional evaluation of
970 argument expressions depending on whether a variable has one of a
971 specified group of values.
973 @code{and} (@pxref{and or}) executes a sequence of expressions in order
974 until either there are no expressions left, or one of them evaluates to
977 @code{or} (@pxref{and or}) executes a sequence of expressions in order
978 until either there are no expressions left, or one of them evaluates to
983 @subsection The Concept of Closure
987 The concept of @dfn{closure} is the idea that a lambda expression
988 ``captures'' the variable bindings that are in lexical scope at the
989 point where the lambda expression occurs. The procedure created by the
990 lambda expression can refer to and mutate the captured bindings, and the
991 values of those bindings persist between procedure calls.
993 This section explains and explores the various parts of this idea in
997 * About Environments:: Names, locations, values and environments.
998 * Local Variables:: Local variables and local environments.
999 * Chaining:: Environment chaining.
1000 * Lexical Scope:: The meaning of lexical scoping.
1001 * Closure:: Explaining the concept of closure.
1002 * Serial Number:: Example 1: a serial number generator.
1003 * Shared Variable:: Example 2: a shared persistent variable.
1004 * Callback Closure:: Example 3: the callback closure problem.
1005 * OO Closure:: Example 4: object orientation.
1008 @node About Environments
1009 @subsubsection Names, Locations, Values and Environments
1014 @cindex top level environment
1015 @cindex environment, top level
1017 We said earlier that a variable name in a Scheme program is associated
1018 with a location in which any kind of Scheme value may be stored.
1019 (Incidentally, the term ``vcell'' is often used in Lisp and Scheme
1020 circles as an alternative to ``location''.) Thus part of what we mean
1021 when we talk about ``creating a variable'' is in fact establishing an
1022 association between a name, or identifier, that is used by the Scheme
1023 program code, and the variable location to which that name refers.
1024 Although the value that is stored in that location may change, the
1025 location to which a given name refers is always the same.
1027 We can illustrate this by breaking down the operation of the
1028 @code{define} syntax into three parts: @code{define}
1032 creates a new location
1035 establishes an association between that location and the name specified
1036 as the first argument of the @code{define} expression
1039 stores in that location the value obtained by evaluating the second
1040 argument of the @code{define} expression.
1043 A collection of associations between names and locations is called an
1044 @dfn{environment}. When you create a top level variable in a program
1045 using @code{define}, the name-location association for that variable is
1046 added to the ``top level'' environment. The ``top level'' environment
1047 also includes name-location associations for all the procedures that are
1048 supplied by standard Scheme.
1050 It is also possible to create environments other than the top level one,
1051 and to create variable bindings, or name-location associations, in those
1052 environments. This ability is a key ingredient in the concept of
1053 closure; the next subsection shows how it is done.
1056 @node Local Variables
1057 @subsubsection Local Variables and Environments
1059 @cindex local variable
1060 @cindex variable, local
1061 @cindex local environment
1062 @cindex environment, local
1064 We have seen how to create top level variables using the @code{define}
1065 syntax (@pxref{Definition}). It is often useful to create variables
1066 that are more limited in their scope, typically as part of a procedure
1067 body. In Scheme, this is done using the @code{let} syntax, or one of
1068 its modified forms @code{let*} and @code{letrec}. These syntaxes are
1069 described in full later in the manual (@pxref{Local Bindings}). Here
1070 our purpose is to illustrate their use just enough that we can see how
1071 local variables work.
1073 For example, the following code uses a local variable @code{s} to
1074 simplify the computation of the area of a triangle given the lengths of
1083 (let ((s (/ (+ a b c) 2)))
1084 (sqrt (* s (- s a) (- s b) (- s c)))))
1087 The effect of the @code{let} expression is to create a new environment
1088 and, within this environment, an association between the name @code{s}
1089 and a new location whose initial value is obtained by evaluating
1090 @code{(/ (+ a b c) 2)}. The expressions in the body of the @code{let},
1091 namely @code{(sqrt (* s (- s a) (- s b) (- s c)))}, are then evaluated
1092 in the context of the new environment, and the value of the last
1093 expression evaluated becomes the value of the whole @code{let}
1094 expression, and therefore the value of the variable @code{area}.
1098 @subsubsection Environment Chaining
1100 @cindex shadowing an imported variable binding
1101 @cindex chaining environments
1103 In the example of the previous subsection, we glossed over an important
1104 point. The body of the @code{let} expression in that example refers not
1105 only to the local variable @code{s}, but also to the top level variables
1106 @code{a}, @code{b}, @code{c} and @code{sqrt}. (@code{sqrt} is the
1107 standard Scheme procedure for calculating a square root.) If the body
1108 of the @code{let} expression is evaluated in the context of the
1109 @emph{local} @code{let} environment, how does the evaluation get at the
1110 values of these top level variables?
1112 The answer is that the local environment created by a @code{let}
1113 expression automatically has a reference to its containing environment
1114 --- in this case the top level environment --- and that the Scheme
1115 interpreter automatically looks for a variable binding in the containing
1116 environment if it doesn't find one in the local environment. More
1117 generally, every environment except for the top level one has a
1118 reference to its containing environment, and the interpreter keeps
1119 searching back up the chain of environments --- from most local to top
1120 level --- until it either finds a variable binding for the required
1121 identifier or exhausts the chain.
1123 This description also determines what happens when there is more than
1124 one variable binding with the same name. Suppose, continuing the
1125 example of the previous subsection, that there was also a pre-existing
1126 top level variable @code{s} created by the expression:
1129 (define s "Some beans, my lord!")
1132 Then both the top level environment and the local @code{let} environment
1133 would contain bindings for the name @code{s}. When evaluating code
1134 within the @code{let} body, the interpreter looks first in the local
1135 @code{let} environment, and so finds the binding for @code{s} created by
1136 the @code{let} syntax. Even though this environment has a reference to
1137 the top level environment, which also has a binding for @code{s}, the
1138 interpreter doesn't get as far as looking there. When evaluating code
1139 outside the @code{let} body, the interpreter looks up variable names in
1140 the top level environment, so the name @code{s} refers to the top level
1143 Within the @code{let} body, the binding for @code{s} in the local
1144 environment is said to @dfn{shadow} the binding for @code{s} in the top
1149 @subsubsection Lexical Scope
1151 The rules that we have just been describing are the details of how
1152 Scheme implements ``lexical scoping''. This subsection takes a brief
1153 diversion to explain what lexical scope means in general and to present
1154 an example of non-lexical scoping.
1156 ``Lexical scope'' in general is the idea that
1160 an identifier at a particular place in a program always refers to the
1161 same variable location --- where ``always'' means ``every time that the
1162 containing expression is executed'', and that
1165 the variable location to which it refers can be determined by static
1166 examination of the source code context in which that identifier appears,
1167 without having to consider the flow of execution through the program as
1171 In practice, lexical scoping is the norm for most programming languages,
1172 and probably corresponds to what you would intuitively consider to be
1173 ``normal''. You may even be wondering how the situation could possibly
1174 --- and usefully --- be otherwise. To demonstrate that another kind of
1175 scoping is possible, therefore, and to compare it against lexical
1176 scoping, the following subsection presents an example of non-lexical
1177 scoping and examines in detail how its behavior differs from the
1178 corresponding lexically scoped code.
1181 @c * Scoping Example:: An example of non-lexical scoping.
1185 @c @node Scoping Example
1186 @subsubheading An Example of Non-Lexical Scoping
1188 To demonstrate that non-lexical scoping does exist and can be useful, we
1189 present the following example from Emacs Lisp, which is a ``dynamically
1193 (defvar currency-abbreviation "USD")
1195 (defun currency-string (units hundredths)
1196 (concat currency-abbreviation
1197 (number-to-string units)
1199 (number-to-string hundredths)))
1201 (defun french-currency-string (units hundredths)
1202 (let ((currency-abbreviation "FRF"))
1203 (currency-string units hundredths)))
1206 The question to focus on here is: what does the identifier
1207 @code{currency-abbreviation} refer to in the @code{currency-string}
1208 function? The answer, in Emacs Lisp, is that all variable bindings go
1209 onto a single stack, and that @code{currency-abbreviation} refers to the
1210 topmost binding from that stack which has the name
1211 ``currency-abbreviation''. The binding that is created by the
1212 @code{defvar} form, to the value @code{"USD"}, is only relevant if none
1213 of the code that calls @code{currency-string} rebinds the name
1214 ``currency-abbreviation'' in the meanwhile.
1216 The second function @code{french-currency-string} works precisely by
1217 taking advantage of this behaviour. It creates a new binding for the
1218 name ``currency-abbreviation'' which overrides the one established by
1219 the @code{defvar} form.
1222 ;; Note! This is Emacs Lisp evaluation, not Scheme!
1223 (french-currency-string 33 44)
1228 Now let's look at the corresponding, @emph{lexically scoped} Scheme
1232 (define currency-abbreviation "USD")
1234 (define (currency-string units hundredths)
1235 (string-append currency-abbreviation
1236 (number->string units)
1238 (number->string hundredths)))
1240 (define (french-currency-string units hundredths)
1241 (let ((currency-abbreviation "FRF"))
1242 (currency-string units hundredths)))
1245 According to the rules of lexical scoping, the
1246 @code{currency-abbreviation} in @code{currency-string} refers to the
1247 variable location in the innermost environment at that point in the code
1248 which has a binding for @code{currency-abbreviation}, which is the
1249 variable location in the top level environment created by the preceding
1250 @code{(define currency-abbreviation @dots{})} expression.
1252 In Scheme, therefore, the @code{french-currency-string} procedure does
1253 not work as intended. The variable binding that it creates for
1254 ``currency-abbreviation'' is purely local to the code that forms the
1255 body of the @code{let} expression. Since this code doesn't directly use
1256 the name ``currency-abbreviation'' at all, the binding is pointless.
1259 (french-currency-string 33 44)
1264 This begs the question of how the Emacs Lisp behaviour can be
1265 implemented in Scheme. In general, this is a design question whose
1266 answer depends upon the problem that is being addressed. In this case,
1267 the best answer may be that @code{currency-string} should be
1268 redesigned so that it can take an optional third argument. This third
1269 argument, if supplied, is interpreted as a currency abbreviation that
1270 overrides the default.
1272 It is possible to change @code{french-currency-string} so that it mostly
1273 works without changing @code{currency-string}, but the fix is inelegant,
1274 and susceptible to interrupts that could leave the
1275 @code{currency-abbreviation} variable in the wrong state:
1278 (define (french-currency-string units hundredths)
1279 (set! currency-abbreviation "FRF")
1280 (let ((result (currency-string units hundredths)))
1281 (set! currency-abbreviation "USD")
1285 The key point here is that the code does not create any local binding
1286 for the identifier @code{currency-abbreviation}, so all occurrences of
1287 this identifier refer to the top level variable.
1291 @subsubsection Closure
1293 Consider a @code{let} expression that doesn't contain any
1297 (let ((s (/ (+ a b c) 2)))
1298 (sqrt (* s (- s a) (- s b) (- s c))))
1302 When the Scheme interpreter evaluates this, it
1306 creates a new environment with a reference to the environment that was
1307 current when it encountered the @code{let}
1310 creates a variable binding for @code{s} in the new environment, with
1311 value given by @code{(/ (+ a b c) 2)}
1314 evaluates the expression in the body of the @code{let} in the context of
1315 the new local environment, and remembers the value @code{V}
1318 forgets the local environment
1321 continues evaluating the expression that contained the @code{let}, using
1322 the value @code{V} as the value of the @code{let} expression, in the
1323 context of the containing environment.
1326 After the @code{let} expression has been evaluated, the local
1327 environment that was created is simply forgotten, and there is no longer
1328 any way to access the binding that was created in this environment. If
1329 the same code is evaluated again, it will follow the same steps again,
1330 creating a second new local environment that has no connection with the
1331 first, and then forgetting this one as well.
1333 If the @code{let} body contains a @code{lambda} expression, however, the
1334 local environment is @emph{not} forgotten. Instead, it becomes
1335 associated with the procedure that is created by the @code{lambda}
1336 expression, and is reinstated every time that that procedure is called.
1337 In detail, this works as follows.
1341 When the Scheme interpreter evaluates a @code{lambda} expression, to
1342 create a procedure object, it stores the current environment as part of
1343 the procedure definition.
1346 Then, whenever that procedure is called, the interpreter reinstates the
1347 environment that is stored in the procedure definition and evaluates the
1348 procedure body within the context of that environment.
1351 The result is that the procedure body is always evaluated in the context
1352 of the environment that was current when the procedure was created.
1354 This is what is meant by @dfn{closure}. The next few subsections
1355 present examples that explore the usefulness of this concept.
1359 @subsubsection Example 1: A Serial Number Generator
1361 This example uses closure to create a procedure with a variable binding
1362 that is private to the procedure, like a local variable, but whose value
1363 persists between procedure calls.
1366 (define (make-serial-number-generator)
1367 (let ((current-serial-number 0))
1369 (set! current-serial-number (+ current-serial-number 1))
1370 current-serial-number)))
1372 (define entry-sn-generator (make-serial-number-generator))
1374 (entry-sn-generator)
1378 (entry-sn-generator)
1383 When @code{make-serial-number-generator} is called, it creates a local
1384 environment with a binding for @code{current-serial-number} whose
1385 initial value is 0, then, within this environment, creates a procedure.
1386 The local environment is stored within the created procedure object and
1387 so persists for the lifetime of the created procedure.
1389 Every time the created procedure is invoked, it increments the value of
1390 the @code{current-serial-number} binding in the captured environment and
1391 then returns the current value.
1393 Note that @code{make-serial-number-generator} can be called again to
1394 create a second serial number generator that is independent of the
1395 first. Every new invocation of @code{make-serial-number-generator}
1396 creates a new local @code{let} environment and returns a new procedure
1397 object with an association to this environment.
1400 @node Shared Variable
1401 @subsubsection Example 2: A Shared Persistent Variable
1403 This example uses closure to create two procedures, @code{get-balance}
1404 and @code{deposit}, that both refer to the same captured local
1405 environment so that they can both access the @code{balance} variable
1406 binding inside that environment. The value of this variable binding
1407 persists between calls to either procedure.
1409 Note that the captured @code{balance} variable binding is private to
1410 these two procedures: it is not directly accessible to any other code.
1411 It can only be accessed indirectly via @code{get-balance} or
1412 @code{deposit}, as illustrated by the @code{withdraw} procedure.
1415 (define get-balance #f)
1424 (set! balance (+ balance amount))
1427 (define (withdraw amount)
1428 (deposit (- amount)))
1443 An important detail here is that the @code{get-balance} and
1444 @code{deposit} variables must be set up by @code{define}ing them at top
1445 level and then @code{set!}ing their values inside the @code{let} body.
1446 Using @code{define} within the @code{let} body would not work: this
1447 would create variable bindings within the local @code{let} environment
1448 that would not be accessible at top level.
1451 @node Callback Closure
1452 @subsubsection Example 3: The Callback Closure Problem
1454 A frequently used programming model for library code is to allow an
1455 application to register a callback function for the library to call when
1456 some particular event occurs. It is often useful for the application to
1457 make several such registrations using the same callback function, for
1458 example if several similar library events can be handled using the same
1459 application code, but the need then arises to distinguish the callback
1460 function calls that are associated with one callback registration from
1461 those that are associated with different callback registrations.
1463 In languages without the ability to create functions dynamically, this
1464 problem is usually solved by passing a @code{user_data} parameter on the
1465 registration call, and including the value of this parameter as one of
1466 the parameters on the callback function. Here is an example of
1467 declarations using this solution in C:
1470 typedef void (event_handler_t) (int event_type,
1473 void register_callback (int event_type,
1474 event_handler_t *handler,
1478 In Scheme, closure can be used to achieve the same functionality without
1479 requiring the library code to store a @code{user-data} for each callback
1485 (define (register-callback event-type handler-proc)
1488 ;; In the application:
1490 (define (make-handler event-type user-data)
1493 <code referencing event-type and user-data>
1496 (register-callback event-type
1497 (make-handler event-type @dots{}))
1500 As far as the library is concerned, @code{handler-proc} is a procedure
1501 with no arguments, and all the library has to do is call it when the
1502 appropriate event occurs. From the application's point of view, though,
1503 the handler procedure has used closure to capture an environment that
1504 includes all the context that the handler code needs ---
1505 @code{event-type} and @code{user-data} --- to handle the event
1510 @subsubsection Example 4: Object Orientation
1512 Closure is the capture of an environment, containing persistent variable
1513 bindings, within the definition of a procedure or a set of related
1514 procedures. This is rather similar to the idea in some object oriented
1515 languages of encapsulating a set of related data variables inside an
1516 ``object'', together with a set of ``methods'' that operate on the
1517 encapsulated data. The following example shows how closure can be used
1518 to emulate the ideas of objects, methods and encapsulation in Scheme.
1521 (define (make-account)
1523 (define (get-balance)
1525 (define (deposit amount)
1526 (set! balance (+ balance amount))
1528 (define (withdraw amount)
1529 (deposit (- amount)))
1534 ((get-balance) get-balance)
1536 ((withdraw) withdraw)
1537 (else (error "Invalid method!")))
1541 Each call to @code{make-account} creates and returns a new procedure,
1542 created by the expression in the example code that begins ``(lambda
1546 (define my-account (make-account))
1553 This procedure acts as an account object with methods
1554 @code{get-balance}, @code{deposit} and @code{withdraw}. To apply one of
1555 the methods to the account, you call the procedure with a symbol
1556 indicating the required method as the first parameter, followed by any
1557 other parameters that are required by that method.
1560 (my-account 'get-balance)
1564 (my-account 'withdraw 5)
1568 (my-account 'deposit 396)
1572 (my-account 'get-balance)
1577 Note how, in this example, both the current balance and the helper
1578 procedures @code{get-balance}, @code{deposit} and @code{withdraw}, used
1579 to implement the guts of the account object's methods, are all stored in
1580 variable bindings within the private local environment captured by the
1581 @code{lambda} expression that creates the account object procedure.
1585 @c TeX-master: "guile.texi"