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
393 string @code{"Name=FSF:Address=Cambridge"}.
395 It is more common, though, to store the procedure value in a variable ---
398 (define make-combined-string
399 (lambda (name address)
400 (string-append "Name=" name ":Address=" address)))
404 --- and then to use the variable name in the procedure invocation:
407 (make-combined-string "FSF" "Cambridge")
411 Which has exactly the same result.
413 It's important to note that procedures created using @code{lambda} have
414 exactly the same status as the standard built in Scheme procedures, and
415 can be invoked, passed around, and stored in variables in exactly the
419 @node Lambda Alternatives
420 @subsubsection Lambda Alternatives
422 Since it is so common in Scheme programs to want to create a procedure
423 and then store it in a variable, there is an alternative form of the
424 @code{define} syntax that allows you to do just that.
426 A @code{define} expression of the form
429 (define (@var{name} [@var{arg1} [@var{arg2} @dots{}]])
430 @var{expression} @dots{})
434 is exactly equivalent to the longer form
438 (lambda ([@var{arg1} [@var{arg2} @dots{}]])
439 @var{expression} @dots{}))
442 So, for example, the definition of @code{make-combined-string} in the
443 previous subsection could equally be written:
446 (define (make-combined-string name address)
447 (string-append "Name=" name ":Address=" address))
450 This kind of procedure definition creates a procedure that requires
451 exactly the expected number of arguments. There are two further forms
452 of the @code{lambda} expression, which create a procedure that can
453 accept a variable number of arguments:
456 (lambda (@var{arg1} @dots{} . @var{args}) @var{expression} @dots{})
458 (lambda @var{args} @var{expression} @dots{})
462 The corresponding forms of the alternative @code{define} syntax are:
465 (define (@var{name} @var{arg1} @dots{} . @var{args}) @var{expression} @dots{})
467 (define (@var{name} . @var{args}) @var{expression} @dots{})
471 For details on how these forms work, see @xref{Lambda}.
473 (It could be argued that the alternative @code{define} forms are rather
474 confusing, especially for newcomers to the Scheme language, as they hide
475 both the role of @code{lambda} and the fact that procedures are values
476 that are stored in variables in the some way as any other kind of value.
477 On the other hand, they are very convenient, and they are also a good
478 example of another of Scheme's powerful features: the ability to specify
479 arbitrary syntactic transformations at run time, which can be applied to
480 subsequently read input.)
483 @node About Expressions
484 @subsection Expressions and Evaluation
486 So far, we have met expressions that @emph{do} things, such as the
487 @code{define} expressions that create and initialize new variables, and
488 we have also talked about expressions that have @emph{values}, for
489 example the value of the procedure invocation expression:
492 (string-append "/home" "/" "andrew")
496 but we haven't yet been precise about what causes an expression like
497 this procedure invocation to be reduced to its ``value'', or how the
498 processing of such expressions relates to the execution of a Scheme
501 This section clarifies what we mean by an expression's value, by
502 introducing the idea of @dfn{evaluation}. It discusses the side effects
503 that evaluation can have, explains how each of the various types of
504 Scheme expression is evaluated, and describes the behaviour and use of
505 the Guile REPL as a mechanism for exploring evaluation. The section
506 concludes with a very brief summary of Scheme's common syntactic
510 * Evaluating:: How a Scheme program is executed.
511 * Tail Calls:: Space-safe recursion.
512 * The REPL:: Interacting with the Guile interpreter.
513 * Syntax Summary:: Common syntactic expressions -- in brief.
518 @subsubsection Evaluating Expressions and Executing Programs
520 In Scheme, the process of executing an expression is known as
521 @dfn{evaluation}. Evaluation has two kinds of result:
525 the @dfn{value} of the evaluated expression
528 the @dfn{side effects} of the evaluation, which consist of any effects of
529 evaluating the expression that are not represented by the value.
532 Of the expressions that we have met so far, @code{define} and
533 @code{set!} expressions have side effects --- the creation or
534 modification of a variable --- but no value; @code{lambda} expressions
535 have values --- the newly constructed procedures --- but no side
536 effects; and procedure invocation expressions, in general, have either
537 values, or side effects, or both.
539 It is tempting to try to define more intuitively what we mean by
540 ``value'' and ``side effects'', and what the difference between them is.
541 In general, though, this is extremely difficult. It is also
542 unnecessary; instead, we can quite happily define the behaviour of a
543 Scheme program by specifying how Scheme executes a program as a whole,
544 and then by describing the value and side effects of evaluation for each
545 type of expression individually.
548 So, some@footnote{These definitions are approximate. For the whole and
549 detailed truth, see @xref{Formal syntax and semantics,R5RS
550 syntax,,r5rs}.} definitions@dots{}
555 A Scheme program consists of a sequence of expressions.
558 A Scheme interpreter executes the program by evaluating these
559 expressions in order, one by one.
566 a piece of literal data, such as a number @code{2.3} or a string
567 @code{"Hello world!"}
571 a procedure invocation expression
573 one of Scheme's special syntactic expressions.
578 The following subsections describe how each of these types of expression
582 @c * Eval Literal:: Evaluating literal data.
583 @c * Eval Variable:: Evaluating variable references.
584 @c * Eval Procedure:: Evaluating procedure invocation expressions.
585 @c * Eval Special:: Evaluating special syntactic expressions.
588 @c @node Eval Literal
590 @subsubheading Evaluating Literal Data
592 When a literal data expression is evaluated, the value of the expression
593 is simply the value that the expression describes. The evaluation of a
594 literal data expression has no side effects.
601 the value of the expression @code{"abc"} is the string value
605 the value of the expression @code{3+4i} is the complex number 3 + 4i
608 the value of the expression @code{#(1 2 3)} is a three-element vector
609 containing the numeric values 1, 2 and 3.
612 For any data type which can be expressed literally like this, the syntax
613 of the literal data expression for that data type --- in other words,
614 what you need to write in your code to indicate a literal value of that
615 type --- is known as the data type's @dfn{read syntax}. This manual
616 specifies the read syntax for each such data type in the section that
617 describes that data type.
619 Some data types do not have a read syntax. Procedures, for example,
620 cannot be expressed as literal data; they must be created using a
621 @code{lambda} expression (@pxref{Creating a Procedure}) or implicitly
622 using the shorthand form of @code{define} (@pxref{Lambda Alternatives}).
625 @c @node Eval Variable
626 @subsubheading Evaluating a Variable Reference
628 When an expression that consists simply of a variable name is evaluated,
629 the value of the expression is the value of the named variable. The
630 evaluation of a variable reference expression has no side effects.
635 (define key "Paul Evans")
639 the value of the expression @code{key} is the string value @code{"Paul
640 Evans"}. If @var{key} is then modified by
647 the value of the expression @code{key} is the numeric value 3.74.
649 If there is no variable with the specified name, evaluation of the
650 variable reference expression signals an error.
653 @c @node Eval Procedure
654 @subsubheading Evaluating a Procedure Invocation Expression
656 This is where evaluation starts getting interesting! As already noted,
657 a procedure invocation expression has the form
660 (@var{procedure} [@var{arg1} [@var{arg2} @dots{}]])
664 where @var{procedure} must be an expression whose value, when evaluated,
667 The evaluation of a procedure invocation expression like this proceeds
672 evaluating individually the expressions @var{procedure}, @var{arg1},
673 @var{arg2}, and so on
676 calling the procedure that is the value of the @var{procedure}
677 expression with the list of values obtained from the evaluations of
678 @var{arg1}, @var{arg2} etc. as its parameters.
681 For a procedure defined in Scheme, ``calling the procedure with the list
682 of values as its parameters'' means binding the values to the
683 procedure's formal parameters and then evaluating the sequence of
684 expressions that make up the body of the procedure definition. The
685 value of the procedure invocation expression is the value of the last
686 evaluated expression in the procedure body. The side effects of calling
687 the procedure are the combination of the side effects of the sequence of
688 evaluations of expressions in the procedure body.
690 For a built-in procedure, the value and side-effects of calling the
691 procedure are best described by that procedure's documentation.
693 Note that the complete side effects of evaluating a procedure invocation
694 expression consist not only of the side effects of the procedure call,
695 but also of any side effects of the preceding evaluation of the
696 expressions @var{procedure}, @var{arg1}, @var{arg2}, and so on.
698 To illustrate this, let's look again at the procedure invocation
702 (string-length (string-append "/home" "/" "andrew"))
705 In the outermost expression, @var{procedure} is @code{string-length} and
706 @var{arg1} is @code{(string-append "/home" "/" "andrew")}.
710 Evaluation of @code{string-length}, which is a variable, gives a
711 procedure value that implements the expected behaviour for
715 Evaluation of @code{(string-append "/home" "/" "andrew")}, which is
716 another procedure invocation expression, means evaluating each of
720 @code{string-append}, which gives a procedure value that implements the
721 expected behaviour for ``string-append''
724 @code{"/home"}, which gives the string value @code{"/home"}
727 @code{"/"}, which gives the string value @code{"/"}
730 @code{"andrew"}, which gives the string value @code{"andrew"}
733 and then invoking the procedure value with this list of string values as
734 its arguments. The resulting value is a single string value that is the
735 concatenation of all the arguments, namely @code{"/home/andrew"}.
738 In the evaluation of the outermost expression, the interpreter can now
739 invoke the procedure value obtained from @var{procedure} with the value
740 obtained from @var{arg1} as its arguments. The resulting value is a
741 numeric value that is the length of the argument string, which is 12.
744 @c @node Eval Special
745 @subsubheading Evaluating Special Syntactic Expressions
747 When a procedure invocation expression is evaluated, the procedure and
748 @emph{all} the argument expressions must be evaluated before the
749 procedure can be invoked. Special syntactic expressions are special
750 because they are able to manipulate their arguments in an unevaluated
751 form, and can choose whether to evaluate any or all of the argument
754 Why is this needed? Consider a program fragment that asks the user
755 whether or not to delete a file, and then deletes the file if the user
759 (if (string=? (read-answer "Should I delete this file?")
764 If the outermost @code{(if @dots{})} expression here was a procedure
765 invocation expression, the expression @code{(delete-file file)}, whose
766 side effect is to actually delete a file, would already have been
767 evaluated before the @code{if} procedure even got invoked! Clearly this
768 is no use --- the whole point of an @code{if} expression is that the
769 @dfn{consequent} expression is only evaluated if the condition of the
770 @code{if} expression is ``true''.
772 Therefore @code{if} must be special syntax, not a procedure. Other
773 special syntaxes that we have already met are @code{define}, @code{set!}
774 and @code{lambda}. @code{define} and @code{set!} are syntax because
775 they need to know the variable @emph{name} that is given as the first
776 argument in a @code{define} or @code{set!} expression, not that
777 variable's value. @code{lambda} is syntax because it does not
778 immediately evaluate the expressions that define the procedure body;
779 instead it creates a procedure object that incorporates these
780 expressions so that they can be evaluated in the future, when that
781 procedure is invoked.
783 The rules for evaluating each special syntactic expression are specified
784 individually for each special syntax. For a summary of standard special
785 syntax, see @xref{Syntax Summary}.
789 @subsubsection Tail calls
793 Scheme is ``properly tail recursive'', meaning that tail calls or
794 recursions from certain contexts do not consume stack space or other
795 resources and can therefore be used on arbitrarily large data or for
796 an arbitrarily long calculation. Consider for example,
812 @code{foo} prints numbers infinitely, starting from the given @var{n}.
813 It's implemented by printing @var{n} then recursing to itself to print
814 @math{@var{n}+1} and so on. This recursion is a tail call, it's the
815 last thing done, and in Scheme such tail calls can be made without
818 Or consider a case where a value is returned, a version of the SRFI-1
819 @code{last} function (@pxref{SRFI-1 Selectors}) returning the last
823 (define (my-last lst)
824 (if (null? (cdr lst))
826 (my-last (cdr lst))))
828 (my-last '(1 2 3)) @result{} 3
831 If the list has more than one element, @code{my-last} applies itself
832 to the @code{cdr}. This recursion is a tail call, there's no code
833 after it, and the return value is the return value from that call. In
834 Scheme this can be used on an arbitrarily long list argument.
837 A proper tail call is only available from certain contexts, namely the
838 following special form positions,
842 @code{and} --- last expression
845 @code{begin} --- last expression
848 @code{case} --- last expression in each clause
851 @code{cond} --- last expression in each clause, and the call to a
852 @code{=>} procedure is a tail call
855 @code{do} --- last result expression
858 @code{if} --- ``true'' and ``false'' leg expressions
861 @code{lambda} --- last expression in body
864 @code{let}, @code{let*}, @code{letrec}, @code{let-syntax},
865 @code{letrec-syntax} --- last expression in body
868 @code{or} --- last expression
872 The following core functions make tail calls,
876 @code{apply} --- tail call to given procedure
879 @code{call-with-current-continuation} --- tail call to the procedure
880 receiving the new continuation
883 @code{call-with-values} --- tail call to the values-receiving
887 @code{eval} --- tail call to evaluate the form
890 @code{string-any}, @code{string-every} --- tail call to predicate on
891 the last character (if that point is reached)
895 The above are just core functions and special forms. Tail calls in
896 other modules are described with the relevant documentation, for
897 example SRFI-1 @code{any} and @code{every} (@pxref{SRFI-1 Searching}).
899 It will be noted there are a lot of places which could potentially be
900 tail calls, for instance the last call in a @code{for-each}, but only
901 those explicitly described are guaranteed.
905 @subsubsection Using the Guile REPL
907 If you start Guile without specifying a particular program for it to
908 execute, Guile enters its standard Read Evaluate Print Loop --- or
909 @dfn{REPL} for short. In this mode, Guile repeatedly reads in the next
910 Scheme expression that the user types, evaluates it, and prints the
913 The REPL is a useful mechanism for exploring the evaluation behaviour
914 described in the previous subsection. If you type @code{string-append},
915 for example, the REPL replies @code{#<primitive-procedure
916 string-append>}, illustrating the relationship between the variable
917 @code{string-append} and the procedure value stored in that variable.
919 In this manual, the notation @result{} is used to mean ``evaluates
920 to''. Wherever you see an example of the form
929 feel free to try it out yourself by typing @var{expression} into the
930 REPL and checking that it gives the expected @var{result}.
934 @subsubsection Summary of Common Syntax
936 This subsection lists the most commonly used Scheme syntactic
937 expressions, simply so that you will recognize common special syntax
938 when you see it. For a full description of each of these syntaxes,
939 follow the appropriate reference.
941 @code{lambda} (@pxref{Lambda}) is used to construct procedure objects.
943 @code{define} (@pxref{Top Level}) is used to create a new variable and
944 set its initial value.
946 @code{set!} (@pxref{Top Level}) is used to modify an existing variable's
949 @code{let}, @code{let*} and @code{letrec} (@pxref{Local Bindings})
950 create an inner lexical environment for the evaluation of a sequence of
951 expressions, in which a specified set of local variables is bound to the
952 values of a corresponding set of expressions. For an introduction to
953 environments, see @xref{About Closure}.
955 @code{begin} (@pxref{begin}) executes a sequence of expressions in order
956 and returns the value of the last expression. Note that this is not the
957 same as a procedure which returns its last argument, because the
958 evaluation of a procedure invocation expression does not guarantee to
959 evaluate the arguments in order.
961 @code{if} and @code{cond} (@pxref{if cond case}) provide conditional
962 evaluation of argument expressions depending on whether one or more
963 conditions evaluate to ``true'' or ``false''.
965 @code{case} (@pxref{if cond case}) provides conditional evaluation of
966 argument expressions depending on whether a variable has one of a
967 specified group of values.
969 @code{and} (@pxref{and or}) executes a sequence of expressions in order
970 until either there are no expressions left, or one of them evaluates to
973 @code{or} (@pxref{and or}) executes a sequence of expressions in order
974 until either there are no expressions left, or one of them evaluates to
979 @subsection The Concept of Closure
983 The concept of @dfn{closure} is the idea that a lambda expression
984 ``captures'' the variable bindings that are in lexical scope at the
985 point where the lambda expression occurs. The procedure created by the
986 lambda expression can refer to and mutate the captured bindings, and the
987 values of those bindings persist between procedure calls.
989 This section explains and explores the various parts of this idea in
993 * About Environments:: Names, locations, values and environments.
994 * Local Variables:: Local variables and local environments.
995 * Chaining:: Environment chaining.
996 * Lexical Scope:: The meaning of lexical scoping.
997 * Closure:: Explaining the concept of closure.
998 * Serial Number:: Example 1: a serial number generator.
999 * Shared Variable:: Example 2: a shared persistent variable.
1000 * Callback Closure:: Example 3: the callback closure problem.
1001 * OO Closure:: Example 4: object orientation.
1004 @node About Environments
1005 @subsubsection Names, Locations, Values and Environments
1010 @cindex top level environment
1011 @cindex environment, top level
1013 We said earlier that a variable name in a Scheme program is associated
1014 with a location in which any kind of Scheme value may be stored.
1015 (Incidentally, the term ``vcell'' is often used in Lisp and Scheme
1016 circles as an alternative to ``location''.) Thus part of what we mean
1017 when we talk about ``creating a variable'' is in fact establishing an
1018 association between a name, or identifier, that is used by the Scheme
1019 program code, and the variable location to which that name refers.
1020 Although the value that is stored in that location may change, the
1021 location to which a given name refers is always the same.
1023 We can illustrate this by breaking down the operation of the
1024 @code{define} syntax into three parts: @code{define}
1028 creates a new location
1031 establishes an association between that location and the name specified
1032 as the first argument of the @code{define} expression
1035 stores in that location the value obtained by evaluating the second
1036 argument of the @code{define} expression.
1039 A collection of associations between names and locations is called an
1040 @dfn{environment}. When you create a top level variable in a program
1041 using @code{define}, the name-location association for that variable is
1042 added to the ``top level'' environment. The ``top level'' environment
1043 also includes name-location associations for all the procedures that are
1044 supplied by standard Scheme.
1046 It is also possible to create environments other than the top level one,
1047 and to create variable bindings, or name-location associations, in those
1048 environments. This ability is a key ingredient in the concept of
1049 closure; the next subsection shows how it is done.
1052 @node Local Variables
1053 @subsubsection Local Variables and Environments
1055 @cindex local variable
1056 @cindex variable, local
1057 @cindex local environment
1058 @cindex environment, local
1060 We have seen how to create top level variables using the @code{define}
1061 syntax (@pxref{Definition}). It is often useful to create variables
1062 that are more limited in their scope, typically as part of a procedure
1063 body. In Scheme, this is done using the @code{let} syntax, or one of
1064 its modified forms @code{let*} and @code{letrec}. These syntaxes are
1065 described in full later in the manual (@pxref{Local Bindings}). Here
1066 our purpose is to illustrate their use just enough that we can see how
1067 local variables work.
1069 For example, the following code uses a local variable @code{s} to
1070 simplify the computation of the area of a triangle given the lengths of
1079 (let ((s (/ (+ a b c) 2)))
1080 (sqrt (* s (- s a) (- s b) (- s c)))))
1083 The effect of the @code{let} expression is to create a new environment
1084 and, within this environment, an association between the name @code{s}
1085 and a new location whose initial value is obtained by evaluating
1086 @code{(/ (+ a b c) 2)}. The expressions in the body of the @code{let},
1087 namely @code{(sqrt (* s (- s a) (- s b) (- s c)))}, are then evaluated
1088 in the context of the new environment, and the value of the last
1089 expression evaluated becomes the value of the whole @code{let}
1090 expression, and therefore the value of the variable @code{area}.
1094 @subsubsection Environment Chaining
1096 @cindex shadowing an imported variable binding
1097 @cindex chaining environments
1099 In the example of the previous subsection, we glossed over an important
1100 point. The body of the @code{let} expression in that example refers not
1101 only to the local variable @code{s}, but also to the top level variables
1102 @code{a}, @code{b}, @code{c} and @code{sqrt}. (@code{sqrt} is the
1103 standard Scheme procedure for calculating a square root.) If the body
1104 of the @code{let} expression is evaluated in the context of the
1105 @emph{local} @code{let} environment, how does the evaluation get at the
1106 values of these top level variables?
1108 The answer is that the local environment created by a @code{let}
1109 expression automatically has a reference to its containing environment
1110 --- in this case the top level environment --- and that the Scheme
1111 interpreter automatically looks for a variable binding in the containing
1112 environment if it doesn't find one in the local environment. More
1113 generally, every environment except for the top level one has a
1114 reference to its containing environment, and the interpreter keeps
1115 searching back up the chain of environments --- from most local to top
1116 level --- until it either finds a variable binding for the required
1117 identifier or exhausts the chain.
1119 This description also determines what happens when there is more than
1120 one variable binding with the same name. Suppose, continuing the
1121 example of the previous subsection, that there was also a pre-existing
1122 top level variable @code{s} created by the expression:
1125 (define s "Some beans, my lord!")
1128 Then both the top level environment and the local @code{let} environment
1129 would contain bindings for the name @code{s}. When evaluating code
1130 within the @code{let} body, the interpreter looks first in the local
1131 @code{let} environment, and so finds the binding for @code{s} created by
1132 the @code{let} syntax. Even though this environment has a reference to
1133 the top level environment, which also has a binding for @code{s}, the
1134 interpreter doesn't get as far as looking there. When evaluating code
1135 outside the @code{let} body, the interpreter looks up variable names in
1136 the top level environment, so the name @code{s} refers to the top level
1139 Within the @code{let} body, the binding for @code{s} in the local
1140 environment is said to @dfn{shadow} the binding for @code{s} in the top
1145 @subsubsection Lexical Scope
1147 The rules that we have just been describing are the details of how
1148 Scheme implements ``lexical scoping''. This subsection takes a brief
1149 diversion to explain what lexical scope means in general and to present
1150 an example of non-lexical scoping.
1152 ``Lexical scope'' in general is the idea that
1156 an identifier at a particular place in a program always refers to the
1157 same variable location --- where ``always'' means ``every time that the
1158 containing expression is executed'', and that
1161 the variable location to which it refers can be determined by static
1162 examination of the source code context in which that identifier appears,
1163 without having to consider the flow of execution through the program as
1167 In practice, lexical scoping is the norm for most programming languages,
1168 and probably corresponds to what you would intuitively consider to be
1169 ``normal''. You may even be wondering how the situation could possibly
1170 --- and usefully --- be otherwise. To demonstrate that another kind of
1171 scoping is possible, therefore, and to compare it against lexical
1172 scoping, the following subsection presents an example of non-lexical
1173 scoping and examines in detail how its behavior differs from the
1174 corresponding lexically scoped code.
1177 @c * Scoping Example:: An example of non-lexical scoping.
1181 @c @node Scoping Example
1182 @subsubheading An Example of Non-Lexical Scoping
1184 To demonstrate that non-lexical scoping does exist and can be useful, we
1185 present the following example from Emacs Lisp, which is a ``dynamically
1189 (defvar currency-abbreviation "USD")
1191 (defun currency-string (units hundredths)
1192 (concat currency-abbreviation
1193 (number-to-string units)
1195 (number-to-string hundredths)))
1197 (defun french-currency-string (units hundredths)
1198 (let ((currency-abbreviation "FRF"))
1199 (currency-string units hundredths)))
1202 The question to focus on here is: what does the identifier
1203 @code{currency-abbreviation} refer to in the @code{currency-string}
1204 function? The answer, in Emacs Lisp, is that all variable bindings go
1205 onto a single stack, and that @code{currency-abbreviation} refers to the
1206 topmost binding from that stack which has the name
1207 ``currency-abbreviation''. The binding that is created by the
1208 @code{defvar} form, to the value @code{"USD"}, is only relevant if none
1209 of the code that calls @code{currency-string} rebinds the name
1210 ``currency-abbreviation'' in the meanwhile.
1212 The second function @code{french-currency-string} works precisely by
1213 taking advantage of this behaviour. It creates a new binding for the
1214 name ``currency-abbreviation'' which overrides the one established by
1215 the @code{defvar} form.
1218 ;; Note! This is Emacs Lisp evaluation, not Scheme!
1219 (french-currency-string 33 44)
1224 Now let's look at the corresponding, @emph{lexically scoped} Scheme
1228 (define currency-abbreviation "USD")
1230 (define (currency-string units hundredths)
1231 (string-append currency-abbreviation
1232 (number->string units)
1234 (number->string hundredths)))
1236 (define (french-currency-string units hundredths)
1237 (let ((currency-abbreviation "FRF"))
1238 (currency-string units hundredths)))
1241 According to the rules of lexical scoping, the
1242 @code{currency-abbreviation} in @code{currency-string} refers to the
1243 variable location in the innermost environment at that point in the code
1244 which has a binding for @code{currency-abbreviation}, which is the
1245 variable location in the top level environment created by the preceding
1246 @code{(define currency-abbreviation @dots{})} expression.
1248 In Scheme, therefore, the @code{french-currency-string} procedure does
1249 not work as intended. The variable binding that it creates for
1250 ``currency-abbreviation'' is purely local to the code that forms the
1251 body of the @code{let} expression. Since this code doesn't directly use
1252 the name ``currency-abbreviation'' at all, the binding is pointless.
1255 (french-currency-string 33 44)
1260 This begs the question of how the Emacs Lisp behaviour can be
1261 implemented in Scheme. In general, this is a design question whose
1262 answer depends upon the problem that is being addressed. In this case,
1263 the best answer may be that @code{currency-string} should be
1264 redesigned so that it can take an optional third argument. This third
1265 argument, if supplied, is interpreted as a currency abbreviation that
1266 overrides the default.
1268 It is possible to change @code{french-currency-string} so that it mostly
1269 works without changing @code{currency-string}, but the fix is inelegant,
1270 and susceptible to interrupts that could leave the
1271 @code{currency-abbreviation} variable in the wrong state:
1274 (define (french-currency-string units hundredths)
1275 (set! currency-abbreviation "FRF")
1276 (let ((result (currency-string units hundredths)))
1277 (set! currency-abbreviation "USD")
1281 The key point here is that the code does not create any local binding
1282 for the identifier @code{currency-abbreviation}, so all occurrences of
1283 this identifier refer to the top level variable.
1287 @subsubsection Closure
1289 Consider a @code{let} expression that doesn't contain any
1293 (let ((s (/ (+ a b c) 2)))
1294 (sqrt (* s (- s a) (- s b) (- s c))))
1298 When the Scheme interpreter evaluates this, it
1302 creates a new environment with a reference to the environment that was
1303 current when it encountered the @code{let}
1306 creates a variable binding for @code{s} in the new environment, with
1307 value given by @code{(/ (+ a b c) 2)}
1310 evaluates the expression in the body of the @code{let} in the context of
1311 the new local environment, and remembers the value @code{V}
1314 forgets the local environment
1317 continues evaluating the expression that contained the @code{let}, using
1318 the value @code{V} as the value of the @code{let} expression, in the
1319 context of the containing environment.
1322 After the @code{let} expression has been evaluated, the local
1323 environment that was created is simply forgotten, and there is no longer
1324 any way to access the binding that was created in this environment. If
1325 the same code is evaluated again, it will follow the same steps again,
1326 creating a second new local environment that has no connection with the
1327 first, and then forgetting this one as well.
1329 If the @code{let} body contains a @code{lambda} expression, however, the
1330 local environment is @emph{not} forgotten. Instead, it becomes
1331 associated with the procedure that is created by the @code{lambda}
1332 expression, and is reinstated every time that that procedure is called.
1333 In detail, this works as follows.
1337 When the Scheme interpreter evaluates a @code{lambda} expression, to
1338 create a procedure object, it stores the current environment as part of
1339 the procedure definition.
1342 Then, whenever that procedure is called, the interpreter reinstates the
1343 environment that is stored in the procedure definition and evaluates the
1344 procedure body within the context of that environment.
1347 The result is that the procedure body is always evaluated in the context
1348 of the environment that was current when the procedure was created.
1350 This is what is meant by @dfn{closure}. The next few subsections
1351 present examples that explore the usefulness of this concept.
1355 @subsubsection Example 1: A Serial Number Generator
1357 This example uses closure to create a procedure with a variable binding
1358 that is private to the procedure, like a local variable, but whose value
1359 persists between procedure calls.
1362 (define (make-serial-number-generator)
1363 (let ((current-serial-number 0))
1365 (set! current-serial-number (+ current-serial-number 1))
1366 current-serial-number)))
1368 (define entry-sn-generator (make-serial-number-generator))
1370 (entry-sn-generator)
1374 (entry-sn-generator)
1379 When @code{make-serial-number-generator} is called, it creates a local
1380 environment with a binding for @code{current-serial-number} whose
1381 initial value is 0, then, within this environment, creates a procedure.
1382 The local environment is stored within the created procedure object and
1383 so persists for the lifetime of the created procedure.
1385 Every time the created procedure is invoked, it increments the value of
1386 the @code{current-serial-number} binding in the captured environment and
1387 then returns the current value.
1389 Note that @code{make-serial-number-generator} can be called again to
1390 create a second serial number generator that is independent of the
1391 first. Every new invocation of @code{make-serial-number-generator}
1392 creates a new local @code{let} environment and returns a new procedure
1393 object with an association to this environment.
1396 @node Shared Variable
1397 @subsubsection Example 2: A Shared Persistent Variable
1399 This example uses closure to create two procedures, @code{get-balance}
1400 and @code{deposit}, that both refer to the same captured local
1401 environment so that they can both access the @code{balance} variable
1402 binding inside that environment. The value of this variable binding
1403 persists between calls to either procedure.
1405 Note that the captured @code{balance} variable binding is private to
1406 these two procedures: it is not directly accessible to any other code.
1407 It can only be accessed indirectly via @code{get-balance} or
1408 @code{deposit}, as illustrated by the @code{withdraw} procedure.
1411 (define get-balance #f)
1420 (set! balance (+ balance amount))
1423 (define (withdraw amount)
1424 (deposit (- amount)))
1439 An important detail here is that the @code{get-balance} and
1440 @code{deposit} variables must be set up by @code{define}ing them at top
1441 level and then @code{set!}ing their values inside the @code{let} body.
1442 Using @code{define} within the @code{let} body would not work: this
1443 would create variable bindings within the local @code{let} environment
1444 that would not be accessible at top level.
1447 @node Callback Closure
1448 @subsubsection Example 3: The Callback Closure Problem
1450 A frequently used programming model for library code is to allow an
1451 application to register a callback function for the library to call when
1452 some particular event occurs. It is often useful for the application to
1453 make several such registrations using the same callback function, for
1454 example if several similar library events can be handled using the same
1455 application code, but the need then arises to distinguish the callback
1456 function calls that are associated with one callback registration from
1457 those that are associated with different callback registrations.
1459 In languages without the ability to create functions dynamically, this
1460 problem is usually solved by passing a @code{user_data} parameter on the
1461 registration call, and including the value of this parameter as one of
1462 the parameters on the callback function. Here is an example of
1463 declarations using this solution in C:
1466 typedef void (event_handler_t) (int event_type,
1469 void register_callback (int event_type,
1470 event_handler_t *handler,
1474 In Scheme, closure can be used to achieve the same functionality without
1475 requiring the library code to store a @code{user-data} for each callback
1481 (define (register-callback event-type handler-proc)
1484 ;; In the application:
1486 (define (make-handler event-type user-data)
1489 <code referencing event-type and user-data>
1492 (register-callback event-type
1493 (make-handler event-type @dots{}))
1496 As far as the library is concerned, @code{handler-proc} is a procedure
1497 with no arguments, and all the library has to do is call it when the
1498 appropriate event occurs. From the application's point of view, though,
1499 the handler procedure has used closure to capture an environment that
1500 includes all the context that the handler code needs ---
1501 @code{event-type} and @code{user-data} --- to handle the event
1506 @subsubsection Example 4: Object Orientation
1508 Closure is the capture of an environment, containing persistent variable
1509 bindings, within the definition of a procedure or a set of related
1510 procedures. This is rather similar to the idea in some object oriented
1511 languages of encapsulating a set of related data variables inside an
1512 ``object'', together with a set of ``methods'' that operate on the
1513 encapsulated data. The following example shows how closure can be used
1514 to emulate the ideas of objects, methods and encapsulation in Scheme.
1517 (define (make-account)
1519 (define (get-balance)
1521 (define (deposit amount)
1522 (set! balance (+ balance amount))
1524 (define (withdraw amount)
1525 (deposit (- amount)))
1530 ((get-balance) get-balance)
1532 ((withdraw) withdraw)
1533 (else (error "Invalid method!")))
1537 Each call to @code{make-account} creates and returns a new procedure,
1538 created by the expression in the example code that begins ``(lambda
1542 (define my-account (make-account))
1549 This procedure acts as an account object with methods
1550 @code{get-balance}, @code{deposit} and @code{withdraw}. To apply one of
1551 the methods to the account, you call the procedure with a symbol
1552 indicating the required method as the first parameter, followed by any
1553 other parameters that are required by that method.
1556 (my-account 'get-balance)
1560 (my-account 'withdraw 5)
1564 (my-account 'deposit 396)
1568 (my-account 'get-balance)
1573 Note how, in this example, both the current balance and the helper
1574 procedures @code{get-balance}, @code{deposit} and @code{withdraw}, used
1575 to implement the guts of the account object's methods, are all stored in
1576 variable bindings within the private local environment captured by the
1577 @code{lambda} expression that creates the account object procedure.
1581 @c TeX-master: "guile.texi"