(by Dorai Sitaram (ds26@gte.com), 1998-2004)
Preface
1 Enter Scheme
2 Data types
2.1 Simple data types
2.1.1 Booleans
2.1.2 Numbers
2.1.3 Characters
2.1.4 Symbols
2.2 Compound data types
2.2.1 Strings
2.2.2 Vectors
2.2.3 Dotted pairs and lists
2.2.4 Conversions between data types
2.3 Other data types
2.4 S-expressions
3 Forms
3.1 Procedures
3.1.1 Procedure parameters
3.1.2 Variable number of arguments
3.2 apply
3.3 Sequencing
4 Conditionals
4.1 when and unless
4.2 cond
4.3 case
4.4 and and or
5 Lexical variables
5.1 let and let*
5.2 fluid-let
6 Recursion
6.1 letrec
6.2 Named let
6.3 Iteration
6.4 Mapping a procedure across a list
7 I/O
7.1 Reading
7.2 Writing
7.3 File ports
7.3.1 Automatic opening and closing of file ports
7.4 String ports
7.5 Loading files
8 Macros
8.1 Specifying the expansion as a template
8.2 Avoiding variable capture inside macros
8.3 fluid-let
9 Structures
9.1 Default initializations
9.2 defstruct defined
10 Alists and tables
11 System interface
11.1 Checking for and deleting files
11.2 Calling operating-system commands
11.3 Environment variables
12 Objects and classes
12.1 A simple object system
12.2 Classes are instances too
12.3 Multiple inheritance
13 Jumps
13.1 call-with-current-continuation
13.2 Escaping continuations
13.3 Tree matching
13.4 Coroutines
13.4.1 Tree-matching with coroutines
14 Nondeterminism
14.1 Description of amb
14.2 Implementing amb in Scheme
14.3 Using amb in Scheme
14.4 Logic puzzles
14.4.1 The Kalotan puzzle
14.4.2 Map coloring
15 Engines
15.1 The clock
15.2 Flat engines
15.3 Nestable engines
16 Shell scripts
16.1 Hello, World!, again
16.2 Scripts with arguments
16.3 Example
17 CGI scripts
17.1 Example: Displaying environment variables
17.2 Example: Displaying selected environment variable
17.3 CGI script utilities
17.4 A calculator via CGI
A Scheme dialects
A.1 Invocation and init files
A.2 Shell scripts
A.3 define-macro
A.4 load-relative
B DOS batch files in Scheme
C Numerical techniques
C.1 Simpson's rule
C.2 Adaptive interval sizes
C.3 Improper integrals
D A clock for infinity
E References
F Index
This is an introduction to the Scheme programming language. It is intended as a quick-start guide, something a novice can use to get a non-trivial working knowledge of the language, before moving on to more comprehensive and in-depth texts.
The text describes an approach to writing a crisp and utilitarian Scheme. Although we will not cover Scheme from abs to zero?, we will not shy away from those aspects of the language that are difficult, messy, nonstandard, or unusual, but nevertheless useful and usable. Such aspects include call-with-current-continuation, system interface, and dialect diversity. Our discussions will be informed by our focus on problem-solving, not by a quest for metalinguistic insight. I have therefore left out many of the staples of traditional Scheme tutorials. There will be no in-depth pedagogy; no dwelling on the semantic appeal of Scheme; no metacircular interpreters; no discussion of the underlying implementation; and no evangelizing about Scheme's virtues. This is not to suggest that these things are unimportant. However, they are arguably not immediately relevant to someone seeking a quick introduction.
How quick though? I do not know if one can teach oneself Scheme in 21 days1, although I have heard it said that the rudiments of Scheme should be a matter of an afternoon's study. The Scheme standard [23] itself, for all its exacting comprehensiveness, is a mere fifty pages long. It may well be that the insight, when it comes, will arrive in its entirety in one afternoon, though there is no telling how many afternoons of mistries must precede it. Until that zen moment, here is my gentle introduction.
Acknowledgment. I thank Matthias Felleisen for introducing me to Scheme and higher-order programming; and Matthew Flatt for creating the robust and pleasant MzScheme implementation used throughout this book.
-- d
1 A fixnum is a machine's idea of a ``small'' integer. Every machine has its own idea of how big a fixnum can be.
The canonical first program is the one that says "Hello, World!" on the console. Using your favorite editor, create a file called hello.scm with the following contents:
;The first program
(begin
(display "Hello, World!")
(newline))
The first line is a comment. When Scheme sees a semicolon, it ignores it and all the following text on the line.
The begin-form is Scheme's way of introducing a sequence of subforms. In this case there are two subforms. The first is a call to thedisplay procedure that outputs its argument (the string "Hello, World!") to the console (or ``standard output''). It is followed by anewline procedure call, which outputs a carriage return.
To run this program, first start your Scheme. This is usually done by typing the name of your Scheme executable at the operating-system command line. Eg, in the case of MzScheme [9], you type
mzscheme
at the operating-system prompt.
This invokes the Scheme listener, which reads your input, evaluates it, prints the result (if any), and then waits for more input from you. For this reason, it is often called the read-eval-print loop. Note that this is not much different from your operating-system command line, which also reads your commands, executes them, and then waits for more. Like the operating system, the Scheme listener has its own prompt -- usually this is ]] ]]> , but could be something else.
At the listener prompt, load the file hello.scm. This is done by typing
(load "hello.scm")
Scheme will now execute the contents of hello.scm, outputting Hello, World! followed by a carriage return. After this, you will get the listener prompt again, waiting for more input from you.
Since you have such an eager listener, you need not always write your programs in a file and load them. Sometimes, it is easier, especially when you are in an exploring mood, to simply type expressions directly at the listener prompt and see what happens. For example, typing the form
(begin (display "Hello, World!")
(newline))
at the Scheme prompt produces
Hello, World!
Actually, you could simply have typed the form "Hello, World!" at the listener, and you would have obtained as result the string
"Hello, World!"
because that is the result of the listener evaluating "Hello, World!".
Other than the fact that the second approach produces a result with double-quotes around it, there is one other significant difference between the last two programs. The first (ie, the one with the begin) does not evaluate to anything -- the Hello, World! it emits is a side-effectproduced by the display and newline procedures writing to the standard output. In the second program, the form "Hello, World!"evaluates to the result, which in this case is the same string as the form.
Henceforth, we will use the notation => to denote evaluation. Thus
E => v
indicates that the form E evaluates to a result value of v. Eg,
(begin
(display "Hello, World!")
(newline))
=>
(ie, nothing or void), although it has the side-effect of writing
Hello, World!
to the standard output. On the other hand,
"Hello, World!"
=> "Hello, World!"
In either case, we are still at the listener. To exit, type
(exit)
and this will land you back at the operating-system command-line (which, as we've seen, is also a kind of listener).
The listener is convenient for interactive testing of programs and program fragments. However it is by no means necessary. You may certainly stick to the tradition of creating programs in their entirety in files, and having Scheme execute them without any explicit ``listening''. In MzScheme, for instance, you could say (at the operating-system prompt)
mzscheme -r hello.scm
and this will produce the greeting without making you deal with the listener. After the greeting, mzscheme will return you to the operating-system prompt. This is almost as if you said
echo Hello, World!
You could even make hello.scm seem like an operating-system command (a shell script or a batch file), but that will have to wait till chapter 16.
A data type is a collection of related values. These collections need not be disjoint, and they are often hierarchical. Scheme has a rich set of data types: some are simple (indivisible) data types and others are compound data types made by combining other data types.
The simple data types of Scheme include booleans, numbers, characters, and symbols.
Scheme's booleans are #t for true and #f for false. Scheme has a predicate procedure called boolean? that checks if its argument is boolean.
(boolean? #t) => #t
(boolean? "Hello, World!") => #f
The procedure not negates its argument, considered as a boolean.
(not #f) => #t
(not #t) => #f
(not "Hello, World!") => #f
The last expression illustrates a Scheme convenience: In a context that requires a boolean, Scheme will treat any value that is not #f as a true value.
Scheme numbers can be integers (eg, 42), rationals (22/7), reals (3.1416), or complex (2+3i). An integer is a rational is a real is a complex number is a number. Predicates exist for testing the various kinds of numberness:
(number? 42) => #t
(number? #t) => #f
(complex? 2+3i) => #t
(real? 2+3i) => #f
(real? 3.1416) => #t
(real? 22/7) => #t
(real? 42) => #t
(rational? 2+3i) => #f
(rational? 3.1416) => #t
(rational? 22/7) => #t
(integer? 22/7) => #f
(integer? 42) => #t
Scheme integers need not be specified in decimal (base 10) format. They can be specified in binary by prefixing the numeral with #b. Thus#b1100 is the number twelve. The octal prefix is #o and the hex prefix is #x. (The optional decimal prefix is #d.)
Numbers can tested for equality using the general-purpose equality predicate eqv?.
(eqv? 42 42) => #t
(eqv? 42 #f) => #f
(eqv? 42 42.0) => #f
However, if you know that the arguments to be compared are numbers, the special number-equality predicate = is more apt.
(= 42 42) => #t
(= 42 #f) -->ERROR!!!
(= 42 42.0) => #t
Other number comparisons allowed are <, <=, ]] ]]> , >=.
(< 3 2) => #f
(>= 4.5 3) => #t
Arithmetic procedures +, -, *, /, expt have the expected behavior:
(+ 1 2 3) => 6
(- 5.3 2) => 3.3
(- 5 2 1) => 2
(* 1 2 3) => 6
(/ 6 3) => 2
(/ 22 7) => 22/7
(expt 2 3) => 8
(expt 4 1/2) => 2.0
For a single argument, - and / return the negation and the reciprocal respectively:
(- 4) => -4
(/ 4) => 1/4
The procedures max and min return the maximum and minimum respectively of the number arguments supplied to them. Any number of arguments can be so supplied.
(max 1 3 4 2 3) => 4
(min 1 3 4 2 3) => 1
The procedure abs returns the absolute value of its argument.
(abs 3) => 3
(abs -4) => 4
This is just the tip of the iceberg. Scheme provides a large and comprehensive suite of arithmetic and trigonometric procedures. For instance,atan, exp, and sqrt respectively return the arctangent, natural antilogarithm, and square root of their argument. Consult R5RS [23] for more details.
Scheme character data are represented by prefixing the character with #. Thus, #\c is the character c. Some non-graphic characters have more descriptive names, eg, #\newline, #\tab. The character for space can be written #\ , or more readably, #\space.
The character predicate is char?:
(char? #\c) => #t
(char? 1) => #f
(char? #\;) => #t
Note that a semicolon character datum does not trigger a comment.
The character data type has its set of comparison predicates: char=?, char<?, char<=?, char>?, char>=?.
(char=? #\a #\a) => #t
(char<? #\a #\b) => #t
(char>=? #\a #\b) => #f
To make the comparisons case-insensitive, use char-ci instead of char in the procedure name:
(char-ci=? #\a #\A) => #t
(char-ci<? #\a #\B) => #t
The case conversion procedures are char-downcase and char-upcase:
(char-downcase #\A) => #\a
(char-upcase #\a) => #\A
The simple data types we saw above are self-evaluating. Ie, if you typed any object from these data types to the listener, the evaluated result returned by the listener will be the same as what you typed in.
#t => #t
42 => 42
#\c => #\c
Symbols don't behave the same way. This is because symbols are used by Scheme programs as identifiers for variables, and thus will evaluate to the value that the variable holds. Nevertheless, symbols are a simple data type, and symbols are legitimate values that Scheme can traffic in, along with characters, numbers, and the rest.
To specify a symbol without making Scheme think it is a variable, you should quote the symbol:
(quote xyz)
=> xyz
Since this type of quoting is very common in Scheme, a convenient abbreviation is provided. The expression
'E
will be treated by Scheme as equivalent to
(quote E)
Scheme symbols are named by a sequence of characters. About the only limitation on a symbol's name is that it shouldn't be mistakable for some other data, eg, characters or booleans or numbers or compound data. Thus, this-is-a-symbol, i18n, <=>, and $!#* are all symbols;16, -i (a complex number!), #t, "this-is-a-string", and (barf) (a list) are not. The predicate for checking symbolness is calledsymbol?:
(symbol? 'xyz) => #t
(symbol? 42) => #f
Scheme symbols are normally case-insensitive. Thus the symbols Calorie and calorie are identical:
(eqv? 'Calorie 'calorie)
=> #t
We can use the symbol xyz as a global variable by using the form define:
(define xyz 9)
This says the variable xyz holds the value 9. If we feed xyz to the listener, the result will be the value held by xyz:
xyz
=> 9
We can use the form set! to change the value held by a variable:
(set! xyz #\c)
Now
xyz
=> #\c
Compound data types are built by combining values from other data types in structured ways.
Strings are sequences of characters (not to be confused with symbols, which are simple data that have a sequence of characters as their name). You can specify strings by enclosing the constituent characters in double-quotes. Strings evaluate to themselves.
"Hello, World!"
=> "Hello, World!"
The procedure string takes a bunch of characters and returns the string made from them:
(string #\h #\e #\l #\l #\o)
=> "hello"
Let us now define a global variable greeting.
(define greeting "Hello; Hello!")
Note that a semicolon inside a string datum does not trigger a comment.
The characters in a given string can be individually accessed and modified. The procedure string-ref takes a string and a (0-based) index, and returns the character at that index:
(string-ref greeting 0)
=> #\H
New strings can be created by appending other strings:
(string-append "E "
"Pluribus "
"Unum")
=> "E Pluribus Unum"
You can make a string of a specified length, and fill it with the desired characters later.
(define a-3-char-long-string (make-string 3))
The predicate for checking stringness is string?.
Strings obtained as a result of calls to string, make-string, and string-append are mutable. The procedure string-set! replaces the character at a given index:
(define hello (string #\H #\e #\l #\l #\o))
hello
=> "Hello"
(string-set! hello 1 #\a)
hello
=> "Hallo"
Vectors are sequences like strings, but their elements can be anything, not just characters. Indeed, the elements can be vectors themselves, which is a good way to generate multidimensional vectors.
Here's a way to create a vector of the first five integers:
(vector 0 1 2 3 4)
=> #(0 1 2 3 4)
Note Scheme's representation of a vector value: a # character followed by the vector's contents enclosed in parentheses.
In analogy with make-string, the procedure make-vector makes a vector of a specific length:
(define v (make-vector 5))
The procedures vector-ref and vector-set! access and modify vector elements. The predicate for checking if something is a vector isvector?.
A dotted pair is a compound value made by combining any two arbitrary values into an ordered couple. The first element is called the car, the second element is called the cdr, and the combining procedure is cons.
(cons 1 #t)
=> (1 . #t)
Dotted pairs are not self-evaluating, and so to specify them directly as data (ie, without producing them via a cons-call), one must explicitly quote them:
'(1 . #t) => (1 . #t)
(1 . #t) -->ERROR!!!
The accessor procedures are car and cdr:
(define x (cons 1 #t))
(car x)
=> 1
(cdr x)
=> #t
The elements of a dotted pair can be replaced by the mutator procedures set-car! and set-cdr!:
(set-car! x 2)
(set-cdr! x #f)
x
=> (2 . #f)
Dotted pairs can contain other dotted pairs.
(define y (cons (cons 1 2) 3))
y
=> ((1 . 2) . 3)
The car of the car of this list is 1. The cdr of the car of this list is 2. Ie,
(car (car y))
=> 1
(cdr (car y))
=> 2
Scheme provides procedure abbreviations for cascaded compositions of the car and cdr procedures. Thus, caar stands for car of car of'', and cdar stands forcdr of car of'', etc.
(caar y)
=> 1
(cdar y)
=> 2
c...r-style abbreviations for upto four cascades are guaranteed to exist. Thus, cadr, cdadr, and cdaddr are all valid. cdadadr might be pushing it.
When nested dotting occurs along the second element, Scheme uses a special notation to represent the resulting expression:
(cons 1 (cons 2 (cons 3 (cons 4 5))))
=> (1 2 3 4 . 5)
Ie, (1 2 3 4 . 5) is an abbreviation for (1 . (2 . (3 . (4 . 5)))). The last cdr of this expression is 5.
Scheme provides a further abbreviation if the last cdr is a special object called the empty list, which is represented by the expression (). The empty list is not considered self-evaluating, and so one should quote it when supplying it as a value in a program:
'() => ()
The abbreviation for a dotted pair of the form (1 . (2 . (3 . (4 . ())))) is
(1 2 3 4)
This special kind of nested dotted pair is called a list. This particular list is four elements long. It could have been created by saying
(cons 1 (cons 2 (cons 3 (cons 4 '()))))
but Scheme provides a procedure called list that makes list creation more convenient. list takes any number of arguments and returns the list containing them:
(list 1 2 3 4)
=> (1 2 3 4)
Indeed, if we know all the elements of a list, we can use quote to specify the list:
'(1 2 3 4)
=> (1 2 3 4)
List elements can be accessed by index.
(define y (list 1 2 3 4))
(list-ref y 0) => 1
(list-ref y 3) => 4
(list-tail y 1) => (2 3 4)
(list-tail y 3) => (4)
list-tail returns the tail of the list starting from the given index.
The predicates pair?, list?, and null? check if their argument is a dotted pair, list, or the empty list, respectively:
(pair? '(1 . 2)) => #t
(pair? '(1 2)) => #t
(pair? '()) => #f
(list? '()) => #t
(null? '()) => #t
(list? '(1 2)) => #t
(list? '(1 . 2)) => #f
(null? '(1 2)) => #f
(null? '(1 . 2)) => #f
Scheme offers many procedures for converting among the data types. We already know how to convert between the character cases usingchar-downcase and char-upcase. Characters can be converted into integers using char->integer, and integers can be converted into characters using integer->char. (The integer corresponding to a character is usually its ascii code.)
(char->integer #\d) => 100
(integer->char 50) => #\2
Strings can be converted into the corresponding list of characters.
(string->list "hello") => (#\h #\e #\l #\l #\o)
Other conversion procedures in the same vein are list->string, vector->list, and list->vector.
Numbers can be converted to strings:
(number->string 16) => "16"
Strings can be converted to numbers. If the string corresponds to no number, #f is returned.
(string->number "16")
=> 16
(string->number "Am I a hot number?")
=> #f
string->number takes an optional second argument, the radix.
(string->number "16" 8) => 14
because 16 in base 8 is the number fourteen.
Symbols can be converted to strings, and vice versa:
(symbol->string 'symbol)
=> "symbol"
(string->symbol "string")
=> string
Scheme contains some other data types. One is the procedure. We have already seen many procedures, eg, display, +, cons. In reality, these are variables holding the procedure values, which are themselves not visible as are numbers or characters:
cons
=> <procedure>
The procedures we have seen thus far are primitive procedures, with standard global variables holding them. Users can create additional procedure values.
Yet another data type is the port. A port is the conduit through which input and output is performed. Ports are usually associated with files and consoles.
In our ``Hello, World!'' program, we used the procedure display to write a string to the console. display can take two arguments, one the value to be displayed, and the other the output port it should be displayed on.
In our program, display's second argument was implicit. The default output port used is the standard output port. We can get the current standard output port via the procedure-call (current-output-port). We could have been more explicit and written
(display "Hello, World!" (current-output-port))
All the data types discussed here can be lumped together into a single all-encompassing data type called the s-expression (s for symbolic). Thus 42, #\c, (1 . 2), #(a b c), "Hello", (quote xyz), (string->number "16"), and (begin (display "Hello, World!") (newline)) are all s-expressions.
The reader will have noted that the Scheme example programs provided thus far are also s-expressions. This is true of all Scheme programs: Programs are data.
Thus, the character datum #\c is a program, or a form. We will use the more general term form instead of program, so that we can deal with program fragments too.
Scheme evaluates the form #\c to the value #\c, because #\c is self-evaluating. Not all s-expressions are self-evaluating. For instance the symbol s-expression xyz evaluates to the value held by the variable xyz. The list s-expression (string->number "16") evaluates to the number 16.
Not all s-expressions are valid programs. If you typed the dotted-pair s-expression (1 . 2) at the Scheme listener, you will get an error.
Scheme evaluates a list form by examining the first element, or head, of the form. If the head evaluates to a procedure, the rest of the form is evaluated to get the procedure's arguments, and the procedure is applied to the arguments.
If the head of the form is a special form, the evaluation proceeds in a manner idiosyncratic to that form. Some special forms we have already seen are begin, define, and set!. begin causes its subforms to be evaluated in order, the result of the entire form being the result of the last subform. define introduces and initializes a variable. set! changes the binding of a variable.
We have seen quite a few primitive Scheme procedures, eg, cons, string->list, and the like. Users can create their own procedures using the special form lambda. For example, the following defines a procedure that adds 2 to its argument:
(lambda (x) (+ x 2))
The first subform, (x), is the list of parameters. The remaining subform(s) constitute the procedure's body. This procedure can be called on an argument, just like a primitive procedure:
((lambda (x) (+ x 2)) 5)
=> 7
If we wanted to call this same procedure many times, we could create a replica using lambda each time, but we can do better. We can use a variable to hold the procedure value:
(define add2
(lambda (x) (+ x 2)))
We can then use the variable add2 each time we need a procedure for adding 2 to its argument:
(add2 4) => 6
(add2 9) => 11
The parameters of a lambda-procedure are specified by its first subform (the form immediately following the head, the symbol lambda). add2is a single-argument -- or unary -- procedure, and so its parameter list is the singleton list (x). The symbol x acts as a variable holding the procedure's argument. Each occurrence of x in the procedure's body refers to the procedure's argument. The variable x is said to be local to the procedure's body.
We can use 2-element lists for 2-argument procedures, and in general, n-element lists for n-argument procedures. The following is a 2-argument procedure that calculates the area of a rectangle. Its two arguments are the length and breadth of the rectangle.
(define area
(lambda (length breadth)
(* length breadth)))
Notice that area multiplies its arguments, and so does the primitive procedure *. We could have simply said:
(define area *)
Some procedures can be called at different times with different numbers of arguments. To do this, the lambda parameter list is replaced by a single symbol. This symbol acts as a variable that is bound to the list of the arguments that the procedure is called on.
In general, the lambda parameter list can be a list of the form (x ...), a symbol, or a dotted pair of the form (x ... . z). In the dotted-pair case, all the variables before the dot are bound to the corresponding arguments in the procedure call, with the single variable after the dot picking up all the remaining arguments as one list.
The Scheme procedure apply lets us call a procedure on a list of its arguments.
(define x '(1 2 3))
(apply + x)
=> 6
In general, apply takes a procedure, followed by a variable number of other arguments, the last of which must be a list. It constructs the argument list by prefixing the last argument with all the other (intervening) arguments. It then returns the result of calling the procedure on this argument list. Eg,
(apply + 1 2 3 x)
=> 12
We used the begin special form to bunch together a group of subforms that need to be evaluated in sequence. Many Scheme forms haveimplicit begins. For example, let's define a 3-argument procedure that displays its three arguments, with spaces between them. A possible definition is:
(define display3
(lambda (arg1 arg2 arg3)
(begin
(display arg1)
(display " ")
(display arg2)
(display " ")
(display arg3)
(newline))))
In Scheme, lambda-bodies are implicit begins. Thus, the begin in display3's body isn't needed, although it doesn't hurt. display3, more simply, is:
(define display3
(lambda (arg1 arg2 arg3)
(display arg1)
(display " ")
(display arg2)
(display " ")
(display arg3)
(newline)))
Like all languages, Scheme provides conditionals. The basic form is the if:
(if test-expression
then-branch
else-branch)
If test-expression evaluates to true (ie, any value other than #f), the then'' branch is evaluated. If not, theelse'' branch is evaluated. The ``else'' branch is optional.
(define p 80)
(if (> p 70)
'safe
'unsafe)
=> safe
(if (< p 90)
'low-pressure) ;no ``else'' branch
=> low-pressure
Scheme provides some other conditional forms for convenience. They can all be defined as macros (chap 8) that expand into if-expressions.
when and unless are convenient conditionals to use when only one branch (the then'' or theelse'' branch) of the basic conditional is needed.
(when (< (pressure tube) 60)
(open-valve tube)
(attach floor-pump tube)
(depress floor-pump 5)
(detach floor-pump tube)
(close-valve tube))
Assuming pressure of tube is less than 60, this conditional will attach floor-pump to tube and depress it 5 times. (attach and depressare some suitable procedures.)
The same program using if would be:
(if (< (pressure tube) 60)
(begin
(open-valve tube)
(attach floor-pump tube)
(depress floor-pump 5)
(detach floor-pump tube)
(close-valve tube)))
Note that when's branch is an implicit begin, whereas if requires an explicit begin if either of its branches has more than one form.
The same behavior can be written using unless as follows:
(unless (>= (pressure tube) 60)
(open-valve tube)
(attach floor-pump tube)
(depress floor-pump 5)
(detach floor-pump tube)
(close-valve tube))
Not all Schemes provide when and unless. If your Scheme does not have them, you can define them as macros (see chap 8).
The cond form is convenient for expressing nested if-expressions, where each ``else'' branch but the last introduces a new if. Thus, the form
(if (char<? c #\c) -1
(if (char=? c #\c) 0
1))
can be rewritten using cond as:
(cond ((char<? c #\c) -1)
((char=? c #\c) 0)
(else 1))
The cond is thus a multi-branch conditional. Each clause has a test and an associated action. The first test that succeeds triggers its associated action. The final else clause is chosen if no other test succeeded.
The cond actions are implicit begins.
A special case of the cond can be compressed into a case expression. This is when every test is a membership test.
(case c
((#\a) 1)
((#\b) 2)
((#\c) 3)
(else 4))
=> 3
The clause whose head contains the value of c is chosen.
Scheme provides special forms for boolean conjunction (and'') and disjunction (or''). (We have already seen (sec 2.1.1) Scheme's boolean negation not, which is a procedure.)
The special form and returns a true value if all its subforms are true. The actual value returned is the value of the final subform. If any of the subforms are false, and returns #f.
(and 1 2) => 2
(and #f 1) => #f
The special form or returns the value of its first true subform. If all the subforms are false, or returns #f.
(or 1 2) => 1
(or #f 1) => 1
Both and and or evaluate their subforms left-to-right. As soon as the result can be determined, and and or will ignore the remaining subforms.
(and 1 #f expression-guaranteed-to-cause-error)
=> #f
(or 1 #f expression-guaranteed-to-cause-error)
=> 1
Scheme's variables have lexical scope, ie, they are visible only to forms within a certain contiguous stretch of program text. The globalvariables we have seen thus far are no exception: Their scope is all program text, which is certainly contiguous.
We have also seen some examples of local variables. These were the lambda parameters, which get bound each time the procedure is called, and whose scope is that procedure's body. Eg,
(define x 9)
(define add2 (lambda (x) (+ x 2)))
x => 9
(add2 3) => 5
(add2 x) => 11
x => 9
Here, there is a global x, and there is also a local x, the latter introduced by procedure add2. The global x is always 9. The local x gets bound to 3 in the first call to add2 and to the value of the global x, ie, 9, in the second call to add2. When the procedure calls return, the global xcontinues to be 9.
The form set! modifies the lexical binding of a variable.
(set! x 20)
modifies the global binding of x from 9 to 20, because that is the binding of x that is visible to set!. If the set! was inside add2's body, it would have modified the local x:
(define add2
(lambda (x)
(set! x (+ x 2))
x))
The set! here adds 2 to the local variable x, and the procedure returns this new value of the local x. (In terms of effect, this procedure is indistinguishable from the previous add2.) We can call add2 on the global x, as before:
(add2 x) => 22
(Remember global x is now 20, not 9!)
The set! inside add2 affects only the local variable used by add2. Although the local variable x got its binding from the global x, the latter is unaffected by the set! to the local x.
x => 20
Note that we had all this discussion because we used the same identifier for a local variable and a global variable. In any text, an identifier named x refers to the lexically closest variable named x. This will shadow any outer or global x's. Eg, in add2, the parameter x shadows the global x.
A procedure's body can access and modify variables in its surrounding scope provided the procedure's parameters don't shadow them. This can give some interesting programs. Eg,
(define counter 0)
(define bump-counter
(lambda ()
(set! counter (+ counter 1))
counter))
The procedure bump-counter is a zero-argument procedure (also called a thunk). It introduces no local variables, and thus cannot shadow anything. Each time it is called, it modifies the global variable counter -- it increments it by 1 -- and returns its current value. Here are some successive calls to bump-counter:
(bump-counter) => 1
(bump-counter) => 2
(bump-counter) => 3
Local variables can be introduced without explicitly creating a procedure. The special form let introduces a list of local variables for use within its body:
(let ((x 1)
(y 2)
(z 3))
(list x y z))
=> (1 2 3)
As with lambda, within the let-body, the local x (bound to 1) shadows the global x (which is bound to 20).
The local variable initializations -- x to 1; y to 2; z to 3 -- are not considered part of the let body. Therefore, a reference to x in the initialization will refer to the global, not the local x:
(let ((x 1)
(y x))
(+ x y))
=> 21
This is because x is bound to 1, and y is bound to the global x, which is 20.
Sometimes, it is convenient to have let's list of lexical variables be introduced in sequence, so that the initialization of a later variable occurs in the lexical scope of earlier variables. The form let* does this:
(let* ((x 1)
(y x))
(+ x y))
=> 2
The x in y's initialization refers to the x just above. The example is entirely equivalent to -- and is in fact intended to be a convenient abbreviation for -- the following program with nested lets:
(let ((x 1))
(let ((y x))
(+ x y)))
=> 2
The values bound to lexical variables can be procedures:
(let ((cons (lambda (x y) (+ x y))))
(cons 1 2))
=> 3
Inside this let body, the lexical variable cons adds its arguments. Outside, cons continues to create dotted pairs.
A lexical variable is visible throughout its scope, provided it isn't shadowed. Sometimes, it is helpful to temporarily set a lexical variable to a certain value. For this, we use the form fluid-let.2
(fluid-let ((counter 99))
(display (bump-counter)) (newline)
(display (bump-counter)) (newline)
(display (bump-counter)) (newline))
This looks similar to a let, but instead of shadowing the global variable counter, it temporarily sets it to 99 before continuing with thefluid-let body. Thus the displays in the body produce
100
101
102
After the fluid-let expression has evaluated, the global counter reverts to the value it had before the fluid-let.
counter => 3
Note that fluid-let has an entirely different effect from let. fluid-let does not introduce new lexical variables like let does. It modifies the bindings of existing lexical variables, and the modification ceases as soon as the fluid-let does.
To drive home this point, consider the program
(let ((counter 99))
(display (bump-counter)) (newline)
(display (bump-counter)) (newline)
(display (bump-counter)) (newline))
which substitutes let for fluid-let in the previous example. The output is now
4
5
6
Ie, the global counter, which is initially 3, is updated by each call to bump-counter. The new lexical variable counter, with its initialization of 99, has no impact on the calls to bump-counter, because although the calls to bump-counter are within the scope of this local counter, the body of bump-counter isn't. The latter continues to refer to the global counter, whose final value is 6.
counter => 6
2 fluid-let is a nonstandard special form. See sec 8.3 for a definition of fluid-let in Scheme.
A procedure body can contain calls to other procedures, not least itself:
(define factorial
(lambda (n)
(if (= n 0) 1
(* n (factorial (- n 1))))))
This recursive procedure calculates the factorial of a number. If the number is 0, the answer is 1. For any other number n, the procedure uses itself to calculate the factorial of n - 1, multiplies that subresult by n, and returns the product.
Mutually recursive procedures are also possible. The following predicates for evenness and oddness use each other:
(define is-even?
(lambda (n)
(if (= n 0) #t
(is-odd? (- n 1)))))
(define is-odd?
(lambda (n)
(if (= n 0) #f
(is-even? (- n 1)))))
These definitions are offered here only as simple illustrations of mutual recursion. Scheme already provides the primitive predicates even?and odd?.
If we wanted the above procedures as local variables, we could try to use a let form:
(let ((local-even? (lambda (n)
(if (= n 0) #t
(local-odd? (- n 1)))))
(local-odd? (lambda (n)
(if (= n 0) #f
(local-even? (- n 1))))))
(list (local-even? 23) (local-odd? 23)))
This won't quite work, because the occurrences of local-even? and local-odd? in the initializations don't refer to the lexical variables themselves. Changing the let to a let* won't work either, for while the local-even? inside local-odd?'s body refers to the correct procedure value, the local-odd? in local-even?'s body still points elsewhere.
To solve problems like this, Scheme provides the form letrec:
(letrec ((local-even? (lambda (n)
(if (= n 0) #t
(local-odd? (- n 1)))))
(local-odd? (lambda (n)
(if (= n 0) #f
(local-even? (- n 1))))))
(list (local-even? 23) (local-odd? 23)))
The lexical variables introduced by a letrec are visible not only in the letrec-body but also within all the initializations. letrec is thus tailor-made for defining recursive and mutually recursive local procedures.
A recursive procedure defined using letrec can describe loops. Let's say we want to display a countdown from 10:
(letrec ((countdown (lambda (i)
(if (= i 0) 'liftoff
(begin
(display i)
(newline)
(countdown (- i 1)))))))
(countdown 10))
This outputs on the console the numbers 10 down to 1, and returns the result liftoff.
Scheme allows a variant of let called named let to write this kind of loop more compactly:
(let countdown ((i 10))
(if (= i 0) 'liftoff
(begin
(display i)
(newline)
(countdown (- i 1)))))
Note the presence of a variable identifying the loop immediately after the let. This program is equivalent to the one written with letrec. You may consider the named let to be a macro (chap 8) expanding to the letrec form.
countdown defined above is really a recursive procedure. Scheme can define loops only through recursion. There are no special looping or iteration constructs.
Nevertheless, the loop as defined above is a genuine loop, in exactly the same way that other languages bill their loops. Ie, Scheme takes special care to ensure that recursion of the type used above will not generate the procedure call/return overhead.
Scheme does this by a process called tail-call elimination. If you look closely at the countdown procedure, you will note that when the recursive call occurs in countdown's body, it is the tail call, or the very last thing done -- each invocation of countdown either does not call itself, or when it does, it does so as its very last act. To a Scheme implementation, this makes the recursion indistinguishable from iteration. So go ahead, use recursion to write loops. It's safe.
Here's another example of a useful tail-recursive procedure:
(define list-position
(lambda (o l)
(let loop ((i 0) (l l))
(if (null? l) #f
(if (eqv? (car l) o) i
(loop (+ i 1) (cdr l)))))))
list-position finds the index of the first occurrence of the object o in the list l. If the object is not found in the list, the procedure returns#f.
Here's yet another tail-recursive procedure, one that reverses its argument list ``in place'', ie, by mutating the contents of the existing list, and without allocating a new one:
(define reverse!
(lambda (s)
(let loop ((s s) (r '()))
(if (null? s) r
(let ((d (cdr s)))
(set-cdr! s r)
(loop d s))))))
(reverse! is a useful enough procedure that it is provided primitively in many Scheme dialects, eg, MzScheme and Guile.)
For some numerical examples of recursion (including iteration), see Appendix C.
A special kind of iteration involves repeating the same action for each element of a list. Scheme offers two procedures for this situation: mapand for-each.
The map procedure applies a given procedure to every element of a given list, and returns the list of the results. Eg,
(map add2 '(1 2 3))
=> (3 4 5)
The for-each procedure also applies a procedure to each element in a list, but returns void. The procedure application is done purely for any side-effects it may cause. Eg,
(for-each display
(list "one " "two " "buckle my shoe"))
has the side-effect of displaying the strings (in the order they appear) on the console.
The procedures applied by map and for-each need not be one-argument procedures. For example, given an n-argument procedure, map takesn lists and applies the procedure to every set of n of arguments selected from across the lists. Eg,
(map cons '(1 2 3) '(10 20 30))
=> ((1 . 10) (2 . 20) (3 . 30))
(map + '(1 2 3) '(10 20 30))
=> (11 22 33)
Scheme has input/output (I/O) procedures that will let you read from an input port or write to an output port. Ports can be associated with the console, files or strings.
Scheme's reader procedures take an optional input port argument. If the port is not specified, the current input port (usually the console) is assumed.
Reading can be character-, line- or s-expression-based. Each time a read is performed, the port's state changes so that the next read will read material following what was already read. If the port has no more material to be read, the reader procedure returns a specific datum called the end-of-file or eof object. This datum is the only value that satisfies the eof-object? predicate.
The procedure read-char reads the next character from the port. read-line reads the next line, returning it as a string (the final newline is not included). The procedure read reads the next s-expression.
Scheme's writer procedures take the object that is to be written and an optional output port argument. If the port is not specified, the current output port (usually the console) is assumed.
Writing can be character- or s-expression-based.
The procedure write-char writes the given character (without the #) to the output port.
The procedures write and display both write the given s-expression to the port, with one difference: write attempts to use a machine-readable format and display doesn't. Eg, write uses double quotes for strings and the #\ syntax for characters. display doesn't.
The procedure newline starts a new line on the output port.
Scheme's I/O procedures do not need a port argument if the port happens to be standard input or standard output. However, if you need these ports explicitly, the zero-argument procedures current-input-port and current-output-port furnish them. Thus,
(display 9)
(display 9 (current-output-port))
have the same behavior.
A port is associated with a file by opening the file. The procedure open-input-file takes a filename argument and returns a new input port associated with it. The procedure open-output-file takes a filename argument and returns a new output port associated with it. It is an error to open an input file that doesn't exist, or to open an output file that already exists.
After you have performed I/O on a port, you should close it with close-input-port or close-output-port.
In the following, assume the file hello.txt contains the single word hello.
(define i (open-input-file "hello.txt"))
(read-char i)
=> #\h
(define j (read i))
j
=> ello
Assume the file greeting.txt does not exist before the following programs are fed to the listener:
(define o (open-output-file "greeting.txt"))
(display "hello" o)
(write-char #\space o)
(display 'world o)
(newline o)
(close-output-port o)
The file greeting.txt will now contain the line:
hello world
Scheme supplies the procedures call-with-input-file and call-with-output-file that will take care of opening a port and closing it after you're done with it.
The procedure call-with-input-file takes a filename argument and a procedure. The procedure is applied to an input port opened on the file. When the procedure completes, its result is returned after ensuring that the port is closed.
(call-with-input-file "hello.txt"
(lambda (i)
(let* ((a (read-char i))
(b (read-char i))
(c (read-char i)))
(list a b c))))
=> (#\h #\e #\l)
The procedure call-with-output-file does the analogous services for an output file.
It is often convenient to associate ports with strings. Thus, the procedure open-input-string associates a port with a given string. Reader procedures on this port will read off the string:
(define i (open-input-string "hello world"))
(read-char i)
=> #\h
(read i)
=> ello
(read i)
=> world
The procedure open-output-string creates an output port that will eventually be used to create a string:
(define o (open-output-string))
(write 'hello o)
(write-char #\, o)
(display " " o)
(display "world" o)
You can now use the procedure get-output-string to get the accumulated string in the string port o:
(get-output-string o)
=> "hello, world"
String ports need not be explicitly closed.
We have already seen the procedure load that loads files containing Scheme code. Loading a file consists in evaluating in sequence every Scheme form in the file. The pathname argument given to load is reckoned relative to the current working directory of Scheme, which is normally the directory in which the Scheme executable was called.
Files can load other files, and this is useful in a large program spanning many files. Unfortunately, unless full pathnames are used, the argument file of a load is dependent on Scheme's current directory. Supplying full pathnames is not always convenient, because we would like to move the program files as a unit (preserving their relative pathnames), perhaps to many different machines.
MzScheme provides the load-relative procedure that greatly helps in fixing the files to be loaded. load-relative, like load, takes a pathname argument. When a load-relative call occurs in a file foo.scm, the path of its argument is reckoned from the directory of the calling file foo.scm. In particular, this pathname is reckoned independent of Scheme's current directory, and thus allows convenient multifile program development.
Users can create their own special forms by defining macros. A macro is a symbol that has a transformer procedure associated with it. When Scheme encounters a macro-expression -- ie, a form whose head is a macro -- , it applies the macro's transformer to the subforms in the macro-expression, and evaluates the result of the transformation.
Ideally, a macro specifies a purely textual transformation from code text to other code text. This kind of transformation is useful for abbreviating an involved and perhaps frequently occurring textual pattern.
A macro is defined using the special form define-macro (but see sec A.3).3 For example, if your Scheme lacks the conditional special formwhen, you could define when as the following macro:
(define-macro when
(lambda (test . branch)
(list 'if test
(cons 'begin branch))))
This defines a when-transformer that would convert a when-expression into the equivalent if-expression. With this macro definition in place, the when-expression
(when (< (pressure tube) 60)
(open-valve tube)
(attach floor-pump tube)
(depress floor-pump 5)
(detach floor-pump tube)
(close-valve tube))
will be converted to another expression, the result of applying the when-transformer to the when-expression's subforms:
(apply
(lambda (test . branch)
(list 'if test
(cons 'begin branch)))
'((< (pressure tube) 60)
(open-valve tube)
(attach floor-pump tube)
(depress floor-pump 5)
(detach floor-pump tube)
(close-valve tube)))
The transformation yields the list
(if (< (pressure tube) 60)
(begin
(open-valve tube)
(attach floor-pump tube)
(depress floor-pump 5)
(detach floor-pump tube)
(close-valve tube)))
Scheme will then evaluate this expression, as it would any other.
As an additional example, here is the macro-definition for when's counterpart unless:
(define-macro unless
(lambda (test . branch)
(list 'if
(list 'not test)
(cons 'begin branch))))
Alternatively, we could invoke when inside unless's definition:
(define-macro unless
(lambda (test . branch)
(cons 'when
(cons (list 'not test) branch))))
Macro expansions can refer to other macros.
A macro transformer takes some s-expressions and produces an s-expression that will be used as a form. Typically this output is a list. In ourwhen example, the output list is created using
(list 'if test
(cons 'begin branch))
where test is bound to the macro's first subform, ie,
(< (pressure tube) 60)
and branch to the rest of the macro's subforms, ie,
((open-valve tube)
(attach floor-pump tube)
(depress floor-pump 5)
(detach floor-pump tube)
(close-valve tube))
Output lists can be quite complicated. It is easy to see that a more ambitious macro than when could lead to quite an elaborate construction process for the output list. In such cases, it is more convenient to specify the macro's output form as a template, with the macro arguments inserted at appropriate places to fill out the template for each particular use of the macro. Scheme provides the backquote syntax to specify such templates. Thus the expression
(list 'IF test
(cons 'BEGIN branch))
is more conveniently written as
`(IF ,test
(BEGIN ,@branch))
We can refashion the when macro-definition as:
(define-macro when
(lambda (test . branch)
`(IF ,test
(BEGIN ,@branch))))
Note that the template format, unlike the earlier list construction, gives immediate visual indication of the shape of the output list. The backquote () introduces a template for a list. The elements of the template appear verbatim in the resulting list, except when they are prefixed by a comma (,') or a comma-splice (`,@'). (For the purpose of illustration, we have written the verbatim elements of the template in UPPER-CASE.)
The comma and the comma-splice are used to insert the macro arguments into the template. The comma inserts the result of evaluating its following expression. The comma-splice inserts the result of evaluating its following expression after splicing it, ie, it removes the outermost set of parentheses. (This implies that an expression introduced by comma-splice must be a list.)
In our example, given the values that test and branch are bound to, it is easy to see that the template will expand to the required
(IF (< (pressure tube) 60)
(BEGIN
(open-valve tube)
(attach floor-pump tube)
(depress floor-pump 5)
(detach floor-pump tube)
(close-valve tube)))
A two-argument disjunction form, my-or, could be defined as follows:
(define-macro my-or
(lambda (x y)
`(if ,x ,x ,y)))
my-or takes two arguments and returns the value of the first of them that is true (ie, non-#f). In particular, the second argument is evaluated only if the first turns out to be false.
(my-or 1 2)
=> 1
(my-or #f 2)
=> 2
There is a problem with the my-or macro as it is written. It re-evaluates the first argument if it is true: once in the if-test, and once again in the ``then'' branch. This can cause undesired behavior if the first argument were to contain side-effects, eg,
(my-or
(begin
(display "doing first argument")
(newline)
#t)
2)
displays "doing first argument" twice.
This can be avoided by storing the if-test result in a local variable:
(define-macro my-or
(lambda (x y)
`(let ((temp ,x))
(if temp temp ,y))))
This is almost OK, except in the case where the second argument happens to contain the same identifier temp as used in the macro definition. Eg,
(define temp 3)
(my-or #f temp)
=> #f
Surely it should be 3! The fiasco happens because the macro uses a local variable temp to store the value of the first argument (#f) and the variable temp in the second argument got captured by the temp introduced by the macro.
To avoid this, we need to be careful in choosing local variables inside macro definitions. We could choose outlandish names for such variables and hope fervently that nobody else comes up with them. Eg,
(define-macro my-or
(lambda (x y)
`(let ((+temp ,x))
(if +temp +temp ,y))))
This will work given the tacit understanding that +temp will not be used by code outside the macro. This is of course an understanding waiting to be disillusioned.
A more reliable, if verbose, approach is to use generated symbols that are guaranteed not to be obtainable by other means. The proceduregensym generates unique symbols each time it is called. Here is a safe definition for my-or using gensym:
(define-macro my-or
(lambda (x y)
(let ((temp (gensym)))
`(let ((,temp ,x))
(if ,temp ,temp ,y)))))
In the macros defined in this document, in order to be concise, we will not use the gensym approach. Instead, we will consider the point about variable capture as having been made, and go ahead with the less cluttered +-as-prefix approach. We will leave it to the astute reader to remember to convert these +-identifiers into gensyms in the manner outlined above.
8.3 fluid-let
Here is a definition of a rather more complicated macro, fluid-let (sec 5.2). fluid-let specifies temporary bindings for a set of already existing lexical variables. Given a fluid-let expression such as
(fluid-let ((x 9) (y (+ y 1)))
(+ x y))
we want the expansion to be
(let ((OLD-X x) (OLD-Y y))
(set! x 9)
(set! y (+ y 1))
(let ((RESULT (begin (+ x y))))
(set! x OLD-X)
(set! y OLD-Y)
RESULT))
where we want the identifiers OLD-X, OLD-Y, and RESULT to be symbols that will not capture variables in the expressions in the fluid-letform.
Here is how we go about fashioning a fluid-let macro that implements what we want:
(define-macro fluid-let
(lambda (xexe . body)
(let ((xx (map car xexe))
(ee (map cadr xexe))
(old-xx (map (lambda (ig) (gensym)) xexe))
(result (gensym)))
(let ,(map (lambda (old-x x)(,old-x ,x))
old-xx xx)
,@(map (lambda (x e)
(set! ,x ,e)) xx ee) (let ((,result (begin ,@body))) ,@(map (lambda (x old-x)(set! ,x ,old-x))
xx old-xx)
,result)))))
The macro's arguments are: xexe, the list of variable/expression pairs introduced by the fluid-let; and body, the list of expressions in the body of the fluid-let. In our example, these are ((x 9) (y (+ y 1))) and ((+ x y)) respectively.
The macro body introduces a bunch of local variables: xx is the list of the variables extracted from the variable/expression pairs. ee is the corresponding list of expressions. old-xx is a list of fresh identifiers, one for each variable in xx. These are used to store the incoming values of the xx, so we can revert the xx back to them once the fluid-let body has been evaluated. result is another fresh identifier, used to store the value of the fluid-let body. In our example, xx is (x y) and ee is (9 (+ y 1)). Depending on how your system implements gensym,old-xx might be the list (GEN-63 GEN-64), and result might be GEN-65.
The output list is created by the macro for our given example looks like
(let ((GEN-63 x) (GEN-64 y))
(set! x 9)
(set! y (+ y 1))
(let ((GEN-65 (begin (+ x y))))
(set! x GEN-63)
(set! y GEN-64)
GEN-65))
which matches our requirement.
3 MzScheme provides define-macro via the defmacro library. Use (require (lib "defmacro.ss")) to load this library.
Chapter 9
Structures
Data that are naturally grouped are called structures. One can use Scheme's compound data types, eg, vectors or lists, to represent structures. Eg, let's say we are dealing with grouped data relevant to a (botanical) tree. The individual elements of the data, or fields, could be: height,girth, age, leaf-shape, and leaf-color, making a total of 5 fields. Such data could be represented as a 5-element vector. The fields could be accessed using vector-ref and modified using vector-set!. Nevertheless, we wouldn't want to be saddled with the burden of remembering which vector index corresponds to which field. That would be a thankless and error-prone activity, especially if fields get excluded or included over the course of time.
We will therefore use a Scheme macro defstruct to define a structure data type, which is basically a vector, but which comes with an appropriate suite of procedures for creating instances of the structure, and for accessing and modifying its fields. Thus, our tree structure could be defined as:
(defstruct tree height girth age leaf-shape leaf-color)
This gives us a constructor procedure named make-tree; accessor procedures for each field, named tree.height, tree.girth, etc; and modifier procedures for each field, named set!tree.height, set!tree.girth, etc. The constructor is used as follows:
(define coconut
(make-tree 'height 30
'leaf-shape 'frond
'age 5))
The constructor's arguments are in the form of twosomes, a field name followed by its initialization. The fields can occur in any order, and may even be missing, in which case their value is undefined.
The accessor procedures are invoked as follows:
(tree.height coconut) => 30
(tree.leaf-shape coconut) => frond
(tree.girth coconut) =>
The tree.girth accessor returns an undefined value, because we did not specify girth for the coconut tree.
The modifier procedures are invoked as follows:
(set!tree.height coconut 40)
(set!tree.girth coconut 10)
If we now access these fields using the corresponding accessors, we will get the new values:
(tree.height coconut) => 40
(tree.girth coconut) => 10
9.1 Default initializations
We can have some initializations done during the definition of the structure itself, instead of per instance. Thus, we could postulate that leaf-shape and leaf-color are by default frond and green respectively. We can always override these defaults by providing explicit initialization in the make-tree call, or by using a field modifier after the structure instance has been created:
(defstruct tree height girth age
(leaf-shape 'frond)
(leaf-color 'green))
(define palm (make-tree 'height 60))
(tree.height palm)
=> 60
(tree.leaf-shape palm)
=> frond
(define plantain
(make-tree 'height 7
'leaf-shape 'sheet))
(tree.height plantain)
=> 7
(tree.leaf-shape plantain)
=> sheet
(tree.leaf-color plantain)
=> green
9.2 defstruct defined
The defstruct macro definition follows:
(define-macro defstruct
(lambda (s . ff)
(let ((s-s (symbol->string s)) (n (length ff)))
(let* ((n+1 (+ n 1))
(vv (make-vector n+1)))
(let loop ((i 1) (ff ff))
(if (<= i n)
(let ((f (car ff)))
(vector-set! vv i
(if (pair? f) (cadr f) '(if #f #f)))
(loop (+ i 1) (cdr ff)))))
(let ((ff (map (lambda (f) (if (pair? f) (car f) f))
ff)))
(begin (define ,(string->symbol (string-append "make-" s-s)) (lambda fvfv (let ((st (make-vector ,n+1)) (ff ',ff)) (vector-set! st 0 ',s) ,@(let loop ((i 1) (r '())) (if (>= i n+1) r (loop (+ i 1) (cons(vector-set! st ,i
,(vector-ref vv i))
r))))
(let loop ((fvfv fvfv))
(if (not (null? fvfv))
(begin
(vector-set! st
(+ (list-position (car fvfv) ff)
1)
(cadr fvfv))
(loop (cddr fvfv)))))
st)))
,@(let loop ((i 1) (procs '()))
(if (>= i n+1) procs
(loop (+ i 1)
(let ((f (symbol->string
(list-ref ff (- i 1)))))
(cons
(define ,(string->symbol (string-append s-s "." f)) (lambda (x) (vector-ref x ,i))) (cons(define ,(string->symbol
(string-append
"set!" s-s "." f))
(lambda (x v)
(vector-set! x ,i v)))
procs))))))
(define ,(string->symbol (string-append s-s "?"))
(lambda (x)
(and (vector? x)
(eqv? (vector-ref x 0) ',s))))))))))
Chapter 10
Alists and tables
An association list, or alist, is a Scheme list of a special format. Each element of the list is a cons cell, the car of which is called a key, the cdr being the value associated with the key. Eg,
((a . 1) (b . 2) (c . 3))
The procedure call (assv k al) finds the cons cell associated with key k in alist al. The keys of the alist are compared against the given kusing the equality predicate eqv?. In general, though we may want a different predicate for key comparison. For instance, if the keys were case-insensitive strings, the predicate eqv? is not very useful.
We now define a structure called table, which is a souped-up alist that allows user-defined predicates on its keys. Its fields are equ andalist.
(defstruct table (equ eqv?) (alist '()))
(The default predicate is eqv? -- as for an ordinary alist -- and the alist is initially empty.)
We will use the procedure table-get to get the value (as opposed to the cons cell) associated with a given key. table-get takes a table and key arguments, followed by an optional default value that is returned if the key was not found in the table:
(define table-get
(lambda (tbl k . d)
(let ((c (lassoc k (table.alist tbl) (table.equ tbl))))
(cond (c (cdr c))
((pair? d) (car d))))))
The procedure lassoc, used in table-get, is defined as:
(define lassoc
(lambda (k al equ?)
(let loop ((al al))
(if (null? al) #f
(let ((c (car al)))
(if (equ? (car c) k) c
(loop (cdr al))))))))
The procedure table-put! is used to update a key's value in the given table:
(define table-put!
(lambda (tbl k v)
(let ((al (table.alist tbl)))
(let ((c (lassoc k al (table.equ tbl))))
(if c (set-cdr! c v)
(set!table.alist tbl (cons (cons k v) al)))))))
The procedure table-for-each calls the given procedure on every key/value pair in the table
(define table-for-each
(lambda (tbl p)
(for-each
(lambda (c)
(p (car c) (cdr c)))
(table.alist tbl))))
Chapter 11
System interface
Useful Scheme programs often need to interact with the underlying operating system.
11.1 Checking for and deleting files
file-exists? checks if its argument string names a file. delete-file deletes its argument file. These procedures are not part of the Scheme standard, but are available in most implementations. These procedures work reliably only for files that are not directories. (Their behavior on directories is dialect-specific.)
file-or-directory-modify-seconds returns the time when its argument file or directory was last modified. Time is reckoned in seconds from 12 AM GMT, 1 January 1970. Eg,
(file-or-directory-modify-seconds "hello.scm")
=> 893189629
assuming that the file hello.scm was last messed with sometime on 21 April 1998.
11.2 Calling operating-system commands
The system procedure executes its argument string as an operating-system command.4 It returns true if the command executed successfully with an exit status 0, and false if it failed to execute or exited with a non-zero status. Any output generated by the command goes to standard output.
(system "ls")
;lists current directory
(define fname "spot")
(system (string-append "test -f " fname))
;tests if file `spot' exists
(system (string-append "rm -f " fname))
;removes `spot'
The last two forms are equivalent to
(file-exists? fname)
(delete-file fname)
11.3 Environment variables
The getenv procedure returns the setting of an operating-system environment variable. Eg,
(getenv "HOME")
=> "/home/dorai"
(getenv "SHELL")
=> "/bin/bash"
4 MzScheme provides the system procedure via the process library. Use (require (lib "process.ss")) to load this library.
Chapter 12
Objects and classes
A class describes a collection of objects that share behavior. The objects described by a class are called the instances of the class. The class specifies the names of the slots that the instance has, although it is up to the instance to populate these slots with particular values. The class also specifies the methods that can be applied to its instances. Slot values can be anything, but method values must be procedures.
Classes are hierarchical. Thus, a class can be a subclass of another class, which is called its superclass. A subclass not only has its own directslots and methods, but also inherits all the slots and methods of its superclass. If a class has a slot or method that has the same name as its superclass's, then the subclass's slot or method is the one that is retained.
12.1 A simple object system
Let us now implement a basic object system in Scheme. We will allow only one superclass per class (single inheritance). If we don't want to specify a superclass, we will use #t as a ``zero'' superclass, one that has neither slots nor methods. The superclass of #t is deemed to be itself.
As a first approximation, it is useful to define classes using a struct called standard-class, with fields for the slot names, the superclass, and the methods. The first two fields we will call slots and superclass respectively. We will use two fields for methods, a method-names field that will hold the list of names of the class's methods, and a method-vector field that will hold the vector of the values of the class's methods.5 Here is the definition of the standard-class:
(defstruct standard-class
slots superclass method-names method-vector)
We can use make-standard-class, the maker procedure of standard-class, to create a new class. Eg,
(define trivial-bike-class
(make-standard-class
'superclass #t
'slots '(frame parts size)
'method-names '()
'method-vector #()))
This is a very simple class. More complex classes will have non-trivial superclasses and methods, which will require a lot of standard initialization that we would like to hide within the class creation process. We will therefore define a macro called create-class that will make the appropriate call to make-standard-class.
(define-macro create-class
(lambda (superclass slots . methods)
(create-class-proc ,superclass (list ,@(map (lambda (slot)',slot) slots))
(list ,@(map (lambda (method) ',(car method)) methods)) (vector ,@(map (lambda (method),(cadr method)) methods)))))
We will defer the definition of the create-class-proc procedure to later.
The procedure make-instance creates an instance of a class by generating a fresh vector based on information enshrined in the class. The format of the instance vector is very simple: Its first element will refer to the class, and its remaining elements will be slot values. make-instance's arguments are the class followed by a sequence of twosomes, where each twosome is a slot name and the value it assumes in the instance.
(define make-instance
(lambda (class . slot-value-twosomes)
;Find `n', the number of slots in `class'.
;Create an instance vector of length `n + 1',
;because we need one extra element in the instance
;to contain the class.
(let* ((slotlist (standard-class.slots class))
(n (length slotlist))
(instance (make-vector (+ n 1))))
(vector-set! instance 0 class)
;Fill each of the slots in the instance
;with the value as specified in the call to
;`make-instance'.
(let loop ((slot-value-twosomes slot-value-twosomes))
(if (null? slot-value-twosomes) instance
(let ((k (list-position (car slot-value-twosomes)
slotlist)))
(vector-set! instance (+ k 1)
(cadr slot-value-twosomes))
(loop (cddr slot-value-twosomes))))))))
Here is an example of instantiating a class:
(define my-bike
(make-instance trivial-bike-class
'frame 'cromoly
'size '18.5
'parts 'alivio))
This binds my-bike to the instance
where
The procedure class-of returns the class of an instance:
(define class-of
(lambda (instance)
(vector-ref instance 0)))
This assumes that class-of's argument will be a class instance, ie, a vector whose first element points to some instantiation of the standard-class. We probably want to make class-of return an appropriate value for any kind of Scheme object we feed to it.
(define class-of
(lambda (x)
(if (vector? x)
(let ((n (vector-length x)))
(if (>= n 1)
(let ((c (vector-ref x 0)))
(if (standard-class? c) c #t))
#t))
#t)))
The class of a Scheme object that isn't created using standard-class is deemed to be #t, the zero class.
The procedures slot-value and set!slot-value access and mutate the values of a class instance:
(define slot-value
(lambda (instance slot)
(let* ((class (class-of instance))
(slot-index
(list-position slot (standard-class.slots class))))
(vector-ref instance (+ slot-index 1)))))
(define set!slot-value
(lambda (instance slot new-val)
(let* ((class (class-of instance))
(slot-index
(list-position slot (standard-class.slots class))))
(vector-set! instance (+ slot-index 1) new-val))))
We are now ready to tackle the definition of create-class-proc. This procedure takes a superclass, a list of slots, a list of method names, and a vector of methods and makes the appropriate call to make-standard-class. The only tricky part is the value to be given to the slotsfield. It can't be just the slots argument supplied via create-class, for a class must include the slots of its superclass as well. We must append the supplied slots to the superclass's slots, making sure that we don't have duplicate slots.
(define create-class-proc
(lambda (superclass slots method-names method-vector)
(make-standard-class
'superclass superclass
'slots
(let ((superclass-slots
(if (not (eqv? superclass #t))
(standard-class.slots superclass)
'())))
(if (null? superclass-slots) slots
(delete-duplicates
(append slots superclass-slots))))
'method-names method-names
'method-vector method-vector)))
The procedure delete-duplicates called on a list s, returns a new list that only includes the last occurrence of each element of s.
(define delete-duplicates
(lambda (s)
(if (null? s) s
(let ((a (car s)) (d (cdr s)))
(if (memv a d) (delete-duplicates d)
(cons a (delete-duplicates d)))))))
Now to the application of methods. We invoke the method on an instance by using the procedure send. send's arguments are the method name, followed by the instance, followed by any arguments the method has in addition to the instance itself. Since methods are stored in the instance's class instead of the instance itself, send will search the instance's class for the method. If the method is not found there, it is looked for in the class's superclass, and so on further up the superclass chain:
(define send
(lambda (method instance . args)
(let ((proc
(let loop ((class (class-of instance)))
(if (eqv? class #t) (error 'send)
(let ((k (list-position
method
(standard-class.method-names class))))
(if k
(vector-ref (standard-class.method-vector class) k)
(loop (standard-class.superclass class))))))))
(apply proc instance args))))
We can now define some more interesting classes:
(define bike-class
(create-class
#t
(frame size parts chain tires)
(check-fit (lambda (me inseam)
(let ((bike-size (slot-value me 'size))
(ideal-size (* inseam 3/5)))
(let ((diff (- bike-size ideal-size)))
(cond ((<= -1 diff 1) 'perfect-fit)
((<= -2 diff 2) 'fits-well)
((< diff -2) 'too-small)
((]]
]]>
diff 2) 'too-big))))))))
Here, bike-class includes a method check-fit, that takes a bike and an inseam measurement and reports on the fit of the bike for a person of that inseam.
Let's redefine my-bike:
(define my-bike
(make-instance bike-class
'frame 'titanium ; I wish
'size 21
'parts 'ultegra
'chain 'sachs
'tires 'continental))
To check if this will fit someone with inseam 32:
(send 'check-fit my-bike 32)
We can subclass bike-class.
(define mtn-bike-class
(create-class
bike-class
(suspension)
(check-fit (lambda (me inseam)
(let ((bike-size (slot-value me 'size))
(ideal-size (- (* inseam 3/5) 2)))
(let ((diff (- bike-size ideal-size)))
(cond ((<= -2 diff 2) 'perfect-fit)
((<= -4 diff 4) 'fits-well)
((< diff -4) 'too-small)
((]]
]]>
diff 4) 'too-big))))))))
mtn-bike-class adds a slot called suspension and uses a slightly different definition for the method check-fit.
12.2 Classes are instances too
It cannot have escaped the astute reader that classes themselves look like they could be the instances of some class (a metaclass, if you will). Note that all classes have some common behavior: each of them has slots, a superclass, a list of method names, and a method vector. make-instance looks like it could be their shared method. This suggests that we could specify this common behavior by another class (which itself should, of course, be a class instance too).
In concrete terms, we could rewrite our class implementation to itself make use of the object-oriented approach, provided we make sure we don't run into chicken-and-egg problems. In effect, we will be getting rid of the class struct and its attendant procedures and rely on the rest of the machinery to define classes as objects.
Let us identify standard-class as the class of which other classes are instances of. In particular, standard-class must be an instance of itself. What should standard-class look like?
We know standard-class is an instance, and we are representing instances by vectors. So it is a vector whose first element holds its class, ie, itself, and whose remaining elements are slot values. We have identified four slots that all classes must have, so standard-class is a 5-element vector.
(define standard-class
(vector 'value-of-standard-class-goes-here
(list 'slots
'superclass
'method-names
'method-vector)
#t
'(make-instance)
(vector make-instance)))
Note that the standard-class vector is incompletely filled in: the symbol value-of-standard-class-goes-here functions as a placeholder. Now that we have defined a standard-class value, we can use it to identify its own class, which is itself:
(vector-set! standard-class 0 standard-class)
Note that we cannot rely on procedures based on the class struct anymore. We should replace all calls of the form
(standard-class? x)
(standard-class.slots c)
(standard-class.superclass c)
(standard-class.method-names c)
(standard-class.method-vector c)
(make-standard-class ...)
by
(and (vector? x) (eqv? (vector-ref x 0) standard-class))
(vector-ref c 1)
(vector-ref c 2)
(vector-ref c 3)
(vector-ref c 4)
(send 'make-instance standard-class ...)
12.3 Multiple inheritance
It is easy to modify the object system to allow classes to have more than one superclass. We redefine the standard-class to have a slot called class-precedence-list instead of superclass. The class-precedence-list of a class is the list of all its superclasses, not just the direct superclasses specified during the creation of the class with create-class. The name implies that the superclasses are listed in a particular order, where superclasses occurring toward the front of the list have precedence over the ones in the back of the list.
(define standard-class
(vector 'value-of-standard-class-goes-here
(list 'slots 'class-precedence-list 'method-names 'method-vector)
'()
'(make-instance)
(vector make-instance)))
Not only has the list of slots changed to include the new slot, but the erstwhile superclass slot is now () instead of #t. This is because theclass-precedence-list of standard-class must be a list. We could have had its value be (#t), but we will not mention the zero class since it is in every class's class-precedence-list.
The create-class macro has to modified to accept a list of direct superclasses instead of a solitary superclass:
(define-macro create-class
(lambda (direct-superclasses slots . methods)
(create-class-proc (list ,@(map (lambda (su),su) direct-superclasses))
(list ,@(map (lambda (slot) ',slot) slots)) (list ,@(map (lambda (method)',(car method)) methods))
(vector ,@(map (lambda (method) `,(cadr method)) methods))
)))
The create-class-proc must calculate the class precedence list from the supplied direct superclasses, and the slot list from the class precedence list:
(define create-class-proc
(lambda (direct-superclasses slots method-names method-vector)
(let ((class-precedence-list
(delete-duplicates
(append-map
(lambda (c) (vector-ref c 2))
direct-superclasses))))
(send 'make-instance standard-class
'class-precedence-list class-precedence-list
'slots
(delete-duplicates
(append slots (append-map
(lambda (c) (vector-ref c 1))
class-precedence-list)))
'method-names method-names
'method-vector method-vector))))
The procedure append-map is a composition of append and map:
(define append-map
(lambda (f s)
(let loop ((s s))
(if (null? s) '()
(append (f (car s))
(loop (cdr s)))))))
The procedure send has to search through the class precedence list left to right when it hunts for a method.
(define send
(lambda (method-name instance . args)
(let ((proc
(let ((class (class-of instance)))
(if (eqv? class #t) (error 'send)
(let loop ((class class)
(superclasses (vector-ref class 2)))
(let ((k (list-position
method-name
(vector-ref class 3))))
(cond (k (vector-ref
(vector-ref class 4) k))
((null? superclasses) (error 'send))
(else (loop (car superclasses)
(cdr superclasses))))
))))))
(apply proc instance args))))
5 We could in theory define methods also as slots (whose values happen to be procedures), but there is a good reason not to. The instances of a class share methods but in general differ in their slot values. In other words, methods can be included in the class definition and don't have to be allocated per instance as slots have to be.
Chapter 13
Jumps
One of the signal features of Scheme is its support for jumps or nonlocal control. Specifically, Scheme allows program control to jump toarbitrary locations in the program, in contrast to the more restrained forms of program control flow allowed by conditionals and procedure calls. Scheme's nonlocal control operator is a procedure named call-with-current-continuation. We will see how this operator can be used to create a breathtaking variety of control idioms.
13.1 call-with-current-continuation
The operator call-with-current-continuation calls its argument, which must be a unary procedure, with a value called the ``current continuation''. If nothing else, this explains the name of the operator. But it is a long name, and is often abbreviated call/cc.6
The current continuation at any point in the execution of a program is an abstraction of the rest of the program. Thus in the program
(+ 1 (call/cc
(lambda (k)
(+ 2 (k 3)))))
the rest of the program, from the point of view of the call/cc-application, is the following program-with-a-hole (with [] representing the hole):
(+ 1 [])
In other words, this continuation is a program that will add 1 to whatever is used to fill its hole.
This is what the argument of call/cc is called with. Remember that the argument of call/cc is the procedure
(lambda (k)
(+ 2 (k 3)))
This procedure's body applies the continuation (bound now to the parameter k) to the argument 3. This is when the unusual aspect of the continuation springs to the fore. The continuation call abruptly abandons its own computation and replaces it with the rest of the program saved in k! In other words, the part of the procedure involving the addition of 2 is jettisoned, and k's argument 3 is sent directly to the program-with-the-hole:
(+ 1 [])
The program now running is simply
(+ 1 3)
which returns 4. In sum,
(+ 1 (call/cc
(lambda (k)
(+ 2 (k 3)))))
=> 4
The above illustrates what is called an escaping continuation, one used to exit out of a computation (here: the (+ 2 []) computation). This is a useful property, but Scheme's continuations can also be used to return to previously abandoned contexts, and indeed to invoke them many times. The ``rest of the program'' enshrined in a continuation is available whenever and how many ever times we choose to recall it, and this is what contributes to the great and sometimes confusing versatility of call/cc. As a quick example, type the following at the listener:
(define r #f)
(+ 1 (call/cc
(lambda (k)
(set! r k)
(+ 2 (k 3)))))
=> 4
The latter expression returns 4 as before. The difference between this use of call/cc and the previous example is that here we also store the continuation k in a global variable r.
Now we have a permanent record of the continuation in r. If we call it on a number, it will return that number incremented by 1:
(r 5)
=> 6
Note that r will abandon its own continuation, which is better illustrated by embedding the call to r inside some context:
(+ 3 (r 5))
=> 6
The continuations provided by call/cc are thus abortive continuations.
13.2 Escaping continuations
Escaping continuations are the simplest use of call/cc and are very useful for programming procedure or loop exits. Consider a procedurelist-product that takes a list of numbers and multiplies them. A straightforward recursive definition for list-product is:
(define list-product
(lambda (s)
(let recur ((s s))
(if (null? s) 1
(* (car s) (recur (cdr s)))))))
There is a problem with this solution. If one of the elements in the list is 0, and if there are many elements after 0 in the list, then the answer is a foregone conclusion. Yet, the code will have us go through many fruitless recursive calls to recur before producing the answer. This is where an escape continuation comes in handy. Using call/cc, we can rewrite the procedure as:
(define list-product
(lambda (s)
(call/cc
(lambda (exit)
(let recur ((s s))
(if (null? s) 1
(if (= (car s) 0) (exit 0)
(* (car s) (recur (cdr s))))))))))
If a 0 element is encountered, the continuation exit is called with 0, thereby avoiding further calls to recur.
13.3 Tree matching
A more involved example of continuation usage is the problem of determining if two trees (arbitrarily nested dotted pairs) have the samefringe, ie, the same elements (or leaves) in the same sequence. Eg,
(same-fringe? '(1 (2 3)) '((1 2) 3))
=> #t
(same-fringe? '(1 2 3) '(1 (3 2)))
=> #f
The purely functional approach is to flatten both trees and check if the results match.
(define same-fringe?
(lambda (tree1 tree2)
(let loop ((ftree1 (flatten tree1))
(ftree2 (flatten tree2)))
(cond ((and (null? ftree1) (null? ftree2)) #t)
((or (null? ftree1) (null? ftree2)) #f)
((eqv? (car ftree1) (car ftree2))
(loop (cdr ftree1) (cdr ftree2)))
(else #f)))))
(define flatten
(lambda (tree)
(cond ((null? tree) '())
((pair? (car tree))
(append (flatten (car tree))
(flatten (cdr tree))))
(else
(cons (car tree)
(flatten (cdr tree)))))))
However, this traverses the trees completely to flatten them, and then again till it finds non-matching elements. Furthermore, even the best flattening algorithms will require conses equal to the total number of leaves. (Destructively modifying the input trees is not an option.)
We can use call/cc to solve the problem without needless traversal and without any consing. Each tree is mapped to a generator, a procedure with internal state that successively produces the leaves of the tree in the left-to-right order that they occur in the tree.
(define tree->generator
(lambda (tree)
(let ((caller '*))
(letrec
((generate-leaves
(lambda ()
(let loop ((tree tree))
(cond ((null? tree) 'skip)
((pair? tree)
(loop (car tree))
(loop (cdr tree)))
(else
(call/cc
(lambda (rest-of-tree)
(set! generate-leaves
(lambda ()
(rest-of-tree 'resume)))
(caller tree))))))
(caller '()))))
(lambda ()
(call/cc
(lambda (k)
(set! caller k)
(generate-leaves))))))))
When a generator created by tree->generator is called, it will store the continuation of its call in caller, so that it can know who to send the leaf to when it finds it. It then calls an internal procedure called generate-leaves which runs a loop traversing the tree from left to right. When the loop encounters a leaf, it will use caller to return the leaf as the generator's result, but it will remember to store the rest of the loop (captured as a call/cc continuation) in the generate-leaves variable. The next time the generator is called, the loop is resumed where it left off so it can hunt for the next leaf.
Note that the last thing generate-leaves does, after the loop is done, is to return the empty list to the caller. Since the empty list is not a valid leaf value, we can use it to tell that the generator has no more leaves to generate.
The procedure same-fringe? maps each of its tree arguments to a generator, and then calls these two generators alternately. It announces failure as soon as two non-matching leaves are found:
(define same-fringe?
(lambda (tree1 tree2)
(let ((gen1 (tree->generator tree1))
(gen2 (tree->generator tree2)))
(let loop ()
(let ((leaf1 (gen1))
(leaf2 (gen2)))
(if (eqv? leaf1 leaf2)
(if (null? leaf1) #t (loop))
#f))))))
It is easy to see that the trees are traversed at most once, and in case of mismatch, the traversals extend only upto the leftmost mismatch. consis not used.
13.4 Coroutines
The generators used above are interesting generalizations of the procedure concept. Each time the generator is called, it resumes its computation, and when it has a result for its caller returns it, but only after storing its continuation in an internal variable so the generator can be resumed again. We can generalize generators further, so that they can mutually resume each other, sending results back and forth amongst themselves. Such procedures are called coroutines [18].
We will view a coroutine as a unary procedure, whose body can contain resume calls. resume is a two-argument procedure used by a coroutine to resume another coroutine with a transfer value. The macro coroutine defines such a coroutine procedure, given a variable name for the coroutine's initial argument, and the body of the coroutine.
(define-macro coroutine
(lambda (x . body)
`(letrec ((+local-control-state
(lambda (,x) ,@body))
(resume
(lambda (c v)
(call/cc
(lambda (k)
(set! +local-control-state k)
(c v))))))
(lambda (v)
(+local-control-state v)))))
A call of this macro creates a coroutine procedure (let's call it A) that can be called with one argument. A has an internal variable called+local-control-state that stores, at any point, the remaining computation of the coroutine. Initially this is the entire coroutine computation. When resume is called -- ie, invoking another coroutine B -- the current coroutine will update its +local-control-statevalue to the rest of itself, stop itself, and then jump to the resumed coroutine B. When coroutine A is itself resumed at some later point, its computation will proceed from the continuation stored in its +local-control-state.
13.4.1 Tree-matching with coroutines
Tree-matching is further simplified using coroutines. The matching process is coded as a coroutine that depends on two other coroutines to supply the leaves of the respective trees:
(define make-matcher-coroutine
(lambda (tree-cor-1 tree-cor-2)
(coroutine dont-need-an-init-arg
(let loop ()
(let ((leaf1 (resume tree-cor-1 'get-a-leaf))
(leaf2 (resume tree-cor-2 'get-a-leaf)))
(if (eqv? leaf1 leaf2)
(if (null? leaf1) #t (loop))
#f))))))
The leaf-generator coroutines remember who to send their leaves to:
(define make-leaf-gen-coroutine
(lambda (tree matcher-cor)
(coroutine dont-need-an-init-arg
(let loop ((tree tree))
(cond ((null? tree) 'skip)
((pair? tree)
(loop (car tree))
(loop (cdr tree)))
(else
(resume matcher-cor tree))))
(resume matcher-cor '()))))
The same-fringe? procedure can now almost be written as
(define same-fringe?
(lambda (tree1 tree2)
(letrec ((tree-cor-1
(make-leaf-gen-coroutine
tree1
matcher-cor))
(tree-cor-2
(make-leaf-gen-coroutine
tree2
matcher-cor))
(matcher-cor
(make-matcher-coroutine
tree-cor-1
tree-cor-2)))
(matcher-cor 'start-ball-rolling))))
Unfortunately, Scheme's letrec can resolve mutually recursive references amongst the lexical variables it introduces only if such variable references are wrapped inside a lambda. And so we write:
(define same-fringe?
(lambda (tree1 tree2)
(letrec ((tree-cor-1
(make-leaf-gen-coroutine
tree1
(lambda (v) (matcher-cor v))))
(tree-cor-2
(make-leaf-gen-coroutine
tree2
(lambda (v) (matcher-cor v))))
(matcher-cor
(make-matcher-coroutine
(lambda (v) (tree-cor-1 v))
(lambda (v) (tree-cor-2 v)))))
(matcher-cor 'start-ball-rolling))))
Note that call/cc is not called directly at all in this rewrite of same-fringe?. All the continuation manipulation is handled for us by thecoroutine macro.
6 If your Scheme does not already have this abbreviation, include (define call/cc call-with-current-continuation) in your initialization code and protect yourself from RSI.
Chapter 14
Nondeterminism
McCarthy's nondeterministic operator amb [25, 4, 33] is as old as Lisp itself, although it is present in no Lisp. amb takes zero or more expressions, and makes a nondeterministic (or ``ambiguous'') choice among them, preferring those choices that cause the program to converge meaningfully. Here we will explore an embedding of amb in Scheme that makes a depth-first selection of the ambiguous choices, and uses Scheme's control operator call/cc to backtrack for alternate choices. The result is an elegant backtracking strategy that can be used for searching problem spaces directly in Scheme without recourse to an extended language. The embedding recalls the continuation strategies used to implement Prolog-style logic programming [16, 7], but is sparer because the operator provided is much like a Scheme boolean operator, does not require special contexts for its use, and does not rely on linguistic infrastructure such as logic variables and unification.
14.1 Description of amb
An accessible description of amb and many example uses are found in the premier Scheme textbook SICP [1]. Informally, amb takes zero or more expressions and nondeterministically returns the value of one of them. Thus,
(amb 1 2)
may evaluate to 1 or 2.
amb called with no expressions has no value to return, and is considered to fail. Thus,
(amb)
-->ERROR!!! amb tree exhausted
(We will examine the wording of the error message later.)
In particular, amb is required to return a value if at least one its subexpressions converges, ie, doesn't fail. Thus,
(amb 1 (amb))
and
(amb (amb) 1)
both return 1.
Clearly, amb cannot simply be equated to its first subexpression, since it has to return a non-failing value, if this is at all possible. However, this is not all: The bias for convergence is more stringent than a merely local choice of amb's subexpressions. amb should furthermore returnthat convergent value that makes the entire program converge. In denotational parlance, amb is an angelic operator.
For example,
(amb #f #t)
may return either #f or #t, but in the program
(if (amb #f #t)
1
(amb))
the first amb-expression must return #t. If it returned #f, the if's ``else'' branch would be chosen, which causes the entire program to fail.
14.2 Implementing amb in Scheme
In our implementation of amb, we will favor amb's subexpressions from left to right. Ie, the first subexpression is chosen, and if it leads to overall failure, the second is picked, and so on. ambs occurring later in the control flow of the program are searched for alternates before backtracking to previous ambs. In other words, we perform a depth-first search of the amb choice tree, and whenever we brush against failure, we backtrack to the most recent node of the tree that offers a further choice. (This is called chronological backtracking.)
We first define a mechanism for setting the base failure continuation:
(define amb-fail '*)
(define initialize-amb-fail
(lambda ()
(set! amb-fail
(lambda ()
(error "amb tree exhausted")))))
(initialize-amb-fail)
When amb fails, it invokes the continuation bound at the time to amb-fail. This is the continuation invoked when all the alternates in the ambchoice tree have been tried and were found to fail.
We define amb as a macro that accepts an indefinite number of subexpressions.
(define-macro amb
(lambda alts...
`(let ((+prev-amb-fail amb-fail))
(call/cc
(lambda (+sk)
,@(map (lambda (alt)
`(call/cc
(lambda (+fk)
(set! amb-fail
(lambda ()
(set! amb-fail +prev-amb-fail)
(+fk 'fail)))
(+sk ,alt))))
alts...)
(+prev-amb-fail))))))
A call to amb first stores away, in +prev-amb-fail, the amb-fail value that was current at the time of entry. This is because the amb-failvariable will be set to different failure continuations as the various alternates are tried.
We then capture the amb's entry continuation +sk, so that when one of the alternates evaluates to a non-failing value, it can immediately exit the amb.
Each alternate alt is tried in sequence (the implicit-begin sequence of Scheme).
First, we capture the current continuation +fk, wrap it in a procedure and set amb-fail to that procedure. The alternate is then evaluated as(+sk alt). If alt evaluates without failure, its return value is fed to the continuation +sk, which immediately exits the amb call. If alt fails, it calls amb-fail. The first duty of amb-fail is to reset amb-fail to the value it had at the time of entry. It then invokes the failure continuation +fk, which causes the next alternate, if any, to be tried.
If all alternates fail, the amb-fail at amb entry, which we had stored in +prev-amb-fail, is called.
14.3 Using amb in Scheme
To choose a number between 1 and 10, one could say
(amb 1 2 3 4 5 6 7 8 9 10)
To be sure, as a program, this will give 1, but depending on the context, it could return any of the mentioned numbers.
The procedure number-between is a more abstract way to generate numbers from a given lo to a given hi (inclusive):
(define number-between
(lambda (lo hi)
(let loop ((i lo))
(if (]]
]]>
i hi) (amb)
(amb i (loop (+ i 1)))))))
Thus (number-between 1 6) will first generate 1. Should that fail, the loop iterates, producing 2. Should that fail, we get 3, and so on, until 6. After 6, loop is called with the number 7, which being more than 6, invokes (amb), which causes final failure. (Recall that (amb) by itself guarantees failure.) At this point, the program containing the call to (number-between 1 6) will backtrack to the chronologically previousamb-call, and try to satisfy that call in another fashion.
The guaranteed failure of (amb) can be used to program assertions.
(define assert
(lambda (pred)
(if (not pred) (amb))))
The call (assert pred) insists that pred be true. Otherwise it will cause the current amb choice point to fail.7
Here is a procedure using assert that generates a prime less than or equal to its argument hi:
(define gen-prime
(lambda (hi)
(let ((i (number-between 2 hi)))
(assert (prime? i))
i)))
This seems devilishly simple, except that when called as a program with any number (say 20), it will produce the uninteresting first solution, ie, 2.
We would certainly like to get all the solutions, not just the first. In this case, we may want all the primes below 20. One way is to explicitly call the failure continuation left after the program has produced its first solution. Thus,
(amb)
=> 3
This leaves yet another failure continuation, which can be called again for yet another solution:
(amb)
=> 5
The problem with this method is that the program is initially called at the Scheme prompt, and successive solutions are also obtained by calling amb at the Scheme prompt. In effect, we are using different programs (we cannot predict how many!), carrying over information from a previous program to the next. Instead, we would like to be able to get these solutions as the return value of a form that we can call in any context. To this end, we define the bag-of macro, which returns all the successful instantiations of its argument. (If the argument never succeeds, bag-of returns the empty list.) Thus, we could say,
(bag-of
(gen-prime 20))
and it would return
(2 3 5 7 11 13 17 19)
The bag-of macro is defined as follows:
(define-macro bag-of
(lambda (e)
`(let ((+prev-amb-fail amb-fail)
(+results '()))
(if (call/cc
(lambda (+k)
(set! amb-fail (lambda () (+k #f)))
(let ((+v ,e))
(set! +results (cons +v +results))
(+k #t))))
(amb-fail))
(set! amb-fail +prev-amb-fail)
(reverse! +results))))
bag-of first saves away its entry amb-fail. It redefines amb-fail to a local continuation +k created within an if-test. Inside the test, thebag-of argument e is evaluated. If e succeeds, its result is collected into a list called +results, and the local continuation is called with the value #t. This causes the if-test to succeed, causing e to be retried at its next backtrack point. More results for e are obtained this way, and they are all collected into +results.
Finally, when e fails, it will call the base amb-fail, which is simply a call to the local continuation with the value #f. This pushes control past the if. We restore amb-fail to its pre-entry value, and return the +results. (The reverse! is simply to produce the results in the order in which they were generated.)
14.4 Logic puzzles
The power of depth-first search coupled with backtracking becomes obvious when applied to solving logic puzzles. These problems are extraordinarily difficult to solve procedurally, but can be solved concisely and declaratively with amb, without taking anything away from the charm of solving the puzzle.
14.4.1 The Kalotan puzzle
The Kalotans are a tribe with a peculiar quirk.8 Their males always tell the truth. Their females never make two consecutive true statements, or two consecutive untrue statements.
An anthropologist (let's call him Worf) has begun to study them. Worf does not yet know the Kalotan language. One day, he meets a Kalotan (heterosexual) couple and their child Kibi. Worf asks Kibi: Are you a boy?'' Kibi answers in Kalotan, which of course Worf doesn't understand. Worf turns to the parents (who know English) for explanation. One of them says:Kibi said: `I am a boy.' '' The other adds: ``Kibi is a girl. Kibi lied.''
Solve for the sex of the parents and Kibi.
--
The solution consists in introducing a bunch of variables, allowing them to take a choice of values, and enumerating the conditions on them as a sequence of assert expressions.
The variables: parent1, parent2, and kibi are the sexes of the parents (in order of appearance) and Kibi; kibi-self-desc is the sex Kibi claimed to be (in Kalotan); kibi-lied? is the boolean on whether Kibi's claim was a lie.
(define solve-kalotan-puzzle
(lambda ()
(let ((parent1 (amb 'm 'f))
(parent2 (amb 'm 'f))
(kibi (amb 'm 'f))
(kibi-self-desc (amb 'm 'f))
(kibi-lied? (amb #t #f)))
(assert
(distinct? (list parent1 parent2)))
(assert
(if (eqv? kibi 'm)
(not kibi-lied?)))
(assert
(if kibi-lied?
(xor
(and (eqv? kibi-self-desc 'm)
(eqv? kibi 'f))
(and (eqv? kibi-self-desc 'f)
(eqv? kibi 'm)))))
(assert
(if (not kibi-lied?)
(xor
(and (eqv? kibi-self-desc 'm)
(eqv? kibi 'm))
(and (eqv? kibi-self-desc 'f)
(eqv? kibi 'f)))))
(assert
(if (eqv? parent1 'm)
(and
(eqv? kibi-self-desc 'm)
(xor
(and (eqv? kibi 'f)
(eqv? kibi-lied? #f))
(and (eqv? kibi 'm)
(eqv? kibi-lied? #t))))))
(assert
(if (eqv? parent1 'f)
(and
(eqv? kibi 'f)
(eqv? kibi-lied? #t))))
(list parent1 parent2 kibi))))
A note on the helper procedures: The procedure distinct? returns true if all the elements in its argument list are distinct, and false otherwise. The procedure xor returns true if only one of its two arguments is true, and false otherwise.
Typing (solve-kalotan-puzzle) will solve the puzzle.
14.4.2 Map coloring
It has been known for some time (but not proven until 1976 [29]) that four colors suffice to color a terrestrial map -- ie, to color the countries so that neighbors are distinguished. To actually assign the colors is still an undertaking, and the following program shows how nondeterministic programming can help.
The following program solves the problem of coloring a map of Western Europe. The problem and a Prolog solution are given in The Art of Prolog [31]. (It is instructive to compare our solution with the book's.)
The procedure choose-color nondeterministically returns one of four colors:
(define choose-color
(lambda ()
(amb 'red 'yellow 'blue 'white)))
In our solution, we create for each country a data structure. The data structure is a 3-element list: The first element of the list is the country's name; the second element is its assigned color; and the third element is the colors of its neighbors. Note we use the initial of the country for its color variable.9 Eg, the list for Belgium is (list 'belgium b (list f h l g)), because -- per the problem statement -- the neighbors of Belgium are France, Holland, Luxembourg, and Germany.
Once we create the lists for each country, we state the (single!) condition they should satisfy, viz, no country should have the color of its neighbors. In other words, for every country list, the second element should not be a member of the third element.
(define color-europe
(lambda ()
;choose colors for each country
(let ((p (choose-color)) ;Portugal
(e (choose-color)) ;Spain
(f (choose-color)) ;France
(b (choose-color)) ;Belgium
(h (choose-color)) ;Holland
(g (choose-color)) ;Germany
(l (choose-color)) ;Luxemb
(i (choose-color)) ;Italy
(s (choose-color)) ;Switz
(a (choose-color)) ;Austria
)
;construct the adjacency list for
;each country: the 1st element is
;the name of the country; the 2nd
;element is its color; the 3rd
;element is the list of its
;neighbors' colors
(let ((portugal
(list 'portugal p
(list e)))
(spain
(list 'spain e
(list f p)))
(france
(list 'france f
(list e i s b g l)))
(belgium
(list 'belgium b
(list f h l g)))
(holland
(list 'holland h
(list b g)))
(germany
(list 'germany g
(list f a s h b l)))
(luxembourg
(list 'luxembourg l
(list f b g)))
(italy
(list 'italy i
(list f a s)))
(switzerland
(list 'switzerland s
(list f i a g)))
(austria
(list 'austria a
(list i s g))))
(let ((countries
(list portugal spain
france belgium
holland germany
luxembourg
italy switzerland
austria)))
;the color of a country
;should not be the color of
;any of its neighbors
(for-each
(lambda (c)
(assert
(not (memq (cadr c)
(caddr c)))))
countries)
;output the color
;assignment
(for-each
(lambda (c)
(display (car c))
(display " ")
(display (cadr c))
(newline))
countries))))))
Type (color-europe) to get a color assignment.
7 SICP names this procedure require. We use the identifier assert in order to avoid confusion with the popular if informal use of the identifier require for something else, viz, an operator that loads code modules on a per-need basis.
8 This puzzle is due to Hunter [19].
9 Spain (España) has e so as not to clash with Switzerland.
Chapter 15
Engines
An engine [17] represents computation that is subject to timed preemption. In other words, an engine's underlying computation is an ordinary thunk that runs as a timer-preemptable process.
An engine is called with three arguments: (1) a number of time units or ticks, (2) a success procedure, and (3) a failure procedure. If the engine computation finishes within the allotted ticks, the success procedure is applied to the computation result and the remaining ticks. If the engine computation could not finish within the allotted ticks, the failure procedure is applied to a new engine representing the unfinished portion of the engine computation.
For example, consider an engine whose underlying computation is a loop that printed the nonnegative integers in sequence. It is created as follows, with the soon-to-be-defined make-engine procedure. make-engine is called on an argument thunk representing the underlying computation, and it returns the corresponding engine:
(define printn-engine
(make-engine
(lambda ()
(let loop ((i 0))
(display i)
(display " ")
(loop (+ i 1))))))
Here is a call to printn-engine:
(define more #f)
(printn-engine 50 list (lambda (ne) (set! more ne)))
=> 0 1 2 3 4 5 6 7 8 9
Ie, the loop gets to print upto a certain number (here 9) and then fails because of the clock interrupt. However, our failure procedure sets a global variable called more to the failed engine, which we can use to resume the loop where the previous engine left off:
(more 50 list (lambda (ne) (set! more ne)))
=> 10 11 12 13 14 15 16 17 18 19
We will now construct engines using call/cc to capture the unfinished computation of a failing engine. First we will construct flat engines, or engines whose computation cannot include the running of other engines. We will later generalize the code to the more general nestableengines or nesters, which can call other engines. But in both cases, we need a timer mechanism, or a clock.
15.1 The clock
Our engines assume the presence of a global clock or interruptable timer that marks the passage of ticks as a program executes. We will assume the following clock interface -- if your Scheme provides any kind of alarm mechanism, it should be an easy matter to rig up a clock of the following type. (Appendix D defines a clock for the Guile [13] dialect of Scheme.)
The internal state of our clock procedure consists of two items:
(1) the number of remaining ticks; and
(2) an interrupt handler to be invoked when the clock runs out of ticks.
clock allows the following operations:
(1) (clock 'set-handler h) sets the interrupt handler to h.
(2) (clock 'set n) resets the clock's remaining ticks to n, returning the previous value.
The number of ticks ranges over the non-negative integers and an atom called infinity. A clock with infinity ticks cannot run out of time and so will not set off the interrupt handler. Such a clock is quiescent or ``already stopped''. To stop a clock, set its ticks to infinity.
The clock handler is set to a thunk. For example,
(clock 'set-handler
(lambda ()
(error "Say goodnight, cat!")))
(clock 'set 9)
This will cause an error to be signaled after 9 ticks have passed, and the message displayed by the signal will be ``Say goodnight, cat!''
15.2 Flat engines
We will first set the clock interrupt handler. Note that the handler is invoked only if a non-quiescent clock runs out of ticks. This happens only during engine computations that are on the brink of failure, for only engines set the clock.
The handler captures the current continuation, which is the rest of the computation of the currently failing engine. This continuation is sent to another continuation stored in the global engine-escape. The engine-escape variable stores the exit continuation of the current engine. Thus the clock handler captures the rest of the failing engine and sends it to an exit point in the engine code, so the requisite failure action can be taken.
(define engine-escape #f)
(define engine-entrance #f)
(clock 'set-handler
(lambda ()
(call/cc engine-escape)))
Let us now look into the innards of the engine code itself. As said, make-engine takes a thunk and fashions an engine out of it:
(define make-engine
(lambda (th)
(lambda (ticks success failure)
(let* ((ticks-left 0)
(engine-succeeded? #f)
(result
(call/cc
(lambda (k)
(set! engine-escape k)
(let ((result
(call/cc
(lambda (k)
(set! engine-entrance k)
(clock 'set ticks)
(let ((v (th)))
(engine-entrance v))))))
(set! ticks-left (clock 'set infinity))
(set! engine-succeeded? #t)
result)))))
(if engine-succeeded?
(success result ticks-left)
(failure
(make-engine
(lambda ()
(result 'resume)))))))))
First we introduce the variables ticks-left and engine-succeeded?. The first will hold the ticks left over should the engine thunk finish in time. The second is a flag that will be used in the engine code to signal if the engine suceeded.
We then run the engine thunk within two nested calls to call/cc. The first call/cc captures the continuation to be used by a failing engine to abort out of its engine computation. This continuation is stored in the global engine-escape. The second call/cc captures an inner continuation that will be used by the return value of the thunk th if it runs to completion. This continuation is stored in the global engine-entrance.
Running through the code, we find that after capturing the continuations engine-escape and engine-entrance, we set the clock's ticks to the time allotted this engine and run the thunk th. If th succeeds, its value v is sent to the continuation engine-entrance, after which the clock is stopped, the remaining ticks ascertained, and the flag engine-succeeded? is set to true. We now go past the engine-escape continuation, and run the final dispatcher in the code: Since we know the engine succeeded, we apply the success procedure to the result and the ticks left.
If the thunk th didn't finish in time though, it will suffer an interrupt. This invokes the clock interrupt handler, which captures the current continuation of the running and now failing thunk and sends it to the continuation engine-escape. This puts the failed-thunk continuation in the outer result variable, and we are now in the final dispatcher in the code: Since engine-succeeded? is still false, we apply thefailure procedure to new engine fashioned out of result.
Notice that when a failed engine is removed, it will traverse the control path charted by the first run of the original engine. Nevertheless, because we have explicitly use the continuations stored in the global variables engine-entrance and engine-escape, and we always set them anew before executing an engine computation, we are assured that the jumps will always come back to the currently executing engine code.
15.3 Nestable engines
In order to generalize the code above to accommodate the nestable type of engine, we need to incorporate into it some tick management that will take care of the apportioning of the right amounts of ticks all the engines in a nested run.
To run a new engine (the child), we need to stop the currently engine (the parent). We then need to assign an appropriate number of ticks to the child. This may not be the same as the ticks assigned by the program text, because it would be unfair for a child to consume more ticks than its parent has left. After the child completes, we need to update the parent's ticks. If the child finished in time, any leftover ticks it has revert to the parent. If ticks were denied from the child because the parent couldn't afford it, then if the child fails, the parent will fail too, but must remember to restart the child with its promised ticks when it (the parent) restarts.
We also need to fluid-let the globals engine-escape and engine-entrance, because each nested engine must have its own pair of these sentinel continuations. As an engine exits (whether through success or failure), the fluid-let will ensure that the next enclosing engine's sentinels take over.
Combining all this, the code for nestable engines looks as follows:
(define make-engine
(lambda (th)
(lambda (ticks s f)
(let* ((parent-ticks
(clock 'set infinity))
;A child can't have more ticks than its parent's
;remaining ticks
(child-available-ticks
(clock-min parent-ticks ticks))
;A child's ticks must be counted against the parent
;too
(parent-ticks-left
(clock-minus parent-ticks child-available-ticks))
;If child was promised more ticks than parent could
;afford, remember how much it was short-changed by
(child-ticks-left
(clock-minus ticks child-available-ticks))
;Used below to store ticks left in clock
;if child completes in time
(ticks-left 0)
(engine-succeeded? #f)
(result
(fluid-let ((*engine-escape* #f)
(*engine-entrance* #f))
(call/cc
(lambda (k)
(set! *engine-escape* k)
(let ((result
(call/cc
(lambda (k)
(set! *engine-entrance* k)
(clock 'set child-available-ticks)
(let ((v (th)))
(*engine-entrance* v))))))
(set! ticks-left
(let ((n (clock 'set *infinity*)))
(if (eqv? n *infinity*) 0 n)))
(set! engine-succeeded? #t)
result))))))
;Parent can reclaim ticks that child didn't need
(set! parent-ticks-left
(clock-plus parent-ticks-left ticks-left))
;This is the true ticks that child has left --
;we include the ticks it was short-changed by
(set! ticks-left
(clock-plus child-ticks-left ticks-left))
;Restart parent with its remaining ticks
(clock 'set parent-ticks-left)
;The rest is now parent computation
(cond
;Child finished in time -- celebrate its success
(engine-succeeded? (s result ticks-left))
;Child failed because it ran out of promised time --
;call failure procedure
((= ticks-left 0)
(f (make-engine (lambda () (result 'resume)))))
;Child failed because parent didn't have enough time,
;ie, parent failed too. If so, when parent is
;resumed, its first order of duty is to resume the
;child with its fair amount of ticks
(else
((make-engine (lambda () (result 'resume)))
ticks-left s f)))))))
Note that we have used the arithmetic operators clock-min, clock-minus, and clock-plus instead of min, -, and +. This is because the values used by the clock arithmetic includes infinity in addition to the integers. Some Scheme dialects provide an infinity value in their arithmetic10 -- if so, you can use the regular arithmetic operators. If not, it is an easy exercise to define the enhanced operators.
10 Eg, in Guile, you can (define infinity (/ 1 0)).
Chapter 16
Shell scripts
It is often convenient to simply write what one wants done into a file or script, and execute the script as though it were any other operating-system shell command. The interface to more weighty programs is often provided in the form of a script, and users frequently build their own scripts or customize existing ones to suit particular needs. Scripting is arguably the most frequent programming task performed. For many users, it is the only programming they will ever do.
Operating systems such as Unix and DOS (the command-line interface provided in Windows) provide such a scripting mechanism, but the scripting language in both cases is very rudimentary. Often a script is just a sequence or batch of commands that one would type to the shell prompt. It saves the user from having to type every one of the shell commands individually each time they require the same or similar sequence to be performed. Some scripting languages throw in a small amount of programmability in the form of a conditional and a loop, but that is about all. This is enough for smallish tasks, but as one's scripts become bigger and more demanding, as scripts invariably seem to do, one often feels the need for a fuller fledged programming language. A Scheme with an adequate operating-system interface makes scripting easy and maintainable.
This section will describe how to write scripts in Scheme. Since there is wide variation in the various Scheme dialects on how to accomplish this, we will concentrate on the MzScheme dialect, and document in appendix A the modifications needed for other dialects. We will also concentrate on the Unix operating system for the moment; appendix B will deal with the DOS counterpart.
16.1 Hello, World!, again
We will now create a Scheme script that says hello to the world. Saying hello is of course not a demanding scripting problem for traditional scripting languages. However, understanding how to transcribe it into Scheme will launch us on the path to more ambitious scripts. First, a conventional Unix hello script is a file, with contents that look like:
echo Hello, World!
It uses the shell command echo. The script can be named hello, made into an executable by doing
chmod +x hello
and placed in one of the directories named in the PATH environment variable. Thereafter, anytime one types
hello
at the shell prompt, one promptly gets the insufferable greeting.
A Scheme hello script will perform the same output using Scheme (using the program in sec 1), but we need something in the file to inform the operating system that it needs to construe the commands in the file as Scheme, and not as its default script language. The Scheme script file, also called hello, looks like:
":"; exec mzscheme -r $0 "$@"
(display "Hello, World!")
(newline))
Everything following the first line is straight Scheme. However, the first line is the magic that makes this into a script. When the user typeshello at the Unix prompt, Unix will read the file as a regular script. The first thing it sees is the ":", which is a shell no-op. The ; is the shell command separator. The next shell command is the exec. exec tells Unix to abandon the current script and run mzscheme -r $0 "$@"instead, where the parameter $0 will be replaced by the name of the script, and the parameter "$@" will be replaced by the list of arguments given by the user to the script. (In this case, there are no such arguments.)
We have now, in effect, transformed the hello shell command into a different shell command, viz,
mzscheme -r /whereveritis/hello
where /whereveritis/hello is the pathname of hello.
mzscheme calls the MzScheme executable. The -r option tells it to load the immediately following argument as a Scheme file after collecting any succeeding arguments into a vector called argv. (In this example, argv will be the null vector.)
Thus, the Scheme script will be run as a Scheme file, and the Scheme forms in the file will have access to the script's original arguments via the vector argv.
Now, Scheme has to tackle the first line in the script, which as we've already seen, was really a well-formed, traditional shell script. The ":"is a self-evaluating string in Scheme and thus harmless. The `;' marks a Scheme comment, and so the exec ... is safely ignored. The rest of the file is of course straight Scheme, and the expressions therein are evaluated in sequence. After all of them have been evaluated, Scheme will exit.
In sum, typing hello at the shell prompt will produce
Hello, World!
and return you to the shell prompt.
16.2 Scripts with arguments
A Scheme script uses the variable argv to refer to its arguments. For example, the following script echoes all its arguments, each on a line:
":"; exec mzscheme -r $0 "$@"
;Put in argv-count the number of arguments supplied
(define argv-count (vector-length argv))
(let loop ((i 0))
(unless (>= i argv-count)
(display (vector-ref argv i))
(newline)
(loop (+ i 1))))
Let's call this script echoall. Calling echoall 1 2 3 will display
1
2
3
Note that the script name ("echoall") is not included in the argument vector.
16.3 Example
Let's now tackle a more substantial problem. We need to transfer files from one computer to another and the only method we have is to use a 3.5'' floppy as a ferry. We need a script split4floppy that will split files larger than 1.44 million bytes into floppy-sized chunks. The script file split4floppy is as follows:
":";exec mzscheme -r $0 "$@"
;floppy-size = number of bytes that will comfortably fit on a
; 3.5" floppy
(define floppy-size 1440000)
;split splits the bigfile f into the smaller, floppy-sized
;subfiles, viz, subfile-prefix.1, subfile-prefix.2, etc.
(define split
(lambda (f subfile-prefix)
(call-with-input-file f
(lambda (i)
(let loop ((n 1))
(if (copy-to-floppy-sized-subfile i subfile-prefix n)
(loop (+ n 1))))))))
;copy-to-floppy-sized-subfile copies the next 1.44 million
;bytes (if there are less than that many bytes left, it
;copies all of them) from the big file to the nth
;subfile. Returns true if there are bytes left over,
;otherwise returns false.
(define copy-to-floppy-sized-subfile
(lambda (i subfile-prefix n)
(let ((nth-subfile (string-append subfile-prefix "."
(number->string n))))
(if (file-exists? nth-subfile) (delete-file nth-subfile))
(call-with-output-file nth-subfile
(lambda (o)
(let loop ((k 1))
(let ((c (read-char i)))
(cond ((eof-object? c) #f)
(else
(write-char c o)
(if (< k floppy-size)
(loop (+ k 1))
#t))))))))))
;bigfile = script's first arg
; = the file that needs splitting
(define bigfile (vector-ref argv 0))
;subfile-prefix = script's second arg
; = the basename of the subfiles
(define subfile-prefix (vector-ref argv 1))
;Call split, making subfile-prefix.{1,2,3,...} from
;bigfile
(split bigfile subfile-prefix)
Script split4floppy is called as follows:
split4floppy largefile chunk
This splits largefile into subfiles chunk.1, chunk.2, ..., such that each subfile fits on a floppy.
After the chunk.i have been ferried over to the target computer, the file largefile can be retrieved by stringing the chunk.i together. This can be done on Unix with:
cat chunk.1 chunk.2 ... > largefile
and on DOS with:
copy /b chunk.1+chunk.2+... largefile
Chapter 17
CGI scripts
(Warning: CGI scripts without appropriate safeguards can compromise your site's security. The scripts presented here are simple examples and are not assured to be secure for actual Web use.)
CGI scripts [27] are scripts that reside on a web server and can be run by a client (browser). The client accesses a CGI script by its URL, just as they would a regular page. The server, recognizing that the URL requested is a CGI script, runs it. How the server recognizes certain URLs as scripts is up to the server administrator. For the purposes of this text, we will assume that they are stored in a distinguished directory called cgi-bin. Thus, the script testcgi.scm on the server www.foo.org would be accessed as http://www.foo.org/cgi-bin/testcgi.scm.
The server runs the CGI script as the user nobody, who cannot be expected to have any PATH knowledge (which is highly subjective anyway). Therefore the introductory magic line for a CGI script written in Scheme needs to be a bit more explicit than the one we used for ordinary Scheme scripts. Eg, the line
":";exec mzscheme -r $0 "$@"
implicitly assumes that there is a particular shell (bash, say), and that there is a PATH, and that mzscheme is in it. For CGI scripts, we will need to be more expansive:
":";exec /usr/local/bin/mzscheme -r $0 "$@"
This gives fully qualified pathnames for the shell and the Scheme executable. The transfer of control from shell to Scheme proceeds as for regular scripts.
17.1 Example: Displaying environment variables
Here is an example Scheme CGI script, testcgi.scm, that outputs the settings of some commonly used CGI environment variables. This information is returned as a new, freshly created, page to the browser. The returned page is simply whatever the CGI script writes to its standard output. This is how CGI scripts talk back to whoever called them -- by giving them a new page.
Note that the script first outputs the line
content-type: text/plain
followed by a blank line. This is standard ritual for a web server serving up a page. These two lines aren't part of what is actually displayed as the page. They are there to inform the browser that the page being sent is plain (ie, un-marked-up) text, so the browser can display it appropriately. If we were producing text marked up in HTML, the content-type would be text/html.
The script testcgi.scm:
":";exec /usr/local/bin/mzscheme -r $0 "$@"
;Identify content-type as plain text.
(display "content-type: text/plain") (newline)
(newline)
;Generate a page with the requested info. This is
;done by simply writing to standard output.
(for-each
(lambda (env-var)
(display env-var)
(display " = ")
(display (or (getenv env-var) ""))
(newline))
'("AUTH_TYPE"
"CONTENT_LENGTH"
"CONTENT_TYPE"
"DOCUMENT_ROOT"
"GATEWAY_INTERFACE"
"HTTP_ACCEPT"
"HTTP_REFERER" ; [sic]
"HTTP_USER_AGENT"
"PATH_INFO"
"PATH_TRANSLATED"
"QUERY_STRING"
"REMOTE_ADDR"
"REMOTE_HOST"
"REMOTE_IDENT"
"REMOTE_USER"
"REQUEST_METHOD"
"SCRIPT_NAME"
"SERVER_NAME"
"SERVER_PORT"
"SERVER_PROTOCOL"
"SERVER_SOFTWARE"))
testcgi.scm can be called directly by opening it on a browser. The URL is:
http://www.foo.org/cgi-bin/testcgi.scm
Alternately, testcgi.scm can occur as a link in an HTML file, which you can click. Eg,
... To view some common CGI environment variables, click
here.
...
However testcgi.scm is launched, it will produce a plain text page containing the settings of the environment variables. An example output:
AUTH_TYPE =
CONTENT_LENGTH =
CONTENT_TYPE =
DOCUMENT_ROOT = /home/httpd/html
GATEWAY_INTERFACE = CGI/1.1
HTTP_ACCEPT = image/gif, image/x-xbitmap, image/jpeg, image/pjpeg, /
HTTP_REFERER =
HTTP_USER_AGENT = Mozilla/3.01Gold (X11; I; Linux 2.0.32 i586)
PATH_INFO =
PATH_TRANSLATED =
QUERY_STRING =
REMOTE_HOST = 127.0.0.1
REMOTE_ADDR = 127.0.0.1
REMOTE_IDENT =
REMOTE_USER =
REQUEST_METHOD = GET
SCRIPT_NAME = /cgi-bin/testcgi.scm
SERVER_NAME = localhost.localdomain
SERVER_PORT = 80
SERVER_PROTOCOL = HTTP/1.0
SERVER_SOFTWARE = Apache/1.2.4
17.2 Example: Displaying selected environment variable
testcgi.scm does not take any input from the user. A more focused script would take an argument environment variable from the user, and output the setting of that variable and none else. For this, we need a mechanism for feeding arguments to CGI scripts. The form tag of HTML provides this capability. Here is a sample HTML page for this purpose:
The user enters the desired environment variable (eg, GATEWAY_INTERFACE) in the textbox and clicks the submit button. This causes all the information in the form -- here, the setting of the parameter envvar to the value GATEWAY_INTERFACE -- to be collected and sent to the CGI script identified by the form, viz, testcgi2.scm. The information can be sent in one of two ways: (1) if the form's method=get (the default), the information is sent via the environment variable called QUERY_STRING; (2) if the form's method=post, the information is available to the CGI script at the latter's standard input port (stdin). Our form uses QUERY_STRING.
It is testcgi2.scm's responsibility to extract the information from QUERY_STRING, and output the answer page accordingly.
The information to the CGI script, whether arriving via an environment variable or through stdin, is formatted as a sequence of parameter/argument pairs. The pairs are separated from each other by the & character. Within a pair, the parameter occurs first and is separated from the argument by the = character. In this case, there is only one parameter/argument pair, viz, envvar=GATEWAY_INTERFACE.
The script testcgi2.scm:
":";exec /usr/local/bin/mzscheme -r $0 "$@"
(display "content-type: text/plain") (newline)
(newline)
;string-index returns the leftmost index in string s
;that has character c
(define string-index
(lambda (s c)
(let ((n (string-length s)))
(let loop ((i 0))
(cond ((>= i n) #f)
((char=? (string-ref s i) c) i)
(else (loop (+ i 1))))))))
;split breaks string s into substrings separated by character c
(define split
(lambda (c s)
(let loop ((s s))
(if (string=? s "") '()
(let ((i (string-index s c)))
(if i (cons (substring s 0 i)
(loop (substring s (+ i 1)
(string-length s))))
(list s)))))))
(define args
(map (lambda (par-arg)
(split #= par-arg))
(split #& (getenv "QUERY_STRING"))))
(define envvar (cadr (assoc "envvar" args)))
(display envvar)
(display " = ")
(display (getenv envvar))
(newline)
Note the use of a helper procedure split to split the QUERY_STRING into parameter/argument pairs along the & character, and then splitting parameter and argument along the = character. (If we had used the post method rather than get, we would have needed to extract the parameters and arguments from the standard input.)
The and are but two of the many different input tags possible in an HTML form. Consult [27] for the full repertoire.
17.3 CGI script utilities
In the example above, the parameter's name or the argument it assumed did not themselves contain any &' or=' characters. In general, they may. To accommodate such characters, and not have them be mistaken for separators, the CGI argument-passing mechanism treats all characters other than letters, digits, and the underscore, as special, and transmits them in an encoded form. A space is encoded as a +'. For other special characters, the encoding is a three-character sequence, and consists of%' followed the special character's hexadecimal code. Thus, the character sequence `20% + 30% = 50%, &c.' will be encoded as
20%25+%2b+30%25+%3d+50%25%2c+%26c%2e
(Space become +';%' becomes %25';+' becomes %2b';=' becomes %3d';,' becomes %2c';&' becomes %26'; and.' becomes `%2e'.)
Instead of dealing anew with the task of getting and decoding the form data in each CGI script, it is convenient to collect some helpful procedures into a library file cgi.scm. testcgi2.scm can then be written more compactly as
":";exec /usr/local/bin/mzscheme -r $0 "$@"
;Load the cgi utilities
(load-relatve "cgi.scm")
(display "content-type: text/plain") (newline)
(newline)
;Read the data input via the form
(parse-form-data)
;Get the envvar parameter
(define envvar (form-data-get/1 "envvar"))
;Display the value of the envvar
(display envvar)
(display " = ")
(display (getenv envvar))
(newline)
This shorter CGI script uses two utility procedures defined in cgi.scm. parse-form-data to read the data supplied by the user via the form. The data consists of parameters and their associated values. form-data-get/1 finds the value associated with a particular parameter.
cgi.scm defines a global table called form-data-table to store form data.
;Load our table definitions
(load-relative "table.scm")
;Define the form-data-table
(define form-data-table (make-table 'equ string=?))
An advantage of using a general mechanism such as the parse-form-data procedure is that we can hide the details of what method (get orpost) was used.
(define parse-form-data
(lambda ()
((if (string-ci=? (or (getenv "REQUEST_METHOD") "GET") "GET")
parse-form-data-using-query-string
parse-form-data-using-stdin))))
The environment variable REQUEST_METHOD tells which method was used to transmit the form data. If the method is GET, then the form data was sent as the string available via another environment variable, QUERY_STRING. The auxiliary procedure parse-form-data-using-query-string is used to pick apart QUERY_STRING:
(define parse-form-data-using-query-string
(lambda ()
(let ((query-string (or (getenv "QUERY_STRING") "")))
(for-each
(lambda (par=arg)
(let ((par/arg (split #= par=arg)))
(let ((par (url-decode (car par/arg)))
(arg (url-decode (cadr par/arg))))
(table-put!
form-data-table par
(cons arg
(table-get form-data-table par '()))))))
(split #& query-string)))))
The helper procedure split, and its helper string-index, are defined as in sec 17.2. As noted, the incoming form data is a sequence of name-value pairs separated by &s. Within each pair, the name comes first, followed by an = character, followed by the value. Each name-value combination is collected into a global table, the form-data-table.
Both name and value are encoded, so we need to decode them using the url-decode procedure to get their actual representation.
(define url-decode
(lambda (s)
(let ((s (string->list s)))
(list->string
(let loop ((s s))
(if (null? s) '()
(let ((a (car s)) (d (cdr s)))
(case a
((#+) (cons #\space (loop d)))
((#%) (cons (hex->char (car d) (cadr d))
(loop (cddr d))))
(else (cons a (loop d)))))))))))
+' is converted into space. A triliteral of the form%xy' is converted, using the procedure hex->char into the character whose ascii encoding is the hex number `xy'.
(define hex->char
(lambda (x y)
(integer->char
(string->number (string x y) 16))))
We still need a form-data parser for the case where the request method is POST. The auxiliary procedure parse-form-data-using-stdindoes this.
(define parse-form-data-using-stdin
(lambda ()
(let* ((content-length (getenv "CONTENT_LENGTH"))
(content-length
(if content-length
(string->number content-length) 0))
(i 0))
(let par-loop ((par '()))
(let ((c (read-char)))
(set! i (+ i 1))
(if (or (]]
]]>
i content-length)
(eof-object? c) (char=? c #=))
(let arg-loop ((arg '()))
(let ((c (read-char)))
(set! i (+ i 1))
(if (or (]]
]]>
i content-length)
(eof-object? c) (char=? c #&))
(let ((par (url-decode
(list->string
(reverse! par))))
(arg (url-decode
(list->string
(reverse! arg)))))
(table-put! form-data-table par
(cons arg (table-get form-data-table
par '())))
(unless (or (]]
]]>
i content-length)
(eof-object? c))
(par-loop '())))
(arg-loop (cons c arg)))))
(par-loop (cons c par))))))))
The POST method sends form data via the script's stdin. The number of characters sent is placed in the environment variableCONTENT_LENGTH. parse-form-data-using-stdin reads the required number of characters from stdin, and populates the form-data-table as before, making sure to decode the parameters' names and values.
It remains to retrieve the values for specific parameters from the form-data-table. Note that the table associates a list with each parameter, in order to accommodate the possibility of multiple values for a parameter. form-data-get retrieves all the values assigned to a parameter. If there is only one value, it returns a singleton containing that value.
(define form-data-get
(lambda (k)
(table-get form-data-table k '())))
form-data-get/1 returns the first (or most significant) value associated with a parameter.
(define form-data-get/1
(lambda (k . default)
(let ((vv (form-data-get k)))
(cond ((pair? vv) (car vv))
((pair? default) (car default))
(else "")))))
In our examples so far, the CGI script has generated plain text. Generally, though, we will want to generate an HTML page. It is not uncommon for a combination of HTML form and CGI script to trigger a series of HTML pages with forms. It is also common to code all the action corresponding to these various forms in a single CGI script. In any case, it is helpful to have a utility procedure that writes out strings in HTML format, ie, with the HTML special characters encoded appropriately:
(define display-html
(lambda (s . o)
(let ((o (if (null? o) (current-output-port)
(car o))))
(let ((n (string-length s)))
(let loop ((i 0))
(unless (>= i n)
(let ((c (string-ref s i)))
(display
(case c
((#<) "<")
((#>) ">")
((#") """)
((#&) "&")
(else c)) o)
(loop (+ i 1)))))))))
17.4 A calculator via CGI
Here is an CGI calculator script, cgicalc.scm, that exploits Scheme's arbitrary-precision arithmetic.
":";exec /usr/local/bin/mzscheme -r $0
;Load the CGI utilities
(load-relative "cgi.scm")
(define uhoh #f)
(define calc-eval
(lambda (e)
(if (pair? e)
(apply (ensure-operator (car e))
(map calc-eval (cdr e)))
(ensure-number e))))
(define ensure-operator
(lambda (e)
(case e
((+) +)
((-) -)
((*) *)
((/) /)
((**) expt)
(else (uhoh "unpermitted operator")))))
(define ensure-number
(lambda (e)
(if (number? e) e
(uhoh "non-number"))))
(define print-form
(lambda ()
(display "<form action="")
(display (getenv "SCRIPT_NAME"))
(display "">
Enter arithmetic expression:
<input type=submit value="Evaluate">
<input type=reset value="Clear">
(define print-page-begin
(lambda ()
(display "content-type: text/html
(define print-page-end
(lambda ()
(display "
(parse-form-data)
(print-page-begin)
(let ((e (form-data-get "arithexp")))
(unless (null? e)
(let ((e1 (car e)))
(display-html e1)
(display "
=> ")
(display-html
(call/cc
(lambda (k)
(set! uhoh
(lambda (s)
(k (string-append "Error: " s))))
(number->string
(calc-eval (read (open-input-string (car e))))))))
(display "
"))))
(print-form)
(print-page-end)
Appendix A
Scheme dialects
All major Scheme dialects implement the R5RS specification [23]. By using only the features documented in the R5RS, one can write Scheme code that is portable across the dialects. However, the R5RS, either for want of consensus or because of inevitable system dependencies, remains silent on several matters that non-trivial programming cannot ignore. The various dialects have therefore had to solve these matters in a non-standard and idiosyncratic manner.
This book uses the MzScheme [9] dialect of Scheme, and thereby uses several features that are nonstandard. The complete list of the dialect-dependent features used in this book is: the command-line (both for opening a listener session and for shell scripts), define-macro, delete-file, file-exists?, file-or-directory-modify-seconds, fluid-let, gensym, getenv, get-output-string, load-relative,open-input-string, open-output-string, read-line, reverse!, system, unless and when.
All but two of these are present in the default environment of MzScheme. The missing two, define-macro and system, are provided in standard MzScheme libraries, which can be explicitly loaded into MzScheme using the forms:
(require (lib "defmacro.ss")) ;provides define-macro
(require (lib "process.ss")) ;provides system
A good place to place these forms is the MzScheme initialization file (or init file), which, on Unix, is the file .mzschemerc in the user's home directory.11
Some of the nonstandard features (eg, file-exists?, delete-file) are in fact de facto standards and are present in many Schemes. Some other features (eg, when, unless) have more or less ``plug-in'' definitions (given in this book) that can be loaded into any Scheme dialect that doesn't have them primitively. The rest require a dialect-specific definition (eg, load-relative).
This chapter describes how to incorporate into your Scheme dialect the nonstandard features used in this book. For further detail about your Scheme dialect, consult the documentation provided by its implementor (appendix E).
A.1 Invocation and init files
Like MzScheme, many Scheme dialects load, if available, an init file, usually supplied in the user's home directory. The init file is a convenient location in which to place definitions for nonstandard features. Eg, the nonstandard procedure file-or-directory-modify-seconds can be added to the Guile [13] dialect of Scheme by putting the following code in Guile's init file, which is ~/.guile:
(define file-or-directory-modify-seconds
(lambda (f)
(vector-ref (stat f) 9)))
Also, the various Scheme dialects have their own distinctively named commands to invoke their respective listeners. The following table lists the invoking commands and init files for some Scheme dialects:
Dialect name Command Init file
Bigloo bigloo ~/.bigloorc
Chicken csi ~/.csirc
Gambit gsi ~/gambc.scm
Gauche gosh ~/.gaucherc
Guile guile ~/.guile
Kawa kawa ~/.kawarc.scm
MIT Scheme (Unix) scheme ~/.scheme.init
MIT Scheme (Win) scheme ~/scheme.ini
MzScheme (Unix, Mac OS X) mzscheme ~/.mzschemerc
MzScheme (Win, Mac OS Classic) mzscheme ~/mzschemerc.ss
SCM scm ~/ScmInit.scm
STk snow ~/.stkrc
A.2 Shell scripts
The initial line for a shell script written in Guile is:
":";exec guile -s $0 "$@"
In the script, the procedure-call (command-line) returns the list of the script's name and arguments. To access just the arguments, take thecdr of this list.
A Gauche [21] shell script starts out as:
":"; exec gosh -- $0 "$@"
In the script, the variable argv holds the list of the script's arguments.
A shell script written in SCM starts out as:
":";exec scm -l $0 "$@"
In the script, the variable argv contains the list of the Scheme executable name, the script's name, the option -l, and the script's arguments. To access just the arguments, take the cdddr of this list.
STk [14] shell scripts start out as:
":";exec snow -f $0 "$@"
In the script, the variable argv contains the list of the script's arguments.
A.3 define-macro
The define-macro used in the text occurs in the Scheme dialects Bigloo [30], Chicken [32], Gambit [6], Gauche [21], Guile, MzScheme and Pocket Scheme [15]. There are minor variations in how macros are defined in the other Scheme dialects. The rest of this section will point out how these other dialects notate the following code fragment:
(define-macro MACRO-NAME
(lambda MACRO-ARGS
MACRO-BODY ...))
In MIT Scheme [26] version 7.7.1 and later, this is written as:
(define-syntax MACRO-NAME
(rsc-macro-transformer
(let ((xfmr (lambda MACRO-ARGS MACRO-BODY ...)))
(lambda (e r)
(apply xfmr (cdr e))))))
In older versions of MIT Scheme:
(syntax-table-define system-global-syntax-table 'MACRO-NAME
(macro MACRO-ARGS
MACRO-BODY ...))
In SCM [20] and Kawa [3]:
(defmacro MACRO-NAME MACRO-ARGS
MACRO-BODY ...)
In STk [14]:
(define-macro (MACRO-NAME . MACRO-ARGS)
MACRO-BODY ...)
A.4 load-relative
The procedure load-relative may be defined for Guile as follows:
(define load-relative
(lambda (f)
(let* ((n (string-length f))
(full-pathname?
(and (]]
]]>
n 0)
(let ((c0 (string-ref f 0)))
(or (char=? c0 #/)
(char=? c0 #~))))))
(basic-load
(if full-pathname? f
(let ((clp (current-load-port)))
(if clp
(string-append
(dirname (port-filename clp)) "/" f)
f)))))))
For SCM:
(define load-relative
(lambda (f)
(let* ((n (string-length f))
(full-pathname?
(and (]]
]]>
n 0)
(let ((c0 (string-ref f 0)))
(or (char=? c0 #/)
(char=? c0 #~))))))
(load (if (and load-pathname full-pathname?)
(in-vicinity (program-vicinity) f)
f)))))
For STk, the following definition for load-relative works only if you discipline yourself to not use load:
(define load-pathname #f)
(define stk%load load)
(define load-relative
(lambda (f)
(fluid-let ((load-pathname
(if (not load-pathname) f
(let* ((n (string-length f))
(full-pathname?
(and (]]
]]>
n 0)
(let ((c0 (string-ref f 0)))
(or (char=? c0 #/)
(char=? c0 #~))))))
(if full-pathname? f
(string-append
(dirname load-pathname)
"/" f))))))
(stk%load load-pathname))))
(define load
(lambda (f)
(error "Don't use load. Use load-relative instead.")))
11 We will use ~/filename to denote the file called filename in the user's home directory.
Appendix B
DOS batch files in Scheme
DOS shell scripts are known as batch files. A conventional DOS batch file that outputs ``Hello, World!'' has the following contents:
echo Hello, World!
It uses the DOS command echo. The batch file is named hello.bat, which identifies it to the operating system as an executable. It may then be placed in one of the directories on the PATH environment variable. Thereafter, anytime one types
hello.bat
or simply
hello
at the DOS prompt, one promptly gets the insufferable greeting.
A Scheme version of the hello batch file will perform the same output using Scheme, but we need something in the file to inform DOS that it needs to construe the commands in the file as Scheme, and not as its default batch language. The Scheme batch file, also called hello.bat, looks like:
;@echo off
;goto :start
:start
echo. > c:_temp.scm
echo (load (find-executable-path "hello.bat" >> c:_temp.scm
echo "hello.bat")) >> c:_temp.scm
mzscheme -r c:_temp.scm %1 %2 %3 %4 %5 %6 %7 %8 %9
goto :eof
|#
(display "Hello, World!")
(newline)
;:eof
The lines upto |# are standard DOS batch. Then follows the Scheme code for the greeting. Finally, there is one more standard DOS batch line, viz, ;:eof.
When the user types hello at the DOS prompt, DOS reads and runs the file hello.bat as a regular batch file. The first line, ;@echo off, turns off the echoing of the commands run -- as we don't want excessive verbiage clouding the effect of our script. The second line, ;goto :start, causes execution to jump forward to the line labeled :start, ie, the fourth line. The three ensuing echo lines create a temporary Scheme file called c:_temp.tmp with the following contents:
(load (find-executable-path "hello.bat" "hello.bat"))
The next batch command is a call to MzScheme. The -r option loads the Scheme file c:_temp.scm. All the arguments (in this example, none) will be available to Scheme in the vector argv. This call to Scheme will evaluate our Scheme script, as we will see below. After Scheme returns, we still need to ensure that the batch file winds up cleanly. The next batch command is goto :eof, which causes control to skirt all the Scheme code and go to the very end of the file, which contains the label ;:eof. The script thus ends.
Now we can see how the call to Scheme does its part, viz, to run the Scheme expressions embedded in the batch file. Loading c:_temp.scmwill cause Scheme to deduce the full pathname of the file hello.bat (using find-executable-path), and to then load hello.bat.
Thus, the Scheme script file will now be run as a Scheme file, and the Scheme forms in the file will have access to the script's original arguments via the vector argv.
Now, Scheme has to skirt the batch commands in the script. This is easily done because these batch commands are either prefixed with a semicolon or are enclosed in #| ... |#, making them Scheme comments.
The rest of the file is of course straight Scheme, and the expressions therein are evaluated in sequence. (The final expression, ;:eof, is a Scheme comment, and causes no harm.) After all the expressions have been evaluated, Scheme will exit.
In sum, typing hello at the DOS prompt will produce
Hello, World!
and return you to the DOS prompt.
Appendix C
Numerical techniques
Recursion (including iteration) combines well with Scheme's mathematical primitive procedures to implement various numerical techniques. As an example, let's implement Simpson's rule, a procedure for finding an approximation for a definite integral.
C.1 Simpson's rule
The definite integral of a function f(x) within an interval of integration [a,b] can be viewed as the area under the curve representing f(x) from the lower limit x = a to the upper limit x = b. In other words, we consider the graph of the curve for f(x) on the x,y-plane, and find the area enclosed between that curve, the x-axis, and the ordinates of f(x) at x = a and x = b.
According to Simpson's rule, we divide the interval of integration [a,b] into n evenly spaced intervals, where n is even. (The larger n is, the better the approximation.) The interval boundaries constitute n + 1 points on the x-axis, viz, x0, x1, ..., xi, xi+1, ..., xn, where x0 = a and xn= b. The length of each interval is h = (b - a)/n, so each xi = a + ih. We then calculate the ordinates of f(x) at the interval boundaries. There are n + 1 such ordinates, viz, y0, ..., yi, ..., yn, where yi = f(xi) = f(a + ih). Simpson's rule approximates the definite integral of f(x) betweena and b with the value12:
We define the procedure integrate-simpson to take four arguments: the integrand f; the x-values at the limits a and b; and the number of intervals n.
(define integrate-simpson
(lambda (f a b n)
;...
The first thing we do in integrate-simpson's body is ensure that n is even -- if it isn't, we simply bump its value by 1.
;...
(unless (even? n) (set! n (+ n 1)))
;...
Next, we put in the local variable h the length of the interval. We introduce two more local variables h*2 and n/2 to store the values of twiceh and half n respectively, as we expect to use these values often in the ensuing calculations.
;...
(let* ((h (/ (- b a) n))
(h*2 (* h 2))
(n/2 (/ n 2))
;...
We note that the sums y1 + y3 + ··· + yn-1 and y2 + y4 + ··· + yn-2 both involve adding every other ordinate. So let's define a local procedure sum-every-other-ordinate-starting-from that captures this common iteration. By abstracting this iteration into a procedure, we avoid having to repeat the iteration textually. This not only reduces clutter, but reduces the chance of error, since we have only one textual occurrence of the iteration to debug.
sum-every-other-ordinate-starting-from takes two arguments: the starting ordinate and the number of ordinates to be summed.
;...
(sum-every-other-ordinate-starting-from
(lambda (x0 num-ordinates)
(let loop ((x x0) (i 0) (r 0))
(if (>= i num-ordinates) r
(loop (+ x h*2)
(+ i 1)
(+ r (f x)))))))
;...
We can now calculate the three ordinate sums, and combine them to produce the final answer. Note that there are n/2 terms in y1 + y3 + ··· +yn-1, and (n/2) - 1 terms in y2 + y4 + ··· + yn-2.
;...
(y0+yn (+ (f a) (f b)))
(y1+y3+...+y.n-1
(sum-every-other-ordinate-starting-from
(+ a h) n/2))
(y2+y4+...+y.n-2
(sum-every-other-ordinate-starting-from
(+ a h*2) (- n/2 1))))
(* 1/3 h
(+ y0+yn
(* 4.0 y1+y3+...+y.n-1)
(* 2.0 y2+y4+...+y.n-2))))))
Let's use integrate-simpson to find the definite integral of the function
We first define
in Scheme's prefix notation.13
(define pi (* 4 (atan 1)))
(define phi
(lambda (x)
(* (/ 1 (sqrt (* 2 pi)))
(exp (- (* 1/2 (* x x)))))))
Note that we exploit the fact that tan-1 1 =
/4 in order to define pi.14
The following calls calculate the definite integrals of phi from 0 to 1, 2, and 3 respectively. They all use 10 intervals.
(integrate-simpson phi 0 1 10)
(integrate-simpson phi 0 2 10)
(integrate-simpson phi 0 3 10)
To four decimal places, these values should be 0.3413, 0.4772, and 0.4987 respectively [2, Table 26.1]. Check to see that our implementation of Simpson's rule does indeed produce comparable values!15
C.2 Adaptive interval sizes
It is not always convenient to specify the number n of intervals. A number that is good enough for one integrand may be woefully inadequate for another. In such cases, it is better to specify the amount of tolerance e we are willing to grant the final answer, and let the program figure out how many intervals are needed. A typical way to accomplish this is to have the program try increasingly better answers by steadily increasing n, and stop when two successive sums differ within e. Thus:
(define integrate-adaptive-simpson-first-try
(lambda (f a b e)
(let loop ((n 4)
(iprev (integrate-simpson f a b 2)))
(let ((icurr (integrate-simpson f a b n)))
(if (<= (abs (- icurr iprev)) e)
icurr
(loop (+ n 2)))))))
Here we calculate successive Simpson integrals (using our original procedure integrate-simpson) for n = 2, 4, .... (Remember that n must be even.) When the integral icurr for the current n differs within e from the integral iprev for the immediately preceding n, we returnicurr.
One problem with this approach is that we don't take into account that only some segments of the function benefit from the addition of intervals. For the other segments, the addition of intervals merely increases the computation without contributing to a better overall answer. For an improved adaptation, we could split the integral into adjacent segments, and improve each segment separately.
(define integrate-adaptive-simpson-second-try
(lambda (f a b e)
(let integrate-segment ((a a) (b b) (e e))
(let ((i2 (integrate-simpson f a b 2))
(i4 (integrate-simpson f a b 4)))
(if (<= (abs (- i2 i4)) e)
i4
(let ((c (/ (+ a b) 2))
(e (/ e 2)))
(+ (integrate-segment a c e)
(integrate-segment c b e))))))))
The initial segment is from a to b. To find the integral for a segment, we calculate the Simpson integrals i2 and i4 with the two smallest interval numbers 2 and 4. If these are within e of each other, we return i4. If not we split the segment in half, recursively calculate the integral separately for each segment, and add. In general, different segments at the same level converge at their own pace. Note that when we integrate a half of a segment, we take care to also halve the tolerance, so that the precision of the eventual sum does not decay.
There are still some inefficiencies in this procedure: The integral i4 recalculates three ordinates already determined by i2, and the integral of each half-segment recalculates three ordinates already determined by i2 and i4. We avoid these inefficiencies by making explicit the sums used for i2 and i4, and by transmitting more parameters in the named-let integrate-segment. This makes for more sharing, both within the body of integrate-segment and across successive calls to integrate-segment:
(define integrate-adaptive-simpson
(lambda (f a b e)
(let* ((h (/ (- b a) 4))
(mid.a.b (+ a (* 2 h))))
(let integrate-segment ((x0 a)
(x2 mid.a.b)
(x4 b)
(y0 (f a))
(y2 (f mid.a.b))
(y4 (f b))
(h h)
(e e))
(let* ((x1 (+ x0 h))
(x3 (+ x2 h))
(y1 (f x1))
(y3 (f x3))
(i2 (* 2/3 h (+ y0 y4 (* 4.0 y2))))
(i4 (* 1/3 h (+ y0 y4 (* 4.0 (+ y1 y3))
(* 2.0 y2)))))
(if (<= (abs (- i2 i4)) e)
i4
(let ((h (/ h 2)) (e (/ e 2)))
(+ (integrate-segment
x0 x1 x2 y0 y1 y2 h e)
(integrate-segment
x2 x3 x4 y2 y3 y4 h e)))))))))
integrate-segment now explicitly sets four intervals of size h, giving five ordinates y0, y1, y2, y3, and y4. The integral i4 uses all of these ordinates, while the integral i2 uses just y0, y2, and y4, with an interval size of twice h. It is easy to verify that the explicit sums used for i2and i4 do correspond to Simpson sums.
Compare the following approximations of
020 ex dx:
(integrate-simpson exp 0 20 10)
(integrate-simpson exp 0 20 20)
(integrate-simpson exp 0 20 40)
(integrate-adaptive-simpson exp 0 20 .001)
(- (exp 20) 1)
The last one is the analytically correct answer. See if you can figure out the smallest n (overshooting is expensive!) such that (integrate-simpson exp 0 20 n) yields a result comparable to that returned by the integrate-adaptive-simpson call.
C.3 Improper integrals
Simpson's rule cannot be directly applied to improper integrals (integrals such that either the value of the integrand is unbounded somewhere within the interval of integration, or the interval of integration is itself unbounded). However, the rule can still be applied for a part of the integral, with the remaining being approximated by other means. For example, consider the
function. For n > 0,
(n) is defined as the following integral with unbounded upper limit:
From this, it follows that (a)
(1) = 1, and (b) for n > 0,
(n + 1) = n
(n). This implies that if we know the value of
in the interval (1, 2), we can find
(n) for any real n > 0. Indeed, if we relax the condition n > 0, we can use result (b) to extend the domain of
(n) to include n < 0, with the understanding that the function will diverge for integer n < 0.16
We first implement a Scheme procedure gamma-1-to-2 that requires its argument n to be within the interval (1, 2). gamma-1-to-2 takes a second argument e for the tolerance.
(define gamma-1-to-2
(lambda (n e)
(unless (< 1 n 2)
(error 'gamma-1-to-2 "argument outside (1, 2)"))
;...
We introduce a local variable gamma-integrand to hold the
-integrand g(x) = xn-1ex:
;...
(let ((gamma-integrand
(let ((n-1 (- n 1)))
(lambda (x)
(* (expt x n-1)
(exp (- x))))))
;...
We now need to integrate g(x) from 0 to
. Clearly we cannot deal with an infinite number of intervals; we therefore use Simpson's rule for only a portion of the interval [0,
), say [0, xc](c for cut-off''). For the remaining,tail'', interval [xc,
), we use a tail-integrand t(x) that reasonably approximates g(x), but has the advantage of being more tractable to analytic solution. Indeed, it is easy to see that for sufficiently large xc, we can replace g(x) by an exponential decay function t(x) = yc e-(x - xc ), where yc = g(xc). Thus:
The first integral can be solved using Simpson's rule, and the second integral is just yc. To find xc, we start with a low-ball value (say 4), and then refine it by successively doubling it until the ordinate at 2xc (ie, g(2xc)) is within a certain tolerance of the ordinate predicted by the tail-integrand (ie, t(2xc)). For both the Simpson integral and the tail-integrand calculation, we will require a tolerance of e/100, an order of 2 less than the given tolerance e, so the overall tolerance is not affected:
;...
(e/100 (/ e 100)))
(let loop ((xc 4) (yc (gamma-integrand 4)))
(let* ((tail-integrand
(lambda (x)
(* yc (exp (- (- x xc))))))
(x1 (* 2 xc))
(y1 (gamma-integrand x1))
(y1-estimated (tail-integrand x1)))
(if (<= (abs (- y1 y1-estimated)) e/100)
(+ (integrate-adaptive-simpson
gamma-integrand
0 xc e/100)
yc)
(loop x1 y1)))))))
We can now write a more general procedure gamma that returns
(n) for any real n:
(define gamma
(lambda (n e)
(cond ((< n 1) (/ (gamma (+ n 1) e) n))
((= n 1) 1)
((< 1 n 2) (gamma-1-to-2 n e))
(else (let ((n-1 (- n 1)))
(* n-1 (gamma n-1 e)))))))
Let us now calculate
(3/2).
(gamma 3/2 .001)
(* 1/2 (sqrt pi))
The second value is the analytically correct answer. (This is because
(3/2) = (1/2)
(1/2), and
(1/2) is known to be
1/2.) You can modifygamma's second argument (the tolerance) to get as close an approximation as you desire.
12 Consult any elementary text on the calculus for an explanation of why this approximation is reasonable.
13
is the probability density of a random variable with a normal or Gaussian distribution, with mean = 0 and standard deviation = 1. The definite integral
0z
(x) dx is the probability that the random variable assumes a value between 0 and z. However, you don't need to know all this in order to understand the example!
14 If Scheme didn't have the atan procedure, we could use our numerical-integration procedure to get an approximation for
01 (1 + x2)-1 dx, which is
/4.
15 By pulling constant factors -- such as (/ 1 (sqrt (* 2 pi))) in phi -- out of the integrand, we could speed up the ordinate calculations within integrate-simpson.
16
(n) for real n > 0 is itself an extension of the ``decrement-then-factorial'' function that maps integer n > 0 to (n - 1)!.
Appendix D
A clock for infinity
The Guile [13] procedure alarm provides an interruptable timer mechanism. The user can set or reset the alarm for some time units, or stop it. When the alarm's timer runs out of this time, it will set off an alarm, whose consequences are user-settable. Guile's alarm is not quite the clock of sec 15.1, but we can modify it easily enough.
The alarm's timer is initially stopped or quiescent, ie, it will not set off an alarm even as time goes by. To set the alarm's time-to-alarm to be nseconds, where n is not 0, run (alarm n). If the timer was already set (but has not yet set off an alarm), the (alarm n) procedure call will return the number of seconds remaining from the previous alarm setting. If there is no previous alarm setting, (alarm n) returns 0.
The procedure call (alarm 0) stops the alarm's timer, ie, the countdown of time is stopped, the timer becomes quiescent and no alarm will go off. (alarm 0) also returns the seconds remaining from a previous alarm setting, if any.
By default, when the alarm's countdown reaches 0, Guile will display a message on the console and exit. More useful behavior can be obtained by using the procedure sigaction, as follows:
(sigaction SIGALRM
(lambda (sig)
(display "Signal ")
(display sig)
(display " raised. Continuing...")
(newline)))
The first argument SIGALRM (which happens to be 14) identifies to sigaction that it is the alarm handler that needs setting.17 The second argument is a unary alarm-handling procedure of the user's choice. In this example, when the alarm goes off, the handler displays "Signal 14 raised. Continuing..." on the console without exiting Scheme. (The 14 is the SIGALRM value that the alarm will pass to its handler. Don't worry about it now.)
From our point of view, this simple timer mechanism poses one problem. A return value of 0 from a call to the procedure alarm is ambiguous: It could either mean that the alarm was quiescent, or that it was just about to run out of time. We could resolve this ambiguity if we could include *infinity*'' in the alarm arithmetic. In other words, we would like a clock that works almost like alarm, except that a quiescent clock is one with *infinity* seconds. This will make many things natural, viz, (1) (clock n) on a quiescent clock returns *infinity*, not 0. (2) To stop the clock, call (clock *infinity*), not (clock 0). (3) (clock 0) is equivalent to setting the clock to an infinitesimally small amount of time, viz, to cause it to raise an alarm instantaneously. In Guile, we can define *infinity* as the followingnumber'':
(define infinity (/ 1 0))
We can define clock in terms of alarm.
(define clock
(let ((stopped? #t)
(clock-interrupt-handler
(lambda () (error "Clock interrupt!"))))
(let ((generate-clock-interrupt
(lambda ()
(set! stopped? #t)
(clock-interrupt-handler))))
(sigaction SIGALRM
(lambda (sig) (generate-clock-interrupt)))
(lambda (msg val)
(case msg
((set-handler)
(set! clock-interrupt-handler val))
((set)
(cond ((= val infinity)
;This is equivalent to stopping the clock.
;This is almost equivalent to (alarm 0), except
;that if the clock is already stopped,
;return infinity.
(let ((time-remaining (alarm 0)))
(if stopped? *infinity*
(begin (set! stopped? #t)
time-remaining))))
((= val 0)
;This is equivalent to setting the alarm to
;go off immediately. This is almost equivalent
;to (alarm 0), except you force the alarm
;handler to run.
(let ((time-remaining (alarm 0)))
(if stopped?
(begin (generate-clock-interrupt)
*infinity*)
(begin (generate-clock-interrupt)
time-remaining))))
(else
;This is equivalent to (alarm n) for n != 0.
;Just remember to return *infinity* if the
;clock was previously quiescent.
(let ((time-remaining (alarm val)))
(if stopped?
(begin (set! stopped? #f) *infinity*)
time-remaining))))))))))
The clock procedure uses three internal state variables:
(1) stopped?, to describe if the clock is stopped;
(2) clock-interrupt-handler, which is a thunk describing the user-specified part of the alarm-handling action; and
(3) generate-clock-interrupt, another thunk which will set stopped? to false before running the user-specified alarm handler.
The clock procedure takes two arguments. If the first argument is set-handler, it uses the second argument as the alarm handler.
If the first argument is set, it sets the time-to-alarm to the second argument, returning the time remaining from a previous setting. The code treats 0, infinity and other values for time differently so that the user gets a mathematically transparent interface to alarm.
17 There are other signals with their corresponding handlers, and sigaction can be used to set these as well.
Appendix E
References
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[25] John McCarthy. A Basis for a Mathematical Theory of Computation. In P Braffort and D Hirschberg, editors, Computer Programming and Formal Systems. North-Holland, 1967.
[26] MIT Scheme Team. MIT Scheme.
[27] NCSA. The Common Gateway Interface.
[28] Christian Queinnec. Lisp in Small Pieces. Cambridge University Press, 1996.
[29] Thomas L Saaty and Paul C Kainen. The Four-Color Problem: Assaults and Conquest. Dover Publications, 1986.
[30] Manuel Serrano. Bigloo.
[31] Leon Sterling and Ehud Shapiro. The Art of Prolog. MIT Press, 2nd edition, 1994.
[32] Felix L Winkelmann. Chicken: A practical and portable Scheme system.
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Last modified 06 April 2022