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MacGambit A. Introduction 0 - 0 B. Using the online help 1247 - 0 C. User interface 2595 C.1. Interacting with the interpreter 2617 C.2. Basic editing 7797 C.3. Special keys 8688 C.4. Arrow keys 9194 C.5. Emacs commands 10642 C.6. Small keyboard emacs mode 11774 C.7. Mouse 12888 C.8. Scrolling 13505 C.9. Editor limitations 13720 - 0 D. Language extensions 13924 D.1. Concurrent evaluation 14059 D.2. Semaphores 15302 D.3. Queues 15838 D.4. Weak Pairs 16665 D.5. Ports 17502 D.6. Symbols 20082 D.7. Evaluation 20862 D.8. Tracing 22400 D.9. Miscellaneous 22798 D.10. Graphics 23861 D.11. Text windows 24963 D.12. Toolbox interface 25444 R4RS 1. Overview of Scheme 29391 1.1. Semantics 29417 1.2. Syntax 32799 1.3. Notation and terminology 33400 1.3.1. Essential and non-essential features 33434 1.3.2. Error situations and unspecified behavior 34047 1.3.3. Entry format 35651 1.3.4. Evaluation examples 38602 1.3.5. Naming conventions 39121 - 0 2. Lexical conventions 39803 2.1. Identifiers 40191 2.2. Whitespace and comments 42089 2.3. Other notations 43131 - 0 3. Basic concepts 44760 3.1. Variables and regions 44782 3.2. True and false 46700 3.3. External representations 47110 3.4. Disjointness of types 49267 3.5. Storage model 49625 - 0 4. Expressions 51311 4.1. Primitive expression types 51881 4.1.1. Variable references 51917 4.1.2. Literal expressions 52322 4.1.3. Procedure calls 53856 4.1.4. Lambda expressions 55381 4.1.5. Conditionals 57790 4.1.6. Assignments 58593 4.2. Derived expression types 59112 4.2.1. Conditionals 59323 4.2.2. Binding constructs 63696 4.2.3. Sequencing 67469 4.2.4. Iteration 68084 4.2.5. Delayed evaluation 71120 4.2.6. Quasiquotation 71633 - 0 5. Program structure 74339 5.1. Programs 74364 5.2. Definitions 75249 5.2.1. Top level definitions 76318 5.2.2. Internal definitions 77229 - 0 6. Standard procedures 78431 6.1. Booleans 78923 6.2. Equivalence predicates 80929 6.3. Pairs and lists 89220 6.4. Symbols 100276 6.5. Numbers 104239 6.5.1. Numerical types 105260 6.5.2. Exactness 106926 6.5.3. Implementation restrictions 108495 6.5.4. Syntax of numerical constants 112972 6.5.5. Numerical operations 114811 6.5.6. Numerical input and output 130979 6.6. Characters 134169 6.7. Strings 139477 6.8. Vectors 145492 6.9. Control features 149072 6.10. Input and output 159159 6.10.1. Ports 159186 6.10.2. Input 162997 6.10.3. Output 166744 6.10.4. System interface 168994 - 0 7. Formal syntax and semantics 170485 A-B abs 121317 acos 126325 and b62459 angle 128861 append 96331 apply 149743 asin 126325 assoc 98905 assq 98905 assv 98905 atan 126325 - 0 begin b67469 boolean? 80637 C c...r 94681 call-with-current-continuation 155293 call-with-input-file 159401 call-with-output-file 159401 car 93467 case b61015 cdr 93828 ceiling 124061 char->integer 138260 char-alphabetic? 137387 char-ci<=? 136667 char-ci<? 136667 char-ci=? 136667 char-ci>=? 136667 char-ci>? 136667 char-downcase 139094 char-lower-case? 137387 char-numeric? 137387 char-ready? 165775 char-upcase 139094 char-upper-case? 137387 char-whitespace? 137387 char<=? 135595 char<? 135595 char=? 135595 char>=? 135595 char>? 135595 char? 135450 clear-graphics i23880 clear-point i23880 close-input-port 162622 close-output-port 162622 compile-file i21236 complex? 115417 cond b59323 cons 92972 cos 126325 current-input-port 160923 current-output-port 160923 D-F define b75249 delay b71120 denominator 123525 display 167307 do b68084 draw-line-to i23880 draw-point i23880 - 0 else b59323 eof-object? 165453 eq? 86628 equal? 88456 eqv? 81368 error i22821 eval i20882 even? 118636 exact->inexact 130105 exact? 117297 exit i23342 exp 126325 expt 128675 - 0 floor 124061 for-each 151309 force 151915 future ib14059 G-L gcd 123005 gensym i20099 get i20412 get-output-string i17517 graphics-text i23880 - 0 if b57790 imag-part 128861 inexact->exact 130105 inexact? 117297 input-port? 160668 integer->char 138260 integer? 115417 - 0 lambda b55381 lcm 123005 length 96095 let b63696 let* b65198 letrec b65878 list 95872 list->string 144753 list->vector 148383 list-ref 97599 list-tail 97282 list? 95436 load 169191 log 126325 M-N magnitude 128861 make-polar 128861 make-queue i15854 make-rectangular 128861 make-semaphore i15322 make-string 141132 make-vector 146787 map 150408 max 119142 member 97915 memq 97915 memv 97915 min 119142 modulo 121486 - 0 negative? 118636 newline 168184 not 80199 null? 95288 number->string 131017 number? 115417 numerator 123525 O-R odd? 118636 open-input-file 162026 open-input-string i17517 open-output-file 162276 open-output-string i17517 open-text-window i24986 or b63065 output-port? 160668 - 0 pair? 92654 peek-char 164546 position-pen i23880 positive? 118636 pp i19384 pretty-print i19384 procedure? 149263 put i20412 - 0 quasiquote b71633 queue-get! i15854 queue-put! i15854 quote b52322 quotient 121486 - 0 rational? 115417 rationalize 125529 read 163015 read-char 164101 real-part 128861 real? 115417 remainder 121486 reverse 96986 round 124061 runtime i23459 S semaphore-signal i15322 semaphore-wait i15322 set! b58593 set-car! 94153 set-cdr! 94507 set-gc-report i23607 sin 126325 sqrt 128454 string 141492 string->list 144753 string->number 132602 string->symbol 103276 string-append 144572 string-ci<=? 142925 string-ci<? 142925 string-ci=? 142462 string-ci>=? 142925 string-ci>? 142925 string-copy 145188 string-fill! 145323 string-length 141637 string-ref 141777 string-set! 141975 string<=? 142925 string<? 142925 string=? 142462 string>=? 142925 string>? 142925 string? 140990 substring 144178 symbol->string 102205 symbol? 101815 T-Z tan 126325 touch i15083 trace ib22400 transcript-off 169825 transcript-on 169825 truncate 124061 - 0 untrace ib22400 - 0 vector 147136 vector->list 148383 vector-fill! 148892 vector-length 147368 vector-ref 147495 vector-set! 147905 vector? 146645 - 0 weak-car i16685 weak-cdr i16685 weak-cons i16685 weak-pair? i16685 weak-set-car! i16685 weak-set-cdr! i16685 with-input-from-file 161130 with-input-from-port i19052 with-input-from-string i18419 with-output-to-file 161130 with-output-to-port i19052 with-output-to-string i18419 write 166763 write-char 168588 - 0 zero? 118636 Others ' b52322 * 119958 + 119958 , b71633 – 120392 / 120392 ; b42089 < 117598 <= 117598 = 117598 => b59323 > 117598 >= 117598 ` b71633 ÛA. Introductionˇ MacGambit is a full implementation of Scheme that conforms to the IEEE-Scheme standard (IEEE P1178) and to the Revised˝4ˇ Report on Scheme (R4RS). The system supports the whole numeric tower (i.e. integer, rational, real and complex numbers). It also has several extensions to the standards including: weak pairs, string ports, property lists, pretty printer, debugger, compiler and multitasking. Macintosh specific features include: a Scheme interface to several Toolbox routines, a drawing window for simple graphics, an online help system and a Scheme oriented editor with an emacs compatibility mode. MacGambit runs on all Macintosh computers but requires at least 2 MB of RAM and System 6 or later. When the program is launched, it grabs most of the memory for its heap and leaves the rest for the Mac's own needs. When running Multifinder or System 7, it is possible to limit the amount of memory allocated by setting the "application memory size" (with the finder's Ícmd-Iˇ command). The latest version of MacGambit can be obtained through the INTERNET from the following anonymous FTP site: Í trex.iro.umontreal.ca:pub/gambitˇ Email concerning MacGambit should be sent to: Í gambit@trex.iro.umontreal.caˇ ÛB. Using the online helpˇ The online help contains two documents. The first document (MacGambit) contains information that is specific to MacGambit. The second document (R4RS) is a definition of the Scheme programming language. The first two menus of the online help window are the respective table of contents of these documents. The remaining menus are an alphabetic index of the procedures and special forms available. Procedures are in plain face, special forms are in bold face and MacGambit specific extensions are in italic. Navigating through the documentation is done either by selecting a topic from one of the help window's menus or by calling the procedure Íhelpˇ. When given the name of a procedure or special form (as a string or symbol), Íhelpˇ will move the help window to the appropriate part of the documentation. The main chapters of R4RS have been reproduced as faithfully as possible including the formatting conventions. However a few sections were omitted for space reasons: the summary, introduction, chapter 7 and appendices. We thank the editors of R4RS, William Clinger and Jonathan Rees, for making the report publicly available. The complete R4RS document can be obtained from the following anonymous FTP sites: Í nexus.yorku.ca:pub/scheme/doc/r4rs.ps.Zˇ Í altdorf.ai.mit.edu:pub/scheme-reports/r4rs.psˇ ÛC. User interfaceˇ ÛC.1. Interacting with the interpreterˇ Interaction with the interpreter's read-eval-print (REP) loop is done inside the "interaction" window. The content of the interaction window can be edited at will by the user. This window also acts as the default output port (and input port). Consequently, the interpreter sends its output to the interaction window. User input and system output are displayed with different fonts. By default, user input is in bold face (but this and other attributes of the window can be changed with the "Styles..." item in the Edit menu). Normally, the user types an expression and then "sends" it to the interpreter to be evaluated. The result of the evaluation is then output to the interaction window. The preferred way of evaluating an expression is to place the insertion point (caret) immediately after the expression to evaluate and then typing Ícmd-returnˇ (i.e. press the Íreturnˇ key while pressing the Ícommandˇ key). An alternative method is to use the Íenterˇ key. When Íenterˇ is pressed, the sequence of "user input" characters immediately preceding the insertion point are sent to the interpreter. Because it doesn't check for a properly formed expression, the Íenterˇ key is useful for programs doing text oriented input. Arbitrary text can also be sent to the interpreter by selecting the text before typing Ícmd-returnˇ or Íenterˇ. These interaction mechanisms also work from windows associated to files. However, the result of evaluation is always displayed in the interaction window. As opposed to most other Lisp systems, MacGambit combines the standard REP loop functions with those of the debugger. In a sense, the user is always interacting with the debugger. When an evaluation error is detected by the interpreter, a message describing the error is displayed and a REP loop of a higher level is started (the topmost REP loop is numbered 0). This REP loop is positionned in the context of the error so that the user can determine the cause of the error and possibly repair the problem and resume the evaluation as though no error had occured. At all times it is possible to examine the frames in the REP loop's continuation (i.e. the call stack). This is useful to locate the source of an error. Expressions typed in to the REP loop are evaluated in the context of the frame currently being examined. This is useful to check the bindings of variables and mutate them (check the examples for details). Special commands accepted by a REP loop are: Ícmd-Rˇ -- Returns from an error or interrupt (the user is prompted for the return value). This value is ignored when returning from an interrupt. Ícmd-Dˇ -- Returns to the previous REP loop (also acts as end-of-file). Ícmd-Tˇ -- Returns to the top-most REP loop. Ícmd-?ˇ -- Gives summary of commands. Ícmd-+ˇ -- Moves to next frame of the continuation and displays it in the same format as Ícmd-Bˇ. Ícmd--ˇ -- Moves to previous frame of the continuation and displays it in the same format as Ícmd-Bˇ. Ícmd-Bˇ -- Displays a summary of each frame in the continuation starting with the current frame. There are 3 columns. The first is the frame number. The second is the procedure that created the frame (and where control will return when this frame is resumed). The last column, if it is present, is the expression whose value is being computed. A frame created by a compiled procedure has a third column only if the procedure was compiled with the DEBUG option. Ícmd-Lˇ -- Lists all non-global variables accessible from the current frame. Ícmd-Iˇ -- Pretty prints the procedure that created the current frame. Ícmd-Yˇ -- Displays subproblem expression for the current frame. Ícmd-.ˇ -- This can be typed at any moment to interrupt the current computation. A new REP loop is started. Ícmd-Jˇ -- Loads a file. Ícmd-Kˇ -- Compiles a file. Here is a transcript of a typical interaction with MacGambit (comments are marked with ";;;" and user input is in bold): ÌMacGambit (v2.0) Ì Ì: Í(define (f x y) (/ (+ x y) 2))Ì Ìf Ì Ì: Í(let ((a 10) (b 20)) Í (* (f a 'b) (f a 100)))Ì ;;; we meant b not 'b Ì*** ERROR -- NUMBER expected Ì(+ 10 'b) Ì Ì1: ;;; typed Ícmd-BÌ to get backtrace Ì0 f (+ x y) Ì-1 (top level) (f a 'b) Ì-2 (top level) (let ((a 10) (b 20)) (* (f a 'b)... Ì-3 ##dynamic-env-bind Ì-4 ##read-eval-print Ì-5 ##dynamic-env-bind Ì-6 ###_kernel.startup Ì Ì1: ;;; typed Ícmd-IÌ to get the procedure that caused the error Ì#[procedure f] = Ì(lambda (x y) (/ (+ x y) 2)) Ì Ì1: ;;; typed Ícmd-LÌ to get the variables accessible here Ìx = 10 Ìy = b Ì Ì1: ;;; typed Ícmd--Ì to move to the previous subproblem Ì-1 (top level) (f a 'b) Ì Ì1-1: ;;; typed Ícmd-LÌ Ìa = 10 Ìb = 20 Ì Ì1-1: ;;; typed Ícmd-+Ì Ì0 f (+ x y) Ì Ì1: ;;; typed Ícmd-RÌ to return from error ÌReturn value: Í(+ x 20)Ì Ì825 Ì Ì: ;;; typed Ícmd-QÌ Ìˇ The file "init.scm" can be used to customize the interpreter. It is loaded just before the initial REP loop is entered. The file is first searched in the folder containing the document being opened and then in the folder containing the interpreter. ÛC.2. Basic editingˇ It is assumed that you are familiar with standard Macintosh editing techniques. If not, you should consult your Getting Started disks and Macintosh users' manuals. On all keyboards the following keys are defined: Í delete -ˇ erase character before cursor position Í tab -ˇ indent current line Í return -ˇ insert a new line and move to the left margin (and then Í ˇ do a Ítabˇ if autoindent is selected for the window) Ícmd-return -ˇ send the expression preceding the insertion point Í enter -ˇ send the user input preceding the insertion point Printable characters which are legal in Scheme programs are simply inserted into the buffer (these are characters in the range of 32 through 126 in the ASCII table). Other characters are simply discarded. However, you can paste arbitrary characters from another application or desk accessory. ÛC.3. Special keysˇ On extended keyboards the following special keys are supported: Í F1 - F4 -ˇ equivalent to Undo, Cut, Copy and Paste Í F5 - F15 -ˇ function keys (not used) Í del> -ˇ erase character after the insertion point Í home -ˇ scroll text to the top of the edit buffer Í end -ˇ scroll text to the bottom of the edit buffer Í page up -ˇ scroll text up a page Í page down -ˇ scroll text down a page Note that these last four do not move the insertion point, just scroll. ÛC.4. Arrow keysˇ Arrow keys (when available) move the insertion point in the corresponding direction: Í left -ˇ move cursor to the left one character Í right -ˇ move cursor to the right one character Í up -ˇ move cursor up one line Í down -ˇ move cursor down one line Arrow keys can be modified with the Íshiftˇ, Íoptionˇ, and Ícommandˇ keys. The Íshiftˇ key may be used to extend the text selection per Apple standards. Each selection has an anchor end and an active end. Generally, the active end is the last end you moved, the anchor end doesn't move. When the Íshiftˇ key is held down, the selection's active end is moved by the arrow keys. The Íoptionˇ key may be used with the arrow keys to move the insertion point left or right by word, or up or down by page. ÍShiftˇ and Íoptionˇ together may be used to move the active end of the selection left or right by words, or up or down by pages. The Ícommandˇ key may be used with the arrow keys to move the insertion point left or right to the beginning or end of the line, or up or down to the beginning or end of the text. ÍShiftˇ and Ícommandˇ together may be used to move the active end of the selection to start or end of the line or text. When Íshiftˇ, Íoptionˇ, and Ícommandˇ are held down together, the up or left arrow will make the beginning of the selection the active end, and the down or right arrow will make the end of the selection the active end. ÛC.5. Emacs commandsˇ A small subset of Emacs compatible command keys are supported by the editor. Some of these commands make use of the Ícontrolˇ key. The Ícontrolˇ key does not exist on small keyboards but it can be simulated by using the Small Keyboard mode (see below). The following table lists the Emacs compatible command keys using the following abbreviations: ÍCˇ = Ícontrolˇ key, ÍMˇ = Íoptionˇ key (Emacs' "meta" key). Commands which move the insertion point: Í C-f -ˇ forward character Í C-M-f -ˇ forward S-expression Í C-b -ˇ backward character Í C-M-b -ˇ backward S-expression Í C-a -ˇ beginning of line Í C-M-a -ˇ beginning of S-expression Í C-m -ˇ select enclosing S-expression Í C-M-m -ˇ select enclosing S-expression Í C-e -ˇ end of line Í C-M-e -ˇ end of S-expression Í C-p -ˇ previous line Í C-n -ˇ next line Commands which modify the buffer: Í C-d -ˇ delete forward (same as Ídel>ˇ key) Í C-del> -ˇ delete to end of line Í C-k -ˇ same as ÍC-del>ˇ Í C-o -ˇ open line Other commands: Í M-return -ˇ same as Ícmd-returnˇ ÛC.6. Small keyboard emacs modeˇ To use Emacs commands on small keyboards without a Ícontrolˇ key, the menu item "Small Keyboard" may be checked in the Edit menu. When it is checked, all keyboard events are interpreted as follows: • the Íoptionˇ key acts as the Ícontrolˇ key • pressing the Íoptionˇ and Ícommandˇ keys simultaneously acts the same as the Ícontrol-optionˇ combination. The original keyboard interpretation is restored by unchecking Small Keyboard mode. Note that Small Keyboard mode has no effect on other events (e.g., mouse modifiers remain as documented earlier). There is one quirk in small keyboard mode: since Íoption-nˇ and Íoption-eˇ are normally "dead keys," MacGambit requires a special keyboard mapping resource (KMAP). For System 6 users, nothing special needs to be done - the KMAP resource is included in the MacGambit application. For System 7 users, you must drag the file "U.S. Live" onto your System file for the MacGambit keyboard mapping to take effect. MacGambit's keyboard mapping will only affect MacGambit, the dead keys will continue to work in other applications. ÛC.7. Mouseˇ The editing action is specified by the number of mouse button clicks: Í single -ˇ position insertion point Í double -ˇ select word Í triple -ˇ select line Dragging after one of these clicks extends the selection by character, word, or line respectively; the anchor point is the original click position, the active end is the other end of the selection. After a click-drag, the active end can be moved with Íshiftˇ clicks or Íshiftˇ arrow keys. The anchor and active ends of the selection can be swapped with Íoption+shift+clickˇ, or Íoption+shift+commandˇ up/down or left/right arrow keys. ÛC.8. Scrollingˇ Holding down Ícommandˇ, Íshiftˇ, Íoptionˇ, and Ícontrolˇ keys speeds up scrolling when mousing in the arrows of the scroll bar. The more keys you hold down the faster it scrolls (exponentially). ÛC.9. Editor limitationsˇ The text size is limited by memory space. There is a limit of 32,000 lines (not characters) per window. The editor has been used with files several hundred kilobytes in size. ÛD. Language extensionsˇ This chapter gives a list of the procedures and special forms supported by MacGambit that are not in R4RS. ÛD.1. Concurrent evaluationˇ Í(future˘ ˇ<expression>Í) ˇsyntax The Ífutureˇ construct is used to implement ˘concurrent evaluationˇ. Í(future ˇ<expression>Í)ˇ creates a task to evaluate <expression> concurrently with the rest of the program (the continuation). The value returned by Ífutureˇ represents the value eventually computed for <expression>. If a task tries to use the value in a strict operation (such as Í+ˇ and Ícarˇ, but not Íconsˇ), the task is suspended until the value is known. Í (define (f n) (expt 3 n)) Í Í (let ((x (future (f 101)))) Í (let ((y (f 100))) Í (/ x y))) ==> 3 Í Í (let ((a 1)) Í (future Í (set! a (/ (f 101) (f 100)))) Í a) ==> 1 ˘orÍ 3 Í Í (define count 0) Í (define (inc) (set! count (+ count 1))) Í (define x (future (let loop () (inc) (loop)))) Í count ==> 1014 Í count ==> 3055 ˘etc.ˇ Í(touch˘ objÍ) ˇprocedure ÍTouchˇ is a strict operation that returns its argument. Í (touch 5) ==> 5 Í (touch (future 5)) ==> 5ˇ ÛD.2. Semaphoresˇ Í(make-semaphore) ˇprocedure Í(semaphore-wait˘ semaphoreÍ) ˇprocedure Í(semaphore-signal˘ semaphoreÍ) ˇprocedure These procedures implement the semaphore data type. Semaphores are generally used to enforce mutual exclusion. ÍSemaphore-waitˇ locks the semaphore and Ísemaphore-signalˇ unlocks it. A task trying to lock a semaphore with Ísemaphore-waitˇ is suspended until the semaphore is unlocked. ÛD.3. Queuesˇ Í(make-queue) ˇprocedure Í(queue-put!˘ queue objÍ) ˇprocedure Í(queue-get!˘ queueÍ) ˇprocedure These procedures implement the queue data type. A queue is a sequence of items. Items are added to the tail of the sequence by Íqueue-put!ˇ. ÍQueue-get!ˇ removes the next element at the head of the sequence. If the sequence is empty, Íqueue-get!ˇ returns Í#fˇ. Otherwise a single element list containing the item is returned. ÍQueue-put!ˇ and Íqueue-get!ˇ are atomic operations. Í (define q (make-queue)) Í (queue-put! q 1) Í (queue-put! q 2) Í (queue-get! q) ==> (1) Í (queue-get! q) ==> (2) Í (queue-get! q) ==> #fˇ ÛD.4. Weak Pairsˇ Í(weak-pair?˘ objÍ) ˇprocedure Í(weak-cons˘ obj¯1˘ obj¯2Í) ˇprocedure Í(weak-car˘ pairÍ) ˇprocedure Í(weak-cdr˘ pairÍ) ˇprocedure Í(weak-set-car!˘ pair objÍ) ˇprocedure Í(weak-set-cdr!˘ pair objÍ) ˇprocedure These procedures are the corresponding pair operations for the "weak pair" data type. Weak pairs are similar to normal pairs except that the object in the car field is "weakly linked" as far as garbage collection is concerned. The car field will be set to Í#fˇ by the garbage collector if it finds that there are only weak links to the object. ÛD.5. Portsˇ Í(open-input-string˘ stringÍ) ˇprocedure Í(open-output-string) ˇprocedure Í(get-output-string˘ portÍ) ˇprocedure These procedures implement string ports. String ports can be used like normal ports. The characters are obtained from (or sent to) a string instead of a file. An output string port accumulates the characters written to the port. The procedure Íget-output-stringˇ extracts the sequence of characters accumulated up to that point and returns them as a string. Í (define ip (open-input-string "(1 2)foo")) Í (define op (open-output-string)) Í (read ip) ==> (1 2) Í (read ip) ==> foo Í (read ip) ==> #[eof] Í (write 'bar op) Í (write '(a b) op) Í (get-output-string op) ==> "bar(a b)"ˇ Í(with-input-from-string˘ string thunkÍ) ˇprocedure Í(with-output-to-string˘ thunkÍ) ˇprocedure The procedure Íwith-input-from-stringˇ is similar to Íwith-input-from-fileˇ except that the characters are obtained from a string. The procedure Íwith-output-to-stringˇ calls the thunk and returns a string containing all characters output to the current output port. Í (with-input-from-string Í "a string" Í (lambda () Í (read-char))) ==> #\a Í Í (with-output-to-string Í (lambda () Í (write (cons 1 2)))) ==> "(1 . 2)"ˇ Í(with-input-from-port˘ port thunkÍ) ˇprocedure Í(with-output-to-port˘ port thunkÍ) ˇprocedure These procedures are respectively similar to Íwith-input-from-fileˇ and Íwith-output-to-fileˇ. The difference is that the first argument is a port instead of a file name. Í(pretty-print˘ objÍ) ˇprocedure Í(pretty-print˘ obj portÍ) ˇprocedure Í(pretty-print˘ obj port kÍ) ˇprocedure Í(pp˘ objÍ) ˇprocedure Í(pp˘ obj portÍ) ˇprocedure Í(pp˘ obj port kÍ) ˇprocedure ÍPretty-printˇ and Íppˇ are similar to Íwriteˇ except that the result is nicely formatted. The argument ˘kˇ specifies the width of the page. If ˘objˇ is a procedure created by the interpreter, Íppˇ will display its definition. ÛD.6. Symbolsˇ Í(gensym) ˇprocedure Í(gensym˘ prefixÍ) ˇprocedure ÍGensymˇ returns a new "uninterned" symbol. ˘Prefixˇ is used as a prefix to the generated name. ˘Prefixˇ is either a string or symbol and it defaults to "g". Í(get˘ symbol propÍ) ˇprocedure Í(put˘ symbol prop objÍ) ˇprocedure ÍGetˇ and Íputˇ access the property list of symbols. ÍPutˇ associates the value ˘objˇ with the property ˘propˇ of the symbol. ÍGetˇ extracts the value associated with the property ˘propˇ of the symbol. ÍGetˇ returns Í#fˇ if ˘propˇ has not been set for the symbol. ˘Propˇ can be any object. ÛD.7. Evaluationˇ Í(eval˘ objÍ) ˇprocedure ÍEvalˇ's argument is a datum representing an expression. ÍEvalˇ evaluates this expression in the global environment and returns the result. Í (eval '(+ 1 2)) ==> 3 Í (eval '(define x 1)) ==> ˘unspecifiedÍ Í x ==> 1ˇ Í(compile-file˘ filename option ...Í) ˇprocedure ˘Filenameˇ should be a string naming an existing file containing Scheme source code. Any of the compilation options described below can be specified after the filename. ÍCompile-fileˇ compiles the source file into an object file which can be loaded with the Íloadˇ procedure or linked into a standalone application by the linker. By convention, source files have a ".scm" extension. Object files have a ".O" extension. The following options are accepted by the compiler: Íverboseˇ -- Generates a trace of the compiler's actions. Íreportˇ -- Produces a global variable usage report. Each global variable used in the program is listed with 4 flags that indicate if the global variable is defined, referenced, mutated and called. Íexpansionˇ -- Shows the source code after macro expansion. Ípvmˇ -- Produces a listing of the PVM code for the program on "<file>.pvm". Íasmˇ -- Produces the assembly language output file "<file>.asm". Ídebugˇ -- Generates code that includes information to aid debugging. Note: The compiler is only available in the full version of MacGambit. ÛD.8. Tracingˇ Í(trace˘ ˇ<name>˘ ...Í) ˇsyntax Í(untrace˘ ˇ<name>˘ ...Í) ˇsyntax ÍTraceˇ starts tracing calls to the specified procedures. ÍUntraceˇ stops the tracing. The form Í(trace)ˇ returns the names of the currently traced procedures and Í(untrace)ˇ stops the tracing on all those procedures. ÛD.9. Miscellaneousˇ Í(error˘ string obj ...Í) ˇprocedure ÍErrorˇ signals an error and causes a new read-eval-print loop to be entered. The message displayed is Ístringˇ followed by the remaining arguments. The continuation of the read-eval-print loop is the same as the one passed to Íerrorˇ. Thus, returning from the read-eval-print loop causes a return from the call to Íerrorˇ. Í (define (real-sqrt x) Í (if (< x 0) Í (error "bad value to real-sqrt:" x) Í (sqrt x)))ˇ Í(exit) ˇprocedure ÍExitˇ causes the program to terminate. Í(runtime) ˇprocedure ÍRuntimeˇ returns the number of seconds since the program was started. Í(set-gc-report˘ booleanÍ) ˇprocedure ÍSet-gc-reportˇ controls the generation of reports on garbage collections. If the argument is true, a brief report of memory usage is generated on every garbage collection. ÛD.10. Graphicsˇ Í(clear-graphics) ˇprocedure Í(position-pen˘ x yÍ) ˇprocedure Í(draw-line-to˘ x yÍ) ˇprocedure Í(draw-point˘ x yÍ) ˇprocedure Í(clear-point˘ x yÍ) ˇprocedure Í(graphics-text˘ string x yÍ) ˇprocedure MacGambit has a "drawing" window which supports simple graphics. This window is initially hidden but it pops up when any of the above procedures are called. The coordinates of the drawing window go from -200 to +200 in both the x (horizontal) and y (vertical) axis. The window is scaled by a factor of 1/2 (i.e. a distance of 10 units corresponds to 5 pixels on the screen). The origin is in the center of the window. Lines are drawn using a "pen". ÍPosition-penˇ sets the position of the pen and calls to Ídraw-line-toˇ move the pen to a new coordinate leaving a line behind. The other procedures do not move the pen. ÛD.11. Text windowsˇ Í(open-text-window˘ stringÍ) ˇprocedure This procedure opens an editable text window with the given title and returns a port to access the window. The port is both an input and output port. Writing to the port displays text in the window. Reading from the port returns the expression (or text) that has been typed in this window and "sent" with Ícmd-returnˇ (or Íenterˇ for text). Closing the port closes the window. ÛD.12. Toolbox interfaceˇ Some of the most common Macintosh Toolbox routines are available as Scheme procedures. BEWARE: these procedures do not check the validity of their arguments so it is easy to crash the system by passing an illegal value. In general the procedures take the same parameters as the corresponding definition in "Inside Macintosh". The notable exception is for Quickdraw procedures. Instead of operating on the "current grafport", the quickdraw procedures take an extra argument that specifies the port to use. This is always the first parameter. Here is a list of the procedures available: Í; Windows Í Í(mac#newwindow bounds title visible procid behind goaway) Í(mac#getnewwindow windowid behind) Í(mac#disposewindow w) Í(mac#selectwindow w) Í(mac#hidewindow w) Í(mac#showwindow w) Í(mac#frontwindow) Í(mac#findwindow pt w-cell) ; w-cell is a pair, the car is the result Í(mac#trackgoaway w pt) Í(mac#dragwindow w pt r) Í(mac#invalrect port r) Í(mac#beginupdate w) Í(mac#endupdate w) Í Í; Quickdraw Í Í(mac#point v h) Í(mac#point-v r) Í(mac#point-h r) Í(mac#point-v-set! r x) Í(mac#point-h-set! r x) Í Í(mac#rect top left bottom right) Í(mac#rect-top r) Í(mac#rect-left r) Í(mac#rect-bottom r) Í(mac#rect-right r) Í(mac#rect-top-set! r x) Í(mac#rect-left-set! r x) Í(mac#rect-bottom-set! r x) Í(mac#rect-right-set! r x) Í Í(mac#openport port) Í(mac#initport port) Í(mac#closeport port) Í(mac#setport port) Í(mac#getport) Í(mac#setorigin port h v) Í(mac#backpat port pat) Í(mac#hidecursor) Í(mac#showcursor) Í(mac#pensize port width height) Í(mac#penmode port mode) Í(mac#penpat port pat) Í(mac#pennormal port) Í(mac#moveto port h v) Í(mac#move port dh dv) Í(mac#lineto port h v) Í(mac#line port dh dv) Í(mac#textfont port font) Í(mac#textface port face) Í(mac#textmode port mode) Í(mac#textsize port size) Í(mac#spaceextra port extra) Í(mac#drawchar port ch) Í(mac#drawstring port s) Í(mac#drawtext port textbuf firstbyte bytecount) ; textbuf is a string Í(mac#charwidth port ch) Í(mac#stringwidth port s) Í(mac#textwidth port textbuf firstbyte bytecount) ; textbuf is a string Í(mac#localtoglobal port pt) Í(mac#globaltolocal port pt) Í(mac#framerect port r) Í(mac#paintrect port r) Í(mac#eraserect port r) Í(mac#invertrect port r) Í(mac#fillrect port r pat) Í(mac#frameroundrect port r ovwd ovht) Í(mac#paintroundrect port r ovwd ovht) Í(mac#eraseroundrect port r ovwd ovht) Í(mac#invertroundrect port r ovwd ovht) Í(mac#fillroundrect port r ovwd ovht pat) Í(mac#frameoval port r) Í(mac#paintoval port r) Í(mac#eraseoval port r) Í(mac#invertoval port r) Í(mac#filloval port r pat) Í(mac#framearc port r startangle arcangle) Í(mac#paintarc port r startangle arcangle) Í(mac#erasearc port r startangle arcangle) Í(mac#invertarc port r startangle arcangle) Í(mac#fillarc port r startangle arcangle pat) Í Í; Menus Í Í(mac#newmenu menuid str) Í(mac#getmenu resourceid) Í(mac#disposemenu themenu) Í(mac#appendmenu themenu str) Í(mac#addresmenu themenu thetype) Í(mac#insertresmenu themenu thetype afteritem) Í(mac#insertmenu themenu beforeid) Í(mac#drawmenubar) Í(mac#deletemenu menuid) Í(mac#clearmenubar) Í(mac#getnewmbar menubarid) Í(mac#getmenubar) Í(mac#setmenubar menulist) Í(mac#menuselect p) Í(mac#menukey ch) Í(mac#hilitemenu menuid) Í(mac#disableitem themenu item) Í(mac#enableitem themenu item) Í(mac#getmhandle menuid) Í Í; Events Í Í(mac#event-what event) Í(mac#event-message event) Í(mac#event-when event) Í(mac#event-where event) Í(mac#event-modifiers event) Í Í(mac#modifiers-button? modifiers) Í(mac#modifiers-command? modifiers) Í(mac#modifiers-shift? modifiers) Í(mac#modifiers-alphalock? modifiers) Í(mac#modifiers-option? modifiers) Í Í; Standard file get/put Í Í(mac#sfgetfile) ; returns a filename or #f Í(mac#sfputfile) ; returns a filename or #f Í Í; Other procedures Í Í(mac#getmouse pt) Í(mac#button) Í(mac#tickcount) Í(mac#delay duration) Í(mac#sysbeep duration) Í(mac#seteventmask themask) Íˇ Û1. Overview of Schemeˇ Û1.1. Semanticsˇ This section gives an overview of Scheme's semantics. A detailed informal semantics is the subject of chapters 3 through 6. For reference purposes, section 7.2 provides a formal semantics of Scheme. Following Algol, Scheme is a statically scoped programming language. Each use of a variable is associated with a lexically apparent binding of that variable. Scheme has latent as opposed to manifest types. Types are associated with values (also called objects) rather than with variables. (Some authors refer to languages with latent types as weakly typed or dynamically typed languages.) Other languages with latent types are APL, Snobol, and other dialects of Lisp. Languages with manifest types (sometimes referred to as strongly typed or statically typed languages) include Algol 60, Pascal, and C. All objects created in the course of a Scheme computation, including procedures and continuations, have unlimited extent. No Scheme object is ever destroyed. The reason that implementations of Scheme do not (usually!) run out of storage is that they are permitted to reclaim the storage occupied by an object if they can prove that the object cannot possibly matter to any future computation. Other languages in which most objects have unlimited extent include APL and other Lisp dialects. Implementations of Scheme are required to be properly tail-recursive. This allows the execution of an iterative computation in constant space, even if the iterative computation is described by a syntactically recursive procedure. Thus with a tail-recursive implementation, iteration can be expressed using the ordinary procedure-call mechanics, so that special iteration constructs are useful only as syntactic sugar. Scheme procedures are objects in their own right. Procedures can be created dynamically, stored in data structures, returned as results of procedures, and so on. Other languages with these properties include Common Lisp and ML. One distinguishing feature of Scheme is that continuations, which in most other languages only operate behind the scenes, also have ``first-class'' status. Continuations are useful for implementing a wide variety of advanced control constructs, including non-local exits, backtracking, and coroutines. See section 6.9. Arguments to Scheme procedures are always passed by value, which means that the actual argument expressions are evaluated before the procedure gains control, whether the procedure needs the result of the evaluation or not. ML, C, and APL are three other languages that always pass arguments by value. This is distinct from the lazy-evaluation semantics of Haskell, or the call-by-name semantics of Algol 60, where an argument expression is not evaluated unless its value is needed by the procedure. Scheme's model of arithmetic is designed to remain as independent as possible of the particular ways in which numbers are represented within a computer. In Scheme, every integer is a rational number, every rational is a real, and every real is a complex number. Thus the distinction between integer and real arithmetic, so important to many programming languages, does not appear in Scheme. In its place is a distinction between exact arithmetic, which corresponds to the mathematical ideal, and inexact arithmetic on approximations. As in Common Lisp, exact arithmetic is not limited to integers. Û1.2. Syntaxˇ Scheme, like most dialects of Lisp, employs a fully parenthesized prefix notation for programs and (other) data; the grammar of Scheme generates a sublanguage of the language used for data. An important consequence of this simple, uniform representation is the susceptibility of Scheme programs and data to uniform treatment by other Scheme programs. The Íreadˇ procedure performs syntactic as well as lexical decomposition of the data it reads. The Íreadˇ procedure parses its input as data (section 7.1.2), not as program. The formal syntax of Scheme is described in section 7.1. Û1.3. Notation and terminologyˇ ¸1.3.1. Essential and non-essential featuresˇ It is required that every implementation of Scheme support features that are marked as being ˘essentialˇ. Features not explicitly marked as essential are not essential. Implementations are free to omit non-essential features of Scheme or to add extensions, provided the extensions are not in conflict with the language reported here. In particular, implementations must support portable code by providing a syntactic mode that preempts no lexical conventions of this report and reserves no identifiers other than those listed as syntactic keywords in section 2.1. ¸1.3.2. Error situations and unspecified behaviorˇ When speaking of an error situation, this report uses the phrase ``an error is signalled'' to indicate that implementations must detect and report the error. If such wording does not appear in the discussion of an error, then implementations are not required to detect or report the error, though they are encouraged to do so. An error situation that implementations are not required to detect is usually referred to simply as ``an error.'' For example, it is an error for a procedure to be passed an argument that the procedure is not explicitly specified to handle, even though such domain errors are seldom mentioned in this report. Implementations may extend a procedure's domain of definition to include such arguments. This report uses the phrase ``may report a violation of an implementation restriction'' to indicate circumstances under which an implementation is permitted to report that it is unable to continue execution of a correct program because of some restriction imposed by the implementation. Implementation restrictions are of course discouraged, but implementations are encouraged to report violations of implementation restrictions. For example, an implementation may report a violation of an implementation restriction if it does not have enough storage to run a program. If the value of an expression is said to be ``unspecified,'' then the expression must evaluate to some object without signalling an error, but the value depends on the implementation; this report explicitly does not say what value should be returned. ¸1.3.3. Entry formatˇ Chapters 4 and 6 are organized into entries. Each entry describes one language feature or a group of related features, where a feature is either a syntactic construct or a built-in procedure. An entry begins with one or more header lines of the form ˘templateÍ ˇessential ˘categoryˇ if the feature is an essential feature, or simply ˘templateÍ ˇ ˘categoryˇ if the feature is not an essential feature. If ˘categoryˇ is ``syntax'', the entry describes an expression type, and the header line gives the syntax of the expression type. Components of expressions are designated by syntactic variables, which are written using angle brackets, for example, <expression>, <variable>. Syntactic variables should be understood to denote segments of program text; for example, <expression> stands for any string of characters which is a syntactically valid expression. The notation <thing˛1ˇ> ... indicates zero or more occurrences of a <thing>, and <thing˛1ˇ> <thing˛2ˇ> ... indicates one or more occurrences of a <thing>. If ˘categoryˇ is ``procedure'', then the entry describes a procedure, and the header line gives a template for a call to the procedure. Argument names in the template are ˘italicizedˇ. Thus the header line Í(vector-ref ˘vectorÍ ˘kÍ) ˇessential procedure indicates that the essential built-in procedure Ívector-refˇ takes two arguments, a vector ˘vectorˇ and an exact non-negative integer ˘kˇ (see below). The header lines Í(make-vector ˘kÍ) ˇessential procedure Í(make-vector ˘kÍ ˘fillÍ) ˇprocedure indicate that in all implementations, the Ímake-vectorˇ procedure must be defined to take one argument, and some implementations will extend it to take two arguments. It is an error for an operation to be presented with an argument that it is not specified to handle. For succinctness, we follow the convention that if an argument name is also the name of a type listed in section 3.4, then that argument must be of the named type. For example, the header line for Ívector-refˇ given above dictates that the first argument to Ívector-refˇ must be a vector. The following naming conventions also imply type restrictions: ˘objÍ ˇany object ˘listˇ, ˘list¯1ˇ, ... ˘list¯jˇ, ...Í ˇlist (see section 6.3) ˘zˇ, ˘z¯1ˇ, ... ˘z¯jˇ, ...Í ˇcomplex number ˘xˇ, ˘x¯1ˇ, ... ˘x¯jˇ, ...Í ˇreal number ˘yˇ, ˘y¯1ˇ, ... ˘y¯jˇ, ...Í ˇreal number ˘qˇ, ˘q¯1ˇ, ... ˘q¯jˇ, ...Í ˇrational number ˘nˇ, ˘n¯1ˇ, ... ˘n¯jˇ, ...Í ˇinteger ˘kˇ, ˘k¯1ˇ, ... ˘k¯jˇ, ...Í ˇexact non-negative integer ¸1.3.4. Evaluation examplesˇ The symbol ``Í==>ˇ'' used in program examples should be read ``evaluates to.'' For example, Í (* 5 8) ==> 40ˇ means that the expression Í(* 5 8)ˇ evaluates to the object Í40ˇ. Or, more precisely: the expression given by the sequence of characters ``Í(* 5 8)ˇ'' evaluates, in the initial environment, to an object that may be represented externally by the sequence of characters ``Í40ˇ''. See section 3.3 for a discussion of external representations of objects. ¸1.3.5. Naming conventionsˇ By convention, the names of procedures that always return a boolean value usually end in ``Í?ˇ''. Such procedures are called predicates. By convention, the names of procedures that store values into previously allocated locations (see section 3.5) usually end in ``Í!ˇ''. Such procedures are called mutation procedures. By convention, the value returned by a mutation procedure is unspecified. By convention, ``Í->ˇ'' appears within the names of procedures that take an object of one type and return an analogous object of another type. For example, Ílist->vectorˇ takes a list and returns a vector whose elements are the same as those of the list. Û2. Lexical conventionsˇ This section gives an informal account of some of the lexical conventions used in writing Scheme programs. For a formal syntax of Scheme, see section 7.1. Upper and lower case forms of a letter are never distinguished except within character and string constants. For example, ÍFooˇ is the same identifier as ÍFOOˇ, and Í#x1ABˇ is the same number as Í#X1abˇ. Û2.1. Identifiersˇ Most identifiers allowed by other programming languages are also acceptable to Scheme. The precise rules for forming identifiers vary among implementations of Scheme, but in all implementations a sequence of letters, digits, and ``extended alphabetic characters'' that begins with a character that cannot begin a number is an identifier. In addition, Í+ˇ, Í-ˇ, and Í...ˇ are identifiers. Here are some examples of identifiers: Í lambda q Í list->vector soup Í + V17a Í <=? a34kTMNs Í the-word-recursion-has-many-meaningsˇ Extended alphabetic characters may be used within identifiers as if they were letters. The following are extended alphabetic characters: Í + - . * / < = > ! ? : $ % _ & ~ ^ˇ See section 7.1.1 for a formal syntax of identifiers. Identifiers have several uses within Scheme programs: • Certain identifiers are reserved for use as syntactic keywords (see below). • Any identifier that is not a syntactic keyword may be used as a variable (see section 3.1). • When an identifier appears as a literal or within a literal (see section 4.1.2), it is being used to denote a ˘symbolˇ (see section 6.4). The following identifiers are syntactic keywords, and should not be used as variables: Í => do or Í and else quasiquote Í begin if quote Í case lambda set! Í cond let unquote Í define let* unquote-splicing Í delay letrecˇ Some implementations allow all identifiers, including syntactic keywords, to be used as variables. This is a compatible extension to the language, but ambiguities in the language result when the restriction is relaxed, and the ways in which these ambiguities are resolved vary between implementations. Û2.2. Whitespace and commentsˇ ˘Whitespaceˇ characters are spaces and newlines. (Implementations typically provide additional whitespace characters such as tab or page break.) Whitespace is used for improved readability and as necessary to separate tokens from each other, a token being an indivisible lexical unit such as an identifier or number, but is otherwise insignificant. Whitespace may occur between any two tokens, but not within a token. Whitespace may also occur inside a string, where it is significant. A semicolon (Í;ˇ) indicates the start of a comment. The comment continues to the end of the line on which the semicolon appears. Comments are invisible to Scheme, but the end of the line is visible as whitespace. This prevents a comment from appearing in the middle of an identifier or number. Í ;;; The FACT procedure computes the factorial Í ;;; of a non-negative integer. Í (define fact Í (lambda (n) Í (if (= n 0) Í 1 ;Base case: return 1 Í (* n (fact (- n 1))))))ˇ Û2.3. Other notationsˇ For a description of the notations used for numbers, see section 6.5. Í. + -ˇ These are used in numbers, and may also occur anywhere in an identifier except as the first character. A delimited plus or minus sign by itself is also an identifier. A delimited period (not occurring within a number or identifier) is used in the notation for pairs (section 6.3), and to indicate a rest-parameter in a formal parameter list (section 4.1.4). A delimited sequence of three successive periods is also an identifier. Í( )ˇ Parentheses are used for grouping and to notate lists (section 6.3). Í'ˇ The single quote character is used to indicate literal data (section 4.1.2). Í`ˇ The backquote character is used to indicate almost-constant data (section 4.2.6). Í, ,@ˇ The character comma and the sequence comma at-sign are used in conjunction with backquote (section 4.2.6). Í"ˇ The double quote character is used to delimit strings (section 6.7). Í\ˇ Backslash is used in the syntax for character constants (section 6.6) and as an escape character within string constants (section 6.7). Í[ ] { }ˇ Left and right square brackets and curly braces are reserved for possible future extensions to the language. Í#ˇ Sharp sign is used for a variety of purposes depending on the character that immediately follows it: Í#tˇ Í#fˇ These are the boolean constants (section 6.1). Í#\ˇ This introduces a character constant (section 6.6). Í#(ˇ This introduces a vector constant (section 6.8). Vector constants are terminated by Í)ˇ . Í#e #i #b #o #d #xˇ These are used in the notation for numbers (section 6.5.4). Û3. Basic conceptsˇ Û3.1. Variables and regionsˇ Any identifier that is not a syntactic keyword (see section 2.1) may be used as a variable. A variable may name a location where a value can be stored. A variable that does so is said to be ˘boundˇ to the location. The set of all visible bindings in effect at some point in a program is known as the ˘environmentˇ in effect at that point. The value stored in the location to which a variable is bound is called the variable's value. By abuse of terminology, the variable is sometimes said to name the value or to be bound to the value. This is not quite accurate, but confusion rarely results from this practice. Certain expression types are used to create new locations and to bind variables to those locations. The most fundamental of these ˘binding constructsˇ is the lambda expression, because all other binding constructs can be explained in terms of lambda expressions. The other binding constructs are Íletˇ, Ílet*ˇ, Íletrecˇ, and Ídoˇ expressions (see sections 4.1.4, 4.2.2, and 4.2.4). Like Algol and Pascal, and unlike most other dialects of Lisp except for Common Lisp, Scheme is a statically scoped language with block structure. To each place where a variable is bound in a program there corresponds a ˘regionˇ of the program text within which the binding is effective. The region is determined by the particular binding construct that establishes the binding; if the binding is established by a lambda expression, for example, then its region is the entire lambda expression. Every reference to or assignment of a variable refers to the binding of the variable that established the innermost of the regions containing the use. If there is no binding of the variable whose region contains the use, then the use refers to the binding for the variable in the top level environment, if any (section 6); if there is no binding for the identifier, it is said to be ˘unboundˇ. Û3.2. True and falseˇ Any Scheme value can be used as a boolean value for the purpose of a conditional test. As explained in section 6.1, all values count as true in such a test except for Í#fˇ. This report uses the word ``true'' to refer to any Scheme value that counts as true, and the word ``false'' to refer to Í#fˇ. ˘Note:ˇ In some implementations the empty list also counts as false instead of true. Û3.3. External representationsˇ An important concept in Scheme (and Lisp) is that of the ˘external representationˇ of an object as a sequence of characters. For example, an external representation of the integer 28 is the sequence of characters ``Í28ˇ'', and an external representation of a list consisting of the integers 8 and 13 is the sequence of characters ``Í(8 13)ˇ''. The external representation of an object is not necessarily unique. The integer 28 also has representations ``Í#e28.000ˇ'' and ``Í#x1cˇ'', and the list in the previous paragraph also has the representations ``Í( 08 13 )ˇ'' and ``Í(8 . (13 . ()))ˇ'' (see section 6.3). Many objects have standard external representations, but some, such as procedures, do not have standard representations (although particular implementations may define representations for them). An external representation may be written in a program to obtain the corresponding object (see Íquoteˇ, section 4.1.2). External representations can also be used for input and output. The procedure Íreadˇ (section 6.10.2) parses external representations, and the procedure Íwriteˇ (section 6.10.3) generates them. Together, they provide an elegant and powerful input/output facility. Note that the sequence of characters ``Í(+ 2 6)ˇ'' is ˘notˇ an external representation of the integer 8, even though it ˘isˇ an expression evaluating to the integer 8; rather, it is an external representation of a three-element list, the elements of which are the symbol Í+ˇ and the integers 2 and 6. Scheme's syntax has the property that any sequence of characters that is an expression is also the external representation of some object. This can lead to confusion, since it may not be obvious out of context whether a given sequence of characters is intended to denote data or program, but it is also a source of power, since it facilitates writing programs such as interpreters and compilers that treat programs as data (or vice versa). The syntax of external representations of various kinds of objects accompanies the description of the primitives for manipulating the objects in the appropriate sections of chapter 6. Û3.4. Disjointness of typesˇ No object satisfies more than one of the following predicates: Í boolean? pair? Í symbol? number? Í char? string? Í vector? procedure?ˇ These predicates define the types ˘booleanˇ, ˘pairˇ, ˘symbolˇ, ˘numberˇ, ˘charˇ (or ˘characterˇ), ˘stringˇ, ˘vectorˇ, and ˘procedureˇ. Û3.5. Storage modelˇ Variables and objects such as pairs, vectors, and strings implicitly denote locations or sequences of locations. A string, for example, denotes as many locations as there are characters in the string. (These locations need not correspond to a full machine word.) A new value may be stored into one of these locations using the Ístring-set!ˇ procedure, but the string continues to denote the same locations as before. An object fetched from a location, by a variable reference or by a procedure such as Ícarˇ, Ívector-refˇ, or Ístring-refˇ, is equivalent in the sense of Íeqv?ˇ (section 6.2) to the object last stored in the location before the fetch. Every location is marked to show whether it is in use. No variable or object ever refers to a location that is not in use. Whenever this report speaks of storage being allocated for a variable or object, what is meant is that an appropriate number of locations are chosen from the set of locations that are not in use, and the chosen locations are marked to indicate that they are now in use before the variable or object is made to denote them. In many systems it is desirable for constants (i.e. the values of literal expressions) to reside in read-only-memory. To express this, it is convenient to imagine that every object that denotes locations is associated with a flag telling whether that object is mutable or immutable. The constants and the strings returned by Ísymbol->stringˇ are then the immutable objects, while all objects created by the other procedures listed in this report are mutable. It is an error to attempt to store a new value into a location that is denoted by an immutable object. Û4. Expressionsˇ A Scheme expression is a construct that returns a value, such as a variable reference, literal, procedure call, or conditional. Expression types are categorized as ˘primitiveˇ or ˘derivedˇ. Primitive expression types include variables and procedure calls. Derived expression types are not semantically primitive, but can instead be explained in terms of the primitive constructs as in section 7.3. They are redundant in the strict sense of the word, but they capture common patterns of usage, and are therefore provided as convenient abbreviations. Û4.1. Primitive expression typesˇ ¸4.1.1. Variable referencesˇ <variable>Í ˇessential syntax An expression consisting of a variable (section 3.1) is a variable reference. The value of the variable reference is the value stored in the location to which the variable is bound. It is an error to reference an unbound variable. Í (define x 28) Í x ==> 28ˇ ¸4.1.2. Literal expressionsˇ Í(quote˘ ˇ<datum>Í) ˇessential syntax Í'ˇ<datum>Í ˇessential syntax <constant>Í ˇessential syntax Í(quote ˇ<datum>Í)ˇ evaluates to <datum>. <Datum> may be any external representation of a Scheme object (see section 3.3). This notation is used to include literal constants in Scheme code. Í (quote a) ==> a Í (quote #(a b c)) ==> #(a b c) Í (quote (+ 1 2)) ==> (+ 1 2)ˇ Í(quote ˇ<datum>Í)ˇ may be abbreviated as Í'ˇ<datum>. The two notations are equivalent in all respects. Í 'a ==> a Í '#(a b c) ==> #(a b c) Í '() ==> () Í '(+ 1 2) ==> (+ 1 2) Í '(quote a) ==> (quote a) Í ''a ==> (quote a)ˇ Numerical constants, string constants, character constants, and boolean constants evaluate ``to themselves''; they need not be quoted. Í '"abc" ==> "abc" Í "abc" ==> "abc" Í '145932 ==> 145932 Í 145932 ==> 145932 Í '#t ==> #t Í #t ==> #tˇ As noted in section 3.5, it is an error to alter a constant (i.e. the value of a literal expression) using a mutation procedure like Íset-car!ˇ or Ístring-set!ˇ. ¸4.1.3. Procedure callsˇ Í(ˇ<operator>Í ˇ<operand˛1ˇ>Í ...) ˇessential syntax A procedure call is written by simply enclosing in parentheses expressions for the procedure to be called and the arguments to be passed to it. The operator and operand expressions are evaluated (in an unspecified order) and the resulting procedure is passed the resulting arguments. Í (+ 3 4) ==> 7 Í ((if #f + *) 3 4) ==> 12ˇ A number of procedures are available as the values of variables in the initial environment; for example, the addition and multiplication procedures in the above examples are the values of the variables Í+ˇ and Í*ˇ. New procedures are created by evaluating lambda expressions (see section 4.1.4). Procedure calls are also called ˘combinationsˇ. ˘Note:ˇ In contrast to other dialects of Lisp, the order of evaluation is unspecified, and the operator expression and the operand expressions are always evaluated with the same evaluation rules. ˘Note:ˇ Although the order of evaluation is otherwise unspecified, the effect of any concurrent evaluation of the operator and operand expressions is constrained to be consistent with some sequential order of evaluation. The order of evaluation may be chosen differently for each procedure call. ˘Note:ˇ In many dialects of Lisp, the empty combination, Í()ˇ, is a legitimate expression. In Scheme, combinations must have at least one subexpression, so Í()ˇ is not a syntactically valid expression. ¸4.1.4. Lambda expressionsˇ Í(lambda˘ ˇ<formals>˘ ˇ<body>Í) ˇessential syntax ˘Syntax:ˇ <Formals> should be a formal arguments list as described below, and <body> should be a sequence of one or more expressions. ˘Semantics:ˇ A lambda expression evaluates to a procedure. The environment in effect when the lambda expression was evaluated is remembered as part of the procedure. When the procedure is later called with some actual arguments, the environment in which the lambda expression was evaluated will be extended by binding the variables in the formal argument list to fresh locations, the corresponding actual argument values will be stored in those locations, and the expressions in the body of the lambda expression will be evaluated sequentially in the extended environment. The result of the last expression in the body will be returned as the result of the procedure call. Í (lambda (x) (+ x x)) ==> ˘a procedureÍ Í ((lambda (x) (+ x x)) 4) ==> 8 Í Í (define reverse-subtract Í (lambda (x y) (- y x))) Í (reverse-subtract 7 10) ==> 3 Í Í (define add4 Í (let ((x 4)) Í (lambda (y) (+ x y)))) Í (add4 6) ==> 10ˇ <Formals> should have one of the following forms: • Í(ˇ<variable˛1ˇ>Í ...)ˇ: The procedure takes a fixed number of arguments; when the procedure is called, the arguments will be stored in the bindings of the corresponding variables. • <variable>: The procedure takes any number of arguments; when the procedure is called, the sequence of actual arguments is converted into a newly allocated list, and the list is stored in the binding of the <variable>. • Í(ˇ<variable˛1ˇ>Í ... ˇ<variable˛n-1ˇ>Í . ˇ<variable˛nˇ>Í)ˇ: If a space-delimited period precedes the last variable, then the value stored in the binding of the last variable will be a newly allocated list of the actual arguments left over after all the other actual arguments have been matched up against the other formal arguments. It is an error for a <variable> to appear more than once in <formals>. Í ((lambda x x) 3 4 5 6) ==> (3 4 5 6) Í ((lambda (x y . z) z) Í 3 4 5 6) ==> (5 6)ˇ Each procedure created as the result of evaluating a lambda expression is tagged with a storage location, in order to make Íeqv?ˇ and Íeq?ˇ work on procedures (see section 6.2). ¸4.1.5. Conditionalsˇ Í(if˘ ˇ<test>˘ ˇ<consequent>˘ ˇ<alternate>Í) ˇessential syntax Í(if˘ ˇ<test>˘ ˇ<consequent>Í) ˇsyntax ˘Syntax:ˇ <Test>, <consequent>, and <alternate> may be arbitrary expressions. ˘Semantics:ˇ An Íifˇ expression is evaluated as follows: first, <test> is evaluated. If it yields a true value (see section 6.1), then <consequent> is evaluated and its value is returned. Otherwise <alternate> is evaluated and its value is returned. If <test> yields a false value and no <alternate> is specified, then the result of the expression is unspecified. Í (if (> 3 2) 'yes 'no) ==> yes Í (if (> 2 3) 'yes 'no) ==> no Í (if (> 3 2) Í (- 3 2) Í (+ 3 2)) ==> 1ˇ ¸4.1.6. Assignmentsˇ Í(set!˘ ˇ<variable>˘ ˇ<expression>Í) ˇessential syntax <Expression> is evaluated, and the resulting value is stored in the location to which <variable> is bound. <Variable> must be bound either in some region enclosing the Íset!ˇ expression or at top level. The result of the Íset!ˇ expression is unspecified. Í (define x 2) Í (+ x 1) ==> 3 Í (set! x 4) ==> ˘unspecifiedÍ Í (+ x 1) ==> 5ˇ Û4.2. Derived expression typesˇ For reference purposes, section 7.3 gives rewrite rules that will convert constructs described in this section into the primitive constructs described in the previous section. ¸4.2.1. Conditionalsˇ Í(cond˘ ˇ<clause˛1ˇ>˘ ˇ<clause˛2ˇ>˘ ...Í) ˇessential syntax ˘Syntax:ˇ Each <clause> should be of the form Í(ˇ<test>Í ˇ<expression>Í ...)ˇ where <test> is any expression. The last <clause> may be an ``else clause,'' which has the form Í(else Íˇ<expression˛1ˇ>Í ˇ<expression˛2ˇ>Í ...).ˇ ˘Semantics:ˇ A Ícondˇ expression is evaluated by evaluating the <test> expressions of successive <clause>s in order until one of them evaluates to a true value (see section 6.1). When a <test> evaluates to a true value, then the remaining <expression>s in its <clause> are evaluated in order, and the result of the last <expression> in the <clause> is returned as the result of the entire Ícondˇ expression. If the selected <clause> contains only the <test> and no <expression>s, then the value of the <test> is returned as the result. If all <test>s evaluate to false values, and there is no else clause, then the result of the conditional expression is unspecified; if there is an else clause, then its <expression>s are evaluated, and the value of the last one is returned. Í (cond ((> 3 2) 'greater) Í ((< 3 2) 'less)) ==> greater Í (cond ((> 3 3) 'greater) Í ((< 3 3) 'less) Í (else 'equal)) ==> equalˇ Some implementations support an alternative <clause> syntax, Í(ˇ<test>Í => ˇ<recipient>Í)ˇ, where <recipient> is an expression. If <test> evaluates to a true value, then <recipient> is evaluated. Its value must be a procedure of one argument; this procedure is then invoked on the value of the <test>. Í (cond ((assv 'b '((a 1) (b 2))) => cadr) Í (else #f)) ==> 2ˇ Í(case˘ ˇ<key>˘ ˇ<clause˛1ˇ>˘ ˇ<clause˛2ˇ>˘ ...Í) ˇessential syntax ˘Syntax:ˇ <Key> may be any expression. Each <clause> should have the form Í((ˇ<datum˛1ˇ>Í Í...) ˇ<expression˛1ˇ>Í ˇ<expression˛2ˇ>Í ...),ˇ where each <datum> is an external representation of some object. All the <datum>s must be distinct. The last <clause> may be an ``else clause,'' which has the form Í(else ˇ<expression˛1ˇ>Í ˇ<expression˛2ˇ>Í ...).ˇ ˘Semantics:ˇ A Ícaseˇ expression is evaluated as follows. <Key> is evaluated and its result is compared against each <datum>. If the result of evaluating <key> is equivalent (in the sense of Íeqv?ˇ; see section 6.2) to a <datum>, then the expressions in the corresponding <clause> are evaluated from left to right and the result of the last expression in the <clause> is returned as the result of the Ícaseˇ expression. If the result of evaluating <key> is different from every <datum>, then if there is an else clause its expressions are evaluated and the result of the last is the result of the Ícaseˇ expression; otherwise the result of the Ícaseˇ expression is unspecified. Í (case (* 2 3) Í ((2 3 5 7) 'prime) Í ((1 4 6 8 9) 'composite)) ==> composite Í (case (car '(c d)) Í ((a) 'a) Í ((b) 'b)) ==> ˘unspecifiedÍ Í (case (car '(c d)) Í ((a e i o u) 'vowel) Í ((w y) 'semivowel) Í (else 'consonant)) ==> consonantˇ Í(and˘ ˇ<test˛1ˇ>˘ ...Í) ˇessential syntax The <test> expressions are evaluated from left to right, and the value of the first expression that evaluates to a false value (see section 6.1) is returned. Any remaining expressions are not evaluated. If all the expressions evaluate to true values, the value of the last expression is returned. If there are no expressions then Í#tˇ is returned. Í (and (= 2 2) (> 2 1)) ==> #t Í (and (= 2 2) (< 2 1)) ==> #f Í (and 1 2 'c '(f g)) ==> (f g) Í (and) ==> #tˇ Í(or˘ ˇ<test˛1ˇ>˘ ...Í) ˇessential syntax The <test> expressions are evaluated from left to right, and the value of the first expression that evaluates to a true value (see section 6.1) is returned. Any remaining expressions are not evaluated. If all expressions evaluate to false values, the value of the last expression is returned. If there are no expressions then Í#fˇ is returned. Í (or (= 2 2) (> 2 1)) ==> #t Í (or (= 2 2) (< 2 1)) ==> #t Í (or #f #f #f) ==> #f Í (or (memq 'b '(a b c)) Í (/ 3 0)) ==> (b c)ˇ ¸4.2.2. Binding constructsˇ The three binding constructs Íletˇ, Ílet*ˇ, and Íletrecˇ give Scheme a block structure, like Algol 60. The syntax of the three constructs is identical, but they differ in the regions they establish for their variable bindings. In a Íletˇ expression, the initial values are computed before any of the variables become bound; in a Ílet*ˇ expression, the bindings and evaluations are performed sequentially; while in a Íletrecˇ expression, all the bindings are in effect while their initial values are being computed, thus allowing mutually recursive definitions. Í(let˘ ˇ<bindings>˘ ˇ<body>Í) ˇessential syntax ˘Syntax:ˇ <Bindings> should have the form Í((ˇ<variable˛1ˇ>Í ˇ<init˛1ˇ>Í) ...),ˇ where each <init> is an expression, and <body> should be a sequence of one or more expressions. It is an error for a <variable> to appear more than once in the list of variables being bound. ˘Semantics:ˇ The <init>s are evaluated in the current environment (in some unspecified order), the <variable>s are bound to fresh locations holding the results, the <body> is evaluated in the extended environment, and the value of the last expression of <body> is returned. Each binding of a <variable> has <body> as its region. Í (let ((x 2) (y 3)) Í (* x y)) ==> 6 Í Í (let ((x 2) (y 3)) Í (let ((x 7) Í (z (+ x y))) Í (* z x))) ==> 35ˇ See also named Íletˇ, section 4.2.4. Í(let*˘ ˇ<bindings>˘ ˇ<body>Í) ˇsyntax ˘Syntax:ˇ <Bindings> should have the form Í((ˇ<variable˛1ˇ>Í ˇ<init˛1ˇ>Í) ...),ˇ and <body> should be a sequence of one or more expressions. ˘Semantics:ˇ ÍLet*ˇ is similar to Íletˇ, but the bindings are performed sequentially from left to right, and the region of a binding indicated by Í(ˇ<variable>Í ˇ<init>Í)ˇ is that part of the Ílet*ˇ expression to the right of the binding. Thus the second binding is done in an environment in which the first binding is visible, and so on. Í (let ((x 2) (y 3)) Í (let* ((x 7) Í (z (+ x y))) Í (* z x))) ==> 70ˇ Í(letrec˘ ˇ<bindings>˘ ˇ<body>Í) ˇessential syntax ˘Syntax:ˇ <Bindings> should have the form Í((ˇ<variable˛1ˇ>Í ˇ<init˛1ˇ>Í) ...),ˇ and <body> should be a sequence of one or more expressions. It is an error for a <variable> to appear more than once in the list of variables being bound. ˘Semantics:ˇ The <variable>s are bound to fresh locations holding undefined values, the <init>s are evaluated in the resulting environment (in some unspecified order), each <variable> is assigned to the result of the corresponding <init>, the <body> is evaluated in the resulting environment, and the value of the last expression in <body> is returned. Each binding of a <variable> has the entire Íletrecˇ expression as its region, making it possible to define mutually recursive procedures. Í (letrec ((even? Í (lambda (n) Í (if (zero? n) Í #t Í (odd? (- n 1))))) Í (odd? Í (lambda (n) Í (if (zero? n) Í #f Í (even? (- n 1)))))) Í (even? 88)) Í ==> #tˇ One restriction on Íletrecˇ is very important: it must be possible to evaluate each <init> without assigning or referring to the value of any <variable>. If this restriction is violated, then it is an error. The restriction is necessary because Scheme passes arguments by value rather than by name. In the most common uses of Íletrecˇ, all the <init>s are lambda expressions and the restriction is satisfied automatically. ¸4.2.3. Sequencingˇ Í(begin˘ ˇ<expression˛1ˇ>˘ ˇ<expression˛2ˇ>˘ ...Í) ˇessential syntax The <expression>s are evaluated sequentially from left to right, and the value of the last <expression> is returned. This expression type is used to sequence side effects such as input and output. Í (define x 0) Í Í (begin (set! x 5) Í (+ x 1)) ==> 6 Í Í (begin (display "4 plus 1 equals ") Í (display (+ 4 1))) ==> ˘unspecifiedÍ Í ˘and printsÍ 4 plus 1 equals 5ˇ ˘Note:ˇ [SICP] uses the keyword Ísequenceˇ instead of Íbeginˇ. ¸4.2.4. Iterationˇ Í(do ((ˇ<variable˛1ˇ>Í ˇ<init˛1ˇ>Í ˇ<step˛1ˇ>Í) ˇsyntax Í Í ...) Í (ˇ<test>Í ˇ<expression>Í ...) Í ˇ<command>Í ...)ˇ ÍDoˇ is an iteration construct. It specifies a set of variables to be bound, how they are to be initialized at the start, and how they are to be updated on each iteration. When a termination condition is met, the loop exits with a specified result value. ÍDoˇ expressions are evaluated as follows: The <init> expressions are evaluated (in some unspecified order), the <variable>s are bound to fresh locations, the results of the <init> expressions are stored in the bindings of the <variable>s, and then the iteration phase begins. Each iteration begins by evaluating <test>; if the result is false (see section 6.1), then the <command> expressions are evaluated in order for effect, the <step> expressions are evaluated in some unspecified order, the <variable>s are bound to fresh locations, the results of the <step>s are stored in the bindings of the <variable>s, and the next iteration begins. If <test> evaluates to a true value, then the <expression>s are evaluated from left to right and the value of the last <expression> is returned as the value of the Ídoˇ expression. If no <expression>s are present, then the value of the Ídoˇ expression is unspecified. The region of the binding of a <variable> consists of the entire Ídoˇ expression except for the <init>s. It is an error for a <variable> to appear more than once in the list of Ídoˇ variables. A <step> may be omitted, in which case the effect is the same as if Í(ˇ<variable>Í ˇ<init>Í Íˇ<variable>Í)ˇ had been written instead of Í(ˇ<variable>Í ˇ<init>Í)ˇ. Í (do ((vec (make-vector 5)) Í (i 0 (+ i 1))) Í ((= i 5) vec) Í (vector-set! vec i i)) ==> #(0 1 2 3 4) Í Í (let ((x '(1 3 5 7 9))) Í (do ((x x (cdr x)) Í (sum 0 (+ sum (car x)))) Í ((null? x) sum))) ==> 25ˇ Í(let˘ ˇ<variable>˘ ˇ<bindings>˘ ˇ<body>Í) ˇsyntax Some implementations of Scheme permit a variant on the syntax of Íletˇ called ``named Íletˇ'' which provides a more general looping construct than Ídoˇ, and may also be used to express recursions. Named Íletˇ has the same syntax and semantics as ordinary Íletˇ except that <variable> is bound within <body> to a procedure whose formal arguments are the bound variables and whose body is <body>. Thus the execution of <body> may be repeated by invoking the procedure named by <variable>. Í (let loop ((numbers '(3 -2 1 6 -5)) Í (nonneg '()) Í (neg '())) Í (cond ((null? numbers) (list nonneg neg)) Í ((>= (car numbers) 0) Í (loop (cdr numbers) Í (cons (car numbers) nonneg) Í neg)) Í ((< (car numbers) 0) Í (loop (cdr numbers) Í nonneg Í (cons (car numbers) neg))))) Í ==> ((6 1 3) (-5 -2))ˇ ¸4.2.5. Delayed evaluationˇ Í(delay˘ ˇ<expression>Í) ˇsyntax The Ídelayˇ construct is used together with the procedure Íforceˇ to implement ˘lazy ˘evaluationˇ or ˘call by needˇ. Í(delay ˇ<expression>Í)ˇ returns an object called a ˘promiseˇ which at some point in the future may be asked (by the Íforceˇ procedure) to evaluate <expression> and deliver the resulting value. See the description of Íforceˇ (section 6.9) for a more complete description of Ídelayˇ. ¸4.2.6. Quasiquotationˇ Í(quasiquote˘ ˇ<template>Í) ˇessential syntax Í`ˇ<template>Í ˇessential syntax ``Backquote'' or ``quasiquote'' expressions are useful for constructing a list or vector structure when most but not all of the desired structure is known in advance. If no commas appear within the <template>, the result of evaluating Í`ˇ<template> is equivalent to the result of evaluating Í'ˇ<template>. If a comma appears within the <template>, however, the expression following the comma is evaluated (``unquoted'') and its result is inserted into the structure instead of the comma and the expression. If a comma appears followed immediately by an at-sign (Í@ˇ), then the following expression must evaluate to a list; the opening and closing parentheses of the list are then ``stripped away'' and the elements of the list are inserted in place of the comma at-sign expression sequence. Í `(list ,(+ 1 2) 4) ==> (list 3 4) Í (let ((name 'a)) `(list ,name ',name)) Í ==> (list a (quote a)) Í `(a ,(+ 1 2) ,@(map abs '(4 -5 6)) b) Í ==> (a 3 4 5 6 b) Í `((foo ,(- 10 3)) ,@(cdr '(c)) . ,(car '(cons))) Í ==> ((foo 7) . cons) Í `#(10 5 ,(sqrt 4) ,@(map sqrt '(16 9)) 8) Í ==> #(10 5 2 4 3 8)ˇ Quasiquote forms may be nested. Substitutions are made only for unquoted components appearing at the same nesting level as the outermost backquote. The nesting level increases by one inside each successive quasiquotation, and decreases by one inside each unquotation. Í `(a `(b ,(+ 1 2) ,(foo ,(+ 1 3) d) e) f) Í ==> (a `(b ,(+ 1 2) ,(foo 4 d) e) f) Í (let ((name1 'x) Í (name2 'y)) Í `(a `(b ,,name1 ,',name2 d) e)) Í ==> (a `(b ,x ,'y d) e)ˇ The notations Í`ˇ<template> and Í(quasiquote ˇ<template>Í)ˇ are identical in all respects. Í,ˇ<expression> is identical to Í(unquote ˇ<expression>Í)ˇ, and Í,@ˇ<expression> is identical to Í(unquote-splicing ˇ<expression>Í)ˇ. The external syntax generated by Íwriteˇ for two-element lists whose car is one of these symbols may vary between implementations. Í (quasiquote (list (unquote (+ 1 2)) 4)) Í ==> (list 3 4) Í '(quasiquote (list (unquote (+ 1 2)) 4)) Í ==> `(list ,(+ 1 2) 4) Í ˘i.e.,Í (quasiquote (list (unquote (+ 1 2)) 4))ˇ Unpredictable behavior can result if any of the symbols Íquasiquoteˇ, Íunquoteˇ, or Íunquote-splicingˇ appear in positions within a <template> otherwise than as described above. Û5. Program structureˇ Û5.1. Programsˇ A Scheme program consists of a sequence of expressions and definitions. Expressions are described in chapter 4; definitions are the subject of the rest of the present chapter. Programs are typically stored in files or entered interactively to a running Scheme system, although other paradigms are possible; questions of user interface lie outside the scope of this report. (Indeed, Scheme would still be useful as a notation for expressing computational methods even in the absence of a mechanical implementation.) Definitions occurring at the top level of a program can be interpreted declaratively. They cause bindings to be created in the top level environment. Expressions occurring at the top level of a program are interpreted imperatively; they are executed in order when the program is invoked or loaded, and typically perform some kind of initialization. Û5.2. Definitionsˇ Definitions are valid in some, but not all, contexts where expressions are allowed. They are valid only at the top level of a <program> and, in some implementations, at the beginning of a <body>. A definition should have one of the following forms: • Í(define ˇ<variable>Í ˇ<expression>Í)ˇ This syntax is essential. • Í(define (ˇ<variable>Í ˇ<formals>Í) ˇ<body>Í)ˇ This syntax is not essential. <Formals> should be either a sequence of zero or more variables, or a sequence of one or more variables followed by a space-delimited period and another variable (as in a lambda expression). This form is equivalent to Í (define ˇ<variable>Í Í (lambda (ˇ<formals>Í) ˇ<body>Í)).ˇ • Í(define (ˇ<variable>Í . ˇ<formal>Í) ˇ<body>Í)ˇ This syntax is not essential. <Formal> should be a single variable. This form is equivalent to Í (define ˇ<variable>Í Í (lambda ˇ<formal>Í ˇ<body>Í)).ˇ • Í(begin ˇ<definition˛1ˇ>Í ...)ˇ This syntax is essential. This form is equivalent to the set of definitions that form the body of the Íbeginˇ. ¸5.2.1. Top level definitionsˇ At the top level of a program, a definition Í (define ˇ<variable>Í ˇ<expression>Í)ˇ has essentially the same effect as the assignment expression Í (set! ˇ<variable>Í ˇ<expression>Í)ˇ if <variable> is bound. If <variable> is not bound, however, then the definition will bind <variable> to a new location before performing the assignment, whereas it would be an error to perform a Íset!ˇ on an unbound variable. Í (define add3 Í (lambda (x) (+ x 3))) Í (add3 3) ==> 6 Í (define first car) Í (first '(1 2)) ==> 1ˇ All Scheme implementations must support top level definitions. Some implementations of Scheme use an initial environment in which all possible variables are bound to locations, most of which contain undefined values. Top level definitions in such an implementation are truly equivalent to assignments. ¸5.2.2. Internal definitionsˇ Some implementations of Scheme permit definitions to occur at the beginning of a <body> (that is, the body of a Ílambdaˇ, Íletˇ, Ílet*ˇ, Íletrecˇ, or Ídefineˇ expression). Such definitions are known as ˘internal definitionsˇ as opposed to the top level definitions described above. The variable defined by an internal definition is local to the <body>. That is, <variable> is bound rather than assigned, and the region of the binding is the entire <body>. For example, Í (let ((x 5)) Í (define foo (lambda (y) (bar x y))) Í (define bar (lambda (a b) (+ (* a b) a))) Í (foo (+ x 3))) ==> 45ˇ A <body> containing internal definitions can always be converted into a completely equivalent Íletrecˇ expression. For example, the Íletˇ expression in the above example is equivalent to Í (let ((x 5)) Í (letrec ((foo (lambda (y) (bar x y))) Í (bar (lambda (a b) (+ (* a b) a)))) Í (foo (+ x 3))))ˇ Just as for the equivalent Íletrecˇ expression, it must be possible to evaluate each <expression> of every internal definition in a <body> without assigning or referring to the value of any <variable> being defined. Û6. Standard proceduresˇ This chapter describes Scheme's built-in procedures. The initial (or ``top level'') Scheme environment starts out with a number of variables bound to locations containing useful values, most of which are primitive procedures that manipulate data. For example, the variable Íabsˇ is bound to (a location initially containing) a procedure of one argument that computes the absolute value of a number, and the variable Í+ˇ is bound to a procedure that computes sums. Û6.1. Booleansˇ The standard boolean objects for true and false are written as Í#tˇ and Í#fˇ. What really matters, though, are the objects that the Scheme conditional expressions (Íifˇ, Ícondˇ, Íandˇ, Íorˇ, Ídoˇ) treat as true or false. The phrase ``a true value'' (or sometimes just ``true'') means any object treated as true by the conditional expressions, and the phrase ``a false value'' (or ``false'') means any object treated as false by the conditional expressions. Of all the standard Scheme values, only Í#fˇ counts as false in conditional expressions. Except for Í#fˇ, all standard Scheme values, including Í#tˇ, pairs, the empty list, symbols, numbers, strings, vectors, and procedures, count as true. ˘Note:ˇ In some implementations the empty list counts as false, contrary to the above. Nonetheless a few examples in this report assume that the empty list counts as true, as in [IEEE-Scheme]. ˘Note:ˇ Programmers accustomed to other dialects of Lisp should be aware that Scheme distinguishes both Í#fˇ and the empty list from the symbol Ínilˇ. Boolean constants evaluate to themselves, so they don't need to be quoted in programs. Í #t ==> #t Í #f ==> #f Í '#f ==> #fˇ Í(not˘ objÍ) ˇessential procedure ÍNotˇ returns Í#tˇ if ˘objˇ is false, and returns Í#fˇ otherwise. Í (not #t) ==> #f Í (not 3) ==> #f Í (not (list 3)) ==> #f Í (not #f) ==> #t Í (not '()) ==> #f Í (not (list)) ==> #f Í (not 'nil) ==> #fˇ Í(boolean?˘ objÍ) ˇessential procedure ÍBoolean?ˇ returns Í#tˇ if ˘objˇ is either Í#tˇ or Í#fˇ and returns Í#fˇ otherwise. Í (boolean? #f) ==> #t Í (boolean? 0) ==> #f Í (boolean? '()) ==> #fˇ Û6.2. Equivalence predicatesˇ A ˘predicateˇ is a procedure that always returns a boolean value (Í#tˇ or Í#fˇ). An ˘equivalence ˘predicateˇ is the computational analogue of a mathematical equivalence relation (it is symmetric, reflexive, and transitive). Of the equivalence predicates described in this section, Íeq?ˇ is the finest or most discriminating, and Íequal?ˇ is the coarsest. ÍEqv?ˇ is slightly less discriminating than Íeq?ˇ. Í(eqv?˘ obj¯1˘ obj¯2Í) ˇessential procedure The Íeqv?ˇ procedure defines a useful equivalence relation on objects. Briefly, it returns Í#tˇ if ˘obj¯1ˇ and ˘obj¯2ˇ should normally be regarded as the same object. This relation is left slightly open to interpretation, but the following partial specification of Íeqv?ˇ holds for all implementations of Scheme. The Íeqv?ˇ procedure returns Í#tˇ if: • ˘obj¯1ˇ and ˘obj¯2ˇ are both Í#tˇ or both Í#fˇ. • ˘obj¯1ˇ and ˘obj¯2ˇ are both symbols and Í (string=? (symbol->string ˘obj¯1Í) Í (symbol->string ˘obj¯2Í)) Í ==> #tˇ ˘Note:ˇ This assumes that neither ˘obj¯1ˇ nor ˘obj¯2ˇ is an ``uninterned symbol'' as alluded to in section 6.4. This report does not presume to specify the behavior of Íeqv?ˇ on implementation-dependent extensions. • ˘obj¯1ˇ and ˘obj¯2ˇ are both numbers, are numerically equal (see Í=ˇ, section 6.5), and are either both exact or both inexact. • ˘obj¯1ˇ and ˘obj¯2ˇ are both characters and are the same character according to the Íchar=?ˇ procedure (section 6.6). • both ˘obj¯1ˇ and ˘obj¯2ˇ are the empty list. • ˘obj¯1ˇ and ˘obj¯2ˇ are pairs, vectors, or strings that denote the same locations in the store (section 3.5). • ˘obj¯1ˇ and ˘obj¯2ˇ are procedures whose location tags are equal (section 4.1.4). The Íeqv?ˇ procedure returns Í#fˇ if: • ˘obj¯1ˇ and ˘obj¯2ˇ are of different types (section 3.4). • one of ˘obj¯1ˇ and ˘obj¯2ˇ is Í#tˇ but the other is Í#fˇ. • ˘obj¯1ˇ and ˘obj¯2ˇ are symbols but Í (string=? (symbol->string ˘obj¯1Í) Í (symbol->string ˘obj¯2Í)) Í ==> #fˇ • one of ˘obj¯1ˇ and ˘obj¯2ˇ is an exact number but the other is an inexact number. • ˘obj¯1ˇ and ˘obj¯2ˇ are numbers for which the Í=ˇ procedure returns Í#fˇ. • ˘obj¯1ˇ and ˘obj¯2ˇ are characters for which the Íchar=?ˇ procedure returns Í#fˇ. • one of ˘obj¯1ˇ and ˘obj¯2ˇ is the empty list but the other is not. • ˘obj¯1ˇ and ˘obj¯2ˇ are pairs, vectors, or strings that denote distinct locations. • ˘obj¯1ˇ and ˘obj¯2ˇ are procedures that would behave differently (return a different value or have different side effects) for some arguments. Í (eqv? 'a 'a) ==> #t Í (eqv? 'a 'b) ==> #f Í (eqv? 2 2) ==> #t Í (eqv? '() '()) ==> #t Í (eqv? 100000000 100000000) ==> #t Í (eqv? (cons 1 2) (cons 1 2))==> #f Í (eqv? (lambda () 1) Í (lambda () 2)) ==> #f Í (eqv? #f 'nil) ==> #f Í (let ((p (lambda (x) x))) Í (eqv? p p)) ==> #tˇ The following examples illustrate cases in which the above rules do not fully specify the behavior of Íeqv?ˇ. All that can be said about such cases is that the value returned by Íeqv?ˇ must be a boolean. Í (eqv? "" "") ==> ˘unspecifiedÍ Í (eqv? '#() '#()) ==> ˘unspecifiedÍ Í (eqv? (lambda (x) x) Í (lambda (x) x)) ==> ˘unspecifiedÍ Í (eqv? (lambda (x) x) Í (lambda (y) y)) ==> ˘unspecifiedˇ The next set of examples shows the use of Íeqv?ˇ with procedures that have local state. ÍGen-counterˇ must return a distinct procedure every time, since each procedure has its own internal counter. ÍGen-loserˇ, however, returns equivalent procedures each time, since the local state does not affect the value or side effects of the procedures. Í (define gen-counter Í (lambda () Í (let ((n 0)) Í (lambda () (set! n (+ n 1)) n)))) Í (let ((g (gen-counter))) Í (eqv? g g)) ==> #t Í (eqv? (gen-counter) (gen-counter)) Í ==> #f Í (define gen-loser Í (lambda () Í (let ((n 0)) Í (lambda () (set! n (+ n 1)) 27)))) Í (let ((g (gen-loser))) Í (eqv? g g)) ==> #t Í (eqv? (gen-loser) (gen-loser)) Í ==> ˘unspecifiedÍ Í Í (letrec ((f (lambda () (if (eqv? f g) 'both 'f))) Í (g (lambda () (if (eqv? f g) 'both 'g))) Í (eqv? f g)) Í ==> ˘unspecifiedÍ Í Í (letrec ((f (lambda () (if (eqv? f g) 'f 'both))) Í (g (lambda () (if (eqv? f g) 'g 'both))) Í (eqv? f g)) Í ==> #fˇ Since it is an error to modify constant objects (those returned by literal expressions), implementations are permitted, though not required, to share structure between constants where appropriate. Thus the value of Íeqv?ˇ on constants is sometimes implementation-dependent. Í (eqv? '(a) '(a)) ==> ˘unspecifiedÍ Í (eqv? "a" "a") ==> ˘unspecifiedÍ Í (eqv? '(b) (cdr '(a b))) ==> ˘unspecifiedÍ Í (let ((x '(a))) Í (eqv? x x)) ==> #tˇ ˘Rationale:ˇ The above definition of Íeqv?ˇ allows implementations latitude in their treatment of procedures and literals: implementations are free either to detect or to fail to detect that two procedures or two literals are equivalent to each other, and can decide whether or not to merge representations of equivalent objects by using the same pointer or bit pattern to represent both. Í(eq?˘ obj¯1˘ obj¯2Í) ˇessential procedure ÍEq?ˇ is similar to Íeqv?ˇ except that in some cases it is capable of discerning distinctions finer than those detectable by Íeqv?ˇ. ÍEq?ˇ and Íeqv?ˇ are guaranteed to have the same behavior on symbols, booleans, the empty list, pairs, and non-empty strings and vectors. ÍEq?ˇ's behavior on numbers and characters is implementation-dependent, but it will always return either true or false, and will return true only when Íeqv?ˇ would also return true. ÍEq?ˇ may also behave differently from Íeqv?ˇ on empty vectors and empty strings. Í (eq? 'a 'a) ==> #t Í (eq? '(a) '(a)) ==> ˘unspecifiedÍ Í (eq? (list 'a) (list 'a)) ==> #f Í (eq? "a" "a") ==> ˘unspecifiedÍ Í (eq? "" "") ==> ˘unspecifiedÍ Í (eq? '() '()) ==> #t Í (eq? 2 2) ==> ˘unspecifiedÍ Í (eq? #\A #\A) ==> ˘unspecifiedÍ Í (eq? car car) ==> #t Í (let ((n (+ 2 3))) Í (eq? n n)) ==> ˘unspecifiedÍ Í (let ((x '(a))) Í (eq? x x)) ==> #t Í (let ((x '#())) Í (eq? x x)) ==> #t Í (let ((p (lambda (x) x))) Í (eq? p p)) ==> #tˇ ˘Rationale:ˇ It will usually be possible to implement Íeq?ˇ much more efficiently than Íeqv?ˇ, for example, as a simple pointer comparison instead of as some more complicated operation. One reason is that it may not be possible to compute Íeqv?ˇ of two numbers in constant time, whereas Íeq?ˇ implemented as pointer comparison will always finish in constant time. ÍEq?ˇ may be used like Íeqv?ˇ in applications using procedures to implement objects with state since it obeys the same constraints as Íeqv?ˇ. Í(equal?˘ obj¯1˘ obj¯2Í) ˇessential procedure ÍEqual?ˇ recursively compares the contents of pairs, vectors, and strings, applying Íeqv?ˇ on other objects such as numbers and symbols. A rule of thumb is that objects are generally Íequal?ˇ if they print the same. ÍEqual?ˇ may fail to terminate if its arguments are circular data structures. Í (equal? 'a 'a) ==> #t Í (equal? '(a) '(a)) ==> #t Í (equal? '(a (b) c) Í '(a (b) c)) ==> #t Í (equal? "abc" "abc") ==> #t Í (equal? 2 2) ==> #t Í (equal? (make-vector 5 'a) Í (make-vector 5 'a)) ==> #t Í (equal? (lambda (x) x) Í (lambda (y) y)) ==> ˘unspecifiedˇ Û6.3. Pairs and listsˇ A ˘pairˇ (sometimes called a ˘dotted pairˇ) is a record structure with two fields called the car and cdr fields (for historical reasons). Pairs are created by the procedure Íconsˇ. The car and cdr fields are accessed by the procedures Ícarˇ and Ícdrˇ. The car and cdr fields are assigned by the procedures Íset-car!ˇ and Íset-cdr!ˇ. Pairs are used primarily to represent lists. A list can be defined recursively as either the empty list or a pair whose cdr is a list. More precisely, the set of lists is defined as the smallest set ˘Xˇ such that • The empty list is in ˘Xˇ. • If ˘listˇ is in ˘Xˇ, then any pair whose cdr field contains ˘listˇ is also in ˘Xˇ. The objects in the car fields of successive pairs of a list are the elements of the list. For example, a two-element list is a pair whose car is the first element and whose cdr is a pair whose car is the second element and whose cdr is the empty list. The length of a list is the number of elements, which is the same as the number of pairs. The empty list is a special object of its own type (it is not a pair); it has no elements and its length is zero. ˘Note:ˇ The above definitions imply that all lists have finite length and are terminated by the empty list. The most general notation (external representation) for Scheme pairs is the ``dotted'' notation Í(˘c¯1Í . ˘c¯2Í)ˇ where ˘c¯1ˇ is the value of the car field and ˘c¯2ˇ is the value of the cdr field. For example Í(4 . 5)ˇ is a pair whose car is 4 and whose cdr is 5. Note that Í(4 . 5)ˇ is the external representation of a pair, not an expression that evaluates to a pair. A more streamlined notation can be used for lists: the elements of the list are simply enclosed in parentheses and separated by spaces. The empty list is written Í()ˇ. For example, Í (a b c d e)ˇ and Í (a . (b . (c . (d . (e . ())))))ˇ are equivalent notations for a list of symbols. A chain of pairs not ending in the empty list is called an ˘improper listˇ. Note that an improper list is not a list. The list and dotted notations can be combined to represent improper lists: Í (a b c . d)ˇ is equivalent to Í (a . (b . (c . d)))ˇ Whether a given pair is a list depends upon what is stored in the cdr field. When the Íset-cdr!ˇ procedure is used, an object can be a list one moment and not the next: Í (define x (list 'a 'b 'c)) Í (define y x) Í y ==> (a b c) Í (list? y) ==> #t Í (set-cdr! x 4) ==> ˘unspecifiedÍ Í x ==> (a . 4) Í (eqv? x y) ==> #t Í y ==> (a . 4) Í (list? y) ==> #f Í (set-cdr! x x) ==> ˘unspecifiedÍ Í (list? x) ==> #fˇ Within literal expressions and representations of objects read by the Íreadˇ procedure, the forms Í'ˇ<datum>, Í`ˇ<datum>, Í,ˇ<datum>, and Í,@ˇ<datum> denote two-element lists whose first elements are the symbols Íquoteˇ, Íquasiquoteˇ, Íunquoteˇ, and Íunquote-splicingˇ, respectively. The second element in each case is <datum>. This convention is supported so that arbitrary Scheme programs may be represented as lists. That is, according to Scheme's grammar, every <expression> is also a <datum> (see section 7.1.2). Among other things, this permits the use of the Íreadˇ procedure to parse Scheme programs. See section 3.3. Í(pair?˘ objÍ) ˇessential procedure ÍPair?ˇ returns Í#tˇ if ˘objˇ is a pair, and otherwise returns Í#fˇ. Í (pair? '(a . b)) ==> #t Í (pair? '(a b c)) ==> #t Í (pair? '()) ==> #f Í (pair? '#(a b)) ==> #fˇ Í(cons˘ obj¯1˘ obj¯2Í) ˇessential procedure Returns a newly allocated pair whose car is ˘obj¯1ˇ and whose cdr is ˘obj¯2ˇ. The pair is guaranteed to be different (in the sense of Íeqv?ˇ) from every existing object. Í (cons 'a '()) ==> (a) Í (cons '(a) '(b c d)) ==> ((a) b c d) Í (cons "a" '(b c)) ==> ("a" b c) Í (cons 'a 3) ==> (a . 3) Í (cons '(a b) 'c) ==> ((a b) . c)ˇ Í(car˘ pairÍ) ˇessential procedure Returns the contents of the car field of ˘pairˇ. Note that it is an error to take the car of the empty list. Í (car '(a b c)) ==> a Í (car '((a) b c d)) ==> (a) Í (car '(1 . 2)) ==> 1 Í (car '()) ==> ˘errorˇ Í(cdr˘ pairÍ) ˇessential procedure Returns the contents of the cdr field of ˘pairˇ. Note that it is an error to take the cdr of the empty list. Í (cdr '((a) b c d)) ==> (b c d) Í (cdr '(1 . 2)) ==> 2 Í (cdr '()) ==> ˘errorˇ Í(set-car!˘ pair objÍ) ˇessential procedure Stores ˘objˇ in the car field of ˘pairˇ. The value returned by Íset-car!ˇ is unspecified. Í (define (f) (list 'not-a-constant-list)) Í (define (g) '(constant-list)) Í (set-car! (f) 3) ==> ˘unspecifiedÍ Í (set-car! (g) 3) ==> ˘errorˇ Í(set-cdr!˘ pair objÍ) ˇessential procedure Stores ˘objˇ in the cdr field of ˘pairˇ. The value returned by Íset-cdr!ˇ is unspecified. Í(caar˘ pairÍ) ˇessential procedure Í(cadr˘ pairÍ) ˇessential procedure . . . Í(cdddar˘ pairÍ) ˇessential procedure Í(cddddr˘ pairÍ) ˇessential procedure These procedures are compositions of Ícarˇ and Ícdrˇ, where for example Ícaddrˇ could be defined by Í (define caddr (lambda (x) (car (cdr (cdr x))))).ˇ Arbitrary compositions, up to four deep, are provided. There are twenty-eight of these procedures in all. Í(null?˘ objÍ) ˇessential procedure Returns Í#tˇ if ˘objˇ is the empty list, otherwise returns Í#fˇ. Í(list?˘ objÍ) ˇessential procedure Returns Í#tˇ if ˘objˇ is a list, otherwise returns Í#fˇ. By definition, all lists have finite length and are terminated by the empty list. Í (list? '(a b c)) ==> #t Í (list? '()) ==> #t Í (list? '(a . b)) ==> #f Í (let ((x (list 'a))) Í (set-cdr! x x) Í (list? x)) ==> #fˇ Í(list˘ obj ...Í) ˇessential procedure Returns a newly allocated list of its arguments. Í (list 'a (+ 3 4) 'c) ==> (a 7 c) Í (list) ==> ()ˇ Í(length˘ listÍ) ˇessential procedure Returns the length of ˘listˇ. Í (length '(a b c)) ==> 3 Í (length '(a (b) (c d e))) ==> 3 Í (length '()) ==> 0ˇ Í(append˘ list ...Í) ˇessential procedure Returns a list consisting of the elements of the first ˘listˇ followed by the elements of the other ˘listˇs. Í (append '(x) '(y)) ==> (x y) Í (append '(a) '(b c d)) ==> (a b c d) Í (append '(a (b)) '((c))) ==> (a (b) (c))ˇ The resulting list is always newly allocated, except that it shares structure with the last ˘listˇ argument. The last argument may actually be any object; an improper list results if the last argument is not a proper list. Í (append '(a b) '(c . d)) ==> (a b c . d) Í (append '() 'a) ==> aˇ Í(reverse˘ listÍ) ˇessential procedure Returns a newly allocated list consisting of the elements of ˘listˇ in reverse order. Í (reverse '(a b c)) ==> (c b a) Í (reverse '(a (b c) d (e (f)))) Í ==> ((e (f)) d (b c) a)ˇ Í(list-tail˘ list kÍ) ˇprocedure Returns the sublist of ˘listˇ obtained by omitting the first ˘kˇ elements. ÍList-tailˇ could be defined by Í (define list-tail Í (lambda (x k) Í (if (zero? k) Í x Í (list-tail (cdr x) (- k 1)))))ˇ Í(list-ref˘ list kÍ) ˇessential procedure Returns the ˘kˇth element of ˘listˇ. (This is the same as the car of Í(list-tail ˘listÍ ˘kÍ)ˇ.) Í (list-ref '(a b c d) 2) ==> c Í (list-ref '(a b c d) Í (inexact->exact (round 1.8))) Í ==> cˇ Í(memq˘ obj listÍ) ˇessential procedure Í(memv˘ obj listÍ) ˇessential procedure Í(member˘ obj listÍ) ˇessential procedure These procedures return the first sublist of ˘listˇ whose car is ˘objˇ, where the sublists of ˘listˇ are the non-empty lists returned by Í(list-tail ˘listÍ ˘kÍ)ˇ for ˘kˇ less than the length of ˘listˇ. If ˘objˇ does not occur in ˘listˇ, then Í#fˇ (not the empty list) is returned. ÍMemqˇ uses Íeq?ˇ to compare ˘objˇ with the elements of ˘listˇ, while Ímemvˇ uses Íeqv?ˇ and Ímemberˇ uses Íequal?ˇ. Í (memq 'a '(a b c)) ==> (a b c) Í (memq 'b '(a b c)) ==> (b c) Í (memq 'a '(b c d)) ==> #f Í (memq (list 'a) '(b (a) c)) ==> #f Í (member (list 'a) Í '(b (a) c)) ==> ((a) c) Í (memq 101 '(100 101 102)) ==> ˘unspecifiedÍ Í (memv 101 '(100 101 102)) ==> (101 102)ˇ Í(assq˘ obj alistÍ) ˇessential procedure Í(assv˘ obj alistÍ) ˇessential procedure Í(assoc˘ obj alistÍ) ˇessential procedure ˘Alistˇ (for ``association list'') must be a list of pairs. These procedures find the first pair in ˘alistˇ whose car field is ˘objˇ, and returns that pair. If no pair in ˘alistˇ has ˘objˇ as its car, then Í#fˇ (not the empty list) is returned. ÍAssqˇ uses Íeq?ˇ to compare ˘objˇ with the car fields of the pairs in ˘alistˇ, while Íassvˇ uses Íeqv?ˇ and Íassocˇ uses Íequal?ˇ. Í (define e '((a 1) (b 2) (c 3))) Í (assq 'a e) ==> (a 1) Í (assq 'b e) ==> (b 2) Í (assq 'd e) ==> #f Í (assq (list 'a) '(((a)) ((b)) ((c)))) Í ==> #f Í (assoc (list 'a) '(((a)) ((b)) ((c)))) Í ==> ((a)) Í (assq 5 '((2 3) (5 7) (11 13))) Í ==> ˘unspecifiedÍ Í (assv 5 '((2 3) (5 7) (11 13))) Í ==> (5 7)ˇ ˘Rationale:ˇ Although they are ordinarily used as predicates, Ímemqˇ, Ímemvˇ, Ímemberˇ, Íassqˇ, Íassvˇ, and Íassocˇ do not have question marks in their names because they return useful values rather than just Í#tˇ or Í#fˇ. Û6.4. Symbolsˇ Symbols are objects whose usefulness rests on the fact that two symbols are identical (in the sense of Íeqv?ˇ) if and only if their names are spelled the same way. This is exactly the property needed to represent identifiers in programs, and so most implementations of Scheme use them internally for that purpose. Symbols are useful for many other applications; for instance, they may be used the way enumerated values are used in Pascal. The rules for writing a symbol are exactly the same as the rules for writing an identifier; see sections 2.1 and 7.1.1. It is guaranteed that any symbol that has been returned as part of a literal expression, or read using the Íreadˇ procedure, and subsequently written out using the Íwriteˇ procedure, will read back in as the identical symbol (in the sense of Íeqv?ˇ). The Ístring->symbolˇ procedure, however, can create symbols for which this write/read invariance may not hold because their names contain special characters or letters in the non-standard case. ˘Note:ˇ Some implementations of Scheme have a feature known as ``slashification'' in order to guarantee write/read invariance for all symbols, but historically the most important use of this feature has been to compensate for the lack of a string data type. Some implementations also have ``uninterned symbols'', which defeat write/read invariance even in implementations with slashification, and also generate exceptions to the rule that two symbols are the same if and only if their names are spelled the same. Í(symbol?˘ objÍ) ˇessential procedure Returns Í#tˇ if ˘objˇ is a symbol, otherwise returns Í#fˇ. Í (symbol? 'foo) ==> #t Í (symbol? (car '(a b))) ==> #t Í (symbol? "bar") ==> #f Í (symbol? 'nil) ==> #t Í (symbol? '()) ==> #f Í (symbol? #f) ==> #fˇ Í(symbol->string˘ symbolÍ) ˇessential procedure Returns the name of ˘symbolˇ as a string. If the symbol was part of an object returned as the value of a literal expression (section 4.1.2) or by a call to the Íreadˇ procedure, and its name contains alphabetic characters, then the string returned will contain characters in the implementation's preferred standard case; some implementations will prefer upper case, others lower case. If the symbol was returned by Ístring->symbolˇ, the case of characters in the string returned will be the same as the case in the string that was passed to Ístring->symbolˇ. It is an error to apply mutation procedures like Ístring-set!ˇ to strings returned by this procedure. The following examples assume that the implementation's standard case is lower case: Í (symbol->string 'flying-fish) Í ==> "flying-fish" Í (symbol->string 'Martin) ==> "martin" Í (symbol->string Í (string->symbol "Malvina")) Í ==> "Malvina"ˇ Í(string->symbol˘ stringÍ) ˇessential procedure Returns the symbol whose name is ˘stringˇ. This procedure can create symbols with names containing special characters or letters in the non-standard case, but it is usually a bad idea to create such symbols because in some implementations of Scheme they cannot be read as themselves. See Ísymbol->stringˇ. The following examples assume that the implementation's standard case is lower case: Í (eq? 'mISSISSIppi 'mississippi) Í ==> #t Í (string->symbol "mISSISSIppi") Í ==> ˇthe symbol with nameÍ "mISSISSIppi" Í (eq? 'bitBlt (string->symbol "bitBlt")) Í ==> #f Í (eq? 'JollyWog Í (string->symbol Í (symbol->string 'JollyWog))) Í ==> #t Í (string=? "K. Harper, M.D." Í (symbol->string Í (string->symbol "K. Harper, M.D."))) Í ==> #tˇ Û6.5. Numbersˇ Numerical computation has traditionally been neglected by the Lisp community. Until Common Lisp there was no carefully thought out strategy for organizing numerical computation, and with the exception of the MacLisp system [Pitman] little effort was made to execute numerical code efficiently. This report recognizes the excellent work of the Common Lisp committee and accepts many of their recommendations. In some ways this report simplifies and generalizes their proposals in a manner consistent with the purposes of Scheme. It is important to distinguish between the mathematical numbers, the Scheme numbers that attempt to model them, the machine representations used to implement the Scheme numbers, and notations used to write numbers. This report uses the types ˘numberˇ, ˘complexˇ, ˘realˇ, ˘rationalˇ, and ˘integerˇ to refer to both mathematical numbers and Scheme numbers. Machine representations such as fixed point and floating point are referred to by names such as ˘fixnumˇ and ˘flonumˇ. ¸6.5.1. Numerical typesˇ Mathematically, numbers may be arranged into a tower of subtypes in which each level is a subset of the level above it: number complex real rational integer For example, 3 is an integer. Therefore 3 is also a rational, a real, and a complex. The same is true of the Scheme numbers that model 3. For Scheme numbers, these types are defined by the predicates Ínumber?ˇ, Ícomplex?ˇ, Íreal?ˇ, Írational?ˇ, and Íinteger?ˇ. There is no simple relationship between a number's type and its representation inside a computer. Although most implementations of Scheme will offer at least two different representations of 3, these different representations denote the same integer. Scheme's numerical operations treat numbers as abstract data, as independent of their representation as possible. Although an implementation of Scheme may use fixnum, flonum, and perhaps other representations for numbers, this should not be apparent to a casual programmer writing simple programs. It is necessary, however, to distinguish between numbers that are represented exactly and those that may not be. For example, indexes into data structures must be known exactly, as must some polynomial coefficients in a symbolic algebra system. On the other hand, the results of measurements are inherently inexact, and irrational numbers may be approximated by rational and therefore inexact approximations. In order to catch uses of inexact numbers where exact numbers are required, Scheme explicitly distinguishes exact from inexact numbers. This distinction is orthogonal to the dimension of type. ¸6.5.2. Exactnessˇ Scheme numbers are either ˘exactˇ or ˘inexactˇ. A number is exact if it was written as an exact constant or was derived from exact numbers using only exact operations. A number is inexact if it was written as an inexact constant, if it was derived using inexact ingredients, or if it was derived using inexact operations. Thus inexactness is a contagious property of a number. If two implementations produce exact results for a computation that did not involve inexact intermediate results, the two ultimate results will be mathematically equivalent. This is generally not true of computations involving inexact numbers since approximate methods such as floating point arithmetic may be used, but it is the duty of each implementation to make the result as close as practical to the mathematically ideal result. Rational operations such as Í+ˇ should always produce exact results when given exact arguments. If the operation is unable to produce an exact result, then it may either report the violation of an implementation restriction or it may silently coerce its result to an inexact value. See section 6.5.3. With the exception of Íinexact->exactˇ, the operations described in this section must generally return inexact results when given any inexact arguments. An operation may, however, return an exact result if it can prove that the value of the result is unaffected by the inexactness of its arguments. For example, multiplication of any number by an exact zero may produce an exact zero result, even if the other argument is inexact. ¸6.5.3. Implementation restrictionsˇ Implementations of Scheme are not required to implement the whole tower of subtypes given in section 6.5.1, but they must implement a coherent subset consistent with both the purposes of the implementation and the spirit of the Scheme language. For example, an implementation in which all numbers are real may still be quite useful. Implementations may also support only a limited range of numbers of any type, subject to the requirements of this section. The supported range for exact numbers of any type may be different from the supported range for inexact numbers of that type. For example, an implementation that uses flonums to represent all its inexact real numbers may support a practically unbounded range of exact integers and rationals while limiting the range of inexact reals (and therefore the range of inexact integers and rationals) to the dynamic range of the flonum format. Furthermore the gaps between the representable inexact integers and rationals are likely to be very large in such an implementation as the limits of this range are approached. An implementation of Scheme must support exact integers throughout the range of numbers that may be used for indexes of lists, vectors, and strings or that may result from computing the length of a list, vector, or string. The Ílengthˇ, Ívector-lengthˇ, and Ístring-lengthˇ procedures must return an exact integer, and it is an error to use anything but an exact integer as an index. Furthermore any integer constant within the index range, if expressed by an exact integer syntax, will indeed be read as an exact integer, regardless of any implementation restrictions that may apply outside this range. Finally, the procedures listed below will always return an exact integer result provided all their arguments are exact integers and the mathematically expected result is representable as an exact integer within the implementation: Í + - * Í quotient remainder modulo Í max min abs Í numerator denominator gcd Í lcm floor ceiling Í truncate round rationalize Í exptˇ Implementations are encouraged, but not required, to support exact integers and exact rationals of practically unlimited size and precision, and to implement the above procedures and the Í/ˇ procedure in such a way that they always return exact results when given exact arguments. If one of these procedures is unable to deliver an exact result when given exact arguments, then it may either report a violation of an implementation restriction or it may silently coerce its result to an inexact number. Such a coercion may cause an error later. An implementation may use floating point and other approximate representation strategies for inexact numbers. This report recommends, but does not require, that the IEEE 32-bit and 64-bit floating point standards be followed by implementations that use flonum representations, and that implementations using other representations should match or exceed the precision achievable using these floating point standards [IEEE]. In particular, implementations that use flonum representations must follow these rules: A flonum result must be represented with at least as much precision as is used to express any of the inexact arguments to that operation. It is desirable (but not required) for potentially inexact operations such as Ísqrtˇ, when applied to exact arguments, to produce exact answers whenever possible (for example the square root of an exact 4 ought to be an exact 2). If, however, an exact number is operated upon so as to produce an inexact result (as by Ísqrtˇ), and if the result is represented as a flonum, then the most precise flonum format available must be used; but if the result is represented in some other way then the representation must have at least as much precision as the most precise flonum format available. Although Scheme allows a variety of written notations for numbers, any particular implementation may support only some of them. For example, an implementation in which all numbers are real need not support the rectangular and polar notations for complex numbers. If an implementation encounters an exact numerical constant that it cannot represent as an exact number, then it may either report a violation of an implementation restriction or it may silently represent the constant by an inexact number. ¸6.5.4. Syntax of numerical constantsˇ The syntax of the written representations for numbers is described formally in section 7.1.1. A number may be written in binary, octal, decimal, or hexadecimal by the use of a radix prefix. The radix prefixes are Í#bˇ (binary), Í#oˇ (octal), Í#dˇ (decimal), and Í#xˇ (hexadecimal). With no radix prefix, a number is assumed to be expressed in decimal. A numerical constant may be specified to be either exact or inexact by a prefix. The prefixes are Í#eˇ for exact, and Í#iˇ for inexact. An exactness prefix may appear before or after any radix prefix that is used. If the written representation of a number has no exactness prefix, the constant may be either inexact or exact. It is inexact if it contains a decimal point, an exponent, or a ``Í#ˇ'' character in the place of a digit, otherwise it is exact. In systems with inexact numbers of varying precisions it may be useful to specify the precision of a constant. For this purpose, numerical constants may be written with an exponent marker that indicates the desired precision of the inexact representation. The letters Ísˇ, Ífˇ, Ídˇ, and Ílˇ specify the use of ˘shortˇ, ˘singleˇ, ˘doubleˇ, and ˘longˇ precision, respectively. (When fewer than four internal inexact representations exist, the four size specifications are mapped onto those available. For example, an implementation with two internal representations may map short and single together and long and double together.) In addition, the exponent marker Íeˇ specifies the default precision for the implementation. The default precision has at least as much precision as ˘doubleˇ, but implementations may wish to allow this default to be set by the user. Í 3.14159265358979F0 Í ˇRound to single:Í 3.141593 Í 0.6L0 Í ˇExtend to long:Í .600000000000000ˇ ¸6.5.5. Numerical operationsˇ The reader is referred to section 1.3.3 for a summary of the naming conventions used to specify restrictions on the types of arguments to numerical routines. The examples used in this section assume that any numerical constant written using an exact notation is indeed represented as an exact number. Some examples also assume that certain numerical constants written using an inexact notation can be represented without loss of accuracy; the inexact constants were chosen so that this is likely to be true in implementations that use flonums to represent inexact numbers. Í(number?˘ objÍ) ˇessential procedure Í(complex?˘ objÍ) ˇessential procedure Í(real?˘ objÍ) ˇessential procedure Í(rational?˘ objÍ) ˇessential procedure Í(integer?˘ objÍ) ˇessential procedure These numerical type predicates can be applied to any kind of argument, including non-numbers. They return Í#tˇ if the object is of the named type, and otherwise they return Í#fˇ. In general, if a type predicate is true of a number then all higher type predicates are also true of that number. Consequently, if a type predicate is false of a number, then all lower type predicates are also false of that number. If ˘zˇ is an inexact complex number, then Í(real? ˘zÍ)ˇ is true if and only if Í(zero? Í(imag-part ˘zÍ))ˇ is true. If ˘xˇ is an inexact real number, then Í(integer? ˘xÍ)ˇ is true if and only if Í(= ˘xÍ (round ˘xÍ))ˇ. Í (complex? 3+4i) ==> #t Í (complex? 3) ==> #t Í (real? 3) ==> #t Í (real? -2.5+0.0i) ==> #t Í (real? #e1e10) ==> #t Í (rational? 6/10) ==> #t Í (rational? 6/3) ==> #t Í (integer? 3+0i) ==> #t Í (integer? 3.0) ==> #t Í (integer? 8/4) ==> #tˇ ˘Note:ˇ The behavior of these type predicates on inexact numbers is unreliable, since any inaccuracy may affect the result. ˘Note:ˇ In many implementations the Írational?ˇ procedure will be the same as Íreal?ˇ, and the Ícomplex?ˇ procedure will be the same as Ínumber?ˇ, but unusual implementations may be able to represent some irrational numbers exactly or may extend the number system to support some kind of non-complex numbers. Í(exact?˘ zÍ) ˇessential procedure Í(inexact?˘ zÍ) ˇessential procedure These numerical predicates provide tests for the exactness of a quantity. For any Scheme number, precisely one of these predicates is true. Í(=˘ z¯1˘ z¯2˘ z¯3˘ ...Í) ˇessential procedure Í(<˘ x¯1˘ x¯2˘ x¯3˘ ...Í) ˇessential procedure Í(>˘ x¯1˘ x¯2˘ x¯3˘ ...Í) ˇessential procedure Í(<=˘ x¯1˘ x¯2˘ x¯3˘ ...Í) ˇessential procedure Í(>=˘ x¯1˘ x¯2˘ x¯3˘ ...Í) ˇessential procedure These procedures return Í#tˇ if their arguments are (respectively): equal, monotonically increasing, monotonically decreasing, monotonically nondecreasing, or monotonically nonincreasing. These predicates are required to be transitive. ˘Note:ˇ The traditional implementations of these predicates in Lisp-like languages are not transitive. ˘Note:ˇ While it is not an error to compare inexact numbers using these predicates, the results may be unreliable because a small inaccuracy may affect the result; this is especially true of Í=ˇ and Ízero?ˇ. When in doubt, consult a numerical analyst. Í(zero?˘ zÍ) ˇessential procedure Í(positive?˘ xÍ) ˇessential procedure Í(negative?˘ xÍ) ˇessential procedure Í(odd?˘ nÍ) ˇessential procedure Í(even?˘ nÍ) ˇessential procedure These numerical predicates test a number for a particular property, returning Í#tˇ or Í#fˇ. See note above. Í(max˘ x¯1˘ x¯2˘ ...Í) ˇessential procedure Í(min˘ x¯1˘ x¯2˘ ...Í) ˇessential procedure These procedures return the maximum or minimum of their arguments. Í (max 3 4) ==> 4 ; exact Í (max 3.9 4) ==> 4.0 ; inexactˇ ˘Note:ˇ If any argument is inexact, then the result will also be inexact (unless the procedure can prove that the inaccuracy is not large enough to affect the result, which is possible only in unusual implementations). If Íminˇ or Ímaxˇ is used to compare numbers of mixed exactness, and the numerical value of the result cannot be represented as an inexact number without loss of accuracy, then the procedure may report a violation of an implementation restriction. Í(+˘ z¯1˘ ...Í) ˇessential procedure Í(*˘ z¯1˘ ...Í) ˇessential procedure These procedures return the sum or product of their arguments. Í (+ 3 4) ==> 7 Í (+ 3) ==> 3 Í (+) ==> 0 Í (* 4) ==> 4 Í (*) ==> 1ˇ Í(-˘ z¯1˘ z¯2Í) ˇessential procedure Í(-˘ zÍ) ˇessential procedure Í(-˘ z¯1˘ z¯2˘ ...Í) ˇprocedure Í(/˘ z¯1˘ z¯2Í) ˇessential procedure Í(/˘ zÍ) ˇessential procedure Í(/˘ z¯1˘ z¯2˘ ...Í) ˇprocedure With two or more arguments, these procedures return the difference or quotient of their arguments, associating to the left. With one argument, however, they return the additive or multiplicative inverse of their argument. Í (- 3 4) ==> -1 Í (- 3 4 5) ==> -6 Í (- 3) ==> -3 Í (/ 3 4 5) ==> 3/20 Í (/ 3) ==> 1/3ˇ Í(abs˘ xÍ) ˇessential procedure ÍAbsˇ returns the magnitude of its argument. Í (abs -7) ==> 7ˇ Í(quotient˘ n¯1˘ n¯2Í) ˇessential procedure Í(remainder˘ n¯1˘ n¯2Í) ˇessential procedure Í(modulo˘ n¯1˘ n¯2Í) ˇessential procedure These procedures implement number-theoretic (integer) division: For positive integers ˘n¯1ˇ and ˘n¯2ˇ, if ˘n¯3ˇ and ˘n¯4ˇ are integers such that ˘n¯1ˇ=˘n¯2˘n¯3ˇ+˘n¯4ˇ and 0 <= ˘n¯4ˇ < ˘n¯2ˇ, then Í (quotient ˘n¯1Í ˘n¯2Í) ==> ˘n¯3Í Í (remainder ˘n¯1Í ˘n¯2Í) ==> ˘n¯4Í Í (modulo ˘n¯1Í ˘n¯2Í) ==> ˘n¯4ˇ For integers ˘n¯1ˇ and ˘n¯2ˇ with ˘n¯2ˇ not equal to 0, Í (= ˘n¯1Í (+ (* ˘n¯2Í (quotient ˘n¯1Í ˘n¯2Í)) Í (remainder ˘n¯1Í ˘n¯2Í))) Í ==> #tˇ provided all numbers involved in that computation are exact. The value returned by Íquotientˇ always has the sign of the product of its arguments. ÍRemainderˇ and Ímoduloˇ differ on negative arguments; the Íremainderˇ is either zero or has the sign of the dividend, while the Ímoduloˇ always has the sign of the divisor: Í (modulo 13 4) ==> 1 Í (remainder 13 4) ==> 1 Í Í (modulo -13 4) ==> 3 Í (remainder -13 4) ==> -1 Í Í (modulo 13 -4) ==> -3 Í (remainder 13 -4) ==> 1 Í Í (modulo -13 -4) ==> -1 Í (remainder -13 -4) ==> -1 Í Í (remainder -13 -4.0) ==> -1.0 ; inexactˇ Í(gcd˘ n¯1˘ ...Í) ˇessential procedure Í(lcm˘ n¯1˘ ...Í) ˇessential procedure These procedures return the greatest common divisor or least common multiple of their arguments. The result is always non-negative. Í (gcd 32 -36) ==> 4 Í (gcd) ==> 0 Í (lcm 32 -36) ==> 288 Í (lcm 32.0 -36) ==> 288.0 ; inexact Í (lcm) ==> 1ˇ Í(numerator˘ qÍ) ˇprocedure Í(denominator˘ qÍ) ˇprocedure These procedures return the numerator or denominator of their argument; the result is computed as if the argument was represented as a fraction in lowest terms. The denominator is always positive. The denominator of 0 is defined to be 1. Í (numerator (/ 6 4)) ==> 3 Í (denominator (/ 6 4)) ==> 2 Í (denominator Í (exact->inexact (/ 6 4))) ==> 2.0ˇ Í(floor˘ xÍ) ˇessential procedure Í(ceiling˘ xÍ) ˇessential procedure Í(truncate˘ xÍ) ˇessential procedure Í(round˘ xÍ) ˇessential procedure These procedures return integers. ÍFloorˇ returns the largest integer not larger than ˘xˇ. ÍCeilingˇ returns the smallest integer not smaller than ˘xˇ. ÍTruncateˇ returns the integer closest to ˘xˇ whose absolute value is not larger than the absolute value of ˘xˇ. ÍRoundˇ returns the closest integer to ˘xˇ, rounding to even when ˘xˇ is halfway between two integers. ˘Rationale:ˇ ÍRoundˇ rounds to even for consistency with the default rounding mode specified by the IEEE floating point standard. ˘Note:ˇ If the argument to one of these procedures is inexact, then the result will also be inexact. If an exact value is needed, the result should be passed to the Íinexact->exactˇ procedure. Í (floor -4.3) ==> -5.0 Í (ceiling -4.3) ==> -4.0 Í (truncate -4.3) ==> -4.0 Í (round -4.3) ==> -4.0 Í Í (floor 3.5) ==> 3.0 Í (ceiling 3.5) ==> 4.0 Í (truncate 3.5) ==> 3.0 Í (round 3.5) ==> 4.0 ; inexact Í Í (round 7/2) ==> 4 ; exact Í (round 7) ==> 7ˇ Í(rationalize˘ x yÍ) ˇprocedure ÍRationalizeˇ returns the ˘simplestˇ rational number differing from ˘xˇ by no more than ˘yˇ. A rational number ˘r¯1ˇ is ˘simplerˇ than another rational number ˘r¯2ˇ if ˘r¯1ˇ = ˘p¯1ˇ/˘q¯1ˇ and ˘r¯2ˇ = ˘p¯2ˇ/˘q¯2ˇ (in lowest terms) and |˘p¯1ˇ| <= |˘p¯2ˇ| and |˘q¯1ˇ| <= |˘q¯2ˇ|. Thus 3/5 is simpler than 4/7. Although not all rationals are comparable in this ordering (consider 2/7 and 3/5) any interval contains a rational number that is simpler than every other rational number in that interval (the simpler 2/5 lies between 2/7 and 3/5). Note that 0 = 0/1 is the simplest rational of all. Í (rationalize Í (inexact->exact .3) 1/10) ==> 1/3 ; exact Í (rationalize .3 1/10) ==> #i1/3 ; inexactˇ Í(exp˘ zÍ) ˇprocedure Í(log˘ zÍ) ˇprocedure Í(sin˘ zÍ) ˇprocedure Í(cos˘ zÍ) ˇprocedure Í(tan˘ zÍ) ˇprocedure Í(asin˘ zÍ) ˇprocedure Í(acos˘ zÍ) ˇprocedure Í(atan˘ zÍ) ˇprocedure Í(atan˘ y xÍ) ˇprocedure These procedures are part of every implementation that supports general real numbers; they compute the usual transcendental functions. ÍLogˇ computes the natural logarithm of ˘zˇ (not the base ten logarithm). ÍAsinˇ, Íacosˇ, and Íatanˇ compute arcsine (sin˝-1ˇ), arccosine (cos˝-1ˇ), and arctangent (tan˝-1ˇ), respectively. The two-argument variant of Íatanˇ computes Í(angle Í(make-rectangular ˘xÍ ˘yÍ))ˇ (see below), even in implementations that don't support general complex numbers. In general, the mathematical functions log, arcsine, arccosine, and arctangent are multiply defined. For nonzero real ˘xˇ, the value of log ˘xˇ is defined to be the one whose imaginary part lies in the range -π (exclusive) to π (inclusive). log 0 is undefined. The value of log ˘zˇ when ˘zˇ is complex is defined according to the formula log ˘zˇ = log magnitude(˘zˇ) + ˘iˇ angle(˘zˇ) With log defined this way, the values of sin˝-1ˇ ˘zˇ, cos˝-1ˇ ˘zˇ, and tan˝-1ˇ ˘zˇ are according to the following formulae: sin˝-1ˇ ˘zˇ = -˘iˇ log(˘izˇ + (1 - ˘z˜2ˇ)˝.5ˇ) cos˝-1ˇ ˘zˇ = π/2 - sin˝-1ˇ ˘zˇ tan˝-1ˇ ˘zˇ = (log (1 + ˘izˇ) - log (1-˘izˇ)) / (2˘iˇ) The above specification follows [CLtL], which in turn cites [Penfield]; refer to these sources for more detailed discussion of branch cuts, boundary conditions, and implementation of these functions. When it is possible these procedures produce a real result from a real argument. Í(sqrt˘ zÍ) ˇprocedure Returns the principal square root of ˘zˇ. The result will have either positive real part, or zero real part and non-negative imaginary part. Í(expt˘ z¯1˘ z¯2Í) ˇprocedure Returns ˘z¯1ˇ raised to the power ˘z¯2ˇ: z1˝z2ˇ = e˝z2 log z1ˇ 0˝0ˇ is defined to be equal to 1. Í(make-rectangular˘ x¯1˘ x¯2Í) ˇprocedure Í(make-polar˘ x¯3˘ x¯4Í) ˇprocedure Í(real-part˘ zÍ) ˇprocedure Í(imag-part˘ zÍ) ˇprocedure Í(magnitude˘ zÍ) ˇprocedure Í(angle˘ zÍ) ˇprocedure These procedures are part of every implementation that supports general complex numbers. Suppose ˘x¯1ˇ, ˘x¯2ˇ, ˘x¯3ˇ, and ˘x¯4ˇ are real numbers and ˘zˇ is a complex number such that ˘zˇ = ˘x¯1ˇ + ˘x¯2˘iˇ = ˘x¯3ˇ . e˝i x4ˇ Then Ímake-rectangularˇ and Ímake-polarˇ return ˘zˇ, Íreal-partˇ returns ˘x¯1ˇ, Íimag-partˇ returns ˘x¯2ˇ, Ímagnitudeˇ returns ˘x¯3ˇ, and Íangleˇ returns ˘x¯4ˇ. In the case of Íangleˇ, whose value is not uniquely determined by the preceding rule, the value returned will be the one in the range -π (exclusive) to π (inclusive). ˘Rationale:ˇ ÍMagnitudeˇ is the same as Íabsˇ for a real argument, but Íabsˇ must be present in all implementations, whereas Ímagnitudeˇ need only be present in implementations that support general complex numbers. Í(exact->inexact˘ zÍ) ˇprocedure Í(inexact->exact˘ zÍ) ˇprocedure ÍExact->inexactˇ returns an inexact representation of ˘zˇ. The value returned is the inexact number that is numerically closest to the argument. If an exact argument has no reasonably close inexact equivalent, then a violation of an implementation restriction may be reported. ÍInexact->exactˇ returns an exact representation of ˘zˇ. The value returned is the exact number that is numerically closest to the argument. If an inexact argument has no reasonably close exact equivalent, then a violation of an implementation restriction may be reported. These procedures implement the natural one-to-one correspondence between exact and inexact integers throughout an implementation-dependent range. See section 6.5.3. ¸6.5.6. Numerical input and outputˇ Í(number->string˘ numberÍ) ˇessential procedure Í(number->string˘ number radixÍ) ˇessential procedure ˘Radixˇ must be an exact integer, either 2, 8, 10, or 16. If omitted, ˘radixˇ defaults to 10. The procedure Ínumber->stringˇ takes a number and a radix and returns as a string an external representation of the given number in the given radix such that Í (let ((number ˘numberÍ) Í (radix ˘radixÍ)) Í (eqv? number Í (string->number (number->string number Í radix) Í radix))) Íˇis true. It is an error if no possible result makes this expression true. If ˘numberˇ is inexact, the radix is 10, and the above expression can be satisfied by a result that contains a decimal point, then the result contains a decimal point and is expressed using the minimum number of digits (exclusive of exponent and trailing zeroes) needed to make the above expression true [howtoprint] [howtoread]; otherwise the format of the result is unspecified. The result returned by Ínumber->stringˇ never contains an explicit radix prefix. ˘Note:ˇ The error case can occur only when ˘numberˇ is not a complex number or is a complex number with a non-rational real or imaginary part. ˘Rationale:ˇ If ˘numberˇ is an inexact number represented using flonums, and the radix is 10, then the above expression is normally satisfied by a result containing a decimal point. The unspecified case allows for infinities, NaNs, and non-flonum representations. Í(string->number˘ stringÍ) ˇessential procedure Í(string->number˘ string radixÍ) ˇessential procedure Returns a number of the maximally precise representation expressed by the given ˘stringˇ. ˘Radixˇ must be an exact integer, either 2, 8, 10, or 16. If supplied, ˘radixˇ is a default radix that may be overridden by an explicit radix prefix in ˘stringˇ (e.g. Í"#o177"ˇ). If ˘radixˇ is not supplied, then the default radix is 10. If ˘stringˇ is not a syntactically valid notation for a number, then Ístring->numberˇ returns Í#fˇ. Í (string->number "100") ==> 100 Í (string->number "100" 16) ==> 256 Í (string->number "1e2") ==> 100.0 Í (string->number "15##") ==> 1500.0ˇ ˘Note:ˇ Although Ístring->numberˇ is an essential procedure, an implementation may restrict its domain in the following ways. ÍString->numberˇ is permitted to return Í#fˇ whenever ˘stringˇ contains an explicit radix prefix. If all numbers supported by an implementation are real, then Ístring->numberˇ is permitted to return Í#fˇ whenever ˘stringˇ uses the polar or rectangular notations for complex numbers. If all numbers are integers, then Ístring->numberˇ may return Í#fˇ whenever the fractional notation is used. If all numbers are exact, then Ístring->numberˇ may return Í#fˇ whenever an exponent marker or explicit exactness prefix is used, or if a Í#ˇ appears in place of a digit. If all inexact numbers are integers, then Ístring->numberˇ may return Í#fˇ whenever a decimal point is used. Û6.6. Charactersˇ Characters are objects that represent printed characters such as letters and digits. Characters are written using the notation Í#\ˇ<character> or Í#\ˇ<character name>. For example: Í#\a ˇ; lower case letter Í#\A ˇ; upper case letter Í#\( ˇ; left parenthesis Í#\ ˇ; the space character Í#\space ˇ; the preferred way to write a space Í#\newline ˇ; the newline character Case is significant in Í#\ˇ<character>, but not in Í#\ˇ<character name>. If <character> in Í#\ˇ<character> is alphabetic, then the character following <character> must be a delimiter character such as a space or parenthesis. This rule resolves the ambiguous case where, for example, the sequence of characters ``Í#\spaceˇ'' could be taken to be either a representation of the space character or a representation of the character ``Í#\sˇ'' followed by a representation of the symbol ``Ípaceˇ.'' Characters written in the Í#\ˇ notation are self-evaluating. That is, they do not have to be quoted in programs. Some of the procedures that operate on characters ignore the difference between upper case and lower case. The procedures that ignore case have ``Í-ciˇ'' (for ``case insensitive'') embedded in their names. Í(char?˘ objÍ) ˇessential procedure Returns Í#tˇ if ˘objˇ is a character, otherwise returns Í#fˇ. Í(char=?˘ char¯1˘ char¯2Í) ˇessential procedure Í(char<?˘ char¯1˘ char¯2Í) ˇessential procedure Í(char>?˘ char¯1˘ char¯2Í) ˇessential procedure Í(char<=?˘ char¯1˘ char¯2Í) ˇessential procedure Í(char>=?˘ char¯1˘ char¯2Í) ˇessential procedure These procedures impose a total ordering on the set of characters. It is guaranteed that under this ordering: • The upper case characters are in order. For example, Í(char<? #\A #\B)ˇ returns Í#tˇ. • The lower case characters are in order. For example, Í(char<? #\a #\b)ˇ returns Í#tˇ. • The digits are in order. For example, Í(char<? #\0 #\9)ˇ returns Í#tˇ. • Either all the digits precede all the upper case letters, or vice versa. • Either all the digits precede all the lower case letters, or vice versa. Some implementations may generalize these procedures to take more than two arguments, as with the corresponding numerical predicates. Í(char-ci=?˘ char¯1˘ char¯2Í) ˇessential procedure Í(char-ci<?˘ char¯1˘ char¯2Í) ˇessential procedure Í(char-ci>?˘ char¯1˘ char¯2Í) ˇessential procedure Í(char-ci<=?˘ char¯1˘ char¯2Í) ˇessential procedure Í(char-ci>=?˘ char¯1˘ char¯2Í) ˇessential procedure These procedures are similar to Íchar=?ˇ et cetera, but they treat upper case and lower case letters as the same. For example, Í(char-ci=? #\A #\a)ˇ returns Í#tˇ. Some implementations may generalize these procedures to take more than two arguments, as with the corresponding numerical predicates. Í(char-alphabetic?˘ charÍ) ˇessential procedure Í(char-numeric?˘ charÍ) ˇessential procedure Í(char-whitespace?˘ charÍ) ˇessential procedure Í(char-upper-case?˘ letterÍ) ˇessential procedure Í(char-lower-case?˘ letterÍ) ˇessential procedure These procedures return Í#tˇ if their arguments are alphabetic, numeric, whitespace, upper case, or lower case characters, respectively, otherwise they return Í#fˇ. The following remarks, which are specific to the ASCII character set, are intended only as a guide: The alphabetic characters are the 52 upper and lower case letters. The numeric characters are the ten decimal digits. The whitespace characters are space, tab, line feed, form feed, and carriage return. Í(char->integer˘ charÍ) ˇessential procedure Í(integer->char˘ nÍ) ˇessential procedure Given a character, Íchar->integerˇ returns an exact integer representation of the character. Given an exact integer that is the image of a character under Íchar->integerˇ, Íinteger->charˇ returns that character. These procedures implement injective order isomorphisms between the set of characters under the Íchar<=?ˇ ordering and some subset of the integers under the Í<=ˇ ordering. That is, if Í (char<=? ˘aÍ ˘bÍ) ==> #t and (<= ˘xÍ ˘yÍ) ==> #tˇ and ˘xˇ and ˘yˇ are in the domain of Íinteger->charˇ, then Í (<= (char->integer ˘aÍ) Í (char->integer ˘bÍ)) ==> #t Í Í (char<=? (integer->char ˘xÍ) Í (integer->char ˘yÍ)) ==> #tˇ Í(char-upcase˘ charÍ) ˇessential procedure Í(char-downcase˘ charÍ) ˇessential procedure These procedures return a character ˘char¯2ˇ such that Í(char-ci=? ˘charÍ ˘char¯2Í)ˇ. In addition, if ˘charˇ is alphabetic, then the result of Íchar-upcaseˇ is upper case and the result of Íchar-downcaseˇ is lower case. Û6.7. Stringsˇ Strings are sequences of characters. Strings are written as sequences of characters enclosed within doublequotes (Í"ˇ). A doublequote can be written inside a string only by escaping it with a backslash (Í\ˇ), as in Í "The word \"recursion\" has many meanings."ˇ A backslash can be written inside a string only by escaping it with another backslash. Scheme does not specify the effect of a backslash within a string that is not followed by a doublequote or backslash. A string constant may continue from one line to the next, but the exact contents of such a string are unspecified. The ˘lengthˇ of a string is the number of characters that it contains. This number is a non-negative integer that is fixed when the string is created. The ˘valid indexesˇ of a string are the exact non-negative integers less than the length of the string. The first character of a string has index 0, the second has index 1, and so on. In phrases such as ``the characters of ˘stringˇ beginning with index ˘startˇ and ending with index ˘endˇ,'' it is understood that the index ˘startˇ is inclusive and the index ˘endˇ is exclusive. Thus if ˘startˇ and ˘endˇ are the same index, a null substring is referred to, and if ˘startˇ is zero and ˘endˇ is the length of ˘stringˇ, then the entire string is referred to. Some of the procedures that operate on strings ignore the difference between upper and lower case. The versions that ignore case have ``Í-ciˇ'' (for ``case insensitive'') embedded in their names. Í(string?˘ objÍ) ˇessential procedure Returns Í#tˇ if ˘objˇ is a string, otherwise returns Í#fˇ. Í(make-string˘ kÍ) ˇessential procedure Í(make-string˘ k charÍ) ˇessential procedure ÍMake-stringˇ returns a newly allocated string of length ˘kˇ. If ˘charˇ is given, then all elements of the string are initialized to ˘charˇ, otherwise the contents of the ˘stringˇ are unspecified. Í(string˘ char ...Í) ˇessential procedure Returns a newly allocated string composed of the arguments. Í(string-length˘ stringÍ) ˇessential procedure Returns the number of characters in the given ˘stringˇ. Í(string-ref˘ string kÍ) ˇessential procedure ˘kˇ must be a valid index of ˘stringˇ. ÍString-refˇ returns character ˘kˇ of ˘stringˇ using zero-origin indexing. Í(string-set!˘ string k charÍ) ˇessential procedure ˘kˇ must be a valid index of ˘stringˇ. ÍString-set!ˇ stores ˘charˇ in element ˘kˇ of ˘stringˇ and returns an unspecified value. Í (define (f) (make-string 3 #\*)) Í (define (g) "***") Í (string-set! (f) 0 #\?) ==> ˘unspecifiedÍ Í (string-set! (g) 0 #\?) ==> ˘errorÍ Í (string-set! (symbol->string 'immutable) Í 0 Í #\?) ==> ˘errorˇ Í(string=?˘ string¯1˘ string¯2Í) ˇessential procedure Í(string-ci=?˘ string¯1˘ string¯2Í) ˇessential procedure Returns Í#tˇ if the two strings are the same length and contain the same characters in the same positions, otherwise returns Í#fˇ. ÍString-ci=?ˇ treats upper and lower case letters as though they were the same character, but Ístring=?ˇ treats upper and lower case as distinct characters. Í(string<?˘ string¯1˘ string¯2Í) ˇessential procedure Í(string>?˘ string¯1˘ string¯2Í) ˇessential procedure Í(string<=?˘ string¯1˘ string¯2Í) ˇessential procedure Í(string>=?˘ string¯1˘ string¯2Í) ˇessential procedure Í(string-ci<?˘ string¯1˘ string¯2Í) ˇessential procedure Í(string-ci>?˘ string¯1˘ string¯2Í) ˇessential procedure Í(string-ci<=?˘ string¯1˘ string¯2Í) ˇessential procedure Í(string-ci>=?˘ string¯1˘ string¯2Í) ˇessential procedure These procedures are the lexicographic extensions to strings of the corresponding orderings on characters. For example, Ístring<?ˇ is the lexicographic ordering on strings induced by the ordering Íchar<?ˇ on characters. If two strings differ in length but are the same up to the length of the shorter string, the shorter string is considered to be lexicographically less than the longer string. Implementations may generalize these and the Ístring=?ˇ and Ístring-ci=?ˇ procedures to take more than two arguments, as with the corresponding numerical predicates. Í(substring˘ string start endÍ) ˇessential procedure ˘Stringˇ must be a string, and ˘startˇ and ˘endˇ must be exact integers satisfying 0 <= ˘startˇ <= ˘endˇ <= Í(string-length ˘stringÍ).ˇ ÍSubstringˇ returns a newly allocated string formed from the characters of ˘stringˇ beginning with index ˘startˇ (inclusive) and ending with index ˘endˇ (exclusive). Í(string-append˘ string ...Í) ˇessential procedure Returns a newly allocated string whose characters form the concatenation of the given strings. Í(string->list˘ stringÍ) ˇessential procedure Í(list->string˘ charsÍ) ˇessential procedure ÍString->listˇ returns a newly allocated list of the characters that make up the given string. ÍList->stringˇ returns a newly allocated string formed from the characters in the list ˘charsˇ. ÍString->listˇ and Ílist->stringˇ are inverses so far as Íequal?ˇ is concerned. Í(string-copy˘ stringÍ) ˇprocedure Returns a newly allocated copy of the given ˘stringˇ. Í(string-fill!˘ string charÍ) ˇprocedure Stores ˘charˇ in every element of the given ˘stringˇ and returns an unspecified value. Û6.8. Vectorsˇ Vectors are heterogenous structures whose elements are indexed by integers. A vector typically occupies less space than a list of the same length, and the average time required to access a randomly chosen element is typically less for the vector than for the list. The ˘lengthˇ of a vector is the number of elements that it contains. This number is a non-negative integer that is fixed when the vector is created. The ˘valid indexesˇ of a vector are the exact non-negative integers less than the length of the vector. The first element in a vector is indexed by zero, and the last element is indexed by one less than the length of the vector. Vectors are written using the notation Í#(˘objÍ ...)ˇ. For example, a vector of length 3 containing the number zero in element 0, the list Í(2 2 2 2)ˇ in element 1, and the string Í"Anna"ˇ in element 2 can be written as following: Í #(0 (2 2 2 2) "Anna")ˇ Note that this is the external representation of a vector, not an expression evaluating to a vector. Like list constants, vector constants must be quoted: Í '#(0 (2 2 2 2) "Anna") Í ==> #(0 (2 2 2 2) "Anna")ˇ Í(vector?˘ objÍ) ˇessential procedure Returns Í#tˇ if ˘objˇ is a vector, otherwise returns Í#fˇ. Í(make-vector˘ kÍ) ˇessential procedure Í(make-vector˘ k fillÍ) ˇprocedure Returns a newly allocated vector of ˘kˇ elements. If a second argument is given, then each element is initialized to ˘fillˇ. Otherwise the initial contents of each element is unspecified. Í(vector˘ obj ...Í) ˇessential procedure Returns a newly allocated vector whose elements contain the given arguments. Analogous to Ílistˇ. Í (vector 'a 'b 'c) ==> #(a b c)ˇ Í(vector-length˘ vectorÍ) ˇessential procedure Returns the number of elements in ˘vectorˇ. Í(vector-ref˘ vector kÍ) ˇessential procedure ˘kˇ must be a valid index of ˘vectorˇ. ÍVector-refˇ returns the contents of element ˘kˇ of ˘vectorˇ. Í (vector-ref '#(1 1 2 3 5 8 13 21) Í 5) Í ==> 8 Í (vector-ref '#(1 1 2 3 5 8 13 21) Í (inexact->exact Í (round (* 2 (acos -1))))) Í ==> 13ˇ Í(vector-set!˘ vector k objÍ) ˇessential procedure ˘kˇ must be a valid index of ˘vectorˇ. ÍVector-set!ˇ stores ˘objˇ in element ˘kˇ of ˘vectorˇ. The value returned by Ívector-set!ˇ is unspecified. Í (let ((vec (vector 0 '(2 2 2 2) "Anna"))) Í (vector-set! vec 1 '("Sue" "Sue")) Í vec) Í ==> #(0 ("Sue" "Sue") "Anna") Í Í (vector-set! '#(0 1 2) 1 "doe") Í ==> ˘errorÍ ; constant vectorˇ Í(vector->list˘ vectorÍ) ˇessential procedure Í(list->vector˘ listÍ) ˇessential procedure ÍVector->listˇ returns a newly allocated list of the objects contained in the elements of ˘vectorˇ. ÍList->vectorˇ returns a newly created vector initialized to the elements of the list ˘listˇ. Í (vector->list '#(dah dah didah)) Í ==> (dah dah didah) Í (list->vector '(dididit dah)) Í ==> #(dididit dah)ˇ Í(vector-fill!˘ vector fillÍ) ˇprocedure Stores ˘fillˇ in every element of ˘vectorˇ. The value returned by Ívector-fill!ˇ is unspecified. Û6.9. Control featuresˇ This chapter describes various primitive procedures which control the flow of program execution in special ways. The Íprocedure?ˇ predicate is also described here. Í(procedure?˘ objÍ) ˇessential procedure Returns Í#tˇ if ˘objˇ is a procedure, otherwise returns Í#fˇ. Í (procedure? car) ==> #t Í (procedure? 'car) ==> #f Í (procedure? (lambda (x) (* x x))) Í ==> #t Í (procedure? '(lambda (x) (* x x))) Í ==> #f Í (call-with-current-continuation procedure?) Í ==> #tˇ Í(apply˘ proc argsÍ) ˇessential procedure Í(apply˘ proc arg¯1˘ ... argsÍ) ˇprocedure ˘Procˇ must be a procedure and ˘argsˇ must be a list. The first (essential) form calls ˘procˇ with the elements of ˘argsˇ as the actual arguments. The second form is a generalization of the first that calls ˘procˇ with the elements of the list Í(append (list ˘arg¯1Í ...) ˘argsÍ)ˇ as the actual arguments. Í (apply + (list 3 4)) ==> 7 Í Í (define compose Í (lambda (f g) Í (lambda args Í (f (apply g args))))) Í Í ((compose sqrt *) 12 75) ==> 30ˇ Í(map˘ proc list¯1˘ list¯2˘ ...Í) ˇessential procedure The ˘listˇs must be lists, and ˘procˇ must be a procedure taking as many arguments as there are ˘listˇs. If more than one ˘listˇ is given, then they must all be the same length. ÍMapˇ applies ˘procˇ element-wise to the elements of the ˘listˇs and returns a list of the results, in order from left to right. The dynamic order in which ˘procˇ is applied to the elements of the ˘listˇs is unspecified. Í (map cadr '((a b) (d e) (g h))) Í ==> (b e h) Í Í (map (lambda (n) (expt n n)) Í '(1 2 3 4 5)) Í ==> (1 4 27 256 3125) Í Í (map + '(1 2 3) '(4 5 6)) ==> (5 7 9) Í Í (let ((count 0)) Í (map (lambda (ignored) Í (set! count (+ count 1)) Í count) Í '(a b c))) ==> ˘unspecifiedˇ Í(for-each˘ proc list¯1˘ list¯2˘ ...Í) ˇessential procedure The arguments to Ífor-eachˇ are like the arguments to Ímapˇ, but Ífor-eachˇ calls ˘procˇ for its side effects rather than for its values. Unlike Ímapˇ, Ífor-eachˇ is guaranteed to call ˘procˇ on the elements of the ˘listˇs in order from the first element to the last, and the value returned by Ífor-eachˇ is unspecified. Í (let ((v (make-vector 5))) Í (for-each (lambda (i) Í (vector-set! v i (* i i))) Í '(0 1 2 3 4)) Í v) ==> #(0 1 4 9 16)ˇ Í(force˘ promiseÍ) ˇprocedure Forces the value of ˘promiseˇ (see Ídelayˇ, section 4.2.5). If no value has been computed for the promise, then a value is computed and returned. The value of the promise is cached (or ``memoized'') so that if it is forced a second time, the previously computed value is returned. Í (force (delay (+ 1 2))) ==> 3 Í (let ((p (delay (+ 1 2)))) Í (list (force p) (force p))) Í ==> (3 3) Í Í (define a-stream Í (letrec ((next Í (lambda (n) Í (cons n (delay (next (+ n 1))))))) Í (next 0))) Í (define head car) Í (define tail Í (lambda (stream) (force (cdr stream)))) Í Í (head (tail (tail a-stream))) Í ==> 2ˇ ÍForceˇ and Ídelayˇ are mainly intended for programs written in functional style. The following examples should not be considered to illustrate good programming style, but they illustrate the property that only one value is computed for a promise, no matter how many times it is forced. Í (define count 0) Í (define p Í (delay (begin (set! count (+ count 1)) Í (if (> count x) Í count Í (force p))))) Í (define x 5) Í p ==> ˘a promiseÍ Í (force p) ==> 6 Í p ==> ˘a promise, stillÍ Í (begin (set! x 10) Í (force p)) ==> 6ˇ Here is a possible implementation of Ídelayˇ and Íforceˇ. Promises are implemented here as procedures of no arguments, and Íforceˇ simply calls its argument: Í (define force Í (lambda (object) Í (object)))ˇ We define the expression Í (delay ˇ<expression>Í)ˇ to have the same meaning as the procedure call Í (make-promise (lambda () ˇ<expression>Í)),ˇ where Ímake-promiseˇ is defined as follows: Í (define make-promise Í (lambda (proc) Í (let ((result-ready? #f) Í (result #f)) Í (lambda () Í (if result-ready? Í result Í (let ((x (proc))) Í (if result-ready? Í result Í (begin (set! result-ready? #t) Í (set! result x) Í result))))))))ˇ ˘Rationale:ˇ A promise may refer to its own value, as in the last example above. Forcing such a promise may cause the promise to be forced a second time before the value of the first force has been computed. This complicates the definition of Ímake-promiseˇ. Various extensions to this semantics of Ídelayˇ and Íforceˇ are supported in some implementations: • Calling Íforceˇ on an object that is not a promise may simply return the object. • It may be the case that there is no means by which a promise can be operationally distinguished from its forced value. That is, expressions like the following may evaluate to either Í#tˇ or to Í#fˇ, depending on the implementation: Í (eqv? (delay 1) 1) ==> ˘unspecifiedÍ Í (pair? (delay (cons 1 2))) ==> ˘unspecifiedˇ • Some implementations may implement ``implicit forcing,'' where the value of a promise is forced by primitive procedures like Ícdrˇ and Í+ˇ: Í (+ (delay (* 3 7)) 13) ==> 34ˇ Í(call-with-current-continuation˘ procÍ) ˇessential procedure ˘Procˇ must be a procedure of one argument. The procedure Ícall-with-current-continuationˇ packages up the current continuation (see the rationale below) as an ``escape procedure'' and passes it as an argument to ˘procˇ. The escape procedure is a Scheme procedure of one argument that, if it is later passed a value, will ignore whatever continuation is in effect at that later time and will give the value instead to the continuation that was in effect when the escape procedure was created. The escape procedure that is passed to ˘procˇ has unlimited extent just like any other procedure in Scheme. It may be stored in variables or data structures and may be called as many times as desired. The following examples show only the most common uses of Ícall-with-current-continuationˇ. If all real programs were as simple as these examples, there would be no need for a procedure with the power of Ícall-with-current-continuationˇ. Í (call-with-current-continuation Í (lambda (exit) Í (for-each (lambda (x) Í (if (negative? x) Í (exit x))) Í '(54 0 37 -3 245 19)) Í #t)) ==> -3 Í Í (define list-length Í (lambda (obj) Í (call-with-current-continuation Í (lambda (return) Í (letrec ((r Í (lambda (obj) Í (cond ((null? obj) 0) Í ((pair? obj) Í (+ (r (cdr obj)) 1)) Í (else (return #f)))))) Í (r obj)))))) Í Í (list-length '(1 2 3 4)) ==> 4 Í Í (list-length '(a b . c)) ==> #fˇ ˘Rationale:ˇ A common use of Ícall-with-current-continuationˇ is for structured, non-local exits from loops or procedure bodies, but in fact Ícall-with-current-continuationˇ is extremely useful for implementing a wide variety of advanced control structures. Whenever a Scheme expression is evaluated there is a ˘continuationˇ wanting the result of the expression. The continuation represents an entire (default) future for the computation. If the expression is evaluated at top level, for example, then the continuation might take the result, print it on the screen, prompt for the next input, evaluate it, and so on forever. Most of the time the continuation includes actions specified by user code, as in a continuation that will take the result, multiply it by the value stored in a local variable, add seven, and give the answer to the top level continuation to be printed. Normally these ubiquitous continuations are hidden behind the scenes and programmers don't think much about them. On rare occasions, however, a programmer may need to deal with continuations explicitly. ÍCall-with-current-continuationˇ allows Scheme programmers to do that by creating a procedure that acts just like the current continuation. Most programming languages incorporate one or more special-purpose escape constructs with names like Íexitˇ, Íreturnˇ, or even Ígotoˇ. In 1965, however, Peter Landin [Landin] invented a general purpose escape operator called the J-operator. John Reynolds [Reynolds] described a simpler but equally powerful construct in 1972. The Ícatchˇ special form described by Sussman and Steele in the 1975 report on Scheme is exactly the same as Reynolds's construct, though its name came from a less general construct in MacLisp. Several Scheme implementors noticed that the full power of the Ícatchˇ construct could be provided by a procedure instead of by a special syntactic construct, and the name Ícall-with-current-continuationˇ was coined in 1982. This name is descriptive, but opinions differ on the merits of such a long name, and some people use the name Ícall/ccˇ instead. Û6.10. Input and outputˇ ¸6.10.1. Portsˇ Ports represent input and output devices. To Scheme, an input port is a Scheme object that can deliver characters upon command, while an output port is a Scheme object that can accept characters. Í(call-with-input-file˘ string procÍ) ˇessential procedure Í(call-with-output-file˘ string procÍ) ˇessential procedure ˘Procˇ should be a procedure of one argument, and ˘stringˇ should be a string naming a file. For Ícall-with-input-fileˇ, the file must already exist; for Ícall-with-output-fileˇ, the effect is unspecified if the file already exists. These procedures call ˘procˇ with one argument: the port obtained by opening the named file for input or output. If the file cannot be opened, an error is signalled. If the procedure returns, then the port is closed automatically and the value yielded by the procedure is returned. If the procedure does not return, then the port will not be closed automatically unless it is possible to prove that the port will never again be used for a read or write operation. ˘Rationale:ˇ Because Scheme's escape procedures have unlimited extent, it is possible to escape from the current continuation but later to escape back in. If implementations were permitted to close the port on any escape from the current continuation, then it would be impossible to write portable code using both Ícall-with-current-continuationˇ and Ícall-with-input-fileˇ or Ícall-with-output-fileˇ. Í(input-port?˘ objÍ) ˇessential procedure Í(output-port?˘ objÍ) ˇessential procedure Returns Í#tˇ if ˘objˇ is an input port or output port respectively, otherwise returns Í#fˇ. Í(current-input-port) ˇessential procedure Í(current-output-port) ˇessential procedure Returns the current default input or output port. Í(with-input-from-file˘ string thunkÍ) ˇprocedure Í(with-output-to-file˘ string thunkÍ) ˇprocedure ˘Thunkˇ must be a procedure of no arguments, and ˘stringˇ must be a string naming a file. For Íwith-input-from-fileˇ, the file must already exist; for Íwith-output-to-fileˇ, the effect is unspecified if the file already exists. The file is opened for input or output, an input or output port connected to it is made the default value returned by Ícurrent-input-portˇ or Ícurrent-output-portˇ, and the ˘thunkˇ is called with no arguments. When the ˘thunkˇ returns, the port is closed and the previous default is restored. ÍWith-input-from-fileˇ and Íwith-output-to-fileˇ return the value yielded by ˘thunkˇ. If an escape procedure is used to escape from the continuation of these procedures, their behavior is implementation dependent. Í(open-input-file˘ filenameÍ) ˇessential procedure Takes a string naming an existing file and returns an input port capable of delivering characters from the file. If the file cannot be opened, an error is signalled. Í(open-output-file˘ filenameÍ) ˇessential procedure Takes a string naming an output file to be created and returns an output port capable of writing characters to a new file by that name. If the file cannot be opened, an error is signalled. If a file with the given name already exists, the effect is unspecified. Í(close-input-port˘ portÍ) ˇessential procedure Í(close-output-port˘ portÍ) ˇessential procedure Closes the file associated with ˘portˇ, rendering the ˘portˇ incapable of delivering or accepting characters. These routines have no effect if the file has already been closed. The value returned is unspecified. ¸6.10.2. Inputˇ Í(read) ˇessential procedure Í(read˘ portÍ) ˇessential procedure ÍReadˇ converts external representations of Scheme objects into the objects themselves. That is, it is a parser for the nonterminal <datum> (see sections 7.1.2 and 6.3). ÍReadˇ returns the next object parsable from the given input ˘portˇ, updating ˘portˇ to point to the first character past the end of the external representation of the object. If an end of file is encountered in the input before any characters are found that can begin an object, then an end of file object is returned. The port remains open, and further attempts to read will also return an end of file object. If an end of file is encountered after the beginning of an object's external representation, but the external representation is incomplete and therefore not parsable, an error is signalled. The ˘portˇ argument may be omitted, in which case it defaults to the value returned by Ícurrent-input-portˇ. It is an error to read from a closed port. Í(read-char) ˇessential procedure Í(read-char˘ portÍ) ˇessential procedure Returns the next character available from the input ˘portˇ, updating the ˘portˇ to point to the following character. If no more characters are available, an end of file object is returned. ˘Portˇ may be omitted, in which case it defaults to the value returned by Ícurrent-input-portˇ. Í(peek-char) ˇessential procedure Í(peek-char˘ portÍ) ˇessential procedure Returns the next character available from the input ˘portˇ, ˘withoutˇ updating the ˘portˇ to point to the following character. If no more characters are available, an end of file object is returned. ˘Portˇ may be omitted, in which case it defaults to the value returned by Ícurrent-input-portˇ. ˘Note:ˇ The value returned by a call to Ípeek-charˇ is the same as the value that would have been returned by a call to Íread-charˇ with the same ˘portˇ. The only difference is that the very next call to Íread-charˇ or Ípeek-charˇ on that ˘portˇ will return the value returned by the preceding call to Ípeek-charˇ. In particular, a call to Ípeek-charˇ on an interactive port will hang waiting for input whenever a call to Íread-charˇ would have hung. Í(eof-object?˘ objÍ) ˇessential procedure Returns Í#tˇ if ˘objˇ is an end of file object, otherwise returns Í#fˇ. The precise set of end of file objects will vary among implementations, but in any case no end of file object will ever be an object that can be read in using Íreadˇ. Í(char-ready?) ˇprocedure Í(char-ready?˘ portÍ) ˇprocedure Returns Í#tˇ if a character is ready on the input ˘portˇ and returns Í#fˇ otherwise. If Íchar-readyˇ returns Í#tˇ then the next Íread-charˇ operation on the given ˘portˇ is guaranteed not to hang. If the ˘portˇ is at end of file then Íchar-ready?ˇ returns Í#tˇ. ˘Portˇ may be omitted, in which case it defaults to the value returned by Ícurrent-input-portˇ. ˘Rationale:ˇ ÍChar-ready?ˇ exists to make it possible for a program to accept characters from interactive ports without getting stuck waiting for input. Any input editors associated with such ports must ensure that characters whose existence has been asserted by Íchar-ready?ˇ cannot be rubbed out. If Íchar-ready?ˇ were to return Í#fˇ at end of file, a port at end of file would be indistinguishable from an interactive port that has no ready characters. ¸6.10.3. Outputˇ Í(write˘ objÍ) ˇessential procedure Í(write˘ obj portÍ) ˇessential procedure Writes a written representation of ˘objˇ to the given ˘portˇ. Strings that appear in the written representation are enclosed in doublequotes, and within those strings backslash and doublequote characters are escaped by backslashes. ÍWriteˇ returns an unspecified value. The ˘portˇ argument may be omitted, in which case it defaults to the value returned by Ícurrent-output-portˇ. Í(display˘ objÍ) ˇessential procedure Í(display˘ obj portÍ) ˇessential procedure Writes a representation of ˘objˇ to the given ˘portˇ. Strings that appear in the written representation are not enclosed in doublequotes, and no characters are escaped within those strings. Character objects appear in the representation as if written by Íwrite-charˇ instead of by Íwriteˇ. ÍDisplayˇ returns an unspecified value. The ˘portˇ argument may be omitted, in which case it defaults to the value returned by Ícurrent-output-portˇ. ˘Rationale:ˇ ÍWriteˇ is intended for producing machine-readable output and Ídisplayˇ is for producing human-readable output. Implementations that allow ``slashification'' within symbols will probably want Íwriteˇ but not Ídisplayˇ to slashify funny characters in symbols. Í(newline) ˇessential procedure Í(newline˘ portÍ) ˇessential procedure Writes an end of line to ˘portˇ. Exactly how this is done differs from one operating system to another. Returns an unspecified value. The ˘portˇ argument may be omitted, in which case it defaults to the value returned by Ícurrent-output-portˇ. Í(write-char˘ charÍ) ˇessential procedure Í(write-char˘ char portÍ) ˇessential procedure Writes the character ˘charˇ (not an external representation of the character) to the given ˘portˇ and returns an unspecified value. The ˘portˇ argument may be omitted, in which case it defaults to the value returned by Ícurrent-output-portˇ. ¸6.10.4. System interfaceˇ Questions of system interface generally fall outside of the domain of this report. However, the following operations are important enough to deserve description here. Í(load˘ filenameÍ) ˇessential procedure ˘Filenameˇ should be a string naming an existing file containing Scheme source code. The Íloadˇ procedure reads expressions and definitions from the file and evaluates them sequentially. It is unspecified whether the results of the expressions are printed. The Íloadˇ procedure does not affect the values returned by Ícurrent-input-portˇ and Ícurrent-output-portˇ. ÍLoadˇ returns an unspecified value. ˘Rationale:ˇ For portability, Íloadˇ must operate on source files. Its operation on other kinds of files necessarily varies among implementations. Í(transcript-on˘ filenameÍ) ˇprocedure Í(transcript-off) ˇprocedure ˘Filenameˇ must be a string naming an output file to be created. The effect of Ítranscript-onˇ is to open the named file for output, and to cause a transcript of subsequent interaction between the user and the Scheme system to be written to the file. The transcript is ended by a call to Ítranscript-offˇ, which closes the transcript file. Only one transcript may be in progress at any time, though some implementations may relax this restriction. The values returned by these procedures are unspecified. Û7. Formal syntax and semanticsˇ Due to formatting restrictions, this chapter is not included in the online help.