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-This is Info file slib.info, produced by Makeinfo-1.64 from the input
-file slib.texi.
-
- This file documents SLIB, the portable Scheme library.
-
- Copyright (C) 1993 Todd R. Eigenschink Copyright (C) 1993, 1994, 1995
-Aubrey Jaffer
-
- Permission is granted to make and distribute verbatim copies of this
-manual provided the copyright notice and this permission notice are
-preserved on all copies.
-
- Permission is granted to copy and distribute modified versions of this
-manual under the conditions for verbatim copying, provided that the
-entire resulting derived work is distributed under the terms of a
-permission notice identical to this one.
-
- Permission is granted to copy and distribute translations of this
-manual into another language, under the above conditions for modified
-versions, except that this permission notice may be stated in a
-translation approved by the author.
-
-
-File: slib.info, Node: Syntactic Closures, Next: Syntax-Case Macros, Prev: Macros That Work, Up: Macros
-
-Syntactic Closures
-==================
-
- `(require 'syntactic-closures)'
-
- - Function: macro:expand EXPRESSION
- - Function: synclo:expand EXPRESSION
- Returns scheme code with the macros and derived expression types of
- EXPRESSION expanded to primitive expression types.
-
- - Function: macro:eval EXPRESSION
- - Function: synclo:eval EXPRESSION
- `macro:eval' returns the value of EXPRESSION in the current top
- level environment. EXPRESSION can contain macro definitions.
- Side effects of EXPRESSION will affect the top level environment.
-
- - Procedure: macro:load FILENAME
- - Procedure: synclo:load FILENAME
- FILENAME should be a string. If filename names an existing file,
- the `macro:load' procedure reads Scheme source code expressions and
- definitions from the file and evaluates them sequentially. These
- source code expressions and definitions may contain macro
- definitions. The `macro:load' procedure does not affect the
- values returned by `current-input-port' and `current-output-port'.
-
-Syntactic Closure Macro Facility
---------------------------------
-
- A Syntactic Closures Macro Facility
-
- by Chris Hanson
-
- 9 November 1991
-
- This document describes "syntactic closures", a low-level macro
-facility for the Scheme programming language. The facility is an
-alternative to the low-level macro facility described in the `Revised^4
-Report on Scheme.' This document is an addendum to that report.
-
- The syntactic closures facility extends the BNF rule for TRANSFORMER
-SPEC to allow a new keyword that introduces a low-level macro
-transformer:
- TRANSFORMER SPEC := (transformer EXPRESSION)
-
- Additionally, the following procedures are added:
- make-syntactic-closure
- capture-syntactic-environment
- identifier?
- identifier=?
-
- The description of the facility is divided into three parts. The
-first part defines basic terminology. The second part describes how
-macro transformers are defined. The third part describes the use of
-"identifiers", which extend the syntactic closure mechanism to be
-compatible with `syntax-rules'.
-
-Terminology
-...........
-
- This section defines the concepts and data types used by the syntactic
-closures facility.
-
- "Forms" are the syntactic entities out of which programs are
- recursively constructed. A form is any expression, any
- definition, any syntactic keyword, or any syntactic closure. The
- variable name that appears in a `set!' special form is also a
- form. Examples of forms:
- 17
- #t
- car
- (+ x 4)
- (lambda (x) x)
- (define pi 3.14159)
- if
- define
-
- An "alias" is an alternate name for a given symbol. It can appear
- anywhere in a form that the symbol could be used, and when quoted
- it is replaced by the symbol; however, it does not satisfy the
- predicate `symbol?'. Macro transformers rarely distinguish
- symbols from aliases, referring to both as identifiers.
-
- A "syntactic" environment maps identifiers to their meanings.
- More precisely, it determines whether an identifier is a syntactic
- keyword or a variable. If it is a keyword, the meaning is an
- interpretation for the form in which that keyword appears. If it
- is a variable, the meaning identifies which binding of that
- variable is referenced. In short, syntactic environments contain
- all of the contextual information necessary for interpreting the
- meaning of a particular form.
-
- A "syntactic closure" consists of a form, a syntactic environment,
- and a list of identifiers. All identifiers in the form take their
- meaning from the syntactic environment, except those in the given
- list. The identifiers in the list are to have their meanings
- determined later. A syntactic closure may be used in any context
- in which its form could have been used. Since a syntactic closure
- is also a form, it may not be used in contexts where a form would
- be illegal. For example, a form may not appear as a clause in the
- cond special form. A syntactic closure appearing in a quoted
- structure is replaced by its form.
-
-Transformer Definition
-......................
-
- This section describes the `transformer' special form and the
-procedures `make-syntactic-closure' and `capture-syntactic-environment'.
-
- - Syntax: transformer EXPRESSION
- Syntax: It is an error if this syntax occurs except as a
- TRANSFORMER SPEC.
-
- Semantics: The EXPRESSION is evaluated in the standard transformer
- environment to yield a macro transformer as described below. This
- macro transformer is bound to a macro keyword by the special form
- in which the `transformer' expression appears (for example,
- `let-syntax').
-
- A "macro transformer" is a procedure that takes two arguments, a
- form and a syntactic environment, and returns a new form. The
- first argument, the "input form", is the form in which the macro
- keyword occurred. The second argument, the "usage environment",
- is the syntactic environment in which the input form occurred.
- The result of the transformer, the "output form", is automatically
- closed in the "transformer environment", which is the syntactic
- environment in which the `transformer' expression occurred.
-
- For example, here is a definition of a push macro using
- `syntax-rules':
- (define-syntax push
- (syntax-rules ()
- ((push item list)
- (set! list (cons item list)))))
-
- Here is an equivalent definition using `transformer':
- (define-syntax push
- (transformer
- (lambda (exp env)
- (let ((item
- (make-syntactic-closure env '() (cadr exp)))
- (list
- (make-syntactic-closure env '() (caddr exp))))
- `(set! ,list (cons ,item ,list))))))
-
- In this example, the identifiers `set!' and `cons' are closed in
- the transformer environment, and thus will not be affected by the
- meanings of those identifiers in the usage environment `env'.
-
- Some macros may be non-hygienic by design. For example, the
- following defines a loop macro that implicitly binds `exit' to an
- escape procedure. The binding of `exit' is intended to capture
- free references to `exit' in the body of the loop, so `exit' must
- be left free when the body is closed:
- (define-syntax loop
- (transformer
- (lambda (exp env)
- (let ((body (cdr exp)))
- `(call-with-current-continuation
- (lambda (exit)
- (let f ()
- ,@(map (lambda (exp)
- (make-syntactic-closure env '(exit)
- exp))
- body)
- (f))))))))
-
- To assign meanings to the identifiers in a form, use
- `make-syntactic-closure' to close the form in a syntactic
- environment.
-
- - Function: make-syntactic-closure ENVIRONMENT FREE-NAMES FORM
- ENVIRONMENT must be a syntactic environment, FREE-NAMES must be a
- list of identifiers, and FORM must be a form.
- `make-syntactic-closure' constructs and returns a syntactic closure
- of FORM in ENVIRONMENT, which can be used anywhere that FORM could
- have been used. All the identifiers used in FORM, except those
- explicitly excepted by FREE-NAMES, obtain their meanings from
- ENVIRONMENT.
-
- Here is an example where FREE-NAMES is something other than the
- empty list. It is instructive to compare the use of FREE-NAMES in
- this example with its use in the `loop' example above: the examples
- are similar except for the source of the identifier being left
- free.
- (define-syntax let1
- (transformer
- (lambda (exp env)
- (let ((id (cadr exp))
- (init (caddr exp))
- (exp (cadddr exp)))
- `((lambda (,id)
- ,(make-syntactic-closure env (list id) exp))
- ,(make-syntactic-closure env '() init))))))
-
- `let1' is a simplified version of `let' that only binds a single
- identifier, and whose body consists of a single expression. When
- the body expression is syntactically closed in its original
- syntactic environment, the identifier that is to be bound by
- `let1' must be left free, so that it can be properly captured by
- the `lambda' in the output form.
-
- To obtain a syntactic environment other than the usage
- environment, use `capture-syntactic-environment'.
-
- - Function: capture-syntactic-environment PROCEDURE
- `capture-syntactic-environment' returns a form that will, when
- transformed, call PROCEDURE on the current syntactic environment.
- PROCEDURE should compute and return a new form to be transformed,
- in that same syntactic environment, in place of the form.
-
- An example will make this clear. Suppose we wanted to define a
- simple `loop-until' keyword equivalent to
- (define-syntax loop-until
- (syntax-rules ()
- ((loop-until id init test return step)
- (letrec ((loop
- (lambda (id)
- (if test return (loop step)))))
- (loop init)))))
-
- The following attempt at defining `loop-until' has a subtle bug:
- (define-syntax loop-until
- (transformer
- (lambda (exp env)
- (let ((id (cadr exp))
- (init (caddr exp))
- (test (cadddr exp))
- (return (cadddr (cdr exp)))
- (step (cadddr (cddr exp)))
- (close
- (lambda (exp free)
- (make-syntactic-closure env free exp))))
- `(letrec ((loop
- (lambda (,id)
- (if ,(close test (list id))
- ,(close return (list id))
- (loop ,(close step (list id)))))))
- (loop ,(close init '())))))))
-
- This definition appears to take all of the proper precautions to
- prevent unintended captures. It carefully closes the
- subexpressions in their original syntactic environment and it
- leaves the `id' identifier free in the `test', `return', and
- `step' expressions, so that it will be captured by the binding
- introduced by the `lambda' expression. Unfortunately it uses the
- identifiers `if' and `loop' within that `lambda' expression, so if
- the user of `loop-until' just happens to use, say, `if' for the
- identifier, it will be inadvertently captured.
-
- The syntactic environment that `if' and `loop' want to be exposed
- to is the one just outside the `lambda' expression: before the
- user's identifier is added to the syntactic environment, but after
- the identifier loop has been added.
- `capture-syntactic-environment' captures exactly that environment
- as follows:
- (define-syntax loop-until
- (transformer
- (lambda (exp env)
- (let ((id (cadr exp))
- (init (caddr exp))
- (test (cadddr exp))
- (return (cadddr (cdr exp)))
- (step (cadddr (cddr exp)))
- (close
- (lambda (exp free)
- (make-syntactic-closure env free exp))))
- `(letrec ((loop
- ,(capture-syntactic-environment
- (lambda (env)
- `(lambda (,id)
- (,(make-syntactic-closure env '() `if)
- ,(close test (list id))
- ,(close return (list id))
- (,(make-syntactic-closure env '()
- `loop)
- ,(close step (list id)))))))))
- (loop ,(close init '())))))))
-
- In this case, having captured the desired syntactic environment,
- it is convenient to construct syntactic closures of the
- identifiers `if' and the `loop' and use them in the body of the
- `lambda'.
-
- A common use of `capture-syntactic-environment' is to get the
- transformer environment of a macro transformer:
- (transformer
- (lambda (exp env)
- (capture-syntactic-environment
- (lambda (transformer-env)
- ...))))
-
-Identifiers
-...........
-
- This section describes the procedures that create and manipulate
-identifiers. Previous syntactic closure proposals did not have an
-identifier data type - they just used symbols. The identifier data
-type extends the syntactic closures facility to be compatible with the
-high-level `syntax-rules' facility.
-
- As discussed earlier, an identifier is either a symbol or an "alias".
-An alias is implemented as a syntactic closure whose "form" is an
-identifier:
- (make-syntactic-closure env '() 'a)
- => an "alias"
-
- Aliases are implemented as syntactic closures because they behave just
-like syntactic closures most of the time. The difference is that an
-alias may be bound to a new value (for example by `lambda' or
-`let-syntax'); other syntactic closures may not be used this way. If
-an alias is bound, then within the scope of that binding it is looked
-up in the syntactic environment just like any other identifier.
-
- Aliases are used in the implementation of the high-level facility
-`syntax-rules'. A macro transformer created by `syntax-rules' uses a
-template to generate its output form, substituting subforms of the
-input form into the template. In a syntactic closures implementation,
-all of the symbols in the template are replaced by aliases closed in
-the transformer environment, while the output form itself is closed in
-the usage environment. This guarantees that the macro transformation
-is hygienic, without requiring the transformer to know the syntactic
-roles of the substituted input subforms.
-
- - Function: identifier? OBJECT
- Returns `#t' if OBJECT is an identifier, otherwise returns `#f'.
- Examples:
- (identifier? 'a)
- => #t
- (identifier? (make-syntactic-closure env '() 'a))
- => #t
- (identifier? "a")
- => #f
- (identifier? #\a)
- => #f
- (identifier? 97)
- => #f
- (identifier? #f)
- => #f
- (identifier? '(a))
- => #f
- (identifier? '#(a))
- => #f
-
- The predicate `eq?' is used to determine if two identifers are
- "the same". Thus `eq?' can be used to compare identifiers exactly
- as it would be used to compare symbols. Often, though, it is
- useful to know whether two identifiers "mean the same thing". For
- example, the `cond' macro uses the symbol `else' to identify the
- final clause in the conditional. A macro transformer for `cond'
- cannot just look for the symbol `else', because the `cond' form
- might be the output of another macro transformer that replaced the
- symbol `else' with an alias. Instead the transformer must look
- for an identifier that "means the same thing" in the usage
- environment as the symbol `else' means in the transformer
- environment.
-
- - Function: identifier=? ENVIRONMENT1 IDENTIFIER1 ENVIRONMENT2
- IDENTIFIER2
- ENVIRONMENT1 and ENVIRONMENT2 must be syntactic environments, and
- IDENTIFIER1 and IDENTIFIER2 must be identifiers. `identifier=?'
- returns `#t' if the meaning of IDENTIFIER1 in ENVIRONMENT1 is the
- same as that of IDENTIFIER2 in ENVIRONMENT2, otherwise it returns
- `#f'. Examples:
-
- (let-syntax
- ((foo
- (transformer
- (lambda (form env)
- (capture-syntactic-environment
- (lambda (transformer-env)
- (identifier=? transformer-env 'x env 'x)))))))
- (list (foo)
- (let ((x 3))
- (foo))))
- => (#t #f)
-
- (let-syntax ((bar foo))
- (let-syntax
- ((foo
- (transformer
- (lambda (form env)
- (capture-syntactic-environment
- (lambda (transformer-env)
- (identifier=? transformer-env 'foo
- env (cadr form))))))))
- (list (foo foo)
- (foobar))))
- => (#f #t)
-
-Acknowledgements
-................
-
- The syntactic closures facility was invented by Alan Bawden and
-Jonathan Rees. The use of aliases to implement `syntax-rules' was
-invented by Alan Bawden (who prefers to call them "synthetic names").
-Much of this proposal is derived from an earlier proposal by Alan
-Bawden.
-
-
-File: slib.info, Node: Syntax-Case Macros, Next: Fluid-Let, Prev: Syntactic Closures, Up: Macros
-
-Syntax-Case Macros
-==================
-
- `(require 'syntax-case)'
-
- - Function: macro:expand EXPRESSION
- - Function: syncase:expand EXPRESSION
- Returns scheme code with the macros and derived expression types of
- EXPRESSION expanded to primitive expression types.
-
- - Function: macro:eval EXPRESSION
- - Function: syncase:eval EXPRESSION
- `macro:eval' returns the value of EXPRESSION in the current top
- level environment. EXPRESSION can contain macro definitions.
- Side effects of EXPRESSION will affect the top level environment.
-
- - Procedure: macro:load FILENAME
- - Procedure: syncase:load FILENAME
- FILENAME should be a string. If filename names an existing file,
- the `macro:load' procedure reads Scheme source code expressions and
- definitions from the file and evaluates them sequentially. These
- source code expressions and definitions may contain macro
- definitions. The `macro:load' procedure does not affect the
- values returned by `current-input-port' and `current-output-port'.
-
- This is version 2.1 of `syntax-case', the low-level macro facility
-proposed and implemented by Robert Hieb and R. Kent Dybvig.
-
- This version is further adapted by Harald Hanche-Olsen
-<hanche@imf.unit.no> to make it compatible with, and easily usable
-with, SLIB. Mainly, these adaptations consisted of:
-
- * Removing white space from `expand.pp' to save space in the
- distribution. This file is not meant for human readers anyway...
-
- * Removed a couple of Chez scheme dependencies.
-
- * Renamed global variables used to minimize the possibility of name
- conflicts.
-
- * Adding an SLIB-specific initialization file.
-
- * Removing a couple extra files, most notably the documentation (but
- see below).
-
- If you wish, you can see exactly what changes were done by reading the
-shell script in the file `syncase.sh'.
-
- The two PostScript files were omitted in order to not burden the SLIB
-distribution with them. If you do intend to use `syntax-case',
-however, you should get these files and print them out on a PostScript
-printer. They are available with the original `syntax-case'
-distribution by anonymous FTP in
-`cs.indiana.edu:/pub/scheme/syntax-case'.
-
- In order to use syntax-case from an interactive top level, execute:
- (require 'syntax-case)
- (require 'repl)
- (repl:top-level macro:eval)
- See the section Repl (*Note Repl::) for more information.
-
- To check operation of syntax-case get
-`cs.indiana.edu:/pub/scheme/syntax-case', and type
- (require 'syntax-case)
- (syncase:sanity-check)
-
- Beware that `syntax-case' takes a long time to load - about 20s on a
-SPARCstation SLC (with SCM) and about 90s on a Macintosh SE/30 (with
-Gambit).
-
-Notes
------
-
- All R4RS syntactic forms are defined, including `delay'. Along with
-`delay' are simple definitions for `make-promise' (into which `delay'
-expressions expand) and `force'.
-
- `syntax-rules' and `with-syntax' (described in `TR356') are defined.
-
- `syntax-case' is actually defined as a macro that expands into calls
-to the procedure `syntax-dispatch' and the core form `syntax-lambda';
-do not redefine these names.
-
- Several other top-level bindings not documented in TR356 are created:
- the "hooks" in `hooks.ss'
-
- the `build-' procedures in `output.ss'
-
- `expand-syntax' (the expander)
-
- The syntax of define has been extended to allow `(define ID)', which
-assigns ID to some unspecified value.
-
- We have attempted to maintain R4RS compatibility where possible. The
-incompatibilities should be confined to `hooks.ss'. Please let us know
-if there is some incompatibility that is not flagged as such.
-
- Send bug reports, comments, suggestions, and questions to Kent Dybvig
-(dyb@iuvax.cs.indiana.edu).
-
-Note from maintainer
---------------------
-
- Included with the `syntax-case' files was `structure.scm' which
-defines a macro `define-structure'. There is no documentation for this
-macro and it is not used by any code in SLIB.
-
-
-File: slib.info, Node: Fluid-Let, Next: Yasos, Prev: Syntax-Case Macros, Up: Macros
-
-Fluid-Let
-=========
-
- `(require 'fluid-let)'
-
- - Syntax: fluid-let `(BINDINGS ...)' FORMS...
-
- (fluid-let ((VARIABLE INIT) ...)
- EXPRESSION EXPRESSION ...)
-
- The INITs are evaluated in the current environment (in some
-unspecified order), the current values of the VARIABLEs are saved, the
-results are assigned to the VARIABLEs, the EXPRESSIONs are evaluated
-sequentially in the current environment, the VARIABLEs are restored to
-their original values, and the value of the last EXPRESSION is returned.
-
- The syntax of this special form is similar to that of `let', but
-`fluid-let' temporarily rebinds existing VARIABLEs. Unlike `let',
-`fluid-let' creates no new bindings; instead it *assigns* the values of
-each INIT to the binding (determined by the rules of lexical scoping)
-of its corresponding VARIABLE.
-
-
-File: slib.info, Node: Yasos, Prev: Fluid-Let, Up: Macros
-
-Yasos
-=====
-
- `(require 'oop)' or `(require 'yasos)'
-
- `Yet Another Scheme Object System' is a simple object system for
-Scheme based on the paper by Norman Adams and Jonathan Rees: `Object
-Oriented Programming in Scheme', Proceedings of the 1988 ACM Conference
-on LISP and Functional Programming, July 1988 [ACM #552880].
-
- Another reference is:
-
- Ken Dickey. Scheming with Objects `AI Expert' Volume 7, Number 10
-(October 1992), pp. 24-33.
-
-* Menu:
-
-* Yasos terms:: Definitions and disclaimer.
-* Yasos interface:: The Yasos macros and procedures.
-* Setters:: Dylan-like setters in Yasos.
-* Yasos examples:: Usage of Yasos and setters.
-
-
-File: slib.info, Node: Yasos terms, Next: Yasos interface, Prev: Yasos, Up: Yasos
-
-Terms
------
-
-"Object"
- Any Scheme data object.
-
-"Instance"
- An instance of the OO system; an "object".
-
-"Operation"
- A METHOD.
-
-*Notes:*
- The object system supports multiple inheritance. An instance can
- inherit from 0 or more ancestors. In the case of multiple
- inherited operations with the same identity, the operation used is
- that from the first ancestor which contains it (in the ancestor
- `let'). An operation may be applied to any Scheme data
- object--not just instances. As code which creates instances is
- just code, there are no "classes" and no meta-ANYTHING. Method
- dispatch is by a procedure call a la CLOS rather than by `send'
- syntax a la Smalltalk.
-
-*Disclaimer:*
- There are a number of optimizations which can be made. This
- implementation is expository (although performance should be quite
- reasonable). See the L&FP paper for some suggestions.
-
-
-File: slib.info, Node: Yasos interface, Next: Setters, Prev: Yasos terms, Up: Yasos
-
-Interface
----------
-
- - Syntax: define-operation `('OPNAME SELF ARG ...`)' DEFAULT-BODY
- Defines a default behavior for data objects which don't handle the
- operation OPNAME. The default default behavior (for an empty
- DEFAULT-BODY) is to generate an error.
-
- - Syntax: define-predicate OPNAME?
- Defines a predicate OPNAME?, usually used for determining the
- "type" of an object, such that `(OPNAME? OBJECT)' returns `#t' if
- OBJECT has an operation OPNAME? and `#f' otherwise.
-
- - Syntax: object `((NAME SELF ARG ...) BODY)' ...
- Returns an object (an instance of the object system) with
- operations. Invoking `(NAME OBJECT ARG ...' executes the BODY of
- the OBJECT with SELF bound to OBJECT and with argument(s) ARG....
-
- - Syntax: object-with-ancestors `(('ANCESTOR1 INIT1`)' ...`)'
- OPERATION ...
- A `let'-like form of `object' for multiple inheritance. It
- returns an object inheriting the behaviour of ANCESTOR1 etc. An
- operation will be invoked in an ancestor if the object itself does
- not provide such a method. In the case of multiple inherited
- operations with the same identity, the operation used is the one
- found in the first ancestor in the ancestor list.
-
- - Syntax: operate-as COMPONENT OPERATION SELF ARG ...
- Used in an operation definition (of SELF) to invoke the OPERATION
- in an ancestor COMPONENT but maintain the object's identity. Also
- known as "send-to-super".
-
- - Procedure: print OBJ PORT
- A default `print' operation is provided which is just `(format
- PORT OBJ)' (*Note Format::) for non-instances and prints OBJ
- preceded by `#<INSTANCE>' for instances.
-
- - Function: size OBJ
- The default method returns the number of elements in OBJ if it is
- a vector, string or list, `2' for a pair, `1' for a character and
- by default id an error otherwise. Objects such as collections
- (*Note Collections::) may override the default in an obvious way.
-
-
-File: slib.info, Node: Setters, Next: Yasos examples, Prev: Yasos interface, Up: Yasos
-
-Setters
--------
-
- "Setters" implement "generalized locations" for objects associated
-with some sort of mutable state. A "getter" operation retrieves a
-value from a generalized location and the corresponding setter
-operation stores a value into the location. Only the getter is named -
-the setter is specified by a procedure call as below. (Dylan uses
-special syntax.) Typically, but not necessarily, getters are access
-operations to extract values from Yasos objects (*Note Yasos::).
-Several setters are predefined, corresponding to getters `car', `cdr',
-`string-ref' and `vector-ref' e.g., `(setter car)' is equivalent to
-`set-car!'.
-
- This implementation of setters is similar to that in Dylan(TM)
-(`Dylan: An object-oriented dynamic language', Apple Computer Eastern
-Research and Technology). Common LISP provides similar facilities
-through `setf'.
-
- - Function: setter GETTER
- Returns the setter for the procedure GETTER. E.g., since
- `string-ref' is the getter corresponding to a setter which is
- actually `string-set!':
- (define foo "foo")
- ((setter string-ref) foo 0 #\F) ; set element 0 of foo
- foo => "Foo"
-
- - Syntax: set PLACE NEW-VALUE
- If PLACE is a variable name, `set' is equivalent to `set!'.
- Otherwise, PLACE must have the form of a procedure call, where the
- procedure name refers to a getter and the call indicates an
- accessible generalized location, i.e., the call would return a
- value. The return value of `set' is usually unspecified unless
- used with a setter whose definition guarantees to return a useful
- value.
- (set (string-ref foo 2) #\O) ; generalized location with getter
- foo => "FoO"
- (set foo "foo") ; like set!
- foo => "foo"
-
- - Procedure: add-setter GETTER SETTER
- Add procedures GETTER and SETTER to the (inaccessible) list of
- valid setter/getter pairs. SETTER implements the store operation
- corresponding to the GETTER access operation for the relevant
- state. The return value is unspecified.
-
- - Procedure: remove-setter-for GETTER
- Removes the setter corresponding to the specified GETTER from the
- list of valid setters. The return value is unspecified.
-
- - Syntax: define-access-operation GETTER-NAME
- Shorthand for a Yasos `define-operation' defining an operation
- GETTER-NAME that objects may support to return the value of some
- mutable state. The default operation is to signal an error. The
- return value is unspecified.
-
-
-File: slib.info, Node: Yasos examples, Prev: Setters, Up: Yasos
-
-Examples
---------
-
- (define-operation (print obj port)
- (format port
- (if (instance? obj) "#<instance>" "~s")
- obj))
-
- (define-operation (SIZE obj)
- (cond
- ((vector? obj) (vector-length obj))
- ((list? obj) (length obj))
- ((pair? obj) 2)
- ((string? obj) (string-length obj))
- ((char? obj) 1)
- (else
- (error "Operation not supported: size" obj))))
-
- (define-predicate cell?)
- (define-operation (fetch obj))
- (define-operation (store! obj newValue))
-
- (define (make-cell value)
- (object
- ((cell? self) #t)
- ((fetch self) value)
- ((store! self newValue)
- (set! value newValue)
- newValue)
- ((size self) 1)
- ((print self port)
- (format port "#<Cell: ~s>" (fetch self)))))
-
- (define-operation (discard obj value)
- (format #t "Discarding ~s~%" value))
-
- (define (make-filtered-cell value filter)
- (object-with-ancestors ((cell (make-cell value)))
- ((store! self newValue)
- (if (filter newValue)
- (store! cell newValue)
- (discard self newValue)))))
-
- (define-predicate array?)
- (define-operation (array-ref array index))
- (define-operation (array-set! array index value))
-
- (define (make-array num-slots)
- (let ((anArray (make-vector num-slots)))
- (object
- ((array? self) #t)
- ((size self) num-slots)
- ((array-ref self index) (vector-ref anArray index))
- ((array-set! self index newValue) (vector-set! anArray index newValue))
- ((print self port) (format port "#<Array ~s>" (size self))))))
-
- (define-operation (position obj))
- (define-operation (discarded-value obj))
-
- (define (make-cell-with-history value filter size)
- (let ((pos 0) (most-recent-discard #f))
- (object-with-ancestors
- ((cell (make-filtered-call value filter))
- (sequence (make-array size)))
- ((array? self) #f)
- ((position self) pos)
- ((store! self newValue)
- (operate-as cell store! self newValue)
- (array-set! self pos newValue)
- (set! pos (+ pos 1)))
- ((discard self value)
- (set! most-recent-discard value))
- ((discarded-value self) most-recent-discard)
- ((print self port)
- (format port "#<Cell-with-history ~s>" (fetch self))))))
-
- (define-access-operation fetch)
- (add-setter fetch store!)
- (define foo (make-cell 1))
- (print foo #f)
- => "#<Cell: 1>"
- (set (fetch foo) 2)
- =>
- (print foo #f)
- => "#<Cell: 2>"
- (fetch foo)
- => 2
-
-
-File: slib.info, Node: Numerics, Next: Procedures, Prev: Macros, Up: Top
-
-Numerics
-********
-
-* Menu:
-
-* Bit-Twiddling:: 'logical
-* Modular Arithmetic:: 'modular
-* Prime Testing and Generation:: 'primes
-* Prime Factorization:: 'factor
-* Random Numbers:: 'random
-* Cyclic Checksum:: 'make-crc
-* Plotting:: 'charplot
-* Root Finding::
-
-
-File: slib.info, Node: Bit-Twiddling, Next: Modular Arithmetic, Prev: Numerics, Up: Numerics
-
-Bit-Twiddling
-=============
-
- `(require 'logical)'
-
- The bit-twiddling functions are made available through the use of the
-`logical' package. `logical' is loaded by inserting `(require
-'logical)' before the code that uses these functions.
-
- - Function: logand N1 N1
- Returns the integer which is the bit-wise AND of the two integer
- arguments.
-
- Example:
- (number->string (logand #b1100 #b1010) 2)
- => "1000"
-
- - Function: logior N1 N2
- Returns the integer which is the bit-wise OR of the two integer
- arguments.
-
- Example:
- (number->string (logior #b1100 #b1010) 2)
- => "1110"
-
- - Function: logxor N1 N2
- Returns the integer which is the bit-wise XOR of the two integer
- arguments.
-
- Example:
- (number->string (logxor #b1100 #b1010) 2)
- => "110"
-
- - Function: lognot N
- Returns the integer which is the 2s-complement of the integer
- argument.
-
- Example:
- (number->string (lognot #b10000000) 2)
- => "-10000001"
- (number->string (lognot #b0) 2)
- => "-1"
-
- - Function: logtest J K
- (logtest j k) == (not (zero? (logand j k)))
-
- (logtest #b0100 #b1011) => #f
- (logtest #b0100 #b0111) => #t
-
- - Function: logbit? INDEX J
- (logbit? index j) == (logtest (integer-expt 2 index) j)
-
- (logbit? 0 #b1101) => #t
- (logbit? 1 #b1101) => #f
- (logbit? 2 #b1101) => #t
- (logbit? 3 #b1101) => #t
- (logbit? 4 #b1101) => #f
-
- - Function: ash INT COUNT
- Returns an integer equivalent to `(inexact->exact (floor (* INT
- (expt 2 COUNT))))'.
-
- Example:
- (number->string (ash #b1 3) 2)
- => "1000"
- (number->string (ash #b1010 -1) 2)
- => "101"
-
- - Function: logcount N
- Returns the number of bits in integer N. If integer is positive,
- the 1-bits in its binary representation are counted. If negative,
- the 0-bits in its two's-complement binary representation are
- counted. If 0, 0 is returned.
-
- Example:
- (logcount #b10101010)
- => 4
- (logcount 0)
- => 0
- (logcount -2)
- => 1
-
- - Function: integer-length N
- Returns the number of bits neccessary to represent N.
-
- Example:
- (integer-length #b10101010)
- => 8
- (integer-length 0)
- => 0
- (integer-length #b1111)
- => 4
-
- - Function: integer-expt N K
- Returns N raised to the non-negative integer exponent K.
-
- Example:
- (integer-expt 2 5)
- => 32
- (integer-expt -3 3)
- => -27
-
- - Function: bit-extract N START END
- Returns the integer composed of the START (inclusive) through END
- (exclusive) bits of N. The STARTth bit becomes the 0-th bit in
- the result.
-
- Example:
- (number->string (bit-extract #b1101101010 0 4) 2)
- => "1010"
- (number->string (bit-extract #b1101101010 4 9) 2)
- => "10110"
-
-
-File: slib.info, Node: Modular Arithmetic, Next: Prime Testing and Generation, Prev: Bit-Twiddling, Up: Numerics
-
-Modular Arithmetic
-==================
-
- `(require 'modular)'
-
- - Function: extended-euclid N1 N2
- Returns a list of 3 integers `(d x y)' such that d = gcd(N1, N2) =
- N1 * x + N2 * y.
-
- - Function: symmetric:modulus N
- Returns `(quotient (+ -1 n) -2)' for positive odd integer N.
-
- - Function: modulus->integer MODULUS
- Returns the non-negative integer characteristic of the ring formed
- when MODULUS is used with `modular:' procedures.
-
- - Function: modular:normalize MODULUS N
- Returns the integer `(modulo N (modulus->integer MODULUS))' in the
- representation specified by MODULUS.
-
-The rest of these functions assume normalized arguments; That is, the
-arguments are constrained by the following table:
-
-For all of these functions, if the first argument (MODULUS) is:
-`positive?'
- Work as before. The result is between 0 and MODULUS.
-
-`zero?'
- The arguments are treated as integers. An integer is returned.
-
-`negative?'
- The arguments and result are treated as members of the integers
- modulo `(+ 1 (* -2 MODULUS))', but with "symmetric"
- representation; i.e. `(<= (- MODULUS) N MODULUS)'.
-
-If all the arguments are fixnums the computation will use only fixnums.
-
- - Function: modular:invertable? MODULUS K
- Returns `#t' if there exists an integer n such that K * n == 1 mod
- MODULUS, and `#f' otherwise.
-
- - Function: modular:invert MODULUS K2
- Returns an integer n such that 1 = (n * K2) mod MODULUS. If K2
- has no inverse mod MODULUS an error is signaled.
-
- - Function: modular:negate MODULUS K2
- Returns (-K2) mod MODULUS.
-
- - Function: modular:+ MODULUS K2 K3
- Returns (K2 + K3) mod MODULUS.
-
- - Function: modular:- MODULUS K2 K3
- Returns (K2 - K3) mod MODULUS.
-
- - Function: modular:* MODULUS K2 K3
- Returns (K2 * K3) mod MODULUS.
-
- The Scheme code for `modular:*' with negative MODULUS is not
- completed for fixnum-only implementations.
-
- - Function: modular:expt MODULUS K2 K3
- Returns (K2 ^ K3) mod MODULUS.
-
-
-File: slib.info, Node: Prime Testing and Generation, Next: Prime Factorization, Prev: Modular Arithmetic, Up: Numerics
-
-Prime Testing and Generation
-============================
-
- `(require 'primes)'
-
- This package tests and generates prime numbers. The strategy used is
-as follows:
-
- First, use trial division by small primes (primes less than 1000)
- to quickly weed out composites with small factors. As a side
- benefit, this makes the test precise for numbers up to one million.
-
- Second, apply the Miller-Rabin primality test to detect (with high
- probability) any remaining composites.
-
- The Miller-Rabin test is a Monte-Carlo test--in other words, it's fast
-and it gets the right answer with high probability. For a candidate
-that *is* prime, the Miller-Rabin test is certain to report "prime"; it
-will never report "composite". However, for a candidate that is
-composite, there is a (small) probability that the Miller-Rabin test
-will erroneously report "prime". This probability can be made
-arbitarily small by adjusting the number of iterations of the
-Miller-Rabin test.
-
- - Function: probably-prime? CANDIDATE
- - Function: probably-prime? CANDIDATE ITER
- Returns `#t' if `candidate' is probably prime. The optional
- parameter `iter' controls the number of iterations of the
- Miller-Rabin test. The probability of a composite candidate being
- mistaken for a prime is at most `(1/4)^iter'. The default value of
- `iter' is 15, which makes the probability less than 1 in 10^9.
-
-
- - Function: primes< START COUNT
- - Function: primes< START COUNT ITER
- - Function: primes> START COUNT
- - Function: primes> START COUNT ITER
- Returns a list of the first `count' odd probable primes less (more)
- than or equal to `start'. The optional parameter `iter' controls
- the number of iterations of the Miller-Rabin test for each
- candidate. The probability of a composite candidate being
- mistaken for a prime is at most `(1/4)^iter'. The default value
- of `iter' is 15, which makes the probability less than 1 in 10^9.
-
-
-* Menu:
-
-* The Miller-Rabin Test:: How the Miller-Rabin test works
-
-
-File: slib.info, Node: The Miller-Rabin Test, Prev: Prime Testing and Generation, Up: Prime Testing and Generation
-
-Theory
-------
-
- Rabin and Miller's result can be summarized as follows. Let `p' (the
-candidate prime) be any odd integer greater than 2. Let `b' (the
-"base") be an integer in the range `2 ... p-1'. There is a fairly
-simple Boolean function--call it `C', for "Composite"--with the
-following properties:
- If `p' is prime, `C(p, b)' is false for all `b' in the range `2
- ... p-1'.
-
- If `p' is composite, `C(p, b)' is false for at most 1/4 of all `b'
- in the range ` 2 ... p-1'. (If the test fails for base `b', `p'
- is called a *strong pseudo-prime to base `b'*.)
-
- For details of `C', and why it fails for at most 1/4 of the potential
-bases, please consult a book on number theory or cryptography such as
-"A Course in Number Theory and Cryptography" by Neal Koblitz, published
-by Springer-Verlag 1994.
-
- There is nothing probablistic about this result. It's true for all
-`p'. If we had time to test `(1/4)p + 1' different bases, we could
-definitively determine the primality of `p'. For large candidates,
-that would take much too long--much longer than the simple approach of
-dividing by all numbers up to `sqrt(p)'. This is where probability
-enters the picture.
-
- Suppose we have some candidate prime `p'. Pick a random integer `b'
-in the range `2 ... p-1'. Compute `C(p,b)'. If `p' is prime, the
-result will certainly be false. If `p' is composite, the probability
-is at most 1/4 that the result will be false (demonstrating that `p' is
-a strong pseudoprime to base `b'). The test can be repeated with other
-random bases. If `p' is prime, each test is certain to return false.
-If `p' is composite, the probability of `C(p,b)' returning false is at
-most 1/4 for each test. Since the `b' are chosen at random, the tests
-outcomes are independent. So if `p' is composite and the test is
-repeated, say, 15 times, the probability of it returning false all
-fifteen times is at most (1/4)^15, or about 10^-9. If the test is
-repeated 30 times, the probability of failure drops to at most 8.3e-25.
-
- Rabin and Miller's result holds for *all* candidates `p'. However,
-if the candidate `p' is picked at random, the probability of the
-Miller-Rabin test failing is much less than the computed bound. This
-is because, for *most* composite numbers, the fraction of bases that
-cause the test to fail is much less than 1/4. For example, if you pick
-a random odd number less than 1000 and apply the Miller-Rabin test with
-only 3 random bases, the computed failure bound is (1/4)^3, or about
-1.6e-2. However, the actual probability of failure is much less--about
-7.2e-5. If you accidentally pick 703 to test for primality, the
-probability of failure is (161/703)^3, or about 1.2e-2, which is almost
-as high as the computed bound. This is because 703 is a strong
-pseudoprime to 161 bases. But if you pick at random there is only a
-small chance of picking 703, and no other number less than 1000 has
-that high a percentage of pseudoprime bases.
-
- The Miller-Rabin test is sometimes used in a slightly different
-fashion, where it can, at least in principle, cause problems. The
-weaker version uses small prime bases instead of random bases. If you
-are picking candidates at random and testing for primality, this works
-well since very few composites are strong pseudo-primes to small prime
-bases. (For example, there is only one composite less than 2.5e10 that
-is a strong pseudo-prime to the bases 2, 3, 5, and 7.) The problem
-with this approach is that once a candidate has been picked, the test is
-deterministic. This distinction is subtle, but real. With the
-randomized test, for *any* candidate you pick--even if your
-candidate-picking procedure is strongly biased towards troublesome
-numbers, the test will work with high probability. With the
-deterministic version, for any particular candidate, the test will
-either work (with probability 1), or fail (with probability 1). It
-won't fail for very many candidates, but that won't be much consolation
-if your candidate-picking procedure is somehow biased toward troublesome
-numbers.
-
-
-File: slib.info, Node: Prime Factorization, Next: Random Numbers, Prev: Prime Testing and Generation, Up: Numerics
-
-Prime Factorization
-===================
-
- `(require 'factor)'
-
- - Function: factor K
- Returns a list of the prime factors of K. The order of the
- factors is unspecified. In order to obtain a sorted list do
- `(sort! (factor k) <)'.
-
- *Note:* The rest of these procedures implement the Solovay-Strassen
-primality test. This test has been superseeded by the faster *Note
-probably-prime?: Prime Testing and Generation. However these are left
-here as they take up little space and may be of use to an
-implementation without bignums.
-
- See Robert Solovay and Volker Strassen, `A Fast Monte-Carlo Test for
-Primality', SIAM Journal on Computing, 1977, pp 84-85.
-
- - Function: jacobi-symbol P Q
- Returns the value (+1, -1, or 0) of the Jacobi-Symbol of exact
- non-negative integer P and exact positive odd integer Q.
-
- - Function: prime? P
- Returns `#f' if P is composite; `#t' if P is prime. There is a
- slight chance `(expt 2 (- prime:trials))' that a composite will
- return `#t'.
-
- - Function: prime:trials
- Is the maxinum number of iterations of Solovay-Strassen that will
- be done to test a number for primality.
-
-
-File: slib.info, Node: Random Numbers, Next: Cyclic Checksum, Prev: Prime Factorization, Up: Numerics
-
-Random Numbers
-==============
-
- `(require 'random)'
-
- - Procedure: random N
- - Procedure: random N STATE
- Accepts a positive integer or real N and returns a number of the
- same type between zero (inclusive) and N (exclusive). The values
- returned have a uniform distribution.
-
- The optional argument STATE must be of the type produced by
- `(make-random-state)'. It defaults to the value of the variable
- `*random-state*'. This object is used to maintain the state of the
- pseudo-random-number generator and is altered as a side effect of
- the `random' operation.
-
- - Variable: *random-state*
- Holds a data structure that encodes the internal state of the
- random-number generator that `random' uses by default. The nature
- of this data structure is implementation-dependent. It may be
- printed out and successfully read back in, but may or may not
- function correctly as a random-number state object in another
- implementation.
-
- - Procedure: make-random-state
- - Procedure: make-random-state STATE
- Returns a new object of type suitable for use as the value of the
- variable `*random-state*' and as a second argument to `random'.
- If argument STATE is given, a copy of it is returned. Otherwise a
- copy of `*random-state*' is returned.
-
- If inexact numbers are support by the Scheme implementation,
-`randinex.scm' will be loaded as well. `randinex.scm' contains
-procedures for generating inexact distributions.
-
- - Procedure: random:uniform STATE
- Returns an uniformly distributed inexact real random number in the
- range between 0 and 1.
-
- - Procedure: random:solid-sphere! VECT
- - Procedure: random:solid-sphere! VECT STATE
- Fills VECT with inexact real random numbers the sum of whose
- squares is less than 1.0. Thinking of VECT as coordinates in
- space of dimension N = `(vector-length VECT)', the coordinates are
- uniformly distributed within the unit N-shere. The sum of the
- squares of the numbers is returned.
-
- - Procedure: random:hollow-sphere! VECT
- - Procedure: random:hollow-sphere! VECT STATE
- Fills VECT with inexact real random numbers the sum of whose
- squares is equal to 1.0. Thinking of VECT as coordinates in space
- of dimension n = `(vector-length VECT)', the coordinates are
- uniformly distributed over the surface of the unit n-shere.
-
- - Procedure: random:normal
- - Procedure: random:normal STATE
- Returns an inexact real in a normal distribution with mean 0 and
- standard deviation 1. For a normal distribution with mean M and
- standard deviation D use `(+ M (* D (random:normal)))'.
-
- - Procedure: random:normal-vector! VECT
- - Procedure: random:normal-vector! VECT STATE
- Fills VECT with inexact real random numbers which are independent
- and standard normally distributed (i.e., with mean 0 and variance
- 1).
-
- - Procedure: random:exp
- - Procedure: random:exp STATE
- Returns an inexact real in an exponential distribution with mean
- 1. For an exponential distribution with mean U use (* U
- (random:exp)).
-