racket/collects/scribblings/reference/sequences.scrbl
2010-10-22 20:15:38 -06:00

586 lines
23 KiB
Racket

#lang scribble/doc
@(require "mz.ss"
(for-syntax racket/base)
scribble/scheme
(for-label racket/generator
racket/mpair))
@(define (info-on-seq where what)
@margin-note{See @secref[where] for information on using @|what| as
sequences.})
@title[#:tag "sequences"]{Sequences}
@guideintro["sequences"]{sequences}
A @deftech{sequence} encapsulates an ordered stream of values. The
elements of a sequence can be extracted with one of the @scheme[for]
syntactic forms or with the procedures returned by
@scheme[sequence-generate].
The sequence datatype overlaps with many other datatypes. Among
built-in datatypes, the sequence datatype includes the following:
@itemize[
@item{strings (see @secref["strings"])}
@item{byte strings (see @secref["bytestrings"])}
@item{lists (see @secref["pairs"])}
@item{mutable lists (see @secref["mpairs"])}
@item{vectors (see @secref["vectors"])}
@item{hash tables (see @secref["hashtables"])}
@item{dictionaries (see @secref["dicts"])}
@item{sets (see @secref["sets"])}
@item{input ports (see @secref["ports"])}
@item{streams (see @secref["streams"])}
]
In addition, @scheme[make-do-sequence] creates a sequence given a thunk
that returns procedures to implement a generator, and the
@scheme[prop:sequence] property can be associated with a structure type.
For most sequence types, extracting elements from a sequence has no
side-effect on the original sequence value; for example, extracting the
sequence of elements from a list does not change the list. For other
sequence types, each extraction implies a side effect; for example,
extracting the sequence of bytes from a port cause the bytes to be read
from the port.
Individual elements of a sequence typically correspond to single values,
but an element may also correspond to multiple values. For example, a
hash table generates two values---a key and its value---for each element
in the sequence.
@; ----------------------------------------------------------------------
@section{Sequence Predicate and Constructors}
@defproc[(sequence? [v any/c]) boolean?]{
Return @scheme[#t] if @scheme[v] can be used as a sequence,
@scheme[#f] otherwise.}
@defproc*[([(in-range [end number?]) sequence?]
[(in-range [start number?] [end number?] [step number? 1]) sequence?])]{
Returns a sequence whose elements are numbers. The single-argument
case @scheme[(in-range end)] is equivalent to @scheme[(in-range 0 end
1)]. The first number in the sequence is @scheme[start], and each
successive element is generated by adding @scheme[step] to the
previous element. The sequence stops before an element that would be
greater or equal to @scheme[end] if @scheme[step] is non-negative, or
less or equal to @scheme[end] if @scheme[step] is negative.
@speed[in-range "number"]}
@defproc[(in-naturals [start exact-nonnegative-integer? 0]) sequence?]{
Returns an infinite sequence of exact integers starting with
@scheme[start], where each element is one more than the preceding
element. @speed[in-naturals "integer"]}
@defproc[(in-list [lst list?]) sequence?]{
Returns a sequence equivalent to @scheme[lst].
@info-on-seq["pairs" "lists"]
@speed[in-list "list"]}
@defproc[(in-mlist [mlst mlist?]) sequence?]{
Returns a sequence equivalent to @scheme[mlst].
@info-on-seq["mpairs" "mutable lists"]
@speed[in-mlist "mutable list"]}
@defproc[(in-vector [vec vector?]
[start exact-nonnegative-integer? 0]
[stop (or/c exact-nonnegative-integer? #f) #f]
[step (and/c exact-integer? (not/c zero?)) 1])
sequence?]{
Returns a sequence equivalent to @scheme[vec] when no optional
arguments are supplied.
@info-on-seq["vectors" "vectors"]
The optional arguments @scheme[start], @scheme[stop], and
@scheme[step] are analogous to @scheme[in-range], except that a
@scheme[#f] value for @scheme[stop] is equivalent to
@scheme[(vector-length vec)]. That is, the first element in the
sequence is @scheme[(vector-ref vec start)], and each successive
element is generated by adding @scheme[step] to index of the previous
element. The sequence stops before an index that would be greater or
equal to @scheme[end] if @scheme[step] is non-negative, or less or
equal to @scheme[end] if @scheme[step] is negative.
If @scheme[start] is less than @scheme[stop] and @scheme[step] is
negative, then the @exnraise[exn:fail:contract:mismatch]. Similarly,
if @scheme[start] is more than @scheme[stop] and @scheme[step] is
positive, then the @exnraise[exn:fail:contract:mismatch]. The
@scheme[start] and @scheme[stop] values are @emph{not} checked against
the size of @scheme[vec], so access can fail when an element is
demanded from the sequence.
@speed[in-vector "vector"]}
@defproc[(in-string [str string?]
[start exact-nonnegative-integer? 0]
[stop (or/c exact-nonnegative-integer? #f) #f]
[step (and/c exact-integer? (not/c zero?)) 1])
sequence?]{
Returns a sequence equivalent to @scheme[str] when no optional
arguments are supplied.
@info-on-seq["strings" "strings"]
The optional arguments @scheme[start], @scheme[stop], and
@scheme[step] are as in @scheme[in-vector].
@speed[in-string "string"]}
@defproc[(in-bytes [bstr bytes?]
[start exact-nonnegative-integer? 0]
[stop (or/c exact-nonnegative-integer? #f) #f]
[step (and/c exact-integer? (not/c zero?)) 1])
sequence?]{
Returns a sequence equivalent to @scheme[bstr] when no optional
arguments are supplied.
@info-on-seq["bytestrings" "byte strings"]
The optional arguments @scheme[start], @scheme[stop], and
@scheme[step] are as in @scheme[in-vector].
@speed[in-bytes "byte string"]}
@defproc[(in-port [r (input-port? . -> . any/c) read]
[in input-port? (current-input-port)])
sequence?]{
Returns a sequence whose elements are produced by calling @scheme[r]
on @scheme[in] until it produces @scheme[eof].}
@defproc[(in-input-port-bytes [in input-port?]) sequence?]{
Returns a sequence equivalent to @scheme[(in-port read-byte in)].}
@defproc[(in-input-port-chars [in input-port?]) sequence?]{
Returns a sequence whose elements are read as characters form
@scheme[in] (equivalent to @scheme[(in-port read-char in)]).}
@defproc[(in-lines [in input-port? (current-input-port)]
[mode (or/c 'linefeed 'return 'return-linefeed 'any 'any-one) 'any])
sequence?]{
Returns a sequence equivalent to
@scheme[(in-port (lambda (p) (read-line p mode)) in)]. Note that the
default mode is @scheme['any], whereas the default mode of
@scheme[read-line] is @scheme['linefeed].}
@defproc[(in-bytes-lines [in input-port? (current-input-port)]
[mode (or/c 'linefeed 'return 'return-linefeed 'any 'any-one) 'any])
sequence?]{
Returns a sequence equivalent to
@scheme[(in-port (lambda (p) (read-bytes-line p mode)) in)]. Note
that the default mode is @scheme['any], whereas the default mode of
@scheme[read-bytes-line] is @scheme['linefeed].}
@defproc[(in-hash [hash hash?]) sequence?]{
Returns a sequence equivalent to @scheme[hash].
@info-on-seq["hashtables" "hash tables"]}
@defproc[(in-hash-keys [hash hash?]) sequence?]{
Returns a sequence whose elements are the keys of @scheme[hash].}
@defproc[(in-hash-values [hash hash?]) sequence?]{
Returns a sequence whose elements are the values of @scheme[hash].}
@defproc[(in-hash-pairs [hash hash?]) sequence?]{
Returns a sequence whose elements are pairs, each containing a key and
its value from @scheme[hash] (as opposed to using @scheme[hash]
directly as a sequence to get the key and value as separate values for
each element).}
@defproc[(in-directory [dir (or/c #f path-string?) #f]) sequence?]{
Return a sequence that produces all of the paths for files,
directories, and links with @racket[dir]. If @racket[dir] is not
@racket[#f], then every produced path starts with @racket[dir] as its
prefix. If @racket[dir] is @racket[#f], then paths in and relative to
the current directory are produced.}
@defproc[(in-producer [producer procedure?] [stop any/c] [args any/c] ...)
sequence?]{
Returns a sequence that contains values from sequential calls to
@scheme[producer]. A @scheme[stop] value returned by
@racket[producer] marks the end of the sequence (and the
@racket[stop] value is not included in the sequence); @scheme[stop]
can be a predicate that is applied to the results of @racket[producer],
or it can be a value that is tested against the result of
with @scheme[eq?]. (You must use a predicate for @racket[stop]
function if the stop value is itself a function or if
@scheme[producer] returns multiple values.)}
@defproc[(in-value [v any/c]) sequence?]{
Returns a sequence that produces a single value: @scheme[v]. This
form is mostly useful for @scheme[let]-like bindings in forms such as
@scheme[for*/list].}
@defproc[(in-indexed [seq sequence?]) sequence?]{
Returns a sequence where each element has two values: the value
produced by @scheme[seq], and a non-negative exact integer starting
with @scheme[0]. The elements of @scheme[seq] must be single-valued.}
@defproc[(in-sequences [seq sequence?] ...) sequence?]{
Returns a sequence that is made of all input sequences, one after the
other. The elements of each @scheme[seq] must all have the same
number of values.}
@defproc[(in-cycle [seq sequence?] ...) sequence?]{
Similar to @scheme[in-sequences], but the sequences are repeated in an
infinite cycle.}
@defproc[(in-parallel [seq sequence?] ...) sequence?]{
Returns a sequence where each element has as many values as the number
of supplied @scheme[seq]s; the values, in order, are the values of
each @scheme[seq]. The elements of each @scheme[seq] must be
single-valued.}
@defproc[(stop-before [seq sequence?] [pred (any/c . -> . any)])
sequence?]{
Returns a sequence that contains the elements of @scheme[seq] (which
must be single-valued), but only until the last element for which
applying @scheme[pred] to the element produces @scheme[#t], after
which the sequence ends.}
@defproc[(stop-after [seq sequence?] [pred (any/c . -> . any)])
sequence?]{
Returns a sequence that contains the elements of @scheme[seq] (which
must be single-valued), but only until the element (inclusive) for
which applying @scheme[pred] to the element produces @scheme[#t],
after which the sequence ends.}
@defproc[(make-do-sequence [thunk (-> (values (any/c . -> . any)
(any/c . -> . any/c)
any/c
(any/c . -> . any/c)
(() () #:rest list? . ->* . any/c)
((any/c) () #:rest list? . ->* . any/c)))])
sequence?]{
Returns a sequence whose elements are generated by the procedures and
initial value returned by the thunk. The generator is defined in terms
of a @defterm{position}, which is initialized to the third result of
the thunk, and the @defterm{element}, which may consist of multiple
values.
The @scheme[thunk] results define the generated elements as follows:
@itemize[
@item{The first result is a @scheme[_pos->element] procedure that takes
the current position and returns the value(s) for the current
element.}
@item{The second result is a @scheme[_next-pos] procedure that takes
the current position and returns the next position.}
@item{The third result is the initial position.}
@item{The fourth result takes the current position and returns a
true result if the sequence includes the value(s) for the current
position, and false if the sequence should end instead of
including the value(s).}
@item{The fifth result is like the fourth result, but it takes the
current element value(s) instead of the current position.}
@item{The sixth result is like the fourth result, but it takes both
the current position and the current element values(s) and
determines a sequence end after the current element is already
included in the sequence.}]
Each of the procedures listed above is called only once per position.
Among the last three procedures, as soon as one of the procedures
returns @scheme[#f], the sequence ends, and none are called again.
Typically, one of the functions determines the end condition, and the
other two functions always return @scheme[#t].}
@defthing[prop:sequence struct-type-property?]{
Associates a procedure to a structure type that takes an instance of
the structure and returns a sequence. If @scheme[v] is an instance of
a structure type with this property, then @scheme[(sequence? v)]
produces @scheme[#t].
@let-syntax[([car (make-element-id-transformer
(lambda (id) #'@schemeidfont{car}))])
@examples[
(define-struct train (car next)
#:property prop:sequence (lambda (t)
(make-do-sequence
(lambda ()
(values train-car
train-next
t
(lambda (t) t)
(lambda (v) #t)
(lambda (t v) #t))))))
(for/list ([c (make-train 'engine
(make-train 'boxcar
(make-train 'caboose
#f)))])
c)]]}
@; ----------------------------------------------------------------------
@section{Sequence Generators}
@defproc[(sequence-generate [seq sequence?])
(values (-> boolean?) (-> any))]{
Returns two thunks to extract elements from the sequence. The first
returns @scheme[#t] if more values are available for the sequence.
The second returns the next element (which may be multiple values)
from the sequence; if no more elements are available, the
@exnraise[exn:fail:contract].}
@; ----------------------------------------------------------------------
@section[#:tag "streams"]{Streams}
@note-lib[racket/stream]
@defthing[empty-stream sequence?]{
A sequence with no elements.}
@defproc[(stream->list [s sequence?]) list?]{
Returns a list whose elements are the elements of the @scheme[s],
which must be a one-valued sequence. If @scheme[s] is infinite, this
function does not terminate.}
@defproc[(stream-cons [v any/c]
...
[s sequence?])
sequence?]{
Returns a sequence whose first element is @scheme[(values v ...)] and whose
remaining elements are the same as @scheme[s].}
@defproc[(stream-first [s sequence?])
(values any/c ...)]{
Returns the first element of @scheme[s].}
@defproc[(stream-rest [s sequence?])
sequence?]{
Returns a sequence equivalent to @scheme[s], except the first element
is omitted.}
@defproc[(stream-length [s sequence?])
exact-nonnegative-integer?]{
Returns the number of elements of @scheme[s]. If @scheme[s] is
infinite, this function does not terminate.}
@defproc[(stream-ref [s sequence?] [i exact-nonnegative-integer?])
(values any/c ...)]{
Returns the @scheme[i]th element of @scheme[s].}
@defproc[(stream-tail [s sequence?] [i exact-nonnegative-integer?])
sequence?]{
Returns a sequence equivalent to @scheme[s], except the first
@scheme[i] elements are omitted.}
@defproc[(stream-append [s sequence?] ...)
sequence?]{
Returns a sequence that contains all elements of each sequence in the
order they appear in the original sequences. The new sequence is
constructed lazily.}
@defproc[(stream-map [f procedure?]
[s sequence?])
sequence?]{
Returns a sequence that contains @scheme[f] applied to each element of
@scheme[s]. The new sequence is constructed lazily.}
@defproc[(stream-andmap [f (-> any/c ... boolean?)]
[s sequence?])
boolean?]{
Returns @scheme[#t] if @scheme[f] returns a true result on every
element of @scheme[s]. If @scheme[s] is infinite and @scheme[f] never
returns a false result, this function does not terminate.}
@defproc[(stream-ormap [f (-> any/c ... boolean?)]
[s sequence?])
boolean?]{
Returns @scheme[#t] if @scheme[f] returns a true result on some
element of @scheme[s]. If @scheme[s] is infinite and @scheme[f] never
returns a true result, this function does not terminate.}
@defproc[(stream-for-each [f (-> any/c ... any)]
[s sequence?])
(void)]{
Applies @scheme[f] to each element of @scheme[s]. If @scheme[s] is
infinite, this function does not terminate.}
@defproc[(stream-fold [f (-> any/c any/c ... any/c)]
[i any/c]
[s sequence?])
(void)]{
Folds @scheme[f] over each element of @scheme[s] with @scheme[i] as
the initial accumulator. If @scheme[s] is infinite, this function
does not terminate.}
@defproc[(stream-filter [f (-> any/c ... boolean?)]
[s sequence?])
sequence?]{
Returns a sequence whose elements are the elements of @scheme[s] for
which @scheme[f] returns a true result. Although the new sequence is
constructed lazily, if @scheme[s] has an infinite number of elements
where @scheme[f] returns a false result in between two elements where
@scheme[f] returns a true result then operations on this sequence will
not terminate during that infinite sub-sequence.}
@defproc[(stream-add-between [s sequence?] [e any/c])
sequence?]{
Returns a sequence whose elements are the elements of @scheme[s]
except in between each is @scheme[e]. The new sequence is constructed
lazily.}
@defproc[(stream-count [f procedure?] [s sequence?])
exact-nonnegative-integer?]{
Returns the number of elements in @scheme[s] for which @scheme[f]
returns a true result. If @scheme[s] is infinite, this function does
not terminate.}
@; ----------------------------------------------------------------------
@section{Iterator Generators}
@defmodule[racket/generator]
@(define generator-eval
(let ([the-eval (make-base-eval)])
(the-eval '(require racket/generator))
the-eval))
@defform[(generator () body ...)]{
Creates a function that returns a value through @scheme[yield], each
time it is invoked. When the generator runs out of values to yield,
the last value it computed will be returned for future invocations of
the generator. Generators can be safely nested.
Note: The first form must be @scheme[()]. In the future, the
@scheme[()] position will hold argument names that are used for the
initial generator call.
@examples[#:eval generator-eval
(define g (generator ()
(let loop ([x '(a b c)])
(if (null? x)
0
(begin
(yield (car x))
(loop (cdr x)))))))
(g)
(g)
(g)
(g)
(g)]
To use an existing generator as a sequence, you should use
@scheme[in-producer] with a stop-value known for the generator.
@examples[#:eval generator-eval
(define my-stop-value (gensym))
(define my-generator (generator ()
(let loop ([x '(a b c)])
(if (null? x)
my-stop-value
(begin
(yield (car x))
(loop (cdr x)))))))
(for/list ([i (in-producer my-generator my-stop-value)])
i)]}
@defform[(infinite-generator body ...)]{
Creates a function similar to @scheme[generator] but when the last
@scheme[body] is executed the function will re-execute all the bodies
in a loop.
@examples[#:eval generator-eval
(define welcome
(infinite-generator
(yield 'hello)
(yield 'goodbye)))
(welcome)
(welcome)
(welcome)
(welcome)]}
@defproc[(in-generator [expr any?] ...) sequence?]{
Returns a generator that can be used as a sequence. The
@scheme[in-generator] procedure takes care of the case when
@scheme[expr] stops producing values, so when the @scheme[expr]
completes, the generator will end.
@examples[#:eval generator-eval
(for/list ([i (in-generator
(let loop ([x '(a b c)])
(when (not (null? x))
(yield (car x))
(loop (cdr x)))))])
i)]}
@defform[(yield expr ...)]{
Saves the point of execution inside a generator and returns a value.
@scheme[yield] can accept any number of arguments and will return them
using @scheme[values].
Values can be passed back to the generator after invoking
@scheme[yield] by passing the arguments to the generator instance.
Note that a value cannot be passed back to the generator until after
the first @scheme[yield] has been invoked.
@examples[#:eval generator-eval
(define my-generator (generator () (yield 1) (yield 2 3 4)))
(my-generator)
(my-generator)]
@examples[#:eval generator-eval
(define pass-values-generator
(generator ()
(let* ([from-user (yield 2)]
[from-user-again (yield (add1 from-user))])
(yield from-user-again))))
(pass-values-generator)
(pass-values-generator 5)
(pass-values-generator 12)]}
@defproc[(generator-state [g any?]) symbol?]{
Returns a symbol that describes the state of the generator.
@itemize[
@item{@scheme['fresh] --- The generator has been freshly created and
has not been invoked yet. Values cannot be passed to a fresh
generator.}
@item{@scheme['suspended] --- Control within the generator has been
suspended due to a call to @scheme[yield]. The generator can
be invoked.}
@item{@scheme['running] --- The generator is currently executing.
This state can only be returned if @scheme[generator-state] is
invoked inside the generator.}
@item{@scheme['done] --- The generator has executed its entire body
and will not call @scheme[yield] anymore.}]
@examples[#:eval generator-eval
(define my-generator (generator () (yield 1) (yield 2)))
(generator-state my-generator)
(my-generator)
(generator-state my-generator)
(my-generator)
(generator-state my-generator)
(my-generator)
(generator-state my-generator)
(define introspective-generator (generator () ((yield 1))))
(introspective-generator)
(introspective-generator
(lambda () (generator-state introspective-generator)))
(generator-state introspective-generator)
(introspective-generator)]}
@defproc[(sequence->generator [s sequence?]) (-> any?)]{
Returns a generator that returns elements from the sequence,
@scheme[s], each time the generator is invoked.}
@defproc[(sequence->repeated-generator [s sequence?]) (-> any?)]{
Returns a generator that returns elements from the sequence,
@scheme[s], similar to @scheme[sequence->generator] but looping over
the values in the sequence when no more values are left.}