656 lines
26 KiB
Racket
656 lines
26 KiB
Racket
#lang scribble/doc
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@(require "mz.ss"
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(for-syntax racket/base)
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scribble/scheme
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(for-label racket/generator
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racket/mpair))
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@(define (info-on-seq where what)
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@margin-note{See @secref[where] for information on using @|what| as
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sequences.})
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@title[#:tag "sequences"]{Sequences}
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@guideintro["sequences"]{sequences}
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A @deftech{sequence} encapsulates an ordered stream of values. The
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elements of a sequence can be extracted with one of the @scheme[for]
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syntactic forms or with the procedures returned by
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@scheme[sequence-generate].
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The sequence datatype overlaps with many other datatypes. Among
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built-in datatypes, the sequence datatype includes the following:
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@itemize[
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@item{strings (see @secref["strings"])}
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@item{byte strings (see @secref["bytestrings"])}
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@item{lists (see @secref["pairs"])}
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@item{mutable lists (see @secref["mpairs"])}
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@item{vectors (see @secref["vectors"])}
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@item{hash tables (see @secref["hashtables"])}
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@item{dictionaries (see @secref["dicts"])}
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@item{sets (see @secref["sets"])}
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@item{input ports (see @secref["ports"])}
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@item{streams (see @secref["streams"])}
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]
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In addition, @scheme[make-do-sequence] creates a sequence given a thunk
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that returns procedures to implement a sequence, and the
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@scheme[prop:sequence] property can be associated with a structure type.
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For most sequence types, extracting elements from a sequence has no
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side-effect on the original sequence value; for example, extracting the
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sequence of elements from a list does not change the list. For other
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sequence types, each extraction implies a side effect; for example,
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extracting the sequence of bytes from a port causes the bytes to be read
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from the port.
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Individual elements of a sequence typically correspond to single values,
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but an element may also correspond to multiple values. For example, a
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hash table generates two values---a key and its value---for each element
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in the sequence.
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@; ----------------------------------------------------------------------
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@section{Sequence Predicate and Constructors}
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@defproc[(sequence? [v any/c]) boolean?]{
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Return @scheme[#t] if @scheme[v] can be used as a sequence,
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@scheme[#f] otherwise.}
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@defproc*[([(in-range [end number?]) sequence?]
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[(in-range [start number?] [end number?] [step number? 1]) sequence?])]{
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Returns a sequence whose elements are numbers. The single-argument
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case @scheme[(in-range end)] is equivalent to @scheme[(in-range 0 end
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1)]. The first number in the sequence is @scheme[start], and each
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successive element is generated by adding @scheme[step] to the
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previous element. The sequence stops before an element that would be
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greater or equal to @scheme[end] if @scheme[step] is non-negative, or
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less or equal to @scheme[end] if @scheme[step] is negative.
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@speed[in-range "number"]}
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@defproc[(in-naturals [start exact-nonnegative-integer? 0]) sequence?]{
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Returns an infinite sequence of exact integers starting with
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@scheme[start], where each element is one more than the preceding
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element. @speed[in-naturals "integer"]}
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@defproc[(in-list [lst list?]) sequence?]{
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Returns a sequence equivalent to @scheme[lst].
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@info-on-seq["pairs" "lists"]
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@speed[in-list "list"]}
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@defproc[(in-mlist [mlst mlist?]) sequence?]{
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Returns a sequence equivalent to @scheme[mlst].
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@info-on-seq["mpairs" "mutable lists"]
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@speed[in-mlist "mutable list"]}
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@defproc[(in-vector [vec vector?]
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[start exact-nonnegative-integer? 0]
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[stop (or/c exact-integer? #f) #f]
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[step (and/c exact-integer? (not/c zero?)) 1])
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sequence?]{
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Returns a sequence equivalent to @scheme[vec] when no optional
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arguments are supplied.
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@info-on-seq["vectors" "vectors"]
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The optional arguments @scheme[start], @scheme[stop], and
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@scheme[step] are analogous to @scheme[in-range], except that a
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@scheme[#f] value for @scheme[stop] is equivalent to
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@scheme[(vector-length vec)]. That is, the first element in the
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sequence is @scheme[(vector-ref vec start)], and each successive
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element is generated by adding @scheme[step] to index of the previous
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element. The sequence stops before an index that would be greater or
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equal to @scheme[end] if @scheme[step] is non-negative, or less or
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equal to @scheme[end] if @scheme[step] is negative.
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If @racket[start] is not a valid index, or @racket[stop]
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is not in [-1, @racket[(vector-length vec)]] then the @exnraise[exn:fail:contract].
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If @scheme[start] is less than @scheme[stop] and @scheme[step] is
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negative, then the @exnraise[exn:fail:contract:mismatch]. Similarly,
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if @scheme[start] is more than @scheme[stop] and @scheme[step] is
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positive, then the @exnraise[exn:fail:contract:mismatch].
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@speed[in-vector "vector"]}
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@defproc[(in-string [str string?]
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[start exact-nonnegative-integer? 0]
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[stop (or/c exact-integer? #f) #f]
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[step (and/c exact-integer? (not/c zero?)) 1])
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sequence?]{
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Returns a sequence equivalent to @scheme[str] when no optional
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arguments are supplied.
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@info-on-seq["strings" "strings"]
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The optional arguments @scheme[start], @scheme[stop], and
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@scheme[step] are as in @scheme[in-vector].
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@speed[in-string "string"]}
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@defproc[(in-bytes [bstr bytes?]
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[start exact-nonnegative-integer? 0]
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[stop (or/c exact-integer? #f) #f]
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[step (and/c exact-integer? (not/c zero?)) 1])
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sequence?]{
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Returns a sequence equivalent to @scheme[bstr] when no optional
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arguments are supplied.
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@info-on-seq["bytestrings" "byte strings"]
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The optional arguments @scheme[start], @scheme[stop], and
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@scheme[step] are as in @scheme[in-vector].
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@speed[in-bytes "byte string"]}
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@defproc[(in-port [r (input-port? . -> . any/c) read]
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[in input-port? (current-input-port)])
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sequence?]{
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Returns a sequence whose elements are produced by calling @scheme[r]
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on @scheme[in] until it produces @scheme[eof].}
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@defproc[(in-input-port-bytes [in input-port?]) sequence?]{
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Returns a sequence equivalent to @scheme[(in-port read-byte in)].}
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@defproc[(in-input-port-chars [in input-port?]) sequence?]{
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Returns a sequence whose elements are read as characters from
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@scheme[in] (equivalent to @scheme[(in-port read-char in)]).}
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@defproc[(in-lines [in input-port? (current-input-port)]
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[mode (or/c 'linefeed 'return 'return-linefeed 'any 'any-one) 'any])
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sequence?]{
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Returns a sequence equivalent to
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@scheme[(in-port (lambda (p) (read-line p mode)) in)]. Note that the
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default mode is @scheme['any], whereas the default mode of
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@scheme[read-line] is @scheme['linefeed].}
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@defproc[(in-bytes-lines [in input-port? (current-input-port)]
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[mode (or/c 'linefeed 'return 'return-linefeed 'any 'any-one) 'any])
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sequence?]{
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Returns a sequence equivalent to
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@scheme[(in-port (lambda (p) (read-bytes-line p mode)) in)]. Note
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that the default mode is @scheme['any], whereas the default mode of
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@scheme[read-bytes-line] is @scheme['linefeed].}
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@defproc[(in-hash [hash hash?]) sequence?]{
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Returns a sequence equivalent to @scheme[hash].
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@examples[
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(define table (hash 'a 1 'b 2))
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(for ([(key value) (in-hash table)])
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(printf "key: ~a value: ~a\n" key value))
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]
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@info-on-seq["hashtables" "hash tables"]}
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@defproc[(in-hash-keys [hash hash?]) sequence?]{
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Returns a sequence whose elements are the keys of @scheme[hash].
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@examples[
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(define table (hash 'a 1 'b 2))
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(for ([key (in-hash-keys table)])
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(printf "key: ~a\n" key))
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]
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}
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@defproc[(in-hash-values [hash hash?]) sequence?]{
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Returns a sequence whose elements are the values of @scheme[hash].
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@examples[
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(define table (hash 'a 1 'b 2))
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(for ([value (in-hash-values table)])
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(printf "value: ~a\n" value))
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]
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}
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@defproc[(in-hash-pairs [hash hash?]) sequence?]{
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Returns a sequence whose elements are pairs, each containing a key and
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its value from @scheme[hash] (as opposed to using @scheme[hash]
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directly as a sequence to get the key and value as separate values for
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each element).
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@examples[
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(define table (hash 'a 1 'b 2))
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(for ([key+value (in-hash-pairs table)])
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(printf "key and value: ~a\n" key+value))
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]
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}
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@defproc[(in-directory [dir (or/c #f path-string?) #f]) sequence?]{
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Return a sequence that produces all of the paths for files,
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directories, and links with @racket[dir]. If @racket[dir] is not
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@racket[#f], then every produced path starts with @racket[dir] as its
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prefix. If @racket[dir] is @racket[#f], then paths in and relative to
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the current directory are produced.}
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@defproc[(in-producer [producer procedure?] [stop any/c] [args any/c] ...)
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sequence?]{
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Returns a sequence that contains values from sequential calls to
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@scheme[producer]. A @scheme[stop] value returned by
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@racket[producer] marks the end of the sequence (and the
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@racket[stop] value is not included in the sequence); @scheme[stop]
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can be a predicate that is applied to the results of @racket[producer],
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or it can be a value that is tested against the result of
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with @scheme[eq?]. (The @racket[stop] argument must be a predicate
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if the stop value is itself a function or if
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@scheme[producer] returns multiple values.)}
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@defproc[(in-value [v any/c]) sequence?]{
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Returns a sequence that produces a single value: @scheme[v]. This
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form is mostly useful for @scheme[let]-like bindings in forms such as
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@scheme[for*/list].}
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@defproc[(in-indexed [seq sequence?]) sequence?]{
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Returns a sequence where each element has two values: the value
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produced by @scheme[seq], and a non-negative exact integer starting
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with @scheme[0]. The elements of @scheme[seq] must be single-valued.}
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@defproc[(in-sequences [seq sequence?] ...) sequence?]{
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Returns a sequence that is made of all input sequences, one after the
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other. The elements of each @scheme[seq] must all have the same
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number of values.}
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@defproc[(in-cycle [seq sequence?] ...) sequence?]{
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Similar to @scheme[in-sequences], but the sequences are repeated in an
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infinite cycle.}
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@defproc[(in-parallel [seq sequence?] ...) sequence?]{
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Returns a sequence where each element has as many values as the number
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of supplied @scheme[seq]s; the values, in order, are the values of
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each @scheme[seq]. The elements of each @scheme[seq] must be
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single-valued.}
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@defproc[(stop-before [seq sequence?] [pred (any/c . -> . any)])
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sequence?]{
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Returns a sequence that contains the elements of @scheme[seq] (which
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must be single-valued), but only until the last element for which
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applying @scheme[pred] to the element produces @scheme[#t], after
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which the sequence ends.}
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@defproc[(stop-after [seq sequence?] [pred (any/c . -> . any)])
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sequence?]{
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Returns a sequence that contains the elements of @scheme[seq] (which
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must be single-valued), but only until the element (inclusive) for
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which applying @scheme[pred] to the element produces @scheme[#t],
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after which the sequence ends.}
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@defproc[(make-do-sequence [thunk (-> (values (any/c . -> . any)
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(any/c . -> . any/c)
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any/c
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(or/c (any/c . -> . any/c) #f)
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(or/c (() () #:rest list? . ->* . any/c) #f)
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(or/c ((any/c) () #:rest list? . ->* . any/c) #f)))])
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sequence?]{
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Returns a sequence whose elements are generated by the procedures and
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initial value returned by the thunk. The sequence is defined in terms
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of a @defterm{position}, which is initialized to the third result of
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the thunk, and the @defterm{element}, which may consist of multiple
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values.
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The @scheme[thunk] results define the generated elements as follows:
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@itemize[
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@item{The first result is a @scheme[_pos->element] procedure that takes
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the current position and returns the value(s) for the current
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element.}
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@item{The second result is a @scheme[_next-pos] procedure that takes
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the current position and returns the next position.}
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@item{The third result is the initial position.}
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@item{The fourth result is a @racket[_continue-with-val?] function that
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takes the current position and returns a
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true result if the sequence includes the value(s) for the current
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position, and false if the sequence should end instead of
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including the value(s). Alternatively, the fourth result can be
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@racket[#f] to indicate that the sequence should always include the
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current value(s).}
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@item{The fifth result is a @racket[_continue-with-pos?] function that is
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like the fourth result, but it takes the
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current element value(s) instead of the current position.
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Alternatively, the fifth result can be
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@racket[#f] to indicate that the sequence should always include the
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value(s) at the current position.}
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@item{The sixth result is a @racket[_continue-after-pos+val?] procedure
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that takes both
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the current position and the current element value(s) and
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determines whether the sequence ends after the current element is already
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included in the sequence.
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Alternatively, the sixth result can be
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@racket[#f] to indicate that the sequence can always continue
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after the current value(s).}]
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Each of the procedures listed above is called only once per position.
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Among the last three procedures, as soon as one of the procedures
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returns @scheme[#f], the sequence ends, and none are called again.
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Typically, one of the functions determines the end condition, and
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@scheme[#f] is used in place of the other two functions.}
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@defthing[prop:sequence struct-type-property?]{
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Associates a procedure to a structure type that takes an instance of
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the structure and returns a sequence. If @scheme[v] is an instance of
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a structure type with this property, then @scheme[(sequence? v)]
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produces @scheme[#t].
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@let-syntax[([car (make-element-id-transformer
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(lambda (id) #'@schemeidfont{car}))])
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@examples[
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(define-struct train (car next)
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#:property prop:sequence (lambda (t)
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(make-do-sequence
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(lambda ()
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(values train-car
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train-next
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t
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(lambda (t) t)
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(lambda (v) #t)
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(lambda (t v) #t))))))
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(for/list ([c (make-train 'engine
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(make-train 'boxcar
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(make-train 'caboose
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#f)))])
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c)]]}
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@; ----------------------------------------------------------------------
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@section{Sequence Generators}
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@defproc[(sequence-generate [seq sequence?])
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(values (-> boolean?) (-> any))]{
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Returns two thunks to extract elements from the sequence. The first
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returns @scheme[#t] if more values are available for the sequence.
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The second returns the next element (which may be multiple values)
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from the sequence; if no more elements are available, the
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@exnraise[exn:fail:contract].}
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@; ----------------------------------------------------------------------
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@section[#:tag "streams"]{Streams}
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@note-lib[racket/stream]
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Warning: the interface that this library implements is dealing with
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sequences, not with lazy lists. (In the future, lazy lists will become
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a valid kind of sequence, hence the naming of these functions.) Note
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also that some of these operations can result in serious efficiency
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penalties, for example, each use of @racket[stream-rest] adds a constant
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overhead for accessing the resulting sequence.
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@defthing[empty-stream sequence?]{
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A sequence with no elements.}
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@defproc[(stream->list [s sequence?]) list?]{
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Returns a list whose elements are the elements of the @scheme[s],
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which must be a one-valued sequence. If @scheme[s] is infinite, this
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function does not terminate.}
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@defproc[(stream-cons [v any/c]
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...
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[s sequence?])
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sequence?]{
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Returns a sequence whose first element is @scheme[(values v ...)] and whose
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remaining elements are the same as @scheme[s].}
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@defproc[(stream-first [s sequence?])
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(values any/c ...)]{
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Returns the first element of @scheme[s].}
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@defproc[(stream-rest [s sequence?])
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sequence?]{
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Returns a sequence equivalent to @scheme[s], except the first element
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is omitted.}
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@defproc[(stream-length [s sequence?])
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exact-nonnegative-integer?]{
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Returns the number of elements of @scheme[s]. If @scheme[s] is
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infinite, this function does not terminate.}
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@defproc[(stream-ref [s sequence?] [i exact-nonnegative-integer?])
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(values any/c ...)]{
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Returns the @scheme[i]th element of @scheme[s].}
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@defproc[(stream-tail [s sequence?] [i exact-nonnegative-integer?])
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sequence?]{
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Returns a sequence equivalent to @scheme[s], except the first
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@scheme[i] elements are omitted.}
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@defproc[(stream-append [s sequence?] ...)
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sequence?]{
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Returns a sequence that contains all elements of each sequence in the
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order they appear in the original sequences. The new sequence is
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constructed lazily.}
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@defproc[(stream-map [f procedure?]
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[s sequence?])
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sequence?]{
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Returns a sequence that contains @scheme[f] applied to each element of
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@scheme[s]. The new sequence is constructed lazily.}
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@defproc[(stream-andmap [f (-> any/c ... boolean?)]
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[s sequence?])
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boolean?]{
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Returns @scheme[#t] if @scheme[f] returns a true result on every
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element of @scheme[s]. If @scheme[s] is infinite and @scheme[f] never
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returns a false result, this function does not terminate.}
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@defproc[(stream-ormap [f (-> any/c ... boolean?)]
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[s sequence?])
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boolean?]{
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Returns @scheme[#t] if @scheme[f] returns a true result on some
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element of @scheme[s]. If @scheme[s] is infinite and @scheme[f] never
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returns a true result, this function does not terminate.}
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@defproc[(stream-for-each [f (-> any/c ... any)]
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[s sequence?])
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(void)]{
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Applies @scheme[f] to each element of @scheme[s]. If @scheme[s] is
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infinite, this function does not terminate.}
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@defproc[(stream-fold [f (-> any/c any/c ... any/c)]
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[i any/c]
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[s sequence?])
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(void)]{
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Folds @scheme[f] over each element of @scheme[s] with @scheme[i] as
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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],
|
|
but with @scheme[e] between each pair of elements in @racket[s].
|
|
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]
|
|
|
|
A @deftech{generator} is a procedure that returns a sequence of
|
|
values, incrementing the sequence each time that the generator is
|
|
called. In particular, the @racket[generator] form implements a
|
|
generator by evaluating a body that calls @racket[yield] to return
|
|
values from the generator.
|
|
|
|
@(define generator-eval
|
|
(let ([the-eval (make-base-eval)])
|
|
(the-eval '(require racket/generator))
|
|
the-eval))
|
|
|
|
|
|
@defproc[(generator? [v any/c]) boolean?]{
|
|
Return @scheme[#t] if @scheme[v] is a @tech{generator},
|
|
@scheme[#f] otherwise.}
|
|
|
|
|
|
@defform[(generator formals body ...+)]{
|
|
Creates a @tech{generator}, where @racket[formals] is like the
|
|
@racket[formals] of @racket[case-lambda] (i.e., the
|
|
@racket[_kw-formals] of @racket[lambda] restricted to non-optional
|
|
and non-keyword arguments).
|
|
|
|
For the first call to a generator, the arguments are bound to the
|
|
@racket[formals] and evaluation of @racket[body] starts. During the
|
|
@tech{dynamic extent} of @racket[body], the generator can return
|
|
immediately using the @racket[yield] function. A second call to the
|
|
generator resumes at the @racket[yield] call, producing the
|
|
arguments of the second call as the results of the @racket[yield],
|
|
and so on. The eventual results of @racket[body] are supplied to an
|
|
implicit final @racket[yield]; after that final @racket[yield],
|
|
calling the generator again returns the same values, but all such
|
|
calls must provide 0 arguments to the generator.
|
|
|
|
@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)]}
|
|
|
|
@defproc[(yield [v any/c] ...) any]{
|
|
Returns @racket[v]s from a generator, saving the point of execution
|
|
inside a generator (i.e., within the @tech{dynamic extent} of a
|
|
@racket[generator] body) to be resumed by the next call to the
|
|
generator. The results of @racket[yield] are the arguments
|
|
that are provided to the next call of the generator.
|
|
|
|
When not in the @tech{dynamic extent} of a @racket[generator],
|
|
@racket[infinite-generator], or @racket[in-generator] body,
|
|
@racket[yield] raises @racket[exn:fail] after evaluating its
|
|
@racket[expr]s.
|
|
|
|
@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)]}
|
|
|
|
@defform[(infinite-generator body ...+)]{
|
|
Like @scheme[generator], but repeats evaluation of the @racket[body]s when
|
|
the last @racket[body] completes without implicitly @racket[yield]ing.
|
|
|
|
@examples[#:eval generator-eval
|
|
(define welcome
|
|
(infinite-generator
|
|
(yield 'hello)
|
|
(yield 'goodbye)))
|
|
(welcome)
|
|
(welcome)
|
|
(welcome)
|
|
(welcome)]}
|
|
|
|
@defform[(in-generator body ...+)]{
|
|
Produces a @tech{sequence} that encapsulates the @tech{generator} formed by
|
|
@racket[(generator () body ...+)]. The values produced by the
|
|
generator form the elements of the sequence.
|
|
|
|
@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)]
|
|
|
|
To use an existing generator as a sequence, 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)]}
|
|
|
|
@defproc[(generator-state [g generator?]) 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 called yet.}
|
|
@item{@scheme['suspended] --- Control within the generator has been
|
|
suspended due to a call to @scheme[yield]. The generator can
|
|
be called.}
|
|
@item{@scheme['running] --- The generator is currently executing.}
|
|
@item{@scheme['done] --- The generator has executed its entire
|
|
body and will continue to produce the same result as from
|
|
the last call.}]
|
|
|
|
@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)]{
|
|
Converts a @tech{sequence} to a @tech{generator}. The generator
|
|
returns the next element of the sequence each time the generator is
|
|
invoked, where each element of the sequence must be a single
|
|
value. When the sequence ends, the generator returns @|void-const|
|
|
as its final result.}
|
|
|
|
@defproc[(sequence->repeated-generator [s sequence?]) (-> any)]{
|
|
Like @scheme[sequence->generator], but when @racket[s] has no further
|
|
values, the generator starts the sequence again (so that the
|
|
generator never stops producing values).}
|
|
|
|
@close-eval[generator-eval]
|