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Specification
The (streams primitive) library provides two mutually-recursive abstract data types: An object of the stream abstract data type is a promise that, when forced, is either stream-null or is an object of type stream-pair. An object of the stream-pair abstract data type contains a stream-car and a stream-cdr, which must be a stream. The essential feature of streams is the systematic suspensions of the recursive promises between the two data types.
α stream
:: (promise stream-null)
| (promise (α stream-pair))
α stream-pair
:: (promise α) × (promise (α stream))
The object stored in the stream-car of a stream-pair is a promise that is forced the first time the stream-car is accessed; its value is cached in case it is needed again. The object may have any type, and different stream elements may have different types. If the stream-car is never accessed, the object stored there is never evaluated. Likewise, the stream-cdr is a promise to return a stream, and is only forced on demand.
This library provides eight operators: constructors for stream-null and stream-pairs, type recognizers for streams and the two kinds of streams, accessors for both fields of a stream-pair, and a lambda that creates procedures that return streams.
Stream-null is a promise that, when forced, is a single object, distinguishable from all other objects, that represents the null stream. Stream-null is immutable and unique.
Stream-cons is a macro that accepts an object and a stream and creates a newly-allocated stream containing a promise that, when forced, is a stream-pair with the object in its stream-car and the stream in its stream-cdr. Stream-cons must be syntactic, not procedural, because neither object nor stream is evaluated when stream-cons is called. Since stream is not evaluated, when the stream-pair is created, it is not an error to call stream-cons with a stream that is not of type stream; however, doing so will cause an error later when the stream-cdr of the stream-pair is accessed. Once created, a stream-pair is immutable; there is no stream-set-car! or stream-set-cdr! that modifies an existing stream-pair. There is no dotted-pair or improper stream as with lists.
Stream? is a procedure that takes an object and returns #t if the object is a stream and #f otherwise. If object is a stream, stream? does not force its promise. If (stream? obj) is #t, then one of (stream-null? obj) and (stream-pair? obj) will be #t and the other will be #f; if (stream? obj) is #f, both (stream-null? obj) and (stream-pair? obj) will be #f.
Stream-null? is a procedure that takes an object and returns #t if the object is the distinguished null stream and #f otherwise. If object is a stream, stream-null? must force its promise in order to distinguish stream-null from stream-pair.
Stream-pair? is a procedure that takes an object and returns #t if the object is a stream-pair constructed by stream-cons and #f otherwise. If object is a stream, stream-pair? must force its promise in order to distinguish stream-null from stream-pair.
Stream-car is a procedure that takes a stream and returns the object stored in the stream-car of the stream. Stream-car signals an error if the object passed to it is not a stream-pair. Calling stream-car causes the object stored there to be evaluated if it has not yet been; the object’s value is cached in case it is needed again.
Stream-cdr is a procedure that takes a stream and returns the stream stored in the stream-cdr of the stream. Stream-cdr signals an error if the object passed to it is not a stream-pair. Calling stream-cdr does not force the promise containing the stream stored in the stream-cdr of the stream.
Stream-lambda creates a procedure that returns a promise to evaluate the body of the procedure. The last body expression to be evaluated must yield a stream. As with normal lambda, args may be a single variable name, in which case all the formal arguments are collected into a single list, or a list of variable names, which may be null if there are no arguments, proper if there are an exact number of arguments, or dotted if a fixed number of arguments is to be followed by zero or more arguments collected into a list. Body must contain at least one expression, and may contain internal definitions preceding any expressions to be evaluated.
(define strm123
(stream-cons 1
(stream-cons 2
(stream-cons 3
stream-null))))
(stream-car strm123) ⇒ 1
(stream-car (stream-cdr strm123) ⇒ 2
(stream-pair?
(stream-cdr
(stream-cons (/ 1 0) stream-null))) ⇒ #f
(stream? (list 1 2 3)) ⇒ #f
(define iter
(stream-lambda (f x)
(stream-cons x (iter f (f x)))))
(define nats (iter (lambda (x) (+ x 1)) 0))
(stream-car (stream-cdr nats)) ⇒ 1
(define stream-add
(stream-lambda (s1 s2)
(stream-cons
(+ (stream-car s1) (stream-car s2))
(stream-add (stream-cdr s1)
(stream-cdr s2)))))
(define evens (stream-add nats nats))
(stream-car evens) ⇒ 0
(stream-car (stream-cdr evens)) ⇒ 2
(stream-car (stream-cdr (stream-cdr evens))) ⇒ 4The (streams derived) library provides useful procedures and syntax that depend on the primitives defined above. In the operator templates given below, an ellipsis ... indicates zero or more repetitions of the preceding subexpression and square brackets […] indicate optional elements. In the type annotations given below, square brackets […] refer to lists, curly braces {…} refer to streams, and nat refers to exact non-negative integers.
It creates a procedure that returns a stream, and may appear anywhere a normal define may appear, including as an internal definition, and may have internal definitions of its own, including other define-streams. The defined procedure takes arguments in the same way as stream-lambda. Define-stream is syntactic sugar on stream-lambda; see also stream-let, which is also a sugaring of stream-lambda.
A simple version of stream-map that takes only a single input stream calls itself recursively:
(define-stream (stream-map proc strm)
(if (stream-null? strm)
stream-null
(stream-cons
(proc (stream-car strm))
(stream-map proc (stream-cdr strm))))))[α] → {α}
List->stream takes a list of objects and returns a newly-allocated stream containing in its elements the objects in the list. Since the objects are given in a list, they are evaluated when list->stream is called, before the stream is created. If the list of objects is null, as in (list->stream '()), the null stream is returned. See also stream.
(define strm123 (list->stream '(1 2 3)))
; fails with divide-by-zero error
(define s (list->stream (list 1 (/ 1 0) -1)))procedure: (port->stream [port]) port → {char} Port->stream takes a port and returns a newly-allocated stream containing in its elements the characters on the port. If port is not given it defaults to the current input port. The returned stream has finite length and is terminated by stream-null.
It looks like one use of port->stream would be this:
(define s ;wrong! (with-input-from-file filename (lambda () (port->stream)))) But that fails, because with-input-from-file is eager, and closes the input port prematurely, before the first character is read. To read a file into a stream, say:
(define-stream (file->stream filename) (let ((p (open-input-file filename))) (stream-let loop ((c (read-char p))) (if (eof-object? c) (begin (close-input-port p) stream-null) (stream-cons c (loop (read-char p))))))) syntax: (stream object ...) Stream is syntax that takes zero or more objects and creates a newly-allocated stream containing in its elements the objects, in order. Since stream is syntactic, the objects are evaluated when they are accessed, not when the stream is created. If no objects are given, as in (stream), the null stream is returned. See also list->stream.
(define strm123 (stream 1 2 3))
; (/ 1 0) not evaluated when stream is created (define s (stream 1 (/ 1 0) -1)) procedure: (stream->list [n] stream) nat × {α} → [α] Stream->list takes a natural number n and a stream and returns a newly-allocated list containing in its elements the first n items in the stream. If the stream has less than n items all the items in the stream will be included in the returned list. If n is not given it defaults to infinity, which means that unless stream is finite stream->list will never return.
(stream->list 10 (stream-map (lambda (x) (* x x)) (stream-from 0))) ⇒ (0 1 4 9 16 25 36 49 64 81) procedure: (stream-append stream ...) {α} ... → {α} Stream-append returns a newly-allocated stream containing in its elements those elements contained in its input streams, in order of input. If any of the input streams is infinite, no elements of any of the succeeding input streams will appear in the output stream; thus, if x is infinite, (stream-append x y) ≡ x. See also stream-concat.
Quicksort can be used to sort a stream, using stream-append to build the output; the sort is lazy; so if only the beginning of the output stream is needed, the end of the stream is never sorted.
(define-stream (qsort lt? strm) (if (stream-null? strm) stream-null (let ((x (stream-car strm)) (xs (stream-cdr strm))) (stream-append (qsort lt? (stream-filter (lambda (u) (lt? u x)) xs)) (stream x) (qsort lt? (stream-filter (lambda (u) (not (lt? u x))) xs)))))) Note also that, when used in tail position as in qsort, stream-append does not suffer the poor performance of append on lists. The list version of append requires re-traversal of all its list arguments except the last each time it is called. But stream-append is different. Each recursive call to stream-append is suspended; when it is later forced, the preceding elements of the result have already been traversed, so tail-recursive loops that produce streams are efficient even when each element is appended to the end of the result stream. This also implies that during traversal of the result only one promise needs to be kept in memory at a time.
procedure: (stream-concat stream) {{α}} ... → {α} Stream-concat takes a stream consisting of one or more streams and returns a newly-allocated stream containing all the elements of the input streams. If any of the streams in the input stream is infinite, any remaining streams in the input stream will never appear in the output stream. See also stream-append.
(stream->list (stream-concat (stream (stream 1 2) (stream) (stream 3 2 1)))) ⇒ (1 2 3 2 1) The permutations of a finite stream can be determined by interleaving each element of the stream in all possible positions within each permutation of the other elements of the stream. Interleave returns a stream of streams with x inserted in each possible position of yy:
(define-stream (interleave x yy) (stream-match yy (() (stream (stream x))) ((y . ys) (stream-append (stream (stream-cons x yy)) (stream-map (lambda (z) (stream-cons y z)) (interleave x ys))))))
(define-stream (perms xs) (if (stream-null? xs) (stream (stream)) (stream-concat (stream-map (lambda (ys) (interleave (stream-car xs) ys)) (perms (stream-cdr xs)))))) procedure: (stream-constant object ...) α ... → {α} Stream-constant takes one or more objects and returns a newly-allocated stream containing in its elements the objects, repeating the objects in succession forever.
(stream-constant 1) ⇒ 1 1 1 ...
(stream-constant #t #f) ⇒ #t #f #t #f #t #f ...
procedure: (stream-drop n stream) procedure nat × {α} → {α} Stream-drop returns the suffix of the input stream that starts at the next element after the first n elements. The output stream shares structure with the input stream; thus, promises forced in one instance of the stream are also forced in the other instance of the stream. If the input stream has less than n elements, stream-drop returns the null stream. See also stream-take.
(define (stream-split n strm) (values (stream-take n strm) (stream-drop n strm))) procedure: (stream-drop-while pred? stream) (α → boolean) × {α} → {α} Stream-drop-while returns the suffix of the input stream that starts at the first element x for which (pred? x) is #f. The output stream shares structure with the input stream. See also stream-take-while.
Stream-unique creates a new stream that retains only the first of any sub-sequences of repeated elements.
(define-stream (stream-unique eql? strm) (if (stream-null? strm) stream-null (stream-cons (stream-car strm) (stream-unique eql? (stream-drop-while (lambda (x) (eql? (stream-car strm) x)) strm))))) procedure: (stream-filter pred? stream) (α → boolean) × {α} → {α} Stream-filter returns a newly-allocated stream that contains only those elements x of the input stream for which (pred? x) is non-#f.
(stream-filter odd? (stream-from 0)) ⇒ 1 3 5 7 9 ... procedure: (stream-fold proc base stream) (α × β → α) × α × {β} → α Stream-fold applies a binary procedure to base and the first element of stream to compute a new base, then applies the procedure to the new base and the next element of stream to compute a succeeding base, and so on, accumulating a value that is finally returned as the value of stream-fold when the end of the stream is reached. Stream must be finite, or stream-fold will enter an infinite loop. See also stream-scan, which is similar to stream-fold, but useful for infinite streams. For readers familiar with other functional languages, this is a left-fold; there is no corresponding right-fold, since right-fold relies on finite streams that are fully-evaluated, at which time they may as well be converted to a list.
Stream-fold is often used to summarize a stream in a single value, for instance, to compute the maximum element of a stream.
(define (stream-maximum lt? strm) (stream-fold (lambda (x y) (if (lt? x y) y x)) (stream-car strm) (stream-cdr strm))) Sometimes, it is useful to have stream-fold defined only on non-null streams:
(define (stream-fold-one proc strm) (stream-fold proc (stream-car strm) (stream-cdr strm))) Stream-minimum can then be defined as:
(define (stream-minimum lt? strm) (stream-fold-one (lambda (x y) (if (lt? x y) x y)) strm)) Stream-fold can also be used to build a stream:
(define-stream (isort lt? strm) (define-stream (insert strm x) (stream-match strm (() (stream x)) ((y . ys) (if (lt? y x) (stream-cons y (insert ys x)) (stream-cons x strm))))) (stream-fold insert stream-null strm)) procedure: (stream-for-each proc stream ...) (α × β × ...) × {α} × {β} ... Stream-for-each applies a procedure element-wise to corresponding elements of the input streams for its side-effects; it returns nothing. Stream-for-each stops as soon as any of its input streams is exhausted.
The following procedure displays the contents of a file:
(define (display-file filename) (stream-for-each display (file->stream filename))) procedure: (stream-from first [step]) number × number → {number} Stream-from creates a newly-allocated stream that contains first as its first element and increments each succeeding element by step. If step is not given it defaults to 1. First and step may be of any numeric type. Stream-from is frequently useful as a generator in stream-of expressions. See also stream-range for a similar procedure that creates finite streams.
Stream-from could be implemented as (stream-iterate (lambda (x) (+ x step)) first).
(define nats (stream-from 0)) ⇒ 0 1 2 ...
(define odds (stream-from 1 2)) ⇒ 1 3 5 ...
procedure: (stream-iterate proc base) (α → α) × α → {α} Stream-iterate creates a newly-allocated stream containing base in its first element and applies proc to each element in turn to determine the succeeding element. See also stream-unfold and stream-unfolds.
(stream-iterate (lambda (x) (+ x 1)) 0) ⇒ 0 1 2 3 4 ...
(stream-iterate (lambda (x) (* x 2)) 1) ⇒ 1 2 4 8 16 ... Given a seed between 0 and 232, exclusive, the following expression creates a stream of pseudo-random integers between 0 and 232, exclusive, beginning with seed, using the method described by Stephen Park and Keith Miller:
(stream-iterate (lambda (x) (modulo (* x 16807) 2147483647)) seed) Successive values of the continued fraction shown below approach the value of the “golden ratio” φ ≈ 1.618:
Continued fraction
The fractions can be calculated by the stream
(stream-iterate (lambda (x) (+ 1 (/ x))) 1)
procedure: (stream-length stream) {α} → nat Stream-length takes an input stream and returns the number of elements in the stream; it does not evaluate its elements. Stream-length may only be used on finite streams; it enters an infinite loop with infinite streams.
(stream-length strm123) ⇒ 3
syntax: (stream-let tag ((var expr) ...) body) Stream-let creates a local scope that binds each variable to the value of its corresponding expression. It additionally binds tag to a procedure which takes the bound variables as arguments and body as its defining expressions, binding the tag with stream-lambda. Tag is in scope within body, and may be called recursively. When the expanded expression defined by the stream-let is evaluated, stream-let evaluates the expressions in its body in an environment containing the newly-bound variables, returning the value of the last expression evaluated, which must yield a stream.
Stream-let provides syntactic sugar on stream-lambda, in the same manner as normal let provides syntactic sugar on normal lambda. However, unlike normal let, the tag is required, not optional, because unnamed stream-let is meaningless.
Stream-member returns the first stream-pair of the input strm with a stream-car x that satisfies (eql? obj x), or the null stream if x is not present in strm.
(define-stream (stream-member eql? obj strm) (stream-let loop ((strm strm)) (cond ((stream-null? strm) strm) ((eql? obj (stream-car strm)) strm) (else (loop (stream-cdr strm)))))) procedure: (stream-map proc stream ...) (α × β ... → ω) × {α} × {β} ... → {ω} Stream-map applies a procedure element-wise to corresponding elements of the input streams, returning a newly-allocated stream containing elements that are the results of those procedure applications. The output stream has as many elements as the minimum-length input stream, and may be infinite.
(define (square x) (* x x))
(stream-map square (stream 9 3)) ⇒ 81 9
(define (sigma f m n) (stream-fold + 0 (stream-map f (stream-range m (+ n 1))))) (sigma square 1 100) ⇒ 338350
In some functional languages, stream-map takes only a single input stream, and stream-zipwith provides a companion function that takes multiple input streams.
syntax: (stream-match stream clause ...) Stream-match provides the syntax of pattern-matching for streams. The input stream is an expression that evaluates to a stream. Clauses are of the form (pattern [fender] expr), consisting of a pattern that matches a stream of a particular shape, an optional fender that must succeed if the pattern is to match, and an expression that is evaluated if the pattern matches. There are four types of patterns:
() — Matches the null stream. (pat0 pat1 ...) — Matches a finite stream with length exactly equal to the number of pattern elements. (pat0 pat1 ... . patrest) — Matches an infinite stream, or a finite stream with length at least as great as the number of pattern elements before the literal dot. pat — Matches an entire stream. Should always appear last in the list of clauses; it’s not an error to appear elsewhere, but subsequent clauses could never match. Each pattern element pati may be either:
An identifier — Matches any stream element. Additionally, the value of the stream element is bound to the variable named by the identifier, which is in scope in the fender and expression of the corresponding clause. Each identifier in a single pattern must be unique. A literal underscore — Matches any stream element, but creates no bindings. The patterns are tested in order, left-to-right, until a matching pattern is found; if fender is present, it must evaluate as non-#f for the match to be successful. Pattern variables are bound in the corresponding fender and expression. Once the matching pattern is found, the corresponding expression is evaluated and returned as the result of the match. An error is signaled if no pattern matches the input stream.
Stream-match is often used to distinguish null streams from non-null streams, binding head and tail:
(define (len strm) (stream-match strm (() 0) ((head . tail) (+ 1 (len tail))))) Fenders can test the common case where two stream elements must be identical; the else pattern is an identifier bound to the entire stream, not a keyword as in cond.
(stream-match strm ((x y . _) (equal? x y) 'ok) (else 'error)) A more complex example uses two nested matchers to match two different stream arguments; (stream-merge lt? . strms) stably merges two or more streams ordered by the lt? predicate:
(define-stream (stream-merge lt? . strms) (define-stream (merge xx yy) (stream-match xx (() yy) ((x . xs) (stream-match yy (() xx) ((y . ys) (if (lt? y x) (stream-cons y (merge xx ys)) (stream-cons x (merge xs yy)))))))) (stream-let loop ((strms strms)) (cond ((null? strms) stream-null) ((null? (cdr strms)) (car strms)) (else (merge (car strms) (apply stream-merge lt? (cdr strms))))))) syntax: (stream-of expr clause ...) Stream-of provides the syntax of stream comprehensions, which generate streams by means of looping expressions. The result is a stream of objects of the type returned by expr. There are four types of clauses:
(var in stream-expr) — Loop over the elements of stream-expr, in order from the start of the stream, binding each element of the stream in turn to var. Stream-from and stream-range are frequently useful as generators for stream-expr. (var is expr) — Bind var to the value obtained by evaluating expr. (pred? expr) — Include in the output stream only those elements x for which (pred? x) is non-#f. The scope of variables bound in the stream comprehension is the clauses to the right of the binding clause (but not the binding clause itself) plus the result expression.
When two or more generators are present, the loops are processed as if they are nested from left to right; that is, the rightmost generator varies fastest. A consequence of this is that only the first generator may be infinite and all subsequent generators must be finite. If no generators are present, the result of a stream comprehension is a stream containing the result expression; thus, (stream-of 1) produces a finite stream containing only the element 1.
(stream-of (* x x) (x in (stream-range 0 10)) (even? x)) ⇒ 0 4 16 36 64
(stream-of (list a b) (a in (stream-range 1 4)) (b in (stream-range 1 3))) ⇒ (1 1) (1 2) (2 1) (2 2) (3 1) (3 2)
(stream-of (list i j) (i in (stream-range 1 5)) (j in (stream-range (+ i 1) 5))) ⇒ (1 2) (1 3) (1 4) (2 3) (2 4) (3 4) procedure: (stream-range first past [step]) number × number × number → {number} Stream-range creates a newly-allocated stream that contains first as its first element and increments each succeeding element by step. The stream is finite and ends before past, which is not an element of the stream. If step is not given it defaults to 1 if first is less than past and -1 otherwise. First, past and step may be of any numeric type. Stream-range is frequently useful as a generator in stream-of expressions. See also stream-from for a similar procedure that creates infinite streams.
(stream-range 0 10) ⇒ 0 1 2 3 4 5 6 7 8 9
(stream-range 0 10 2) → 0 2 4 6 8
Successive elements of the stream are calculated by adding step to first, so if any of first, past or step are inexact, the length of the output stream may differ from (ceiling (- (/ (- past first) step) 1).
procedure: (stream-ref stream n) {α} × nat → α Stream-ref returns the nth element of stream, counting from zero. An error is signaled if n is greater than or equal to the length of stream.
(define (fact n) (stream-ref (stream-scan * 1 (stream-from 1)) n)) procedure: (stream-reverse stream) {α} → {α} Stream-reverse returns a newly-allocated stream containing the elements of the input stream but in reverse order. Stream-reverse may only be used with finite streams; it enters an infinite loop with infinite streams. Stream-reverse does not force evaluation of the elements of the stream.
(define s (stream 1 (/ 1 0) -1)) (define r (stream-reverse s)) (stream-ref r 0) (stream-ref r 2) 1 (stream-ref r 1) error: division by zero procedure: (stream-scan proc base stream) (α × β → α) × α × {β} → {α} Stream-scan accumulates the partial folds of an input stream into a newly-allocated output stream. The output stream is the base followed by (stream-fold proc base (stream-take i stream)) for each of the first i elements of stream.
(stream-scan + 0 (stream-from 1)) ⇒ (stream 0 1 3 6 10 15 ...)
(stream-scan * 1 (stream-from 1)) ⇒ (stream 1 1 2 6 24 120 ...) procedure: (stream-take n stream) nat × {α} → {α} Stream-take takes a non-negative integer n and a stream and returns a newly-allocated stream containing the first n elements of the input stream. If the input stream has less than n elements, so does the output stream. See also stream-drop.
Mergesort splits a stream into two equal-length pieces, sorts them recursively and merges the results:
(define-stream (msort lt? strm) (let* ((n (quotient (stream-length strm) 2)) (ts (stream-take n strm)) (ds (stream-drop n strm))) (if (zero? n) strm (stream-merge lt? (msort < ts) (msort < ds))))) procedure: (stream-take-while pred? stream) (α → boolean) × {α} → {α} Stream-take-while takes a predicate and a stream and returns a newly-allocated stream containing those elements x that form the maximal prefix of the input stream for which (pred? x) is non-#f. See also stream-drop-while.
(stream-car (stream-reverse (stream-take-while (lambda (x) (< x 1000)) primes))) ⇒ 997 procedure: (stream-unfold map pred? gen base) (α → β) × (α → boolean) × (α → α) × α → {β} Stream-unfold is the fundamental recursive stream constructor. It constructs a stream by repeatedly applying gen to successive values of base, in the manner of stream-iterate, then applying map to each of the values so generated, appending each of the mapped values to the output stream as long as (pred? base) is non-#f. See also stream-iterate and stream-unfolds.
The expression below creates the finite stream 0 1 4 9 16 25 36 49 64 81. Initially the base is 0, which is less than 10, so map squares the base and the mapped value becomes the first element of the output stream. Then gen increments the base by 1, so it becomes 1; this is less than 10, so map squares the new base and 1 becomes the second element of the output stream. And so on, until the base becomes 10, when pred? stops the recursion and stream-null ends the output stream.
(stream-unfold (lambda (x) (expt x 2)) ; map (lambda (x) (< x 10)) ; pred? (lambda (x) (+ x 1)) ; gen 0) ; base procedure: (stream-unfolds proc seed) (α → (values α × β ...)) × α → (values {β} ...) Stream-unfolds returns n newly-allocated streams containing those elements produced by successive calls to the generator proc, which takes the current seed as its argument and returns n+1 values
(proc seed → seed result0 ... resultn-1
where the returned seed is the input seed to the next call to the generator and resulti indicates how to produce the next element of the ith result stream:
(value) — value is the next car of the result stream #f — no value produced by this iteration of the generator proc for the result stream () — the end of the result stream It may require multiple calls of proc to produce the next element of any particular result stream. See also stream-iterate and stream-unfold.
Stream-unfolds is especially useful when writing expressions that return multiple streams. For instance, (stream-partition pred? strm) is equivalent to
(values (stream-filter pred? strm) (stream-filter (lambda (x) (not (pred? x))) strm)) but only tests pred? once for each element of strm.
(define (stream-partition pred? strm) (stream-unfolds (lambda (s) (if (stream-null? s) (values s '() '()) (let ((a (stream-car s)) (d (stream-cdr s))) (if (pred? a) (values d (list a) #f) (values d #f (list a)))))) strm))
(call-with-values (lambda () (stream-partition odd? (stream-range 1 6))) (lambda (odds evens) (list (stream->list odds) (stream->list evens)))) ⇒ ((1 3 5) (2 4)) procedure: (stream-zip stream ...) {α} × {β} × ... → {[α β ...]} Stream-zip takes one or more input streams and returns a newly-allocated stream in which each element is a list (not a stream) of the corresponding elements of the input streams. The output stream is as long as the shortest input stream, if any of the input streams is finite, or is infinite if all the input streams are infinite.
A common use of stream-zip is to add an index to a stream, as in (stream-finds eql? obj strm), which returns all the zero-based indices in strm at which obj appears; (stream-find eql? obj strm) returns the first such index, or #f if obj is not in strm.
(define-stream (stream-finds eql? obj strm) (stream-of (car x) (x in (stream-zip (stream-from 0) strm)) (eql? obj (cadr x))))
(define (stream-find eql? obj strm) (stream-car (stream-append (stream-finds eql? obj strm) (stream #f))))
(stream-find char=? #\l (list->stream (string->list "hello"))) ⇒ 2
(stream-find char=? #\l (list->stream (string->list "goodbye"))) ⇒ #f Stream-find is not as inefficient as it looks; although it calls stream-finds, which finds all matching indices, the matches are computed lazily, and only the first match is needed for stream-find.