## SRFI-127: Lazy Sequences

Lazy sequences (or lseqs, pronounced "ell-seeks") are a generalization of lists. In particular, an lseq is either a proper list or a dotted list whose last cdr is a SRFI 121 generator. A generator is a procedure that can be invoked with no arguments in order to lazily supply additional elements of the lseq. When a generator has no more elements to return, it returns an end-of-file object. Consequently, lazy sequences cannot reliably contain end-of-file objects.

This SRFI provides a set of procedures suitable for operating on lazy sequences based on SRFI-1.

## TOC »

## SRFI Description

For a full description of this SRFI, see the full SRFI document. This documentation covers the API only.

## Lazy Sequences

The templates given below obey the following conventions for procedure formals:

- lseq
- A lazy sequence
- x, y, a, b
- Any value
- object, value
- Any value
- n, i
- A natural number (an integer >= 0)
- proc
- A procedure
- pred
- A procedure whose return value is treated as a boolean
- generator
- A procedure with no arguments that returns a sequence of values
- =
- A boolean procedure taking two arguments

To interpret the examples, pretend that they are executed on a Scheme that prints lazy sequences with the syntax of lists, truncating them when they get too long.

### Constructors

Every list constructor procedure is also an lseq constructor procedure. The procedure `generator->lseq` constructs an lseq based on the values of a generator. In order to prepend a value to an lseq, simply use cons; to prepend more than one value, use SRFI 1's `cons*`.

`generator->lseq``generator`procedureReturns an lseq whose elements are the values generated by

`generator`. The exact behavior is as follows:`generator`is invoked with no arguments to produce an object`obj`.- If
`obj`is an end-of-file object, the empty list is returned. - Otherwise, a newly allocated pair whose car is
`obj`and whose cdr is`generator`is returned.

(generator->lseq (make-iota-generator +inf.0 1)) ;=> (1 2 3 ...)

### Predicates

`lseq?``x`procedureReturns

`#t`if`x`is an lseq. This procedure may also return`#t`if x is an improper list whose last cdr is a procedure that requires arguments, since there is no portable way to examine a procedure to determine how many arguments it requires. Otherwise it returns`#f`.

`lseq=?``elt=?``lseq1``lseq2`procedureDetermines lseq equality, given an element-equality procedure. Two lseqs are equal if they are of the same length, and their corresponding elements are equal, as determined by

`elt=?`. When`elt=?`is called, its first argument is always from`lseq1`and its second argument is from`lseq2`.The dynamic order in which the

`elt=?`procedure is applied to pairs of elements is not specified.The

`elt=?`procedure must be consistent with`eq?`. This implies that two lseqs which are`eq?`are always`lseq=?`, as well; implementations may exploit this fact to "short-cut" the element-by-element equality tests.

### Selectors

`lseq-car``lseq`procedure`lseq-first``lseq`procedureThese procedures are synonymous. They return the first element of

`lseq`. They are included for completeness, as they are the same as`car`. It is an error to apply them to an empty`lseq`.

`lseq-cdr``lseq`procedure`lseq-rest``lseq`procedureThese procedures are synonymous. They return an lseq with the contents of

`lseq`except for the first element. The exact behavior is as follows:- If lseq is a pair whose cdr is a procedure, then the procedure is invoked with no arguments to produce an object
`obj`.- If
`obj`is an end-of-file object, then the cdr of lseq is set to the empty list, which is returned. - If
`obj`is any other object, then a new pair is allocated whose car is`obj`and whose cdr is the cdr of lseq (i.e. the procedure). The cdr of lseq is set to the newly allocated pair, which is returned.

- If
- If lseq is a pair whose cdr is not a procedure, then the cdr is returned.
- If lseq is not a pair, it is an error.

Implementations that inline cdr are advised to inline

`lseq-cdr`if possible.- If lseq is a pair whose cdr is a procedure, then the procedure is invoked with no arguments to produce an object

`lseq-ref``lseq``i`procedureReturns the ith element of

`lseq`. (This is the same as`(lseq-first (lseq-drop lseq i))`). It is an error if i >= n, where`n`is the length of`lseq`.(lseq-ref '(a b c d) 2) ;=> c

`lseq-take``lseq``i`procedure`lseq-drop``lseq``i`procedure`lseq-take`lazily returns the first`i`elements of`lseq`.`lseq-drop`returns all but the first`i`elements of`lseq`.(lseq-take '(a b c d e) 2) ;=> (a b) (lseq-drop '(a b c d e) 2) ;=> (c d e)

`lseq-drop`is exactly equivalent to performing`i``lseq-rest`operations on`lseq`.

### The Whole Lazy Sequence

`lseq-realize``lseq`procedureRepeatedly applies

`lseq-cdr`to`lseq`until its generator (if there is one) has been exhausted, and returns`lseq`, which is now guaranteed to be a proper list. This procedure can be called on an arbitrary lseq before passing it to a procedure which only accepts lists. However, if the generator never returns an end-of-file object,`lseq-realize`will never return.

`lseq->generator``lseq`procedureReturns a generator which when invoked will return all the elements of

`lseq`, including any that have not yet been realized.

`lseq-length``lseq`procedureReturns the length of its argument, which is the non-negative integer n such that

`lseq-rest`applied n times to the`lseq`produces an empty lseq.`lseq`must be finite, or this procedure will not return.

`lseq-append``lseq``...`procedureReturns an lseq that lazily contains all the elements of all the lseqs in order.

`lseq-zip``lseq1``lseq2``...`procedureIf

`lseq-zip`is passed n lseqs, it lazily returns an lseq each element of which is an n-element list comprised of the corresponding elements from the lseqs. If any of the lseqs are finite in length, the result is as long as the shortest lseq.(lseq-zip '(one two three) (generator->lseq (make-iota-generator +inf.0 1 1)) (generator->lseq (make-repeating-generator) '(odd even)))) ;=> ((one 1 odd) (two 2 even) (three 3 odd)) (lseq-zip '(1 2 3)) ;=> ((1) (2) (3))

### Mapping and Filtering

`lseq-map``proc``lseq1``lseq2``...`procedureThe

`lseq-map`procedure lazily applies`proc`element-wise to the corresponding elements of the lseqs, where`proc`is a procedure taking as many arguments as there are lseqs and returning a single value, and returns an lseq of the results in order. The dynamic order in which`proc`is applied to the elements of the lseqs is unspecified.(lseq-map (lambda (x) (lseq-car (lseq-cdr x))) '((a b) (d e) (g h))) ;=> (b e h) (lseq-map (lambda (n) (expt n n)) (make-iota-generator +inf.0 1 1) ;=> (1 4 27 256 3125 ...) (lseq-map + '(1 2 3) '(4 5 6)) => (5 7 9) (let ((count 0)) (lseq-map (lambda (ignored) (set! count (+ count 1)) count) '(a b))) ;=> (1 2) or (2 1)

`lseq-for-each``proc``lseq1``lseq2``...`procedureThe arguments to

`lseq-for-each`are like the arguments to`lseq-map`, but`lseq-for-each`calls`proc`for its side effects rather than for its values. Unlike`lseq-map`,`lseq-for-each`is guaranteed to call`proc`on the elements of the lseqs in order from the first element(s) to the last, and the value returned by`lseq-for-each`is unspecified. If none of the lseqs are finite, lseq-for-each never returns.(let ((v (make-vector 5))) (lseq-for-each (let ((count 0)) (lambda (i) (vector-set! v count (* i i)) (set! count (+ count 1)))) '(0 1 2 3 4)) v) ;=> (#0 1 2 3 4)

`lseq-filter``pred``lseq`procedure`lseq-remove``pred``lseq`procedureThe procedure

`lseq-filter`lazily returns an lseq that contains only the elements of`lseq`that satisfy`pred`.The procedure

`lseq-remove`is the same as`lseq-filter`, except that it returns elements that do not satisfy`pred`. These procedures are guaranteed to call`pred`on the elements of the lseqs in sequence order.(lseq-filter odd? (generator->lseq (make-range-generator 1 5))) ;=> (1 3) (lseq-remove odd? (generator->lseq (make-range-generator 1 5))) ;=> (2 4)

### Searching

The following procedures all search lseqs for the leftmost element satisfying some criterion.

`lseq-find``pred``lseq`procedureReturn the first element of

`lseq`that satisfies predicate`pred`, or`#f`if no element does. It cannot reliably be applied to lseqs that include`#f`as an element; use`lseq-find-tail`instead. The predicate is guaranteed to be evaluated on the elements of lseq in sequence order, and only as often as necessary.(lseq-find even? '(3 1 4 1 5 9 2 6)) ;=> 4

`lseq-find-tail``pred``lseq`procedureReturns the longest tail of

`lseq`whose first element satisfies`pred`, or`#f`if no element does. The predicate is guaranteed to be evaluated on the elements of lseq in sequence order, and only as often as necessary.`lseq-find-tail`can be viewed as a general-predicate variant of the`lseq-member`function.Examples:

(lseq-find-tail even? '(3 1 37 -8 -5 0 0)) ;=> (-8 -5 0 0) (lseq-find-tail even? '(3 1 37 -5)) ;=> #f ;; equivalent to (lseq-member elt lseq) (lseq-find-tail (lambda (elt) (equal? x elt)) lseq)

`lseq-take-while``pred``lseq`procedureLazily returns the longest initial prefix of

`lseq`whose elements all satisfy the predicate`pred`.(lseq-take-while even? '(2 18 3 10 22 9)) ;=> (2 18)

`lseq-drop-while``pred``lseq`procedureDrops the longest initial prefix of

`lseq`whose elements all satisfy the predicate pred, and returns the rest of the lseq.(lseq-drop-while even? '(2 18 3 10 22 9)) ;=> (3 10 22 9)

Note that

`lseq-drop-while`is essentially`lseq-find-tail`where the sense of the predicate is inverted:`lseq-find-tail`searches until it finds an element satisfying the predicate;`lseq-drop-while`searches until it finds an element that doesn't satisfy the predicate.

`lseq-any``pred``lseq1``lseq2``...`procedureApplies

`pred`to successive elements of the lseqs, returning true if`pred`returns true on any application. If an application returns a true value,`lseq-any`immediately returns that value. Otherwise, it iterates until a true value is produced or one of the lseqs runs out of values; in the latter case,`lseq-any`returns`#f`. It is an error if`pred`does not accept the same number of arguments as there are lseqs and return a boolean result.Note the difference between

`lseq-find`and`lseq-any`--`lseq-find`returns the element that satisfied the predicate;`lseq-any`returns the true value that the predicate produced.Like

`lseq-every`,`lseq-any`'s name does not end with a question mark -- this is to indicate that it does not return a simple boolean (`#t`or`#f`), but a general value.(lseq-any integer? '(a 3 b 2.7)) ;=> #t (lseq-any integer? '(a 3.1 b 2.7)) ;=> #f (lseq-any < '(3 1 4 1 5) '(2 7 1 8 2)) ;=> #t (define (factorial n) (cond ((< n 0) #f) ((= n 0) 1) (else (* n (factorial (- n 1)))))) (lseq-any factorial '(-1 -2 3 4)) ;=> 6

`lseq-every``pred``lseq1``lseq2``...`procedureApplies

`pred`to successive elements of the lseqs, returning true if the predicate returns true on every application. If an application returns a false value,`lseq-every`immediately returns that value. Otherwise, it iterates until a false value is produced or one of the lseqs runs out of values; in the latter case,`lseq-every`returns the last value returned by`pred`, or`#t`if`pred`was never invoked. It is an error if`pred`does not accept the same number of arguments as there are lseqs and return a boolean result.Like

`lseq-any`,`lseq-every`'s name does not end with a question mark -- this is to indicate that it does not return a simple boolean (`#t`or`#f`), but a general value.(lseq-every factorial '(1 2 3 4)) ;=> 24

`lseq-index``pred``lseq1``lseq2``...`procedureReturn the index of the leftmost element that satisfies

`pred`.Applies

`pred`to successive elements of the lseqs, returning an index usable with`lseq-ref`if the predicate returns true. Otherwise, it iterates until one of the lseqs runs out of values, in which case`#f`is returned. It is an error if`pred`does not accept the same number of arguments as there are lseqs and return a boolean result.The iteration stops when one of the lseqs runs out of values; in this case,

`lseq-index`returns`#f`.(lseq-index even? '(3 1 4 1 5 9)) ;=> 2 (lseq-index < '(3 1 4 1 5 9 2 5 6) '(2 7 1 8 2)) ;=> 1 (lseq-index = '(3 1 4 1 5 9 2 5 6) '(2 7 1 8 2)) ;=> #f

`lseq-member``x``lseq``#!optional``pred`procedure`lseq-memq``x``lseq`procedure`lseq-memv``x``lseq`procedureThese procedures return the longest tail of

`lseq`whose first element is`x`, where the tails of`lseq`are the non-empty lseqs returned by`(lseq-drop lseq i)`for`i`less than the length of`lseq`. If`x`does not occur in`lseq`, then`#f`is returned.`lseq-memq`uses`eq?`to compare`x`with the elements of`lseq`, while`lseq-memv`uses`eqv?`, and`lseq-member`uses`pred`, which defaults to`equal?`.(lseq-memq 'a '(a b c)) ;=> (a b c) (lseq-memq 'b '(a b c)) ;=> (b c) (lseq-memq 'a '(b c d)) ;=> #f (lseq-memq (list 'a) '(b (a) c)) ;=> #f (lseq-member (list 'a) '(b (a) c)) ;=> ((a) c) (lseq-memq 101 '(100 101 102)) ;=> *unspecified* (lseq-memv 101 '(100 101 102)) ;=> (101 102)

The equality procedure is used to compare the elements ei of

`lseq`to the key`x`in this way: the first argument is always`x`, and the second argument is one of the lseq elements. Thus one can reliably find the first element of lseq that is greater than five with`(lseq-member 5 lseq <)`Note that fully general lseq searching may be performed with the

`lseq-find-tail`procedure, e.g.(lseq-find-tail even? lseq) ; Find the first elt with an even key.

## Repository

## Version History

- 1.2
- Removes hardcoded .so extension from setup files.
- 1.1
- Fixes typo in meta file.
- 1.0
- Initial release

## License

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