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## 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 »

## Installation

$ chicken-install srfi-127

or

$ chicken-install srfi-127 -test

if you want to run the tests for the egg in addition.

## 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

Copyright (C) John Cowan (2015-2016). All Rights Reserved.

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.