## 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.

## 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*`.

*[procedure]*

`(generator->lseq generator)`

Returns 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

*[procedure]*

`(lseq? x)`

Returns `#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`.

*[procedure]*

`(lseq=? elt=? lseq1 lseq2)`

Determines 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

*[procedure]*

`(lseq-car lseq)`

*[procedure]*

`(lseq-first lseq)`

These 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`.

*[procedure]*

`(lseq-cdr lseq)`

*[procedure]*

`(lseq-rest lseq)`

These 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.

*[procedure]*

`(lseq-ref lseq i)`

Returns 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

*[procedure]*

`(lseq-take lseq i)`

*[procedure]*

`(lseq-drop lseq i)`

`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

*[procedure]*

`(lseq-realize lseq)`

Repeatedly 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.

*[procedure]*

`(lseq->generator lseq)`

Returns a generator which when invoked will return all the elements of `lseq`, including any that have not yet been realized.

*[procedure]*

`(lseq-length lseq)`

Returns 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.

*[procedure]*

`(lseq-append lseq ...)`

Returns an lseq that lazily contains all the elements of all the lseqs in order.

*[procedure]*

`(lseq-zip lseq1 lseq2 ...)`

If `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

*[procedure]*

`(lseq-map proc lseq1 lseq2 ...)`

The `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)

*[procedure]*

`(lseq-for-each proc lseq1 lseq2 ...)`

The 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)

*[procedure]*

`(lseq-filter pred lseq)`

*[procedure]*

`(lseq-remove pred lseq)`

The 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.

*[procedure]*

`(lseq-find pred lseq)`

Return 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

*[procedure]*

`(lseq-find-tail pred lseq)`

Returns 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)

*[procedure]*

`(lseq-take-while pred lseq)`

Lazily 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)

*[procedure]*

`(lseq-drop-while pred lseq)`

Drops 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.

*[procedure]*

`(lseq-any pred lseq1 lseq2 ...)`

Applies `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

*[procedure]*

`(lseq-every pred lseq1 lseq2 ...)`

Applies `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

*[procedure]*

`(lseq-index pred lseq1 lseq2 ...)`

Return 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

*[procedure]*

`(lseq-member x lseq [ pred ])`

*[procedure]*

`(lseq-memq x lseq)`

*[procedure]*

`(lseq-memv x lseq)`

These 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.

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