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## 9.26 `gauche.sequence` - Sequence framework

Module: gauche.sequence

Provides a generic operations on sequences. A sequence is a collection with ordered elements. Besides all the operations applicable on collections, you can associate integer index to each element, and apply order-aware operations on the elements.

This module inherits `gauche.collection` (See section `gauche.collection` - Collection framework). All the collection generic operations can be applied to a sequence as well.

Among Gauche builtin class, lists, vectors and strings are sequences and the specialized methods are defined for them. Other extension types, such as SRFI-4 uniform vector, have the methods as well.

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### 9.26.1 Fundamental sequence accessors

Method: ref (seq <sequence>) index :optional fallback

Returns index-th element of the sequence seq. This method enables uniform access for any sequence types.

When index is less than zero, or greater than or equal to the size of the sequence, fallback is returned if provided, or an error is signaled if not.

 ```(ref '(a b c) 1) ⇒ b (ref '#(a b c) 1) ⇒ b (ref "abc" 1) ⇒ #\b ```
Method: (setter ref) (seq <sequence>) index value

Sets value to the index-th element of the sequence seq. This is the uniform sequence modifier.

Note: Some sequences may not support arbitrary modification by index. For example, if you have a sequence representing a set of sorted integers, you cannot modify i-th element with arbitrary value. Yet such sequence may provide other means of modification, such as inserting or deleting elements.

 ```(let ((x (list 'a 'b 'c))) (set! (ref x 1) 'z) x) ⇒ (a z c) (let ((x (vector 'a 'b 'c))) (set! (ref x 1) 'z) x) ⇒ #(a z c) (let ((x (string #\a #\b #\c))) (set! (ref x 1) #\z) x) ⇒ "azc" ```
Method: referencer (seq <sequence>)
Method: modifier (seq <sequence>)

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### 9.26.2 Slicing sequence

Method: subseq (seq <sequence>) :optional start end

Retrieve a subsequence of the sequence seq, from start-th element (inclusive) to end-th element (exclusive). If end is omitted, up to the end of sequence is taken. The type of the returned sequence is the same as seq.

 ```(subseq '(a b c d e) 1 4) ⇒ (b c d) (subseq '#(a b c d e) 1 4) ⇒ #(b c d) (subseq "abcde" 1 4) ⇒ "bcd" (subseq '(a b c d e) 3) ⇒ (d e) ```
Method: (setter subseq) (seq <sequence>) start end value-seq
Method: (setter subseq) (seq <sequence>) start value-seq

Sets the elements of value-seq from the start-th element (inclusive) to the end-th element (exclusive) of the sequence seq. Value-seq can be any sequence, but its size must be larger than (end - start).

In the second form, end is figured out by the length of value-seq.

 ```(define s (vector 'a 'b 'c 'd 'e)) (set! (subseq s 1 4) '(4 5 6)) s ⇒ #(a 4 5 6 e) (set! (subseq s 0) "ab") s ⇒ #(#\a #\b 5 6 e) ```

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### 9.26.3 Mapping over sequences

You can use extended `fold`, `map`, `for-each` and other generic functions on sequences, since a sequence is also a collection. However, sometimes you want to have index as well as the element itself during iteration. There are several generic functions for it.

Method: fold-with-index kons knil (seq <sequence>) …

Like generic `fold`, except kons is given the index within seq, as the first argument, as well as each element from seqs and the accrued value.

 ```(fold-with-index acons '() '(a b c)) ⇒ ((2 . c) (1 . b) (0 . a)) ```
Method: map-with-index proc (seq <sequence>) …
Method: map-to-with-index class proc (seq <sequence>) …
Method: for-each-with-index proc (seq <sequence>) …

Like `map`, `map-to` and `for-each`, except proc receives the index as the first argument.

 ```(map-with-index list '(a b c d) '(e f g h)) ⇒ ((0 a e) (1 b f) (2 c g) (3 d h)) (map-to-with-index cons '(a b c d)) ⇒ #((0 . a) (1 . b) (2 . c) (3 . d)) ```
Method: find-with-index pred (seq <sequence>)

Finds the first element in seq that satisfies pred like `find`, but returns two values, the index of the element and the element itself. If no element satisfies pred, two `#f`’s are returned.

 ```(find-with-index char-upper-case? "abraCadabra") ⇒ 4 and #\C (find-with-index char-numeric? "abraCadabra") ⇒ #f and #f ```
Method: find-index pred (seq <sequence>)

Like `find`, but returns the index of the first element that satisfies pred in seq, instead of the element itself. If no element in seq satisfies pred, `#f` is returned.

 ```(find-index char-upper-case? "abraCadabra") ⇒ 4 (find-index char-numeric? "abraCadabra") ⇒ #f ```

See also `list-index` in SRFI-1 (See section List utilities).

Method: fold-right kons knil (seq <sequence>) …

Generalization of `fold-right` on lists. Like `fold`, this method applies a higher-order function kons over given sequence(s), passing the "seed" value whose default is knil. The difference between `fold` and `fold-right` is the associative order of elements on which kons is applied.

When we have one sequence, `[E0, E1, ..., En]`, `fold` and `fold-right` work as follows, respectively.

 ```fold: (kons En (kons En-1 (kons ... (kons E1 (kons E1 knil)) ...))) fold-right (kons E0 (kons E1 (kons ... (kons En-1 (kons En knil)) ...))) ```

This method isn’t defined on `<collection>`, since collections don’t care the order of elements.

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### 9.26.4 Other operations over sequences

#### Selection and searching

Note that selection and searching methods for collections can also be applied to sequences. See Selection and searching in collection.

#### Grouping

Generic function: group-sequence seq :key key test

Groups consecutive elements in a sequence seq which have the common key value. A key value of an element is obtained by applying the procedure key to the element; the default procedure is `identity`. For each element in seq, key is applied exactly once. The equal-ness of keys are compared by test procedure, whose default is `eqv?`.

 ```(group-sequence '(1 1 1 2 3 4 4 2 2 3 1 1 3)) ⇒ ((1 1 1) (2) (3) (4 4) (2 2) (3) (1 1) (3)) (group-sequence '(1 1 1 2 3 4 4 2 2 3 1 1 3) :key (cut modulo <> 2))) ⇒ ((1 1 1) (2) (3) (4 4 2 2) (3 1 1 3)) (group-sequence '#("a" "a" "b" "b" "c" "d" "d") :test string=?) ⇒ (("a" "a") ("b" "b") ("c") ("d" "d")) (group-sequence "aabbcdd" :test char=?) ⇒ ((#\a #\a) (#\b #\b) (#\c) (#\d #\d)) ```

This method is similar to Haskell’s `group`. If you want to group elements that are not adjacent, use `group-collection` (See section Selection and searching in collection).

#### Permutation and shuffling

Generic function: permute (src <sequence>) (permuter <sequence>) :optional fallback

Returns a newly created sequence of the same type as src, in which the elements are permuted from src according to permuter.

Permuter is a sequence of exact integers. When the k-th element of permuter is i, the k-th element of the result is `(ref src i)`. Therefore, the size of the result sequence is the same as the size of permuter. Permuter can be any kind of sequence, unrelated to the type of src.

It is allowed that the same index i can appear more than once in permuter.

 ```(permute '(a b c d) '(3 2 0 1)) ⇒ (d c a b) (permute '(a b c d) '(0 2)) ⇒ (a c) (permute '(a b c d) '(0 0 1 1 2 2)) ⇒ (a a b b c c) ```

If an integer in permuter is out of the valid range as the index of src, then an error is signaled unless fallback is given. If fallback is given, what value is used depends on the result of `(ref src i fallback)`—which usually returns fallback for the out-of-range index i.

 ```(permute '#(a b c) '(3 2 1 0) 'foo) ⇒ #(foo c b a) (permute "!,HWdelor" #(2 5 6 6 7 1 -1 3 7 8 6 4 0) #\space) ⇒ "Hello, World!" ```
Generic function: permute-to (class <class>) (src <sequence>) (permuter <sequence>) :optional fallback

Like `permute`, but the result will be an instance of the given class instead of the class of src.

 ```(permute-to '(#\a #\b #\c #\d #\r) '(0 1 4 0 2 0 3 0 1 4 0)) ⇒ "abracadabra" ```
Generic function: permute! (src <sequence>) (permuter <sequence>) :optional fallback

Also like `permute`, but the result is stored back to src. Src must be a mutable sequence, and the length of src and permuter must be the same.

Generic function: shuffle (src <sequence>) :optional random-source

Returns a new sequence of the same type and size as src, in which elements are randomly permuted.

 ```(shuffle '(a b c d e)) ⇒ (e b d c a) (shuffle "abcde") ⇒ "bacde" ```

This generic function uses `srfi-27` (See section `srfi-27` - Sources of Random Bits). By default it uses `default-random-source`, but you can pass an alternative random source by the optional argument.

Generic function: shuffle-to (class <class>) (src <sequence>) :optional random-source

Like `shuffle`, except that the result will be an instance of class instead of the class of src.

Generic function: shuffle! (src <sequence>) :optional random-source

Like `shuffle`, but the result is stored back to src. Src must be a mutable sequence.

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### 9.26.5 Implementing sequence

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