43: Vector library

by Taylor Campbell


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Table of Contents

1. Abstract

This SRFI proposes a comprehensive and complete library of vector operations accompanied by a freely available and complete reference implementation. The reference implementation is unencumbered by copyright, and useable with no modifications on any Scheme system that is R5RS-compliant. It also provides several hooks for implementation-specific optimization as well.

Because this SRFI is more of a library or module specification than a request for additions to readers or any other internal implementation detail, in an implementation that supports a module or structure or package or library or unit (et cetera) systems, these procedures should be contained in a module / structure / package / library / unit called vector-lib.

2. Rationale

R5RS provides very few list-processing procedures, for which reason SRFI 1 (list-lib) exists. However, R5RS provides even fewer vector operations — while it provides mapping, appending, et cetera operations for lists, it specifies only nine vector manipulation operations —:

Many Scheme implementations provide several vector operations beyond the miniscule set that R5RS defines (the typical vector-append, vector-map, et cetera), but often these procedures have different names, take arguments in different orders, don't take the same number of arguments, or have some other flaw that makes them unportable. For this reason, this SRFI is proposed.

It should be noted that no vector sorting procedures are provided by this SRFI, because there already is a SRFI for such a purpose (SRFI 32 (sort-lib)), which includes routines for sorting not only vectors but also lists.

3. Procedure Index

Here is an index of the procedures provided by this package. Those marked by bold are provided in R5RS and those marked by bold italic are defined by R5RS but are modified from their original definitions.

· Constructors

make-vector vector
vector-unfold vector-unfold-right
vector-copy vector-reverse-copy
vector-append vector-concatenate

· Predicates


· Selectors


· Iteration

vector-fold vector-fold-right
vector-map vector-map!

· Searching

vector-index vector-index-right
vector-skip vector-skip-right
vector-any vector-every

· Mutators

vector-set! vector-swap!
vector-copy! vector-reverse-copy!

· Conversion

vector->list reverse-vector->list
list->vector reverse-list->vector

4. Procedures

In this section containing specifications of procedures, the following notation is used to specify parameters and return values:

(f arg1 arg2 ···) -> something
Indicates a function f takes the parameters arg1 arg2 ··· and returns a value of the type something. If something is unspecified, then what f returns is implementation-dependant; this SRFI does not specify what it returns, and in order to write portable code, the return value should be ignored.

The argument in this place must be a vector, i.e. it must satisfy the predicate vector?.

i, j, start, size
The argument in this place must be a nonnegative integer, i.e. it must satisfy the predicates integer? and either zero? or positive?. The third case of it indicates the index at which traversal begins; the fourth case of it indicates the size of a vector.

The argument in this place must be a positive integer, i.e. it must satisfy the predicates integer? and positive?. This indicates the index directly before which traversal will stop — processing will occur until the the index of the vector is end. It is the closed right side of a range.

The argument in this place must be a function of one or more arguments, returning exactly one value.

The argument in this place must be a function of one or more arguments that returns one value, which is treated as a boolean.

x, y, z, seed, knil, fill, key, value
The argument in this place may be any Scheme value.

Indicates that something is an optional argument; it needn't necessarily be applied. Something needn't necessarily be one thing; for example, this usage of it is perfectly valid:

   [start [end]]

and is indeed used quite often.

something ···
Indicates that zero or more somethings are allowed to be arguments.

something1 something2 ···
Indicates that at least one something must be arguments.

something1 something2 ··· somethingn
Exactly equivalent to the previous argument notation, but this also indicates that n will be used later in the procedure description.

It should be noted that all of the procedures that iterate across multiple vectors in parallel stop iterating and produce the final result when the end of the shortest vector is reached. The sole exception is vector=, which automatically returns #f if the vectors' lengths vary.

4.1. Constructors

(make-vector size [fill]) -> vector
[R5RS] Creates and returns a vector of size size, optionally filling it with fill. The default value of fill is unspecified.


(make-vector 5 3)
#(3 3 3 3 3)

(vector x ···) -> vector
[R5RS] Creates and returns a vector whose elements are x ···.


(vector 0 1 2 3 4)
#(0 1 2 3 4)

(vector-unfold f length initial-seed ···) -> vector
The fundamental vector constructor. Creates a vector whose length is length and iterates across each index k between 0 and length, applying f at each iteration to the current index and current seeds, in that order, to receive n + 1 values: first, the element to put in the kth slot of the new vector and n new seeds for the next iteration. It is an error for the number of seeds to vary between iterations.


(vector-unfold (λ (i x) (values x (- x 1)))
                 10 0)

#(0 -1 -2 -3 -4 -5 -6 -7 -8 -8)

Construct a vector of the sequence of integers in the range [0,n).
(vector-unfold values n)
#(0 1 2 ··· n-2 n-1)

Copy vector.

(vector-unfold (λ (i) (vector-ref vector i))
                 (vector-length vector))

(vector-unfold-right f length initial-seed ···) -> vector
Like vector-unfold, but it uses f to generate elements from right-to-left, rather than left-to-right.


Construct a vector in reverse of the integers in the range [0,n).

(vector-unfold-right (λ (i x) (values x (+ x 1))) n 0)
#(n-1 n-2 ··· 2 1 0)

Reverse vector.

(vector-unfold-right (λ (i x) (values (vector-ref vector x) (+ x 1)))
                       (vector-length vector)

(vector-copy vec [start [end [fill]]]) -> vector
Allocates a new vector whose length is end - start and fills it with elements from vec, taking elements from vec starting at index start and stopping at index end. start defaults to 0 and end defaults to the value of (vector-length vec). If end extends beyond the length of vec, the slots in the new vector that obviously cannot be filled by elements from vec are filled with fill, whose default value is unspecified.


(vector-copy '#(a b c d e f g h i))
#(a b c d e f g h i)

(vector-copy '#(a b c d e f g h i) 6)
#(g h i)

(vector-copy '#(a b c d e f g h i) 3 6)
#(d e f)

(vector-copy '#(a b c d e f g h i) 6 12 'x)
#(g h i x x x)

(vector-reverse-copy vec [start [end]]) -> vector
Like vector-copy, but it copies the elements in the reverse order from vec.


(vector-reverse-copy '#(5 4 3 2 1 0) 1 5)
#(1 2 3 4)

(vector-append vec ···) -> vector
Returns a newly allocated vector that contains all elements in order from the subsequent locations in vec ···.


(vector-append '#(x) '#(y))
#(x y)

(vector-append '#(a) '#(b c d))
#(a b c d)

(vector-append '#(a #(b)) '#(#(c)))
#(a #(b) #(c))

(vector-concatenate list-of-vectors) -> vector
Appends each vector in list-of-vectors. This is equivalent to:

(apply vector-append list-of-vectors)

However, it may be implemented better.


(vector-concatenate '(#(a b) #(c d)))
#(a b c d)

4.2. Predicates

(vector? x) -> boolean
[R5RS] Disjoint type predicate for vectors: this returns #t if x is a vector, and #f if otherwise.


(vector? '#(a b c))

(vector? '(a b c))

(vector? #t)

(vector? '#())

(vector? '())

(vector-empty? vec) -> boolean
Returns #t if vec is empty, i.e. its length is 0, and #f if not.


(vector-empty? '#(a))

(vector-empty? '#(()))

(vector-empty? '#(#()))

(vector-empty? '#())

(vector= elt=? vec ···) -> boolean
Vector structure comparator, generalized across user-specified element comparators. Vectors a and b are considered equal by vector= iff their lengths are the same, and for each respective elements Ea and Eb, (elt=? Ea Eb) returns a true value. Elt=? is always applied to two arguments. Element comparison must be consistent with eq; that is, if (eq? Ea Eb) results in a true value, then (elt=? Ea Eb) must also result in a true value. This may be exploited to avoid unnecessary element comparisons. (The reference implementation does, but it does not consider the situation where elt=? is in fact itself eq? to avoid yet more unnecessary comparisons.)

If there are only zero or one vector arguments, #t is automatically returned. The dynamic order in which comparisons of elements and of vectors are performed is left completely unspecified; do not rely on a particular order.


(vector= eq? '#(a b c d) '#(a b c d))

(vector= eq? '#(a b c d) '#(a b d c))

(vector= = '#(1 2 3 4 5) '#(1 2 3 4))

(vector= = '#(1 2 3 4) '#(1 2 3 4))

The two trivial cases.

(vector= eq?)

(vector= eq? '#(a))

Note the fact that we don't use vector literals in the next two — it is unspecified whether or not literal vectors with the same external representation are eq?.

(vector= eq? (vector (vector 'a)) (vector (vector 'a)))

(vector= equal? (vector (vector 'a)) (vector (vector 'a)))

4.3. Selectors

(vector-ref vec i) -> value
[R5RS] Vector element dereferencing: returns the value that the location in vec at i is mapped to in the store. Indexing is based on zero. I must be within the range [0, (vector-length vec)).


(vector-ref '#(a b c d) 2)

(vector-length vec) -> exact nonnegative integer
[R5RS] Returns the length of vec, the number of locations reachable from vec. (The careful word 'reachable' is used to allow for 'vector slices,' whereby vec refers to a larger vector that contains more locations that are unreachable from vec. This SRFI does not define vector slices, but later SRFIs may.)


(vector-length '#(a b c))

4.4. Iteration

(vector-fold kons knil vec1 vec2 ···) -> value
The fundamental vector iterator. Kons is iterated over each index in all of the vectors, stopping at the end of the shortest; kons is applied as (kons i state (vector-ref vec1 i) (vector-ref vec2 i) ···) where state is the current state value — the current state value begins with knil, and becomes whatever kons returned at the respective iteration —, and i is the current index.

The iteration is strictly left-to-right.


Find the longest string's length in vector-of-strings.
(vector-fold (λ (index len str) (max (string-length str) len))
               0 vector-of-strings)

Produce a list of the reversed elements of vec.
(vector-fold (λ (index tail elt) (cons elt tail))
               '() vec)

Count the number of even numbers in vec.
(vector-fold (λ (index counter n)
                 (if (even? n) (+ counter 1) counter))
               0 vec)

(vector-fold-right kons knil vec1 vec2 ···) -> value
Similar to vector-fold, but it iterates right to left instead of left to right.


Convert a vector to a list.
(vector-fold-right (λ (index tail elt) (cons elt tail))
                     '() '#(a b c d))

(a b c d)

(vector-map f vec1 vec2 ···) -> vector
Constructs a new vector of the shortest size of the vector arguments. Each element at index i of the new vector is mapped from the old vectors by (f i (vector-ref vec1 i) (vector-ref vec2 i) ···). The dynamic order of application of f is unspecified.


(vector-map (λ (i x) (* x x))
              (vector-unfold (λ (i x) (values x (+ x 1))) 4 1))

#(1 4 9 16)

(vector-map (λ (i x y) (* x y))
              (vector-unfold (λ (i x) (values x (+ x 1))) 5 1)
              (vector-unfold (λ (i x) (values x (- x 1))) 5 5))

#(5 8 9 8 5)

(let ((count 0))
   (vector-map (λ (ignored-index ignored-elt)
                 (set! count (+ count 1))
               '#(a b)))
#(1 2) OR #(2 1)

(vector-map (λ (i elt) (+ i elt)) '#(1 2 3 4))
#(1 3 5 7)

(vector-map! f vec1 vec2 ···) -> unspecified
Similar to vector-map, but rather than mapping the new elements into a new vector, the new mapped elements are destructively inserted into vec1. Again, the dynamic order of application of f unspecified, so it is dangerous for f to apply either vector-ref or vector-set! to vec1 in f.

(vector-for-each f vec1 vec2 ···) -> unspecified
Simple vector iterator: applies f to each index in the range [0, length), where length is the length of the smallest vector argument passed, and the respective list of parallel elements from vec1 vec2 ··· at that index. In contrast with vector-map, f is reliably applied to each subsequent elements, starting at index 0, in the vectors.


(vector-for-each (λ (i x) (display x) (newline))
                 '#("foo" "bar" "baz" "quux" "zot"))

(vector-count pred? vec1 vec2 ···) -> exact nonnegative integer
Counts the number of parallel elements in the vectors that satisfy pred?, which is applied, for each index i in the range [0, length) — where length is the length of the smallest vector argument —, to i and each parallel element in the vectors at that index, in order.


(vector-count (λ (i elt) (even? elt)) '#(3 1 4 1 5 9 2 5 6))

(vector-count (λ (i x y) (< x y)) '#(1 3 6 9) '#(2 4 6 8 10 12))

4.5. Searching

(vector-index pred? vec1 vec2 ···) -> exact nonnegative integer or #f
Finds & returns the index of the first elements in vec1 vec2 ··· that satisfy pred?. If no matching element is found by the end of the shortest vector, #f is returned.


(vector-index even? '#(3 1 4 1 5 9))

(vector-index < '#(3 1 4 1 5 9 2 5 6) '#(2 7 1 8 2))

(vector-index = '#(3 1 4 1 5 9 2 5 6) '#(2 7 1 8 2))

(vector-index-right pred? vec1 vec2 ···) -> exact nonnegative integer or #f
Like vector-index, but it searches right-to-left, rather than left-to-right, and all of the vectors must have the same length.

(vector-skip pred? vec1 vec2 ···) -> exact nonnegative integer or #f
Finds & returns the index of the first elements in vec1 vec2 ··· that do not satisfy pred?. If all the values in the vectors satisfy pred? until the end of the shortest vector, this returns #f. This is equivalent to:

(vector-index (λ (x1 x2 ···) (not (pred? x1 x1 ···)))
                    vec1 vec2 ···)


(vector-skip number? '#(1 2 a b 3 4 c d))

(vector-skip-right pred? vec1 vec2 ···) -> exact nonnegative integer or #f
Like vector-skip, but it searches for a non-matching element right-to-left, rather than left-to-right, and all of the vectors must have the same length. This is equivalent to:

(vector-index-right (λ (x1 x2 ···) (not (pred? x1 x1 ···)))
                          vec1 vec2 ···)

(vector-binary-search vec value cmp) -> exact nonnegative integer or #f
Similar to vector-index and vector-index-right, but instead of searching left to right or right to left, this performs a binary search. cmp should be a procedure of two arguments and return a negative integer, which indicates that its first argument is less than its second, zero, which indicates that they are equal, or a positive integer, which indicates that the first argument is greater than the second argument. An example cmp might be:

(λ (char1 char2)
  (cond ((char<? char1 char2) -1)
        ((char=? char1 char2) 0)
        (else 1)))

(vector-any pred? vec1 vec2 ···) -> value or #f
Finds the first set of elements in parallel from vec1 vec2 ··· for which pred? returns a true value. If such a parallel set of elements exists, vector-any returns the value that pred? returned for that set of elements. The iteration is strictly left-to-right.

(vector-every pred? vec1 vec2 ···) -> value or #f
If, for every index i between 0 and the length of the shortest vector argument, the set of elements (vector-ref vec1 i) (vector-ref vec2 i) ··· satisfies pred?, vector-every returns the value that pred? returned for the last set of elements, at the last index of the shortest vector. The iteration is strictly left-to-right.

4.6. Mutators

(vector-set! vec i value) -> unspecified
[R5RS] Assigns the contents of the location at i in vec to value.

(vector-swap! vec i j) -> unspecified
Swaps or exchanges the values of the locations in vec at i & j.

(vector-fill! vec fill [start [end]]) -> unspecified
[R5RS+] Assigns the value of every location in vec between start, which defaults to 0 and end, which defaults to the length of vec, to fill.

(vector-reverse! vec [start [end]]) -> unspecified
Destructively reverses the contents of the sequence of locations in vec between start and end. Start defaults to 0 and end defaults to the length of vec. Note that this does not deeply reverse.

(vector-copy! target tstart source [sstart [send]]) -> unspecified
Copies a block of elements from source to target, both of which must be vectors, starting in target at tstart and starting in source at sstart, ending when send - sstart elements have been copied. It is an error for target to have a length less than tstart + (send - sstart). Sstart defaults to 0 and send defaults to the length of source.

(vector-reverse-copy! target tstart source [sstart [send]]) -> unspecified
Like vector-copy!, but this copies the elements in the reverse order. It is an error if target and source are identical vectors and the target & source ranges overlap; however, if tstart = sstart, vector-reverse-copy! behaves as (vector-reverse! target tstart send) would.

4.7. Conversion

(vector->list vec [start [end]]) -> proper-list
[R5RS+] Creates a list containing the elements in vec between start, which defaults to 0, and end, which defaults to the length of vec.

(reverse-vector->list vec [start [end]]) -> proper-list
Like vector->list, but the resulting list contains the elements in reverse between the the specified range.

(list->vector proper-list) -> vector
[R5RS+] Creates a vector of elements from proper-list.

(reverse-list->vector proper-list) -> vector
Like list->vector, but the resulting list contains the elements in reverse of proper-list.

5. Reference Implementation

With this SRFI comes a complete reference implementation. It is licensed under a very open copyright with which no implementors should have any legal issues.

The reference implementation has only one non-R5RS dependency: SRFI 23's error procedure.

This reference implementation of all the procedures described in this SRFI can be found here.

6. Acknowledgements

Thanks to Olin Shivers for his wonderfully complete list and string packages; to all the members of the #scheme IRC channel on Freenode who nitpicked a great deal, but also helped quite a lot in general, and helped test the reference implementation in various Scheme systems; to Michael Burschik for his numerous comments; to Sergei Egorov for helping to narrow down the procedures; to Mike Sperber for putting up with an extremely overdue draft; to Felix Winkelmann for continually bugging me about finishing up the SRFI so that it would be only overdue and not withdrawn; and to everyone else who gave questions, comments, thoughts, or merely attention to the SRFI.

7. References

R5RS: The Revised5 Report on Scheme
R. Kelsey, W. Clinger, J. Rees (editors).
Higher-Order and Symbolic Computation, Vol. 11, No. 1, September, 1998
ACM SIGPLAN Notices, Vol. 33, No. 9, October, 1998
Available at: http://www.schemers.org/Documents/Standards/R5RS/

SRFI: Scheme Request for Implementation
The SRFI website can be found at: https://srfi.schemers.org/
The SRFIs mentioned in this document are described later.

SRFI 1: List Library
A SRFI of list processing procedures, written by Olin Shivers.
Available at: https://srfi.schemers.org/srfi-1/

SRFI 13: String Library
A SRFI of string processing procedures, written by Olin Shivers.
Available at: https://srfi.schemers.org/srfi-13/

SRFI 23: Error Reporting Mechanism
A SRFI that defines a new primitive (error) for reporting that an error occurred, written by Stephan Houben.
Available at: https://srfi.schemers.org/srfi-23/

SRFI 32: Sort Libraries (draft)
A SRFI of list and vector sorting routines, written by Olin Shivers.
Available at: https://srfi.schemers.org/srfi-32/

8. Copyright

Copyright (C) Taylor Campbell (2003). 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.


Editor: Mike Sperber