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4.10 Pairs and Lists

Pairs and Lists in The Racket Guide introduces pairs and lists.

A pair combines exactly two values. The first value is accessed with the car procedure, and the second value is accessed with the cdr procedure. Pairs are not mutable (but see Mutable Pairs and Lists).

A list is recursively defined: it is either the constant null, or it is a pair whose second value is a list.

A list can be used as a single-valued sequence (see Sequences). The elements of the list serve as elements of the sequence. See also in-list.

Cyclic data structures can be created using only immutable pairs via read or make-reader-graph. If starting with a pair and using some number of cdrs returns to the starting pair, then the pair is not a list.

See Reading Pairs and Lists for information on reading pairs and lists and Printing Pairs and Lists for information on printing pairs and lists.

Returns #t if v is a pair, #f otherwise.

Examples:

Returns #t if v is the empty list, #f otherwise.

Examples:

Returns a newly allocated pair whose first element is a and second element is d. When d is a list, the allocated pair is also a list.

Examples:

> (cons 1 2)

'(1 . 2)

> (cons 1 '())

'(1)

Returns the first element of the pair p.

Examples:

> (car '(1 2))

1

> (car '(2 . 3))

2

Returns the second element of the pair p.

Examples:

> (cdr '(1 2))

'(2)

> (cdr '(2 . 3))

3

The empty list.

Examples:

Returns #t if v is a list: either the empty list, or a pair whose second element is a list. This procedure effectively takes constant time due to internal caching (so that any necessary traversals of pairs can in principle count as an extra cost of allocating the pairs).

Examples:

Returns a newly allocated list containing the vs as its elements.

Examples:

Like

, but the last argument is used as the tail of the result, instead of the final element. The result is a list only if the last argument is a list.

Examples:

Creates a list of

elements by applying

to the integers from

to

in order. If

is the resulting list, then

is the value produced by

.

Examples:

Returns the number of elements in lst. This function takes time proportional to that length.

Examples:

Returns the element of

at position

, where the list’s first element is position

. If the list has

or fewer elements, then the

exception is raised.

The lst argument need not actually be a list; lst must merely start with a chain of at least (add1 pos) pairs.

This function takes time proportional to pos.

Examples:

Returns the list after the first

elements of

. If the list has fewer than

elements, then the

exception is raised.

The lst argument need not actually be a list; lst must merely start with a chain of at least pos pairs.

This function takes time proportional to pos.

Examples:

When given all list arguments, the result is a list that contains all of the elements of the given lists in order. The last argument is used directly in the tail of the result.

The last argument need not be a list, in which case the result is an “improper list.”

This function takes time proportional to the length of all arguments (added together) except the last argument.

Examples:

Returns a list that has the same elements as lst, but in reverse order.

This function takes time proportional to the length of lst.

Example:

Applies proc to the elements of the lsts from the first elements to the last. The proc argument must accept the same number of arguments as the number of supplied lsts, and all lsts must have the same number of elements. The result is a list containing each result of proc in order.

Examples:

'(2 3 4 5)

> (map (lambda (number1 number2)          (+ number1 number2))        '(1 2 3 4)        '(10 100 1000 10000))

'(11 102 1003 10004)

Similar to

in the sense that

is applied to each element of

, but

The andmap function is actually closer to foldl than map, since andmap doesn’t produce a list. Still, (andmap f (list x y z)) is equivalent to (and (f x) (f y) (f z)) in the same way that (map f (list x y z)) is equivalent to (list (f x) (f y) (f z)).

• the result is #f if any application of proc produces #f, in which case proc is not applied to later elements of the lsts; and

• the result is that of proc applied to the last elements of the lsts; more specifically, the application of proc to the last elements in the lsts is in tail position with respect to the andmap call.

If the lsts are empty, then #t is returned.

Examples:

Similar to

in the sense that

is applied to each element of

, but

To continue the andmap note above, (ormap f (list x y z)) is equivalent to (or (f x) (f y) (f z)).

• the result is #f if every application of proc produces #f; and

• the result is that of the first application of proc producing a value other than #f, in which case proc is not applied to later elements of the lsts; the application of proc to the last elements of the lsts is in tail position with respect to the ormap call.

If the lsts are empty, then #f is returned.

Examples:

Similar to

, but

is called only for its effect, and its result (which can be any number of values) is ignored.

Example:

Like

,

applies a procedure to the elements of one or more lists. Whereas

combines the return values into a list,

combines the return values in an arbitrary way that is determined by

.

If foldl is called with n lists, then proc must take n+1 arguments. The extra argument is the combined return values so far. The proc is initially invoked with the first item of each list, and the final argument is init. In subsequent invocations of proc, the last argument is the return value from the previous invocation of proc. The input lsts are traversed from left to right, and the result of the whole foldl application is the result of the last application of proc. If the lsts are empty, the result is init.

Unlike foldr, foldl processes the lsts in constant space (plus the space for each call to proc).

Examples:

> (foldl cons '() '(1 2 3 4))

'(4 3 2 1)

> (foldl + 0 '(1 2 3 4))

10

> (foldl (lambda (a b result)            (* result (- a b)))          1          '(1 2 3)          '(4 5 6))

-27

Like

, but the lists are traversed from right to left. Unlike

,

processes the

s in space proportional to the length of

s (plus the space for each call to

).

Examples:

The bindings in this section are provided by the sequence-tools-lib package, which acts as an extension to the base sequence libraries.

Like

, but produces a list containing all the results of applying

as well as the initial accumulator.

Examples:

Examples:

Returns a list with the elements of lst for which pred produces a true value. The pred procedure is applied to each element from first to last.

Example:

Returns a list that is like lst, omitting the first element of lst that is equal to v using the comparison procedure proc (which must accept two arguments), with v as the first argument and an element in lst as the second argument. If no element in lst is equal to v (according to proc), lst is returned unchanged.

Examples:

Changed in version 8.2.0.2 of package base: Guaranteed that the output is eq? to lst if no removal occurs.

Examples:

> (remq 2 (list 1 2 3 4 5))

'(1 3 4 5)

> (remq '(2) (list '(1) '(2) '(3)))

'((1) (2) (3))

> (remq "2" (list "1" "2" "3"))

'("1" "3")

> (remq #\c (list #\a #\b #\c))

'(#\a #\b)

Examples:

> (remv 2 (list 1 2 3 4 5))

'(1 3 4 5)

> (remv '(2) (list '(1) '(2) '(3)))

'((1) (2) (3))

> (remv "2" (list "1" "2" "3"))

'("1" "3")

> (remv #\c (list #\a #\b #\c))

'(#\a #\b)

Examples:

Added in version 8.5.0.3 of package base.

Like

, but removes from

every instance of every element of

.

Example:

Changed in version 8.2.0.2 of package base: Guaranteed that the output is eq? to lst if no removal occurs.

Example:

Example:

Examples:

Added in version 8.5.0.3 of package base.

Returns a list sorted according to the less-than? procedure, which takes two elements of lst and returns a true value if the first is less (i.e., should be sorted earlier) than the second.

The sort is stable; if two elements of lst are “equal” (i.e., less-than? does not return a true value when given the pair in either order), then the elements preserve their relative order from lst in the output list. To preserve this guarantee, use sort with a strict comparison functions (e.g., < or string<?; not <= or string<=?).

Because of the peculiar fact that the IEEE-754 number system specifies that +nan.0 is neither greater nor less than nor equal to any other number, sorting lists containing this value may produce a surprising result.

The #:key argument extract-key is used to extract a key value for comparison from each list element, where #f is replaced by (lambda (x) x) That is, the full comparison procedure is essentially

(lambda (x y)   (less-than? (extract-key x) (extract-key y)))

By default, extract-key is applied to two list elements for every comparison, but if cache-keys? is true, then the extract-key function is used exactly once for each list item. Supply a true value for cache-keys? when extract-key is an expensive operation; for example, if file-or-directory-modify-seconds is used to extract a timestamp for every file in a list, then cache-keys? should be #t to minimize file-system calls, but if extract-key is car, then cache-keys? should be #f. As another example, providing extract-key as (lambda (x) (random)) and #t for cache-keys? effectively shuffles the list.

Examples:

> (sort '(1 3 4 2) <)

'(1 2 3 4)

> (sort '("aardvark" "dingo" "cow" "bear") string<?)

'("aardvark" "bear" "cow" "dingo")

'(("aardvark") ("bear") ("cow") ("dingo"))

Locates the first element of lst that is equal to v according to is-equal?. If such an element exists, the tail of lst starting with that element is returned. Otherwise, the result is #f.

The lst argument need not actually be a list; lst must merely start with a chain of pairs until a matching element is found. If no matching element is found, then lst must be a list (and not a cyclic list). The result can be a non-list in the case that an element is found and the returned tail of lst is a non-list.

Examples:

Examples:

Added in version 8.5.0.3 of package base.

Examples:

Like

, but finds an element using

.

Examples:

Like

, but finds an element using the predicate

; an element is found when

applied to the element returns a true value.

Example:

Like

, but returns the element or

instead of a tail of

or

.

Notably, if #f is an element of lst, then the result of #f is ambiguous: it may indicate that no element satisfies proc, or may indicate that the element #f satisfies proc.

Example:

Locates the first element of

whose

is equal to

according to

. If such an element exists, the pair (i.e., an element of

) is returned. Otherwise, the result is

.

The lst argument need not actually be a list of pairs; lst must merely start with a chain of pairs contains pairs until a matching element is found. If no matching element is found, then lst must be a list of pairs (and not a cyclic list).

Examples:

Examples:

Added in version 8.5.0.3 of package base.

Like

, but finds an element using

.

Example:

Like

, but finds an element using

.

Example:

Like

, but finds an element using the predicate

; an element is found when

applied to the

of an

element returns a true value.

Example:

Example:

> (cdar '((7 6 5 4 3 2 1) 8 9))

'(6 5 4 3 2 1)

Example:

> (caaar '(((6 5 4 3 2 1) 7) 8 9))

6

Example:

> (caadr '(9 (7 6 5 4 3 2 1) 8))

7

Example:

> (cadar '((7 6 5 4 3 2 1) 8 9))

6

Example:

> (cdaar '(((6 5 4 3 2 1) 7) 8 9))

'(5 4 3 2 1)

Example:

> (cdadr '(9 (7 6 5 4 3 2 1) 8))

'(6 5 4 3 2 1)

Example:

> (cddar '((7 6 5 4 3 2 1) 8 9))

'(5 4 3 2 1)

Example:

> (caaaar '((((5 4 3 2 1) 6) 7) 8 9))

5

Example:

> (caaadr '(9 ((6 5 4 3 2 1) 7) 8))

6

Example:

> (caadar '((7 (5 4 3 2 1) 6) 8 9))

5

Example:

> (caaddr '(9 8 (6 5 4 3 2 1) 7))

6

Example:

> (cadaar '(((6 5 4 3 2 1) 7) 8 9))

5

Example:

> (cadadr '(9 (7 6 5 4 3 2 1) 8))

6

Example:

> (caddar '((7 6 5 4 3 2 1) 8 9))

5

Example:

> (cdaaar '((((5 4 3 2 1) 6) 7) 8 9))

'(4 3 2 1)

Example:

> (cdaadr '(9 ((6 5 4 3 2 1) 7) 8))

'(5 4 3 2 1)

Example:

> (cdadar '((7 (5 4 3 2 1) 6) 8 9))

'(4 3 2 1)

Example:

> (cdaddr '(9 8 (6 5 4 3 2 1) 7))

'(5 4 3 2 1)

Example:

> (cddaar '(((6 5 4 3 2 1) 7) 8 9))

'(4 3 2 1)

Example:

> (cddadr '(9 (7 6 5 4 3 2 1) 8))

'(5 4 3 2 1)

Example:

> (cdddar '((7 6 5 4 3 2 1) 8 9))

'(4 3 2 1)

The empty list.

Examples:

Example:

Examples:

The same as

, but only for lists (that are not empty).

Example:

> (first '(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15))

1

The same as

, but only for lists (that are not empty).

Example:

> (rest '(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15))

'(2 3 4 5 6 7 8 9 10 11 12 13 14 15)

Returns the second element of the list.

Example:

> (second '(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15))

2

Returns the third element of the list.

Example:

> (third '(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15))

3

Returns the fourth element of the list.

Example:

> (fourth '(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15))

4

Returns the fifth element of the list.

Example:

> (fifth '(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15))

5

Returns the sixth element of the list.

Example:

> (sixth '(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15))

6

Returns the seventh element of the list.

Example:

> (seventh '(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15))

7

Returns the eighth element of the list.

Example:

> (eighth '(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15))

8

Returns the ninth element of the list.

Example:

> (ninth '(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15))

9

Returns the tenth element of the list.

Example:

> (tenth '(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15))

10

Returns the eleventh element of the list.

Example:

> (eleventh '(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15))

11

Added in version 8.15.0.3 of package base.

Returns the twelfth element of the list.

Example:

> (twelfth '(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15))

12

Added in version 8.15.0.3 of package base.

Returns the thirteenth element of the list.

Example:

> (thirteenth '(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15))

13

Added in version 8.15.0.3 of package base.

Returns the fourteenth element of the list.

Example:

> (fourteenth '(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15))

14

Added in version 8.15.0.3 of package base.

Returns the fifteenth element of the list.

Example:

> (fifteenth '(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15))

15

Added in version 8.15.0.3 of package base.

Returns the last element of the list.

This function takes time proportional to the length of lst.

Example:

> (last '(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15))

15

Returns the last pair of a (possibly improper) list.

This function takes time proportional to the “length” of p.

Example:

Returns a newly constructed list of length k, holding v in all positions.

Example:

> (make-list 7 'foo)

'(foo foo foo foo foo foo foo)

Returns a list that is the same as

except at the specified index. The element at the specified index is

.

This function takes time proportional to pos.

Added in version 6.3 of package base.

Returns a list that is the same as lst except at the specified index. The element at the specified index is value.

This function takes time proportional to pos.

Example:

> (list-set '(zero one two) 2 "two")

'(zero one "two")

Added in version 6.3 of package base.

Like

, but returns the index of the first element found instead of the tail of the list.

Example:

Added in version 6.7.0.3 of package base.

Like

but with the predicate-searching behavior of

.

Example:

Added in version 6.7.0.3 of package base.

Like

, but returns the a list of all the indexes where the element occurs in the list instead of just the first one.

Example:

Added in version 6.7.0.3 of package base.

Example:

Added in version 6.7.0.3 of package base.

Returns a fresh list whose elements are the first

elements of

. If

has fewer than

elements, the

exception is raised.

The lst argument need not actually be a list; lst must merely start with a chain of at least pos pairs.

This function takes time proportional to pos.

Examples:

> (take '(1 2 3 4 5) 2)

'(1 2)

> (take 'non-list 0)

'()

Returns the same result as

(values (take lst pos) (drop lst pos))

except that it can be faster, but it will still take time proportional to pos.

Returns a fresh list whose elements are taken successively from lst as long as they satisfy pred. The returned list includes up to, but not including, the first element in lst for which pred returns #f.

The lst argument need not actually be a list; the chain of pairs in lst will be traversed until a non-pair is encountered.

Examples:

Drops elements from the front of lst as long as they satisfy pred.

Examples:

Returns the same result as

(values (takef lst pred) (dropf lst pred))

except that it can be faster.

Returns the

’s

-length tail. If

has fewer than

elements, then the

exception is raised.

The lst argument need not actually be a list; lst must merely end with a chain of at least pos pairs.

This function takes time proportional to the length of lst.

Examples:

Returns a fresh list whose elements are the prefix of

, dropping its

-length tail. If

has fewer than

elements, then the

exception is raised.

The lst argument need not actually be a list; lst must merely end with a chain of at least pos pairs.

This function takes time proportional to the length of lst.

Examples:

Returns the same result as

(values (drop-right lst pos) (take-right lst pos))

except that it can be faster, but it will still take time proportional to the length of lst.

Examples:

True if l is a prefix of r.

Added in version 6.3 of package base.

Returns the longest common prefix of l and r.

Added in version 6.3 of package base.

Returns the tails of l and r with the common prefix removed.

Added in version 6.3 of package base.

Returns the longest common prefix together with the tails of l and r with the common prefix removed.

Added in version 6.3 of package base.

(add-between   lst             v            [ #:before-first before-first             #:before-last before-last             #:after-last after-last             #:splice? splice?])   →   list?

  lst : list?   v : any/c   before-first : list? = '()   before-last : any/c = v   after-last : list? = '()   splice? : any/c = #f

Returns a list with the same elements as lst, but with v between each pair of elements in lst; the last pair of elements will have before-last between them, instead of v (but before-last defaults to v).

If splice? is true, then v and before-last should be lists, and the list elements are spliced into the result. In addition, when splice? is true, before-first and after-last are inserted before the first element and after the last element respectively.

Examples:

> (add-between '(x y z) 'and)

'(x and y and z)

> (add-between '(x) 'and)

'(x)

> (add-between '("a" "b" "c" "d") "," #:before-last "and")

'("a" "," "b" "," "c" "and" "d")

> (add-between '(x y z) '(-) #:before-last '(- -)                #:before-first '(begin) #:after-last '(end LF)                #:splice? #t)

'(begin x - y - - z end LF)

Examples:

> (append* '(a) '(b) '((c) (d)))

'(a b c d)

'("Alpha" ", " "Beta" ", " "Gamma")

Flattens an arbitrary S-expression structure of pairs into a list. More precisely,

is treated as a binary tree where pairs are interior nodes, and the resulting list contains all of the non-

leaves of the tree in the same order as an inorder traversal.

Examples:

Returns the first duplicate item in lst. More precisely, it returns the first x such that there was a previous y where (same? (extract-key x) (extract-key y)).

If no duplicate is found, then failure-result determines the result:

• If failure-result is a procedure, it is called (through a tail call) with no arguments to produce the result.

• Otherwise, failure-result is returned as the result.

The same? argument should be an equivalence predicate such as equal? or eqv?. The procedures equal?, eqv?, eq?, and equal-always? automatically use a dictionary for speed.

Examples:

Added in version 6.3 of package base.
Changed in version 6.11.0.2: Added the #:default optional argument.

Returns a list that has all items in lst, but without duplicate items, where same? determines whether two elements of the list are equivalent. The resulting list is in the same order as lst, and for any item that occurs multiple times, the first one is kept.

The #:key argument extract-key is used to extract a key value from each list element, so two items are considered equal if (same? (extract-key x) (extract-key y)) is true.

Like check-duplicates, if the same? argument is one of equal?, eqv?, eq?, and equal-always?, the operation can be specialized to improve performance.

Examples:

Like

, except that, if

returns

, that element is omitted from the resulting list. In other words,

is equivalent to

, but more efficient, because

avoids building the intermediate list.

Example:

Example:

Similar to

, except that two values are returned: the items for which

returns a true value, and the items for which

returns

.

The result is the same as

(values (filter pred lst) (filter (negate pred) lst))

but pred is applied to each item in lst only once.

Example:

Similar to

, but returns lists.

The resulting list holds numbers starting at start and whose successive elements are computed by adding step to their predecessor until end (excluded) is reached. If no starting point is provided, 0 is used. If no step argument is provided, 1 is used.

Like in-range, a range application can provide better performance when it appears directly in a for clause.

Examples:

> (range 10)

'(0 1 2 3 4 5 6 7 8 9)

> (range 10 20)

'(10 11 12 13 14 15 16 17 18 19)

> (range 20 40 2)

'(20 22 24 26 28 30 32 34 36 38)

> (range 20 10 -1)

'(20 19 18 17 16 15 14 13 12 11)

> (range 10 15 1.5)

'(10 11.5 13.0 14.5)

Changed in version 6.7.0.4 of package base: Adjusted to cooperate with for in the same way that in-range does.

The resulting list holds numbers starting at start and whose successive elements are computed by adding step to their predecessor until end (included) is reached. If no step argument is provided, 1 is used.

Like in-inclusive-range, an inclusive-range application can provide better performance when it appears directly in a for clause.

Examples:

Added in version 8.0.0.13 of package base.

Example:

Like

, but the meaning of the

predicate is reversed: the result is a list of all items for which

returns

.

Example:

Returns a list with all elements from lst, randomly shuffled.

Examples:

> (shuffle '(1 2 3 4 5 6))

'(3 2 1 4 5 6)

> (shuffle '(1 2 3 4 5 6))

'(5 4 6 2 3 1)

> (shuffle '(1 2 3 4 5 6))

'(6 4 2 3 1 5)

Return a list of all combinations of elements in the input list (a.k.a. the

powerset of

). If

is given, limit results to combinations of

elements.

Examples:

Returns a sequence of all combinations of elements in the input list, or all combinations of length

if

is given. Builds combinations one-by-one instead of all at once.

Examples:

Returns a list of all permutations of the input list. Note that this function works without inspecting the elements, and therefore it ignores repeated elements (which will result in repeated permutations). Raises an error if the input list contains more than 256 elements.

Examples:

Returns a sequence of all permutations of the input list. It is equivalent to

but much faster since it builds the permutations one-by-one on each iteration. Raises an error if the input list contains more than 256 elements.

Returns the first element in the list

that minimizes the result of

. Signals an error on an empty list. See also

.

Examples:

> (argmin car '((3 pears) (1 banana) (2 apples)))

'(1 banana)

> (argmin car '((1 banana) (1 orange)))

'(1 banana)

Returns the first element in the list

that maximizes the result of

. Signals an error on an empty list. See also

.

Examples:

> (argmax car '((3 pears) (1 banana) (2 apples)))

'(3 pears)

> (argmax car '((3 pears) (3 oranges)))

'(3 pears)

Groups the given list into equivalence classes, with equivalence being determined by

. Within each equivalence class,

preserves the ordering of the original list. Equivalence classes themselves are in order of first appearance in the input.

Example:

> (group-by (lambda (x) (modulo x 3)) '(1 2 1 2 54 2 5 43 7 2 643 1 2 0))

'((1 1 43 7 643 1) (2 2 2 5 2 2) (54 0))

Added in version 6.3 of package base.

Computes the n-ary cartesian product of the given lists.

Examples:

> (cartesian-product '(1 2 3) '(a b c))

'((1 a) (1 b) (1 c) (2 a) (2 b) (2 c) (3 a) (3 b) (3 c))

> (cartesian-product '(4 5 6) '(d e f) '(#t #f))

'((4 d #t)

  (4 d #f)

  (4 e #t)

  (4 e #f)

  (4 f #t)

  (4 f #f)

  (5 d #t)

  (5 d #f)

  (5 e #t)

  (5 e #f)

  (5 f #t)

  (5 f #f)

  (6 d #t)

  (6 d #f)

  (6 e #t)

  (6 e #f)

  (6 f #t)

  (6 f #f))

Added in version 6.3 of package base.

Returns a list that is like lst, omitting the first element of lst for which pred produces a true value.

Added in version 6.3 of package base.

Like

, but removes all the elements for which

produces a true value.

Added in version 6.3 of package base.

The bindings in this section are provided by the sequence-tools-lib package, which acts as an extension to the base sequence libraries.

Returns a list of sliding windows such that each window contains size elements with the window sliding step positions on each iteration. If the number of remaining elements is less than size, then those elements are dropped.

Examples:

> (windows 3 1 '(1 2 3 4))

'((1 2 3) (2 3 4))

> (windows 2 3 '(1 2 3))

'((1 2))

> (windows 1 2 '(1 2 3 4))

'((1) (3))

Returns a list such that each element is a sublist (slice) that is constructed from comparing each pair of adjacent elements. All pairs of elements that satisfy proc will be grouped together into a slice, otherwise the element will start a new slice.

Examples:

Returns a value like

, with

created by

replaced with the values that they contain, and with

created by

with an immutable hash table. No part of

is mutated; instead, parts of

are copied as necessary to construct the resulting graph, where at most one copy is created for any given value.

Since the copied values can be immutable, and since the copy is also immutable, make-reader-graph can create cycles involving only immutable pairs, vectors, boxes, and hash tables.

Only the following kinds of values are copied and traversed to detect placeholders:

• pairs

• vectors, both mutable and immutable

• boxes, both mutable and immutable

• hash tables, both mutable and immutable

• instances of a prefab structure type

• placeholders created by make-placeholder and make-hash-placeholder

Due to these restrictions, make-reader-graph creates exactly the same sort of cyclic values as read.

Example:

Changes the value of ph to v.

Returns the value of ph.

Added in version 8.5.0.3 of package base.

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