# Title

Immutable Deques

# Author

Kevin Wortman, John Cowan

# Status

This SRFI is currently in final status. Here is an explanation of each status that a SRFI can hold. To provide input on this SRFI, please send email to `srfi-134@nospamsrfi.schemers.org`. To subscribe to the list, follow these instructions. You can access previous messages via the mailing list archive.

- Received: 2015/12/9
- 60-day deadline: 2016/2/7
- Draft #1 published: 2015/12/9
- Draft #2 published: 2016/1/20
- Draft #3 published: 2016/1/31
- Draft #4 published: 2016/2/6
- Draft #5 published: 2016/2/9 (mostly code changes)
- Draft #6 published: 2016/4/7
- Draft #7 published: 2016/4/12
- Draft #8 published: 2016/5/9
- Draft #9 published: 2016/5/28
- Finalized: 2016/7/1

# Abstract

This SRFI defines immutable deques. A deque is a double-ended queue, a sequence which allows elements to be added or removed efficiently from either end. A structure is immutable when all its operations leave the structure unchanged. Note that none of the procedures specified here ends with an exclamation point.

# Rationale

A double-ended queue, or deque (pronounced "deck") is a sequential data structure which allows elements to be added or removed from either end in amortized O(1) time. It is a generalization of both a queue and a stack, and can be used as either by disregarding the irrelevant procedures.

This SRFI describes immutable deques, or ideques. Immutable structures are sometimes called persistent and are closely related to pure functional (a.k.a. pure) structures. The availability of immutable data structures facilitates writing efficient programs in the pure-functional style. Immutable deques can also be seen as a bidirectional generalization of immutable lists, and some of the procedures documented below are most useful in that context. Unlike the immutable lists of SRFI 116, it is efficient to produce modified versions of an ideque; unlike the list queues of SRFI 117, it is possible to efficiently return an updated version of an ideque without mutating any earlier versions of it.

The specification was designed jointly by Kevin Wortman and John Cowan. John Cowan is the editor and shepherd. The two-list implementation was written by John Cowan.

# Procedure index

Constructors: `ideque, ideque-tabulate, ideque-unfold, ideque-unfold-right`

Predicates: `ideque?, ideque-empty?, ideque=, ideque-any, ideque-every`

Queue operations: `ideque-front, ideque-back, ideque-remove-front, ideque-remove-back, ideque-add-front, ideque-add-back`

Other accessors: `ideque-ref, ideque-take, ideque-take-right, ideque-drop, ideque-drop-right, ideque-split-at`

The whole ideque: `ideque-length, ideque-append, ideque-reverse, ideque-count, ideque-zip`

Mapping: `ideque-map, ideque-filter-map, ideque-for-each, ideque-for-each-right, ideque-fold, ideque-fold-right, ideque-append-map`

Filtering: `ideque-filter, ideque-remove, ideque-partition`

Searching: `ideque-find, ideque-find-right, ideque-take-while, ideque-take-while-right, ideque-drop-while, ideque-drop-while-right, ideque-span, ideque-break`

Conversion: `list->ideque, ideque->list, generator->ideque, ideque->generator`

# Specification

We specify required time efficiency upper bounds using big-O notation. We note when, in some cases, there is "slack" between the required bound and the theoretically optimal bound for an operation. Implementations may use data structures with amortized time bounds, but should document which bounds hold in only an amortized sense.

Deques are disjoint from all other Scheme types.

## Constructors

`(ideque` element ...`)`

Returns an ideque containing the elements. The first element (if any) will be at the front of the ideque and the last element (if any) will be at the back. Takes O(n) time, where n is the number of elements.

`(ideque-tabulate` n proc`)`

Invokes the predicate proc on every exact integer from 0 (inclusive) to n (exclusive). Returns an ideque containing the results in order of generation. Takes O(n) time.

`(ideque-unfold` stop? mapper successor seed`)`

Invokes the predicate stop? on seed. If it returns false, generate the next result by applying mapper to seed, generate the next seed by applying successor to seed, and repeat this algorithm with the new seed. If stop? returns true, return an ideque containing the results in order of accumulation. Takes O(n) time.

`(ideque-unfold-right` stop? mapper successor seed`)`

Invokes the predicate stop? on seed. If it returns false, generate the next result by applying mapper to seed, generate the next seed by applying successor to seed, and repeat the algorithm with the new seed. If stop? returns true, return an ideque containing the results in reverse order of accumulation. Takes O(n) time.

## Predicates

`(ideque?` x`)`

Returns `#t` if x is an ideque, and `#f` otherwise. Takes O(1) time.

`(ideque-empty?` ideque`)`

Returns `#t` if ideque contains zero elements, and `#f` otherwise. Takes O(1) time.

`(ideque=` elt= ideque ...`)`

Determines ideque equality, given an element-equality procedure. Ideque A equals ideque B if they are of the same length, and their corresponding elements are equal, as determined by elt=. If the element-comparison procedure's first argument is from idequei, then its second argument is from idequei+1, i.e. it is always called as `(`elt= a b`)` for a an element of ideque A, and b an element of ideque B.

In the n-ary case, every idequei is compared to idequei+1 (as opposed, for example, to comparing ideque1 to every idequei, for i > 1). If there are zero or one ideque arguments, `ideque=` simply returns true. The name does not end in a question mark for compatibility with the SRFI-1 procedure `list=`.

Note that the dynamic order in which the elt= procedure is applied to pairs of elements is not specified. For example, if `ideque=` is applied to three ideques, A, B, and C, it may first completely compare A to B, then compare B to C, or it may compare the first elements of A and B, then the first elements of B and C, then the second elements of A and B, and so forth.

The equality procedure must be consistent with `eq?`. Note that this implies that two ideques which are `eq?` are always `ideque=`, as well; implementations may exploit this fact to "short-cut" the element-by-element comparisons.

`(ideque-any` pred ideque`)`

`(ideque-every` pred ideque`)`

Invokes pred on the elements of the ideque in order until one call returns a true/false value, which is then returned. If there are no elements, returns `#f`/`#t`. Takes O(n) time.

## Queue operations

`(ideque-front` ideque`)`

`(ideque-back` ideque`)`

Returns the front/back element of ideque. It is an error for ideque to be empty. Takes O(1) time.

`(ideque-remove-front` ideque`)`

`(ideque-remove-back` ideque`)`

Returns an ideque with the front/back element of ideque removed. It is an error for ideque to be empty. Takes O(1) time.

`(ideque-add-front` ideque obj`)`

`(ideque-add-back` ideque obj`)`

Returns an ideque with obj pushed to the front/back of ideque. Takes O(1) time.

## Other accessors

`(ideque-ref` ideque n`)`

Returns the nth element of ideque. It is an error unless n is less than the length of ideque. Takes O(n) time.

`(ideque-take` ideque n`)`

`(ideque-take-right` ideque n`)`

Returns an ideque containing the first/last n elements of ideque. It is an error if n is greater than the length of ideque. Takes O(n) time.

`(ideque-drop` ideque n`)`

`(ideque-drop-right` ideque n`)`

Returns an ideque containing all but the first/last n elements of ideque. It is an error if n is greater than the length of ideque. Takes O(n) time.

`(ideque-split-at` ideque n`)`

Returns two values, the results of `(ideque-take` ideque n`)` and `(ideque-drop` ideque n`)` respectively, but may be more efficient. Takes O(n) time.

## The whole ideque

`(ideque-length` ideque`)`

Returns the length of ideque as an exact integer. May take O(n) time, though O(1) is optimal.

`(ideque-append` ideque ...`)`

Returns an ideque with the contents of the ideque followed by the others, or an empty ideque if there are none. Takes O(kn) time, where k is the number of ideques and n is the number of elements involved, though O(k log n) is possible.

`(ideque-reverse` ideque`)`

Returns an ideque containing the elements of ideque in reverse order. Takes O(1) time.

`(ideque-count` pred ideque`)`

Pred is a procedure taking a single value and returning a single value. It is applied element-wise to the elements of ideque, and a count is tallied of the number of elements that produce a true value. This count is returned. Takes O(n) time. The dynamic order of calls to pred is unspecified.

`(ideque-zip` ideque1 ideque2 ...`)`

Returns an ideque of lists (not ideques) each of which contains the corresponding elements of ideques in the order specified. Terminates when all the elements of any of the ideques have been processed. Takes O(kn) time, where k is the number of ideques and n is the number of elements in the shortest ideque.

## Mapping

`(ideque-map` proc ideque`)`

Applies proc to the elements of ideque and returns an ideque containing the results in order. The dynamic order of calls to proc is unspecified. Takes O(n) time.

`(ideque-filter-map` proc ideque`)`

Applies proc to the elements of ideque and returns an ideque containing the true (i.e. non-`#f`) results in order. The dynamic order of calls to proc is unspecified. Takes O(n) time.

`(ideque-for-each` proc ideque`)`

`(ideque-for-each-right` proc ideque`)`

Applies proc to the elements of ideque in forward/reverse order and returns an unspecified result. Takes O(n) time.

`(ideque-fold` proc nil ideque`)`

`(ideque-fold-right` proc nil ideque`)`

Invokes proc on the elements of ideque in forward/reverse order, passing the result of the previous invocation as a second argument. For the first invocation, nil is used as the second argument. Returns the result of the last invocation, or nil if there was no invocation. Takes O(n) time.

`(ideque-append-map` proc ideque`)`

Applies proc to the elements of ideque. It is an error if the result is not a list. Returns an ideque containing the elements of the lists in order. Takes O(n) time, where n is the number of elements in all the lists returned.

## Filtering

`(ideque-filter` pred ideque`)`

`(ideque-remove` pred ideque`)`

Returns an ideque containing the elements of ideque that do/do not satisfy pred. Takes O(n) time.

`(ideque-partition` proc ideque`)`

Returns two values, the results of `(ideque-filter` pred ideque`)` and `(ideque-remove` pred ideque`)` respectively, but may be more efficient. Takes O(n) time.

## Searching

`(ideque-find` pred ideque [ failure ]`)`

`(ideque-find-right` pred ideque [ failure ]`)`

Returns the first/last element of ideque that satisfies pred. If there is no such element, returns the result of invoking the thunk failure; the default thunk is `(lambda () #f)`. Takes O(n) time.

`(ideque-take-while` pred ideque`)`

`(ideque-take-while-right` pred ideque`)`

Returns an ideque containing the longest initial/final prefix of elements in ideque all of which satisfy pred. Takes O(n) time.

`(ideque-drop-while` pred ideque`)`

`(ideque-drop-while-right` pred ideque`)`

Returns an ideque which omits the longest initial/final prefix of elements in ideque all of which satisfy pred, but includes all other elements of ideque. Takes O(n) time.

`(ideque-span` pred ideque`)`

`(ideque-break` pred ideque`)`

Returns two values, the initial prefix of the elements of ideque which do/do not satisfy pred, and the remaining elements. Takes O(n) time.

## Conversion

`(list->ideque` list`)`

`(ideque->list` ideque`)`

Conversion between ideque and list structures. FIFO order is preserved, so the front of a list corresponds to the front of an ideque. Each operation takes O(n) time.

`(generator->ideque` generator`)`

`(ideque->generator` ideque`)`

Conversion between SRFI 121 generators and ideques. Each operation takes O(n) time. A generator is a procedure that is called repeatedly with no arguments to generate consecutive values, and returns an end-of-file object when it has no more values to return.

# Implementation

The sample implementation is in the in the `ideque-2list` subdirectory of the repository for this SRFI. It is an implementation based on two Scheme lists, one for the front and another (in reverse element order) for the back. The cost of `ideque-front`, `ideque-back`, `ideque-remove-front`, and `ideque-remove-back` are amortized O(1). An implementation based on finger trees may be added later.

# Copyright

Copyright (C) John Cowan, Kevin Wortman (2015). 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.