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Higher-Order Functions

This module adds some useful higher-order functions, additional to the standard Higher-Order Functions provided by the official specification.

Removed: Some functions have been removed in favor of new XQuery 4 standard functions:

BaseX 10	XQuery 4
`hof:drop-while`	`fn:subsequence-where`
`hof:id`, `hof:const`	`fn:identity`
`hof:until`	`fn:while-do`, `fn:do-until`
`hof:take-while`	`fn:take-while`

Conventions

All functions in this module are assigned to the http://basex.org/modules/hof namespace, which is statically bound to the hof prefix.

Loops

`hof:fold-left1`

Signature

Signature	hof:fold-left1( $input as item()+, $action as fn(item(), item()) as item() ) as item()*
Summary	Works the same as `fn:fold-left`, but does not need a seed, because the sequence must be non-empty.
Examples	`hof:fold-left1(1 to 10, op('+'))` Result: `55` `hof:fold-left1((), fn($a, $b) { $a + $b })` Raises `XPTY0004`, because `$seq` has to be non-empty.

hof:fold-left1(
  $input   as item()+,
  $action  as fn(item()*, item()) as item()*
) as item()*

Summary Works the same as fn:fold-left, but does not need a seed, because the sequence must be non-empty.

Examples

hof:fold-left1(1 to 10, op('+'))

Result: 55

hof:fold-left1((), fn($a, $b) { $a + $b })

Raises XPTY0004, because $seq has to be non-empty.

`hof:scan-left`

Signature

Signature	hof:scan-left( $input as item(), $zero as item(), $action as fn(item(), item()) as item() ) as item()*
Summary	This function is similar to `fn:fold-left`, but it returns a list of successive reduced values from the left. It is equivalent to: `declare function hof:scan-left($input, $acc, $action) { if (empty($input)) then $acc else ( $acc, hof:scan-left(tail($input), $action($acc, head($input)), $action) ) };`
Examples	`hof:scan-left(1 to 5, 0, op('+'))` Result: `0, 1, 3, 6, 10, 15`. Computes triangular numbers.

hof:scan-left(
  $input   as item()*,
  $zero    as item()*,
  $action  as fn(item()*, item()) as item()*
) as item()*

Summary

This function is similar to fn:fold-left, but it returns a list of successive reduced values from the left. It is equivalent to:

declare function hof:scan-left($input, $acc, $action) {
  if (empty($input)) then $acc else (
    $acc,
    hof:scan-left(tail($input), $action($acc, head($input)), $action)
  )
};

Examples

hof:scan-left(1 to 5, 0, op('+'))

Result: 0, 1, 3, 6, 10, 15. Computes triangular numbers.

Sorting

`hof:top-k-by`

Signature

Signature	hof:top-k-by( $input as item(), $key as fn(item()) as item(), $k as xs:integer ) as item()
Summary	Returns the `$k` items in `$input` that are greatest when sorted by the result of `$key` applied to the item. The function is a much more efficient implementation of the following scheme: `let $results := ( for $item in $input order by $key($item) descending return $item ) return subsequence($results, 1, $k)`
Examples	`hof:top-k-by(1 to 1000, identity#1, 5)` Result: `1000, 999, 998, 997, 996` `hof:top-k-by(1 to 1000, fn { -. }, 3)` Result: `1, 2, 3` `hof:top-k-by(<x a='1' b='2' c='3'/>/@*, xs:integer#1, 2)/local-name()` Result: `'c', 'b'`

hof:top-k-by(
  $input  as item()*,
  $key    as fn(item()) as item(),
  $k      as xs:integer
) as item()*

Summary

Returns the $k items in $input that are greatest when sorted by the result of $key applied to the item. The function is a much more efficient implementation of the following scheme:

let $results := (
  for $item in $input
  order by $key($item) descending
  return $item
)
return subsequence($results, 1, $k)

Examples

hof:top-k-by(1 to 1000, identity#1, 5)

Result: 1000, 999, 998, 997, 996

hof:top-k-by(1 to 1000, fn { -. }, 3)

Result: 1, 2, 3

hof:top-k-by(<x a='1' b='2' c='3'/>/@*, xs:integer#1, 2)/local-name()

Result: 'c', 'b'

`hof:top-k-with`

Signature

Signature	hof:top-k-with( $input as item(), $comparator as fn(item(), item()) as xs:boolean, $k as xs:integer ) as item()
Summary	Returns the `$k` items in `$input` that are greatest when sorted in the order of the less-than predicate `$comparator`. The function is a general version of `hof:top-k-by`.
Examples	`hof:top-k-with(1 to 1000, fn($a, $b) { $a lt $b }, 5)` Result: `1000, 999, 998, 997, 996` `hof:top-k-with(-5 to 5, fn($a, $b) { abs($a) gt abs($b) }, 5)` Result: `0, 1, -1, 2, -2`

hof:top-k-with(
  $input       as item()*,
  $comparator  as fn(item(), item()) as xs:boolean,
  $k           as xs:integer
) as item()*

Summary Returns the $k items in $input that are greatest when sorted in the order of the less-than predicate $comparator. The function is a general version of hof:top-k-by.

Examples

hof:top-k-with(1 to 1000, fn($a, $b) { $a lt $b }, 5)

Result: 1000, 999, 998, 997, 996

hof:top-k-with(-5 to 5, fn($a, $b) { abs($a) gt abs($b) }, 5)

Result: 0, 1, -1, 2, -2

Changelog

Version 11.0

Removed: hof:until (replaced with fn:while-do/fn:do-until, hof:id/hof:const (replaced with fn:identity, hof:drop-while (replaced with fn:subsequence-where), hof:take-while (replaced with fn:take-while)

Version 9.5

Added: hof:drop-while

Version 8.1

Added: hof:scan-left, hof:take-while

Version 7.2

Added: hof:top-k-by, hof:top-k-with
Removed: hof:iterate

Version 7.0

Added: The module was added with Version 7.0.

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