Higher-Order Functions Module

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

With Version 11, many functions have been removed in favor of new features of XQuery 4:

BaseX 10 XQuery 4
hof:drop-while fn:items-starting-where
hof:id fn:identity
hof:until fn:iterate-while
hof:take-while fn:items-before

Conventions[edit]

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

Loops[edit]

hof:fold-left1[edit]

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

hof:scan-left[edit]

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

Sorting[edit]

hof:top-k-by[edit]

Signature 
hof:top-k-by(
  $input  as item()*,
  $key    as function(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: 
(for $item in $input
 order by $key($item) descending
 return $item
)[position() <= $k]
Examples
  • hof:top-k-by(1 to 1000, hof:id#1, 5) returns 1000 999 998 997 996
  • hof:top-k-by(1 to 1000, function($x) { -$x }, 3) returns 1 2 3
  • hof:top-k-by(<x a='1' b='2' c='3'/>/@*, xs:integer#1, 2)/node-name() returns c b

hof:top-k-with[edit]

Signature 
hof:top-k-with(
  $input       as item()*,
  $comparator  as function(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 $comparator. The function is a general version of hof:top-k-by.
Examples
  • hof:top-k-with(1 to 1000, function($a, $b) { $a lt $b }, 5) returns 1000 999 998 997 996
  • hof:top-k-with(-5 to 5, function($a, $b) { abs($a) gt abs($b) }, 5) returns 0 1 -1 2 -2

Identity[edit]

hof:const[edit]

Signature 
hof:const(
  $input   as item()*,
  $ignore  as item()*
) as item()*
Summary Returns its first argument unchanged and ignores the second. This function isn’t useful on its own, but can be used as argument to other higher-order functions, e.g., when a function combining two values is expected and one only wants to retain the left one.
Examples
  • hof:const(42, 1337) returns 42.
  • With higher-order functions:
let $zip-sum := function($f, $seq1, $seq2) {
  sum(for-each-pair($seq1, $seq2, $f))
}
let $sum-all  := $zip-sum(function($a, $b) { $a + $b }, ?, ?)
let $sum-left := $zip-sum(hof:const#2, ?, ?)
return (
  $sum-all((1, 1, 1, 1, 1), 1 to 5),
  $sum-left((1, 1, 1, 1, 1), 1 to 5)
)
  • Another use-case: When inserting a key into a map, $f decides how to combine the new value with a possibly existing old one. hof:const here means ignoring the old value, so that's normal insertion.
let $insert-with := function($f, $map, $k, $v) {
  let $old := $map($k)
  let $new := if($old) then $f($v, $old) else $v
  return map:merge(($map, map:entry($k, $new)))
}
let $map := map { 'foo': 1 }
let $add := $insert-with(function($a, $b) { $a + $b }, ?, ?, ?)
let $ins := $insert-with(hof:const#2, ?, ?, ?)
return (
  $add($map, 'foo', 2)('foo'),
  $ins($map, 'foo', 42)('foo')
)

returns 3 42

Changelog[edit]

Version 11.0
  • Removed: hof:until (replaced with fn:iterate-while, hof:if (replaced with fn:identity, hof:drop-while (replaced with fn:items-starting-where), hof:take-while (replaced with fn:items-before)
Version 9.5
Version 8.1
Version 7.2
Version 7.0
  • module added
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