Higher-Order Functions Module

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

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	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

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

hof:top-k-by

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

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

hof:const

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

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

• 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

• module added