Higher-Order Functions Module

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

Conventions

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

Functions

hof:id

Signatures	hof:id($expr as item()*) as item()*
Summary	Returns its argument unchanged. This function isn't useful on its own, but can be used as argument to other higher-order functions.
Examples	hof:id(1 to 5) returns 1 2 3 4 5 With higher-order functions: let $sort-by := function($f, $seq) { for $x in $seq order by $f($x) return $x } let $sort := $sort-by(hof:id#1, ?), $reverse-sort := $sort-by(function($x) { -$x }, ?) return ( $sort((1, 5, 3, 2, 4)), '|', $reverse-sort((1, 5, 3, 2, 4)) ) returns: 1 2 3 4 5 | 5 4 3 2 1

hof:const

Signatures	hof:const($expr as item()*, $ignored 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, $seq2) { sum(map-pairs($f, $seq1, $seq2)) } let $sum-all := $zip-sum(function($a, $b) { $a + $b }, ?, ?), $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), $new := if($old) then $f($v, $old) else $v return map:new(($map, map { $k: $new })) } let $map := map { 'foo': 1 } let $add := $insert-with(function($a, $b) {$a + $b}, ?, ?, ?), $insert := $insert-with(hof:const#2, ?, ?, ?) return ( $add($map, 'foo', 2)('foo'), $insert($map, 'foo', 42)('foo') ) returns 3 42

hof:fold-left1

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

hof:until

Signatures	hof:until($pred as function(item()*) as xs:boolean, $f as function(item()*) as item()*, $start as item()*) as item()*
Summary	Applies the function $f to the initial value $start until the predicate $pred applied to the result returns true().
Examples	hof:until(function($x) { $x ge 1000 }, function($y) { 2 * $y }, 1) returns 1024. Calculating the square-root of a number by iteratively improving an initial guess: let $sqrt := function($x as xs:double) as xs:double { hof:until( function($res) { abs($res * $res - $x) < 0.00001 }, function($guess) { ($guess + $x div $guess) div 2 }, $x ) } return $sqrt(25) returns 5.000000000053722.

hof:scan-left

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

hof:take-while

Template:Mark:

Signatures	hof:take-while($seq as item()*, $pred as function(item()) as xs:boolean) as item()*
Summary	The function returns items of $seq as long as the predicate $pred is satisfied. It is equivalent to: declare function hof:take-while($seq, $pred) { if(empty($seq) or not($pred(head($seq)))) then () else ( head($seq), hof:take-while(tail($seq), $pred) ) };
Examples	Computes at most 100 random integers, but stops if an integer is smaller than 10: hof:take-while( for $i in 1 to 100 return random:integer(50), function($x) { $x >= 10 } )

hof:top-k-by

Signatures	hof:top-k-by($seq as item()*, $sort-key as function(item()) as item(), $k as xs:integer) as item()*
Summary	Returns the $k items in $seq that are greatest when sorted by the result of $f applied to the item. The function is a much more efficient implementation of the following scheme: (for $x in $seq order by $sort-key($x) descending return $x )[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

Signatures	hof:top-k-with($seq as item()*, $lt as function(item(), item()) as xs:boolean, $k as xs:integer) as item()*
Summary	Returns the $k items in $seq that are greatest when sorted in the order of the less-than predicate $lt. The function is a general version of hof:top-k-by($seq, $sort-key, $k).
Examples	hof:top-k-with(1 to 1000, function($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

Changelog

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