Higher-Order Functions Module

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Revision as of 12:40, 12 December 2017 by CG (talk | contribs) (→‎hof:until)
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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.

Loops

hof:fold-left1

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

hof: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 $start and, subsequently, to the last result of this function until the predicate function $pred (applied to the initial value or the subsequent results) returns true().
Examples
  • hof:until(function($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.

  • The evaluation of the predicate is pre-fixed, thus every cycle starts with the evaluation of the predicate first.
declare function local:pred($res) { true() };
declare function local:loop($val) { $val + 1 };

hof:until(local:pred#1, local:loop#1, 0)

returns 0.

hof:scan-left

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

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), $pred)
  )
};
Examples
  • Computes at most 100 random integers, but stops if an integer is smaller than 10:
hof:take-while(
  (1 to 100) ! random:integer(50),
  function($x) { $x >= 10 }
)

Sorting

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

IDs

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 := sort(?, (), hof:id#1)
let $reverse-sort := sort(?, (), function($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, $seq2) {
  sum(for-each-pair($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 8.1
Version 7.2
Version 7.0
  • module added